ISO/TR 6336-30

Calculation of load capacity of spur and helical gears — Part 30: Calculation examples for the application of ISO 6336 parts 1,2,3,5

ISO/TR 6336-30:2017 presents worked examples that apply exclusively the approximation methods for the determination of specific influential factors, such as the dynamic factor, Kv, and the load distributions factors KHα, KHβ, etc., where full analytical calculation procedures are provided within the referenced parts of ISO 6336. Worked examples covering the more advanced analysis techniques and methods are outside the scope of this document. The example calculations presented in this document are provided for guidance on the application of ISO 6336‑1, ISO 6336‑2, ISO 6336‑3 and ISO 6336‑5. Any of the values, safety factors or the data presented are not to be taken as recommended criteria for real gearing. Data presented within this document are for the purpose of aiding the application of the calculation procedures of ISO 6336‑1, ISO 6336‑2, ISO 6336‑3 and ISO 6336‑5.

Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale — Partie 30: Exemples d'application de l'ISO 6336 parties 1, 2, 3, 5

ISO 6336-30:2017 fournit des exemples pratiques qui appliquent exclusivement les méthodes d'approximation permettant de déterminer des facteurs d'influence spécifiques, tels que le facteur dynamique, KV, et les facteurs de distribution de charge, KHα, KHβ, etc., pour lesquelles des méthodes de calcul analytiques complètes sont fournies dans les documents ISO 6336 référencés. Les exemples pratiques couvrant des méthodes et des techniques d'analyse plus avancées ne relèvent pas du domaine d'application du présent document. Les exemples de calcul donnés dans le présent document sont fournis à titre indicatif pour l'application de l'ISO 6336‑1, de l'ISO 6336‑2, de l'ISO 6336‑3 et de l'ISO 6336‑5. Aucune des valeurs, aucun des coefficients de sécurité, ni aucune des données présentés ne sauraient être interprétés comme des critères recommandés pour des engrenages réels. Les données qui figurent dans le présent document visent à faciliter l'application des méthodes de calcul de l'ISO 6336‑1, de l'ISO 6336‑2, de l'ISO 6336‑3 et de l'ISO 6336‑5.

General Information

• Status: Not Published
• ICS: 21.200 - Gears
• Technical Committee: ISO/TC 60/SC 2 - Gear capacity calculation
• Drafting Committee: ISO/TC 60/SC 2 - Gear capacity calculation
• Current Stage: 6000 - International Standard under publication
• Completion Date: 10-Nov-2022

RELATIONS

• Revises: ISO/TR 6336-30:2017 - Calculation of load capacity of spur and helical gears — Part 30: Calculation examples for the application of ISO 6336 parts 1,2,3,5
• Effective Date: 06-Jun-2022

Standards Content (sample)

TECHNICAL ISO/TR
REPORT 6336-30
Second edition
Calculation of load capacity of spur
and helical gears —
Part 30:
Calculation examples for the
application of ISO 6336 parts 1,2,3,5
Calcul de la capacité de charge des engrenages cylindriques à
dentures droite et hélicoïdale —
Partie 30: Exemples d'application de l'ISO 6336 parties 1, 2, 3, 5
PROOF/ÉPREUVE
Reference number
ISO/TR 6336-30:2022(E)
© ISO 2022
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ISO/TR 6336-30:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
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ISO/TR 6336-30:2022(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction .................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms, definitions, symbols and units ......................................................................................................................................... 1

3.1 Terms and definitions ...................................................................................................................................................................... 1

3.2 Symbols and units ............................................................................................................................................................................... 1

4 Worked examples ................................................................................................................................................................................................ 6

4.1 General ........................................................................................................................................................................................................... 6

4.2 Qualifying comments ........................................................................................................................................... ............................. 6

4.2.1 Calculation of base pitch deviation, f ........................................................................................................... 6

4.2.2 Calculation of running-in allowance, y , for the transverse load factors K
α Hα

and K ......................................................................................................................................................................................... 6

4.2.3 Calculation of mesh stiffness, c ........................................................................................................................... 7

4.2.4 Application of lubricant film Z , Z and Z , hardness Z and size Z
L v R W X

influence factors ................................................................................................................................................................. 7

4.2.5 Calculation of the permissible contact stress in the limited life range (Z

and Z ) ...................................................................................................................................................................................... 7

4.2.6 Application of work hardening factor, Z .................................................................................................... 7

4.2.7 Determination of Rz......................................................................................................................................................... 8

4.2.8 Facewidth for calculations involving double helical gears ........................................................... 8

4.2.9 Calculation of ε for double helical gears ...................................................................................................... 8

4.2.10 Calculation of f and f .......................................................................................................................................... 8

Hβ5 Hβ

4.2.11 Helix tolerance f and f for double helical gears.......................................................................... 8

Hβ5 Hβ

4.2.12 Calculation of root diameter, d ............................................................................................................................. 8

4.2.13 Calculations for internal gears............................................................................................................................... 8

4.2.14 Rounding of values ........................................................................................................................................................... 8

4.2.15 Deviations of values ......................................................................................................................................................... 8

4.2.16 Nominal and generated values............................................................................................................................... 9

4.2.17 ISO 1328-1 ................................................................................................................................................................................ 9

4.2.18 Values for reference only ................................... ........................................................................................................ .. 9

4.3 Example 1: Single helical case carburized gear pair ............................................................................................. 9

4.4 Example 2: Single helical through-hardened gear pair ...................................................................................13

4.5 Example 3: Spur through-hardened gear pair ......................................................................................................... 17

4.6 Example 4: Spur case carburized gear pair ............................................................................................................... 21

4.7 Example 5: Spur gear pair with an induction hardened pinion and through-

hardened cast gear ........................................................................................................................................................................... 25

4.8 Example 6: Spur internal through-hardened gear pair ...................................................................................29

4.9 Example 7: Double helical through-hardened wrought gear pair ......................................................... 33

4.10 Example 8: Single helical case carburized gear pair.......................................................................................... 37

Annex A (informative) Example 1 detailed calculation ................................................................................................................43

Bibliography .............................................................................................................................................................................................................................63

iii
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ISO/TR 6336-30:2022(E)
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 of 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

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear

capacity calculation.

This second edition cancels and replaces the first edition (ISO 6336-30:2017), which has been

technically revised according to ISO 6336-1:2019, ISO 6336-2:2019, ISO 6336-3:2019.

The main changes are as follows:

— introduction of tooth flank correction factor (auxiliary factor, see ISO 6336-2:2019) f ;

ZCa
— introduction of load distribution influence factor f ;
— modification of the helix angle factor Y ;

— calculation of tooth form factor Y and stress correction factor Y generated with a shaper cutter;

F S
— update to the qualifying comments in 4.2;
— update to the input variables (additional values, modified values).
A list of all parts in the ISO 6336 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
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ISO/TR 6336-30:2022(E)
Introduction

The ISO 6336 series consists of International Standards, Technical Specifications (TS) and Technical

Reports (TR) under the general title Calculation of load capacity of spur and helical 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 6336-1 to ISO 6336-19 cover fatigue analyses for gear rating. The

procedures described in ISO 6336-20 to ISO 6336-29 are predominantly related to the tribological

behaviour of the lubricated flank surface contact. ISO 6336-30 to ISO 6336-39 include example

calculations. The ISO 6336 series allows the addition of new parts under appropriate numbers to reflect

knowledge gained in the future.

Requesting standardized calculations according to ISO 6336 without referring to specific parts requires

the use of only those parts that are designated as International Standards (see Table 1 for listing).

When requesting further calculations, the relevant part or parts of ISO 6336 need to be specified. Use

of a Technical Specification as acceptance criteria for a specific design needs to be agreed in advance

between manufacturer and purchaser.
Table 1 — Overview of ISO 6336
Technical
International Technical
Calculation of load capacity of spur and helical gears Specifica-
Standard Report
tion
Part 1: Basic principles, introduction and general influence factors X
Part 2: Calculation of surface durability (pitting) X
Part 3: Calculation of tooth bending strength X
Part 4: Calculation of tooth flank fracture load capacity X
Part 5: Strength and quality of materials X
Part 6: Calculation of service life under variable load X
Part 20: Calculation of scuffing load capacity — Flash temperature
method
Part 21: Calculation of scuffing load capacity — Integral temperature
method
Part 22: Calculation of micropitting load capacity
(replaces: ISO/TR 15144-1)
Part 30: Calculation examples for the application of ISO 6336‑1,
ISO 6336‑2, ISO 6336‑3 and, ISO 6336‑5
Part 31: Calculation examples of micropitting load capacity
(replaces: ISO/TR 15144-2)

NOTE At the time of publication of this document, some of the parts listed here were under development. Consult the ISO

website.

This document provides worked examples for the application of the calculation procedures defined in

ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5. The example calculations cover the application to

spur, helical and double helical, external and internal cylindrical involute gears for both high speed

and low speed operating conditions, determining the ISO safety factors against tooth flank pitting and

tooth root bending strength for each gear set. The calculation procedures used are consistent with

those presented in ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5, unless qualifying comments are

provided. Where qualifying comments have been included in this document, they reflect areas of the

calculation procedures presented in the current standards where points of clarification are required

or editorial errors have been identified. The changes defined within the qualifying comments will be

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ISO/TR 6336-30:2022(E)

implemented in future revisions of ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5. No additional

calculations are presented here that are outside of the referenced documents.

Eight worked examples are presented with the necessary input data for each gear set provided at the

beginning of the calculation. Calculation details are presented in full for one worked example, with all

following examples having summarized results data presented in tabular format.

For all calculations in this document, the flank tolerance classes according to ISO 1328-1 are applied.

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TECHNICAL REPORT ISO/TR 6336-30:2022(E)
Calculation of load capacity of spur and helical gears —
Part 30:
Calculation examples for the application of ISO 6336 parts
1,2,3,5
1 Scope

This document presents worked examples that apply exclusively the approximation methods for the

determination of specific influential factors, such as the dynamic factor, K , and the load distributions

factors K , K , etc., where full analytical calculation procedures are provided within the referenced

Hα Hβ
parts of ISO 6336.

Worked examples covering the more advanced analysis techniques and methods are not applicable to

this document.

The example calculations presented in this document are provided for guidance on the application

of ISO 6336-1:2019, ISO 6336-2:2019, ISO 6336-3:2019 and ISO 6336-5:2016. Any of the values, safety

factors or the data presented do not represent recommended criteria for real gearing. Data presented

within this document are for the purpose of aiding the application of the calculation procedures of

ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5.
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 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336 (all parts), Calculation of load capacity of spur and helical gears
3 Terms, definitions, symbols and units
3.1 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 1122-1, ISO 6336 (all parts)

and the following apply.

ISO and IEC maintain terminology 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/
3.2 Symbols and units

The units of length metre, millimetre and micrometre are chosen in accordance with common practice.

The conversions of the units are already included in the given formulae. All symbols used in this

document are given in Table 2.
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ISO/TR 6336-30:2022(E)
Table 2 — Symbols
Symbol Description Unit
A Flank tolerance class —
a Centre distance mm
B Non-dimensional parameter —
B Non-dimensional parameter —
B Non-dimensional parameter —
B Constant —
B Constant —
b Facewidth (total facewidth if double helical) mm
b Facewidth per helical if double helical (b/2) mm
b Contact facewidth mm
eff
b Web thickness mm
C Tip relief μm
C Basic rack factor —
C Root relief µm
C Correction factor —
C Gear blank factor —
C Constant —
C Constant —
C Constant —
C Constant —
C Constant —
C Constant —
C Constant —
C Lubrication film factor exponent —
C Roughness factor exponent —
c Mean value of mesh stiffness per unit facewidth N/(mm·μm)
c Mean value of mesh stiffness per unit facewidth N/(mm·μm)
c′ Maximum tooth stiffness per unit facewidth of gear pair N/(mm·μm)
′ Theoretical single stiffness N/(mm·μm)
D Ball diameter mm
d Reference diameter mm
d Tip diameter mm
d Virtual tip diameter mm
d Base circle diameter mm
d Virtual base diameter mm
d Virtual outer single tooth contact diameter mm
d Root form diameter (based on x ) mm
Ff E
d Root diameter (based on x ) mm
f E
d Mean tooth diameter mm
d Start of active profile diameter mm
d Virtual reference diameter mm
d External shaft diameter mm
d Internal shaft diameter mm
shi
d Working pitch diameter mm
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ISO/TR 6336-30:2022(E)
TTaabbllee 22 ((ccoonnttiinnueuedd))
Symbol Description Unit
E Young's modulus N/mm
E Auxiliary value (for form factor for pinion or wheel) —
1,2
F Mean transverse tangential load N
F Nominal tangential load at the reference cylinder N
F Determinant tangential load N
F Initial equivalent misalignment μm
F Effective equivalent misalignment (after running-in) μm
f Effective profile deviation after running-in μm
fαeff
f Profile form deviation (see ISO 1328-1) μm
f Helix slope deviation (see ISO 1328-1) μm
f Mesh misalignment μm

f Transverse base pitch deviation (the values of f can be used for calculations in μm

pb pT
accordance with the ISO 6336 series, using tolerances according to ISO 1328-1)
f Effective transverse base pitch deviation after running-in μm
pbeff
f Single pitch tolerance (see ISO 1328-1, ISO 6336 refers to f as f ) μm
pT pT pt
f Equivalent misalignment μm
f Shaft deformation under specific load μm
sh0
f Tooth flank correction factor (auxiliary factor, see ISO 6336-2:2019) —
ZCa
f Load distribution influence factor —
G Auxiliary value (for form factor) —
H Auxiliary value (for form factor) —
h Tooth depth mm
h Bending moment arm mm
h Basic rack dedendum mm
h Tip chamfer mm
K Constant —
K Application factor —
K Transverse load factor —
K Face load factor —
K Transverse load factor —
K Face load factor —
K Dynamic factor —
K Mesh load factor —
k Number of teeth spanned —
L Auxiliary notch parameter —
l Bearing span mm
M Dimension between balls mm
m Normal module mm
m Reduced gear pair mass per unit facewidth kg/mm
red
N Resonance ratio —
N Exponent —
N Number of load cycles —
N Number of meshes —
n Rotation speed of pinion (or wheel) min
1,2
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ISO/TR 6336-30:2022(E)
TTaabbllee 22 ((ccoonnttiinnueuedd))
Symbol Description Unit
n Resonance speed min
p Virtual base pitch mm
pr As cut basic rack undercut mm
q Material allowance for finishing mm
q Notch parameter —
q Notch parameter of standard reference test piece —
q′ Flexibility of pair of meshing teeth (mm·μm)/N
Ra Arithmetic mean roughness value, Ra = 1/6 Rz μm
Rz Mean peak-to-valley roughness (ISO 4287:1997 including ISO 4287:1997/ μm
Cor 1:1998, ISO 4287:1997/Cor 2:2005, ISO 4287:1997/Amd 1:2009 and
ISO 4288:1996 )
Rz Mean relative peak-to-valley roughness for gear pair μm
S Safety factor for bending —
S Tooth root normal chord mm
S Safety factor for surface durability —
s Bearing span offset mm
s Residual fillet undercut, sp=−rq mm
pr pr
T Nominal torque at pinion/wheel Nm
1,2
v Circumferential velocity at the reference cylinder m/s
v Pitch line velocity m/s
W Span measurement mm
x Nominal profile shift coefficient —
x Generating profile shift coefficient —
x Generating profile shift coefficient (pre-finishing) —
E,V
x Pinion cutter profile shift coefficient —
Y Rim thickness factor —
Y Deep tooth factor —
Y Tooth form factor —
Y Life factor (tooth root stress) —
Y Life factor for reference test conditions (tooth root stress) —
Y Relative surface factor —
RrelT
Y Stress correction factor —

Y Stress correction factor, relevant to the dimensions of the reference test gears —

Y Size factor —
Y Helix angle factor —
Y Relative notch sensitivity factor for reference stress —
δrelT
y Running-in allowance μm
y Running-in allowance μm
y Running-in allowance μm
Z Single pair tooth contact factor —
Z Single pair tooth contact factor —
Z Elasticity factor
Nm/ m
Z Zone factor —
Z Lubricant factor —
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ISO/TR 6336-30:2022(E)
TTaabbllee 22 ((ccoonnttiinnueuedd))
Symbol Description Unit
Z Life factor (contact stress) —
Z Life factor for reference test conditions (contact stress) —
Z Roughness factor —
Z Work hardening factor —
Z Size factor —
Z Velocity factor —
Z Helix angle factor —
Z Contact ratio factor —
z Number of teeth —
z Virtual number of teeth —
z Pinion cutter number of teeth —
α Normal pressure angle °
α Virtual form factor pressure angle °
α Virtual load direction angle °
Fen
α Transverse pressure angle °
α Transverse working pressure angle °
β Helix angle (without subscript, at reference cylinder) °
γ Auxiliary angle °
ε Transverse contact ratio —
ε Virtual contact ratio —
ε Overlap ratio —
ε Total contact ratio —
θ Auxiliary value (for form factor) rad
ν Poisson's ratio —
ν Lubrication viscosity mm /s
ρ Material density kg/m
ρ Radius of curvature mm
ρ Pinion cutter tip radius coefficient —
aP0
ρ Radius of root fillet mm
ρ Root fillet radius of the basic rack for cylindrical gears mm
ρ Relative radius of curvature mm
red
ρ′ Slip layer thickness mm
σ Nominal tooth root stress N/mm
σ Tooth root stress N/mm
σ Allowable stress number (bending) N/mm
Flim
σ Permissible bending stress N/mm
σ Permissible bending stress (long life) N/mm
FPlonglife
σ Permissible bending stress (reference condition) N/mm
FPref
σ Contact stress N/mm
σ Allowable stress number (surface) N/mm
H lim
σ Nominal contact stress at pitch point N/mm
σ Permissible contact stress N/mm
σ Permissible contact stress (long life) N/mm
HPlonglife
σ Permissible contact stress (reference) N/mm
HPref
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ISO/TR 6336-30:2022(E)
TTaabbllee 22 ((ccoonnttiinnueuedd))
Symbol Description Unit
σ Yield stress N/mm
σ Proof stress N/mm
0,2
χ* Relative stress gradient in root of a notch mm
Stress gradient – smooth, polished test piece mm
* Stress gradient for reference test piece mm
Cancelled and replaced by ISO 21920-2:2021.
Cancelled and replaced by ISO 21920-3:2021.
4 Worked examples
4.1 General

Clause 4 presents examples for the calculation of the safety factor for surface durability, S , and safety

factor for tooth breakage, S . For all examples, where various calculation methods are presented for the

determination of specific influencing factors, the approximate methods detailed in the ISO 6336 series

are applied. Where a specific method is used to calculate an influence parameter, the method used is

denoted as a subscript to that factor (as defined in ISO 6336-1).

The calculations results in specific aspects of the rating procedure to highlight the influence of specific

gear pair geometry, quality or application.

For example 1 in 4.3, the full calculation procedure is presented including the formulae. For all

subsequent calculations, only the tabulated input and results data are provided.

In a number of areas, points of clarification of the procedure or specific criteria that differ slightly from

the definitions provided in ISO 6336-1, ISO 6336-2 and ISO 6336-3 are incorporated within the example

calculations. The points reflect the true intention of the procedures of ISO 6336-1, ISO 6336-2 and

ISO 6336-3 and are defined in 4.2.

NOTE 1 The calculations and results presented were performed using computer-based procedures. If the

calculations are performed manually, it is possible that small differences between the results appear.

NOTE 2 In the presented results, all values for K factors are presented with rounding to two decimal places

(X,XX); however, for the actual calculations, the results for each factor have been used with unrounded values.

4.2 Qualifying comments
4.2.1 Calculation of base pitch deviation, f

The value calculated for f is by means of Formula (1), and is applied without rounding:

ff=⋅cos()α (1)
pb pT t
where f is provided by ISO 1328-1.

4.2.2 Calculation of running-in allowance, y , for the transverse load factors K and K

α Hα Fα

The following criteria defined in ISO 6336-1:2019, 8.3.1, are applied only for the calculation of K and

K :

— The base pitch deviation, f , accounts for the total effect of all gear tooth deviations which affect

the transverse load factor. If, nevertheless, the profile form deviation, f , is greater than the base

pitch deviation, the profile form deviation f is used instead of the base pitch deviation f .

fα pb
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ISO/TR 6336-30:2022(E)

— If profile modifications compensate for the deflections of the teeth at the actual load level, 50 % of

the base pitch deviation f and its corresponding running-in value y ( f ) respectively the profile

pb α pb

form deviation f and its corresponding running-in value y ( f ) is used for the calculation of K .

fα α fα Hα
This reduction applies for examples 1 and 4 of this document.

The criteria listed above do not apply for determining f and f for the calculation of K according to

pb fα v
ISO 6336-1:2019, 6.5.4.
4.2.3 Calculation of mesh stiffness, c

The calculation of mesh stiffness, c , in accordance with method B of ISO 6336-1:2019, 9.3.3, is applied

for all example calculations. For all c calculations, the use of the nominal profile shift coefficient, x, and

nominal basic rack dedendum, h , is applied. The generating profile shift coefficient, x , is not used,

fP E

even where x is used for other strength calculations associated with the tooth root. Virtual number of

teeth of helical gears were calculated with Formula (16) of ISO 6336-3:2019 rather than approximate

formula given in Formula (81) of ISO 6336-1:2019.

4.2.4 Application of lubricant film Z , Z and Z , hardness Z and size Z influence factors

L v R W X

According to the ISO 6336 series, the permissible contact stress numbers for static and reference

condition, including all relevant influence factors as defined, will be calculated. For limited life, linear

interpolation on a log–log scale, following the procedure of Z , between these two values is applied.

The linear interpolation on a log-log-scale for limited life leads to a value Z , which can be different to

the value Z .

The displayed values of Z , Z , Z , Z and Z in the output tables of this document show the interpolated

L v R W X
values of each Z-factor.
4.2.5 Calculation of the permiss
...

ISO/TR 6336-30:2022(E)
ISO TC 60/SC 2/WG 6
Date: 2022-09-1510-13

Calculation of load capacity of spur and helical gears — Part 30: Calculation examples for the

application of ISO 6336 parts 1,2,3,5
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ISO/TR 6336-30:2022(E)
© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part

of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or

mechanical, including photocopying, or posting on the internet or an intranet, without prior written

permission. Permission can be requested from either ISO at the address below or ISO’s member body

in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.orgwww.iso.org
Published in Switzerland
ii © ISO 2022 – All rights reserved
ii © ISO 2022 – All rights reserved
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ISO/TR 6336-30:2022(E)
Contents

Foreword ............................................................................................................................................................. v

Introduction ...................................................................................................................................................... vi

1 Scope ....................................................................................................................................................... 1

2 Normative references ....................................................................................................................... 1

3 Terms, definitions, symbols and units ......................................................................................... 1

3.1 Terms and definitions ....................................................................................................................... 1

3.2 Symbols and units .............................................................................................................................. 1

4 Worked examples ............................................................................................................................... 7

4.1 General ................................................................................................................................................... 7

4.2 Qualifying comments ......................................................................................................................... 8

4.2.1 Calculation of base pitch deviation, f ...................................................................................... 8

4.2.2 Calculation of running-in allowance, y , for the transverse load factors K and K

α Hα Fα

.................................................................................................................................................................. 8

4.2.3 Calculation of mesh stiffness, c .................................................................................................... 8

4.2.4 Application of lubricant film Z , Z and Z , hardness Z and size Z influence

L v R W X

factors .................................................................................................................................................... 8

4.2.5 Calculation of the permissible contact stress in the limited life range (Z and Z ) .. 8

N NT

4.2.6 Application of work hardening factor, Z ................................................................................. 9

4.2.7 Determination of Rz ........................................................................................................................... 9

4.2.8 Face width for calculations involving double helical gears .................................................. 9

4.2.9 Calculation of ε for double helical gears ................................................................................... 9

4.2.10 Calculation of f and f ............................................................................................................. 9

Hβ5 Hβ

4.2.11 Helix tolerance f and f for double helical gears ........................................................... 9

Hβ5 Hβ

4.2.12 Calculation of root diameter, d ..................................................................................................... 9

4.2.13 Calculations for internal gears .................................................................................................... 10

4.2.14 Rounding of values .......................................................................................................................... 10

4.2.15 Deviations of values ........................................................................................................................ 10

4.2.16 Nominal and generated values .................................................................................................... 10

4.2.17 ISO 1328-1:2013 .............................................................................................................................. 10

4.2.18 Values for reference only .............................................................................................................. 10

4.3 Example 1: Single helical case carburized gear pair ............................................................ 10

4.4 Example 2: Single helical through-hardened gear pair ....................................................... 15

4.5 Example 3: Spur through-hardened gear pair ....................................................................... 20

4.6 Example 4: Spur case carburized gear pair ............................................................................. 25

4.7 Example 5: Spur gear pair with an induction hardened pinion and through-hardened

cast gear .............................................................................................................................................. 29

4.8 Example 6: Spur internal through-hardened gear pair ....................................................... 34

4.9 Example 7: Double helical through-hardened wrought gear pair ................................... 39

4.10 Example 8: Single helical case carburized gear pair ............................................................ 44

Annex A (informative) Example 1 detailed calculation ................................................................... 50

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ISO/TR 6336-30:2022(E)

A.1 General ................................................................................................................................................ 50

A.2 Defined data ...................................................................................................................................... 50

A.3 ISO 6336-5:2016 — Allowable stress values for contact and bending ........................... 51

A.4 Application data ............................................................................................................................... 51

A.5 Load data ............................................................................................................................................ 52

A.6 Supplementary calculations ......................................................................................................... 52

A.7 ISO 6336-2:2019 — Contact ratio factor .................................................................................. 54

A.8 ISO 6336-1:2019 — Basic principles, introduction and general influence factors .... 54

A.8.1 Determination of dynamic factor, k ......................................................................................... 54

A.8.2 Determination of face load factors, K and K .................................................................. 58

Hβ Fβ

A.8.3 Determination of transverse load factors, K and K .................................................... 59

Hα Fα

A.9 ISO 6336-2:2019 — Calculation of surface durability (pitting) ........................................ 59

A.9.1 Determination of contact stress, σ .......................................................................................... 59

A.9.2 Determination of permissible contact stress, σ ............................................................... 60

A.10 ISO 6336-3:2019 — Calculation of tooth bending strength ............................................... 63

A.10.1 Determination of tooth root stress, σ ..................................................................................... 63

A.10.2 Determination of permissible tooth root stress, σ .......................................................... 68

Bibliography .................................................................................................................................................... 71

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ISO/TR 6336-30:2022(E)
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 of 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

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear

capacity calculation.

This second edition cancels and replaces the first edition (ISO 6336-30:2017), which has been technically

revised according to ISO 6336-1:2019, ISO 6336-2:2019, ISO 6336-3:2019.
The main changes are as follows:

— introduction of tooth flank correction factor (auxiliary factor, see ISO 6336-2:2019) f ;

ZCa
— introduction of load distribution influence factor f ;
— modification of the helix angle factor Y ;

— calculation of tooth form factor Y and stress correction factor Y generated with a shaper cutter;

F S
— update to the qualifying comments in chapter 4.2;
— update to the input variables (additional values, modified values)).
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ISO/TR 6336-30:2022(E)
A list of all parts in the ISO 6336 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
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ISO/TR 6336-30:2022(E)
Introduction

The ISO 6336 series consists of International Standards, Technical Specifications (TS) and Technical

Reports (TR) under the general title Calculation of load capacity of spur and helical 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 6336-1 to ISO 6336-19 cover fatigue analyses for gear rating. The

procedures described in ISO 6336-20 to ISO 6336-29 are predominantly related to the tribological

behaviour of the lubricated flank surface contact. ISO 6336-30 to ISO 6336-39 include example

calculations. The ISO 6336 series allows the addition of new parts under appropriate numbers to reflect

knowledge gained in the future.

Requesting standardized calculations according to ISO 6336 without referring to specific parts requires

the use of only those parts that are designated as International Standards (see Table 1 for listing). When

requesting further calculations, the relevant part or parts of ISO 6336 need to be specified. Use of a

Technical Specification as acceptance criteria for a specific design needs to be agreed in advance between

manufacturer and purchaser.
Table 1 — Overview of ISO 6336
International Technical Technical
Calculation of load capacity of spur and helical gears
Standard Specification Report
Part 1: Basic principles, introduction and general influence factors X
Part 2: Calculation of surface durability (pitting) X
Part 3: Calculation of tooth bending strength X
Part 4: Calculation of tooth flank fracture load capacity X
Part 5: Strength and quality of materials X
Part 6: Calculation of service life under variable load X
Part 20: Calculation of scuffing load capacity — Flash temperature
method
Part 21: Calculation of scuffing load capacity — Integral temperature
method
Part 22: Calculation of micropitting load capacity
(replaces: ISO/TR 15144-1)
Part 30: Calculation examples for the application of ISO 6336-1,
X
ISO 6336-2, ISO 6336-3 and, ISO 6336-5
Part 31: Calculation examples of micropitting load capacity
X
(replaces: ISO/TR 15144-2)
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ISO/TR 6336-30:2022(E)

NOTE At the time of publication of this document, some of the parts listed here were under development. Consult the ISO

website.

This document provides worked examples for the application of the calculation procedures defined in

ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5. The example calculations cover the application to

spur, helical and double helical, external and internal cylindrical involute gears for both high speed and

low speed operating conditions, determining the ISO safety factors against tooth flank pitting and tooth

root bending strength for each gear set. The calculation procedures used are consistent with those

presented in ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5, unless qualifying comments are

provided. Where qualifying comments have been included in this document, they reflect areas of the

calculation procedures presented in the current standards where points of clarification are required or

editorial errors have been identified. The changes defined within the qualifying comments will be

implemented in future releasesrevisions of ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5. No

additional calculations are presented here that are outside of the referenced documents.

Eight worked examples are presented with the necessary input data for each gear set provided at the

beginning of the calculation. Calculation details are presented in full for one worked example, with all

following examples having summarized results data presented in tabular format.

For all calculations in this document, the flank tolerance classes according to ISO 1328-1:2013 are

applied.
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TECHNICAL REPORT ISO/TR 6336-30:2022(E)
Calculation of load capacity of spur and helical gears —
Part 30: Calculation examples for the application of ISO 6336-
parts 1,
ISO 6336-2, ISO 6336-3 and, ISO 6336-,5
1 Scope

This document presents worked examples that apply exclusively the approximation methods for the

determination of specific influential factors, such as the dynamic factor, K , and the load distributions

factors K , K , etc., where full analytical calculation procedures are provided within the referenced

Hα Hβ
parts of ISO 6336.

Worked examples covering the more advanced analysis techniques and methods are outside the scope

ofnot applicable to this document.

The example calculations presented in this document are provided for guidance on the application of

ISO 6336-1:2019, ISO 6336-2:2019, ISO 6336-3:2019 and ISO 6336-5:2016. Any of the values, safety

factors or the data presented do not represent recommended criteria for real gearing. Data presented

within this document are for the purpose of aiding the application of the calculation procedures of

ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5.
2 Normative references
There are no normative references in this document.

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 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336 (all parts), Calculation of load capacity of spur and helical gears
3 Terms, definitions, symbols and units
3.1 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 1122-1 and, ISO 6336 (all parts)

are appliedand the following apply.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https://www.iso.org/obphttps://www.iso.org/obp

— IEC Electropedia: available at https://www.electropedia.org/
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ISO/TR 6336-30:2022(E)
3.2 Symbols and units

The units of length metre, millimetre and micrometre are chosen in accordance with common practice.

The conversions of the units are already included in the given formulae. All symbols used in this

document are given in Table 2.
Table 2 — Symbols used in this document
Symbol Description Unit
A Flank tolerance class —
a Centre distance mm
B Non-dimensional parameter —
B Non-dimensional parameter —
B Non-dimensional parameter —
B Constant —
B Constant —
b Facewidth (total facewidth if double helical) mm
b Facewidth per helical if double helical (b/2) mm
b Contact facewidth mm
eff
b Web thickness mm
C Tip relief μm
C Basic rack factor —
C Root relief µm
C Correction factor —
C Gear blank factor —
C Constant —
C Constant —
C Constant —
C Constant —
C Constant —
C Constant —
C Constant —
C Lubrication film factor exponent —
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ISO/TR 6336-30:2022(E)
Symbol Description Unit
C Roughness factor exponent —
c Mean value of mesh stiffness per unit facewidth N/(mm·μm)
c Mean value of mesh stiffness per unit facewidth N/(mm·μm)
c′ Maximum tooth stiffness per unit facewidth of gear pair N/(mm·μm)
𝑐𝑐 ′ Theoretical single stiffness N/(mm·μm)
th th
D Ball diameter mm
d Reference diameter mm
d Tip diameter mm
d Virtual tip diameter mm
d Base circle diameter mm
d Virtual base diameter mm
d Virtual outer single tooth contact diameter mm
d Root form diameter (based on x ) mm
Ff E
d Root diameter (based on x ) mm
f E
d Mean tooth diameter mm
d Start of active profile diameter mm
d Virtual reference diameter mm
d External shaft diameter mm
d Internal shaft diameter mm
shi
d Working pitch diameter mm
E Young's modulus 2
N/mm
E Auxiliary value (for form factor for pinion or wheel) —
1,2
F Mean transverse tangential load N
F Nominal tangential load at the reference cylinder N
F Determinant tangential load N
F Initial equivalent misalignment μm
F Effective equivalent misalignment (after running-in) μm
f Effective profile deviation after running-in μm
fαeff
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ISO/TR 6336-30:2022(E)
Symbol Description Unit
f Profile form deviation (see ISO 1328-1:2013) μm
f Helix slope deviation (see ISO 1328-1:2013) μm
f Mesh misalignment μm
f Transverse base pitch deviation (the values of f maycan be used for μm
calculations in accordance with the ISO 6336 series, using tolerances complying
withaccording to ISO 1328-1:2013)
f Effective transverse base pitch deviation after running-in μm
pbeff
f Single pitch tolerance (see ISO 1328-1:2013, ISO 6336 refers to f as f ) μm
pT pT pt
f Equivalent misalignment μm
f Shaft deformation under specific load μm
sh0
f Tooth flank correction factor (auxiliary factor, see ISO 6336-2:2019) —
ZCa
f Load distribution influence factor —
G Auxiliary value (for form factor) —
H Auxiliary value (for form factor) —
h Tooth depth mm
h Bending moment arm mm
h Basic rack dedendum mm
h Tip chamfer mm
K Constant —
K Application factor —
K Transverse load factor —
K Face load factor —
K Transverse load factor —
K Face load factor —
K Dynamic factor —
K Mesh load factor —
k Number of teeth spanned —
L Auxiliary notch parameter —
l Bearing span mm
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ISO/TR 6336-30:2022(E)
Symbol Description Unit
M Dimension between balls mm
m Normal module mm
m Reduced gear pair mass per unit facewidth kg/mm
red
N Resonance ratio —
N Exponent —
N Number of load cycles —
N Number of meshes —
n Rotation speed of pinion (or wheel) −1
1,2 min
n Resonance speed −1
E1 min
p Virtual base pitch mm
pr As cut basic rack undercut mm
q Material allowance for finishing mm
q Notch parameter —
q Notch parameter of standard reference test piece —
q′ Flexibility of pair of meshing teeth (mm·μm)/N
Ra Arithmetic mean roughness value, Ra = 1/6 Rz μm
Rz Mean peak-to-valley roughness (ISO 4287:19971997 including μm
ISO 4287:1997/Cor 1:1998, ISO 4287:1997/Cor 2:2005,
ISO 4287:1997/Amd 1:2009 and ISO 4288:19961996 )
Rz Mean relative peak-to-valley roughness for gear pair μm
S Safety factor for bending —
S Tooth root normal chord mm
S Safety factor for surface durability —
s Bearing span offset mm
s Residual fillet undercut, 𝑠𝑠 =𝑝𝑝𝑝𝑝−𝑞𝑞 s pr− q mm
pr pr pr
T Nominal torque at pinion/wheel Nm
1,2
v Circumferential velocity at the reference cylinder m/s
v Pitch line velocity m/s
W Span measurement mm
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ISO/TR 6336-30:2022(E)
Symbol Description Unit
x Nominal profile shift coefficient —
x Generating profile shift coefficient —
x Generating profile shift coefficient (pre-finishing) —
E,V
x Pinion cutter profile shift coefficient —
Y Rim thickness factor —
Y Deep tooth factor —
Y Tooth form factor —
Y Life factor (tooth root stress) —
Y Life factor for reference test conditions (tooth root stress) —
Y Relative surface factor —
RrelT
Y Stress correction factor —

Y Stress correction factor, relevant to the dimensions of the reference test gears —

Y Size factor —
Y Helix angle factor —
Y Relative notch sensitivity factor for reference stress —
δrelT
y Running-in allowance μm
y Running-in allowance μm
y Running-in allowance μm
Z Single pair tooth contact factor —
Z Single pair tooth contact factor —
Z Elasticity factor 2
E �𝑁𝑁/𝑚𝑚𝑚𝑚
N / mm
Z Zone factor —
Z Lubricant factor —
Z Life factor (contact stress) —
Z Life factor for reference test conditions (contact stress) —
Z Roughness factor —
Z Work hardening factor —
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ISO/TR 6336-30:2022(E)
Symbol Description Unit
Z Size factor —
Z Velocity factor —
Z Helix angle factor —
Z Contact ratio factor —
z Number of teeth —
z Virtual number of teeth —
z Pinion cutter number of teeth —
α Normal pressure angle °
α Virtual form factor pressure angle °
α Virtual load direction angle °
Fen
α Transverse pressure angle °
α Transverse working pressure angle °
β Helix angle (without subscript, at reference cylinder) °
γ Auxiliary angle °
ε Transverse contact ratio —
ε Virtual contact ratio —
ε Overlap ratio —
ε Total contact ratio —
θ Auxiliary value (for form factor) rad
ν Poisson's ratio —
ν Lubrication viscosity 2
40 mm /s
ρ Material density 3
kg/m
ρ Radius of curvature mm
ρ Pinion cutter tip radius coefficient —
aP0
ρ Radius of root fillet mm
ρ Root fillet radius of the basic rack for cylindrical gears mm
ρ Relative radius of curvature mm
red
ρ′ Slip layer thickness mm
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ISO/TR 6336-30:2022(E)
Symbol Description Unit
σ Nominal tooth root stress 2
FO N/mm
σ Tooth root stress 2
F N/mm
σ Allowable stress number (bending) 2
Flim N/mm
σ Permissible bending stress 2
FP N/mm
σ Permissible bending stress (long life) 2
FPlonglife N/mm
σ Permissible bending stress (reference condition) 2
FPref N/mm
σ Contact stress 2
H N/mm
σ Allowable stress number (surface) 2
H lim N/mm
σ Nominal contact stress at pitch point 2
HO N/mm
σ Permissible contact stress 2
HP N/mm
σ Permissible contact stress (long life) 2
HPlonglife N/mm
σ Permissible contact stress (reference) 2
HPref N/mm
σ Yield stress 2
s N/mm
σ Proof stress 2
0,2 N/mm
χ* Relative stress gradient in root of a notch -1
∗ Stress gradient – smooth, polished test piece -1
𝜒𝜒 χ
∗ * Stress gradient for reference test piece -1
𝜒𝜒 χ mm
T T
1 Pinion —
2 Cancelled and replaced by ISO 21920-2:2021. Wheel —
Deleted Cells
Cancelled and replaced by ISO 21920-3:2021.
1 – 9 General numbering —
94 Worked examples
9.14.1 General

This clauseClause 4 presents examples for the calculation of the safety factor for surface durability, S ,

and safety factor for tooth breakage, S . For all examples, where various calculation methods are

presented for the determination of specific influencing factors, the approximate methods detailed in the

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ISO/TR 6336-30:2022(E)

ISO 6336 series are applied. Where a specific method is used to calculate an influence parameter, the

method used is denoted as a subscript to that factor (as defined in ISO 6336-1).

The calculations results in specific aspects of the rating procedure to highlight the influence of specific

gear pair geometry, quality or application.
, the full calculation procedure is presented including the formulae. For all
For example 1 in 4.3
subsequent calculations, only the tabulated input and results data are provided.

In a number of areas, points of clarification of the procedure or specific criteria that differ slightly from

the definitions provided in ISO 6336-1, ISO 6336-2 and ISO 6336-3 are incorporated within the example

calculations. The points reflect the true intention of the procedures of ISO 6336-1, ISO 6336-2 and

ISO 6336-3 and are defined in 4.2.

NOTE 1 The calculations and results presented were performed using computer-based procedures. If the

calculations are performed manually, it is possible that small differences between the results can appear.

NOTE 2 In the presented results, all values for K factors are presented with rounding to two decimal places (X,XX);

however, for the actual calculations, the results for each factor have been used with unrounded values.

9.24.2 Qualifying comments
9.2.14.2.1 Calculation of base pitch deviation, f

The value calculated for f is by means of Formula (1), and is applied without rounding:

𝑓𝑓 =𝑓𝑓 ⋅ cos(𝛼𝛼 ) ff⋅cosα (1)
( )
pb pT 𝑡𝑡 pb pT t
where f is provided by ISO 1328-1:2013.

9.2.24.2.2 Calculation of running-in allowance, y , for the transverse load factors K and

α Hα

The following criteria defined in ISO 6336-1:2019, 8.3.1, are applied only for the calculation of K and

K :

— The base pitch deviation, f , accounts for the total effect of all gear tooth deviations which affect the

transverse load factor. If, nevertheless, the profile form deviation, f , is greater than the base pitch

deviation,
...