# ISO 10300-1:2014

(Main)## Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors

## Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors

ISO 10300-1:2014 specifies the methods of calculation of the load capacity of bevel gears, the formulae and symbols used for calculation, and the general factors influencing load conditions. The formulae are intended to establish uniformly acceptable methods for calculating the pitting resistance and bending strength of straight, helical (skew), spiral bevel, Zerol and hypoid gears. They are applicable equally to tapered depth and uniform depth teeth. The term "bevel gear" refers to all of these gear types; if not the case, the specific forms are identified. The formulae take into account the known major factors influencing pitting on the tooth flank and fractures in the tooth root. The rating formulae are not applicable to other types of gear tooth deterioration such as plastic yielding, micropitting, case crushing, welding, and wear. The bending strength formulae are applicable to fractures at the tooth fillet, but not to those on the active flank surfaces, to failures of the gear rim or of the gear blank through the web and hub. Pitting resistance and bending strength rating systems for a particular type of bevel gears can be established by selecting proper values for the factors used in the general formulae. If necessary, the formulae allow for the inclusion of new factors at a later date. The rating system of ISO 10300 (all parts) is based on virtual cylindrical gears and restricted to bevel gears whose virtual cylindrical gears have transverse contact ratios of εvα

## Calcul de la capacité de charge des engrenages coniques — Partie 1: Introduction et facteurs généraux d'influence

## Izračun nosilnosti stožčastih zobnikov - 1. del: Uvod in koeficienti

Ta del standarda ISO 10300 določa metode za izračun nosilnosti stožčastih zobnikov, formule in simbole, uporabljene za izračun, ter splošne dejavnike, ki vplivajo na pogoje nosilnosti. Formule iz ISO 10300 (vsi deli) so namenjene določanju splošno sprejemljivih metod za izračun odpornosti proti jamičenju in upogibne trdnosti ravnih, valjastih (poševnih), spiralnih stožčastih, Zerol in

hipoidnih zobnikov. Uporabljajo se tudi za stožčaste zobe in zobe enakomerne velikosti. V nadaljevanju izraz »stožčasti zobnik« pomeni vse vrste zobnikov; v nasprotnem primeru so navedene posebne oblike zobnikov. V formulah se upoštevajo glavni znani dejavniki, ki vplivajo na jamičenje zobnih bokov in razpoke v zobnem korenu. Formule za ocenjevanje se ne uporabljajo za druge vrste okvar zobnikovih zob, kot so nastajanje plastičnih deformacij in mikro jamic, uničenje ohišja, varjenje in obraba. Formule upogibne trdnosti se uporabljajo za razpoke na zobnih kotih, vendar ne za tiste z aktivnimi zobnimi boki, in za deformacije zobatega venca ali zobnikovega telesa prek mreže in pesta. Sisteme za ocenjevanje odpornosti proti jamičenju in upogibne trdnosti za določeno vrsto stožčastih zobnikov je mogoče določiti z izbiro ustreznih vrednosti za faktorje, ki se uporabljajo v splošnih formulah. Formule po potrebi omogočajo vključitev novih faktorjev na poznejši datum. Upoštevati je treba, da se ISO 10300 (vsi deli) ne uporablja za stožčaste zobnike z neustreznim kontaktnim vzorcem pod obremenitvijo (glej dodatek D).

Formule v tem delu standarda ISO 10300 temeljijo na umišljenih valjastih zobnikih in so omejene na stožčaste zobnike z umišljenimi valjastimi zobniki s profilno stopnjo prekrivanja εvα < 2. Poleg tega se navedena razmerja uporabljajo za stožčaste zobnike, pri katerih je vsota koeficientov profilnega premika zobatega kolesca in kolesa nič (glej ISO 23509).

OPOZORILO – Uporabnika opozarjamo, da naj bi se pri uporabi formul za velike povprečne srednje spiralne kote (βm1 + βm2)/2 > 45°, za kote efektivnega tlaka αe > 30° in/ali za veliko širino zoba b > 13 mmn izračunan rezultat ISO 10300 (vsi deli) potrdil z izkušnjami.

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### Standards Content (Sample)

INTERNATIONAL ISO

STANDARD 10300-1

Second edition

2014-04-01

Calculation of load capacity of bevel

gears —

Part 1:

Introduction and general influence

factors

Calcul de la capacité de charge des engrenages coniques —

Partie 1: Introduction et facteurs généraux d’influence

Reference number

ISO 10300-1:2014(E)

©

ISO 2014

---------------------- Page: 1 ----------------------

ISO 10300-1:2014(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2014

All rights reserved. Unless otherwise specified, 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

Case postale 56 • CH-1211 Geneva 20

Tel. + 41 22 749 01 11

Fax + 41 22 749 09 47

E-mail copyright@iso.org

Web www.iso.org

Published in Switzerland

ii © ISO 2014 – All rights reserved

---------------------- Page: 2 ----------------------

ISO 10300-1:2014(E)

Contents Page

Foreword .iv

Introduction .v

1 Scope . 1

2 Normative references . 1

3 Terms and definitions . 2

4 Symbols and units . 2

5 Application . 8

5.1 Calculation methods . 8

5.2 Safety factors . 9

5.3 Rating factors . 9

5.4 Further factors to be considered .10

5.5 Further influence factors in the basic formulae .11

6 External force and application factor, K .12

A

6.1 Nominal tangential force, torque, power.12

6.2 Variable load conditions .12

6.3 Application factor, K .

A 13

7 Dynamic factor, K .13

v

7.1 General .13

7.2 Design .14

7.3 Manufacturing .14

7.4 Transmission error .14

7.5 Dynamic response .15

7.6 Resonance .15

7.7 Calculation methods for K .

v 15

8 Face load factors, K , K .25

Hβ Fβ

8.1 General documents.25

8.2 Method A .25

8.3 Method B .25

8.4 Method C .26

9 Transverse load factors, K , K .27

Hα Fα

9.1 General comments .27

9.2 Method A .28

9.3 Method B .28

9.4 Method C .30

9.5 Running-in allowance, y .

α 31

Annex A (normative) Calculation of virtual cylindrical gears — Method B1 .35

Annex B (normative) Calculation of virtual cylindrical gears — Method B2 .47

Annex C (informative) Values for application factor, K .53

A

Annex D (informative) Contact patterns .54

Bibliography .58

© ISO 2014 – All rights reserved iii

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ISO 10300-1:2014(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. www.iso.org/directives

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any

patent rights identified during the development of the document will be in the Introduction and/or on

the ISO list of patent declarations received. www.iso.org/patents

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the meaning of ISO specific terms and expressions related to conformity

assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers

to Trade (TBT) see the following URL: Foreword - Supplementary information

The committee responsible for this document is ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity

calculation.

This second edition cancels and replaces the first edition (ISO 10300-1:2001), which has been technically

revised.

ISO 10300 consists of the following parts, under the general title Calculation of load capacity of bevel

gears:

— Part 1: Introduction and general influence factors

— Part 2: Calculation of surface durability (pitting)

— Part 3: Calculation of tooth root strength

iv © ISO 2014 – All rights reserved

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ISO 10300-1:2014(E)

Introduction

When ISO 10300:2001 (all parts, withdrawn) became due for (its first) revision, the opportunity was

taken to include hypoid gears, since previously the series only allowed for calculating the load capacity

of bevel gears without offset axes. The former structure is retained, i.e. three parts of the ISO 10300

series, together with ISO 6336-5, and it is intended to establish general principles and procedures for

rating of bevel gears. Moreover, ISO 10300 (all parts) is designed to facilitate the application of future

knowledge and developments, as well as the exchange of information gained from experience.

Several calculation methods, i.e. A, B and C, are specified, which stand for decreasing accuracy and

reliability from A to C because of simplifications implemented in formulae and factors. The approximate

methods in ISO 10300 (all parts) are used for preliminary estimates of gear capacity where the final

details of the gear design are not yet known. More detailed methods are intended for the recalculation

of the load capacity limits when all important gear data are given.

ISO 10300 (all parts) does not provide an upgraded calculation procedure as a method A, although it

would be available, such as finite element or boundary element methods combined with sophisticated

tooth contact analyses. The majority of Working Group 13 decided that neither is it sufficient for an

International Standard to simply refer to such a complex computer program, nor does it make sense to

explain it step by step in an International Standard.

On the other hand, by means of such a computer program, a new calculation procedure for bevel and

hypoid gears on the level of method B was developed and checked. It is part of the ISO 10300 series as

submethod B1. Besides, if the hypoid offset, a, is zero, method B1 becomes identical to the set of proven

formulae of the former version of ISO 10300 (all parts):2001.

In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, an annex, called: “Calculation

of virtual cylindrical gears — Method B2”, is included in this part of ISO 10300. Additionally, ISO 10300-2

is supplemented by a separate clause: “Gear flank rating formulae — Method B2”; regarding ISO 10300-3,

it was agreed that the former method B2, which uses the Lewis parabola to determine the critical section

in the root and not the 30° tangent at the tooth fillet as method B1 does, now be extended by the AGMA

methods for rating the strength of bevel gears and hypoid gears. It was necessary to present a new,

clearer structure of the three parts, which is illustrated in Figure 1 (of this part of ISO 10300). Note,

ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when method B2.

The procedures covered by ISO 10300 (all parts) are based on both testing and theoretical studies, but

it is possible that the results obtained from its rating calculations might not be in good agreement with

certain, previously accepted, gear calculation methods.

ISO 10300 (all parts) provides calculation procedures by which different gear designs can be compared.

It is neither meant to ensure the performance of assembled gear drive systems nor intended for use by

the average engineer. Rather, it is aimed at the experienced gear designer capable of selecting reasonable

values for the factors in these formulae, based on knowledge of similar designs and on awareness of the

effects of the items discussed.

NOTE Contrary to cylindrical gears, where the contact is usually linear, bevel gears are generally manufactured

with profile and lengthwise crowning: i.e. the tooth flanks are curved on all sides and the contact develops an

elliptical pressure surface. This is taken into consideration when determining the load factors by the fact that the

rectangular zone of action (in the case of spur and helical gears) is replaced by an inscribed parallelogram for

method B1 and an inscribed ellipse for method B2 (see Annex A for method B1 and Annex B for method B2). The

conditions for bevel gears, different from cylindrical gears in their contact, are thus taken into consideration by

the longitudinal and transverse load distribution factors.

© ISO 2014 – All rights reserved v

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ISO 10300-1:2014(E)

Key

a

One set of formulae for both, bevel and hypoid gears.

b

Separate sets of formulae for bevel and for hypoid gears.

Figure 1 — Structure of calculation methods in ISO 10300 (all parts)

vi © ISO 2014 – All rights reserved

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INTERNATIONAL STANDARD ISO 10300-1:2014(E)

Calculation of load capacity of bevel gears —

Part 1:

Introduction and general influence factors

1 Scope

This part of ISO 10300 specifies the methods of calculation of the load capacity of bevel gears, the

formulae and symbols used for calculation, and the general factors influencing load conditions.

The formulae in ISO 10300 (all parts) are intended to establish uniformly acceptable methods for

calculating the pitting resistance and bending strength of straight, helical (skew), spiral bevel, Zerol and

hypoid gears. They are applicable equally to tapered depth and uniform depth teeth. Hereinafter, the

term “bevel gear” refers to all of these gear types; if not the case, the specific forms are identified.

The formulae take into account the known major factors influencing pitting on the tooth flank and

fractures in the tooth root. The rating formulae are not applicable to other types of gear tooth deterioration

such as plastic yielding, micropitting, case crushing, welding, and wear. The bending strength formulae

are applicable to fractures at the tooth fillet, but not to those on the active flank surfaces, to failures

of the gear rim or of the gear blank through the web and hub. Pitting resistance and bending strength

rating systems for a particular type of bevel gears can be established by selecting proper values for the

factors used in the general formulae. If necessary, the formulae allow for the inclusion of new factors at

a later date. Note, ISO 10300 (all parts) is not applicable to bevel gears which have an inadequate contact

pattern under load (see Annex D).

The rating system of ISO 10300 (all parts) is based on virtual cylindrical gears and restricted to bevel

gears whose virtual cylindrical gears have transverse contact ratios of ε < 2. Additionally, the given

vα

relations are valid for bevel gears of which the sum of profile shift coefficients of pinion and wheel is

zero (see ISO 23509).

WARNING — The user is cautioned that when the formulae are used for large average mean spiral

angles (β +β )/2 > 45°, for effective pressure angles α > 30° and/or for large face widths

m1 m2 e

b > 13 m , the calculated results of ISO 10300 (all parts) should be confirmed by experience.

mn

2 Normative references

The following documents, in whole or in part, are normatively referenced in this document and are

indispensable to its application. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

ISO 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry

ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials

ISO 10300-2:2014, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability

(pitting)

ISO 10300-3:2014, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength

ISO 17485, Bevel gears — ISO system of accuracy

ISO 23509:2006, Bevel and hypoid gear geometry

© ISO 2014 – All rights reserved 1

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ISO 10300-1:2014(E)

3 Terms and definitions

For the purposes of this part of ISO 10300, terms and definitions given in ISO 1122-1 and ISO 23509

apply.

4 Symbols and units

For the purposes of this document, the symbols given in ISO 701, ISO 17485 and ISO 23509 apply.

Table 1 contains symbols and their units which are used at more than one places of ISO 10300 (all parts).

Other symbols, especially those of auxiliary variables, which are used in equations following closely

after their definitions, are not listed in Table 1. Table 2 contains general subscripts used in ISO 10300

(all parts).

Table 1 — Symbols and units used in ISO 10300 (all parts)

Symbol Description or term Unit

a hypoid offset mm

a relative hypoid offset —

rel

a centre distance of virtual cylindrical gear pair mm

v

a centre distance of virtual cylindrical gear pair in normal section mm

vn

b face width mm

b relative base face width —

b

b calculated effective face width mm

ce

b effective face width (e.g. measured length of contact pattern) mm

eff

b face width of virtual cylindrical gears mm

v

b effective face width of virtual cylindrical gears mm

v,eff

c empirical parameter to determine the dynamic factor —

v

c mean value of mesh stiffness per unit face width N/(mm ⋅ µm)

γ

c mesh stiffness for average conditions N/(mm ⋅ µm)

γ0

c’ single stiffness N/(mm ⋅ µm)

c ’ single stiffness for average conditions N/(mm ⋅ µm)

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

d base diameter of virtual cylindrical gear in normal section mm

vbn

d root diameter of virtual cylindrical gear mm

vf

d reference diameter of virtual cylindrical gear in normal section mm

vn

e exponent for the distribution of the load peaks along the lines of contact —

f distance from the centre of the zone of action to a contact line mm

f maximum distance to middle contact line mm

max

f maximum distance to middle contact line at right side of contact pattern mm

maxB

f maximum distance to middle contact line at left side of contact pattern mm

max0

2 © ISO 2014 – All rights reserved

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ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

f single pitch deviation µm

pt

f effective pitch deviation µm

p,eff

g length of contact line (method B2) mm

c

g length of path of contact of virtual cylindrical gear in transverse section mm

vα

g relative length of action in normal section —

vαn

g relative length of action to point of load application (method B2) —

J

g relative length of action within the contact ellipse —

η

h mean addendum mm

am

h tool addendum mm

a0

h mean dedendum mm

fm

h dedendum of the basic rack profile mm

fP

h mean whole depth used for bevel spiral angle factor mm

m

h relative mean virtual dedendum —

vfm

h bending moment arm for tooth root stress (load application at tooth tip) mm

Fa

h load height from critical section (method B2) mm

N

′

k contact shift factor —

l length of contact line (method B1) mm

b

l theoretical length of contact line mm

b0

l theoretical length of middle contact line mm

bm

m outer transverse module mm

et

m mean normal module mm

mn

m mean transverse module mm

mt

m mass per unit face width reduced to the line of action of dynamically equiva-

red

kg/mm

lent cylindrical gears

m* relative individual gear mass per unit face width referred to line of action kg/mm

–1

n rotational speed min

–1

n resonance speed of pinion min

E1

p peak load N/mm

p transverse base pitch (method B2) mm

et

p maximum peak load N/mm

max

p* relative peak load for calculating the load sharing factor (method B1) —

p relative mean normal pitch —

mn

p relative mean normal base pitch —

nb

p transverse base pitch of virtual cylindrical gear (method B1) mm

vet

q exponent in the formula for lengthwise curvature factor —

q notch parameter —

s

r cutter radius mm

c0

r tooth fillet radius at the root in mean section mm

mf

r mean pitch radius mm

mpt

r mean transverse radius to point of load application (method B2) mm

my 0

r relative mean virtual tip radius —

va

© ISO 2014 – All rights reserved 3

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ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

r relative mean virtual pitch radius —

vn

s mean normal circular thickness mm

mn

s amount of protuberance at the tool mm

pr

s tooth root chord in calculation section mm

Fn

s one-half tooth thickness at critical section (method B2) mm

N

u gear ratio of bevel gear —

u gear ratio of virtual cylindrical gear —

v

v tangential speed at outer end (heel) of the reference cone m/s

et

v maximum pitch line velocity at operating pitch diameter m/s

et,max

v sliding velocity in the mean point P m/s

g

v sliding velocity parallel to the contact line m/s

g,par

v sliding velocity vertical to the contact line m/s

g,vert

v tangential speed at mid-face width of the reference cone m/s

mt

v sum of velocities in the mean point P m/s

Σ

v sum of velocities in profile direction m/s

Σh

v sum of velocities in lengthwise direction m/s

Σl

v sum of velocities vertical to the contact line m/s

Σ,vert

w angle of contact line relative to the root cone °

x profile shift coefficient —

hm

x thickness modification coefficient —

sm

x tooth strength factor (method B2) mm

N

x distance from mean section to point of load application mm

oo

y running-in allowance for pitch deviation related to the polished test piece µm

p

y location of point of load application for maximum bending stress on path of

J

mm

action (method B2)

y location of point of load application on path of action for maximum root

3

mm

stress

y running-in allowance for pitch error µm

α

z number of teeth —

z number of teeth of virtual cylindrical gear —

v

z number of teeth of virtual cylindrical gear in normal section —

vn

z number of blade groups of the cutter —

0

A auxiliary factor for calculating the dynamic factor K —

v-C

A* related area for calculating the load sharing factor Z mm

LS

A outer tooth thickness allowance mm

sne

B accuracy grade according to ISO 17485 —

C correction factor of tooth stiffness for non average conditions —

F

C correction factor for the length of contact lines —

lb

C , C , constants for determining lubricant film factors

ZL ZR

—

C

ZV

2

E modulus of elasticity, Young’s modulus N/mm

E, G, H auxiliary variables for tooth form factor (method B1) —

4 © ISO 2014 – All rights reserved

---------------------- Page: 10 ----------------------

ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

F auxiliary variable for mid-zone factor —

F nominal tangential force at mid-face width of the reference cone N

mt

F determinant tangential force at mid-face width of the reference cone N

mtH

F nominal normal force N

n

F nominal tangential force of virtual cylindrical gears N

vmt

HB Brinell hardness —

K constant; factor for calculating the dynamic factor K —

v─B

K dynamic factor —

v

K * preliminary dynamic factor for non-hypoid gears —

v

K application factor —

A

K lengthwise curvature factor for bending stress —

F0

K transverse load factor for bending stress —

Fα

K face load factor for bending stress —

Fβ

K transverse load factor for contact stress —

Hα

K * preliminary transverse load factor for contact stress for non-hypoid gears —

Hα

K face load factor for contact stress —

Hβ

K mounting factor —

Hβ-be

N reference speed related to resonance speed n —

E1

N number of load cycles —

L

P nominal power kW

Ra = CLA = AA arithmetic average roughness µm

R outer cone distance mm

e

R mean cone distance mm

m

R relative mean back cone distance —

mpt

Rz mean roughness µm

Rz mean roughness for gear pairs with relative curvature radius ρ = 10 mm µm

10 rel

S safety factor for bending stress (against breakage) —

F

S minimum safety factor for bending stress —

F,min

S safety factor for contact stress (against pitting) —

H

S minimum safety factor for contact stress —

H,min

T nominal torque of pinion and wheel Nm

1,2

W wheel mean slot width mm

m2

Y tooth form factor of pinion and wheel (method B2) —

1,2

Y stress concentration and stress correction factor (method B2) —

f

Y inertia factor (bending) —

i

Y root stress adjustment factor (method B2) —

A

Y bevel spiral angle factor —

BS

Y tooth form factor for load application at the tooth tip (method B1) —

Fa

Y combined tooth form factor for generated gears —

FS

Y bending strength geometry factor (method B2) —

J

Y load sharing factor (bending) —

LS

© ISO 2014 – All rights reserved 5

---------------------- Page: 11 ----------------------

ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

Y life factor (bending) —

NT

Y relative surface condition factor —

R,Rel T

Y stress correction factor for load application at the tooth tip —

Sa

Y stress correction factor for dimensions of the standard test gear —

ST

Y size factor for tooth root stress —

X

Y relative notch sensitivity factor —

δ,rel T

Y contact ratio factor for bending (method B1) —

ε

Z inertia factor (pitting) —

i

Z speed factor —

v

Z contact stress adjustment factor (method B2) —

A

2 1/2

Z elasticity factor (N/mm )

E

Z face width factor —

FW

Z hypoid factor —

Hyp

Z pitting resistance geometry factor (method B2) —

I

Z bevel gear factor (method B1) —

K

Z lubricant factor —

L

Z load sharing factor (method B1) —

LS

Z mid-zone factor —

M-B

Z life factor (pitting) —

NT

Z roughness factor for contact stress —

R

Z bevel slip factor —

S

Z work hardening factor —

W

Z size factor —

X

α adjusted pressure angle (method B2) °

a

α normal pressure angle at tooth tip °

an

α effective pressure angle in transverse section °

et

α effective pressure angle for drive side/coast side °

eD,C

α limit pressure angle in wheel root coordinates (method B2) °

f

α limit pressure angle °

lim

α generated pressure angle for drive side/coast side °

nD,C

α transverse pressure angle of virtual cylindrical gears °

vet

α load application angle at tooth tip of virtual cylindrical gear (method B1) °

Fan

α normal pressure angle at point of load application (method B2) °

L

β mean base spiral angle °

bm

β mean spiral angle °

m

β helix angle of virtual gear (method B1), virtual spiral angle (method B2) °

v

β helix angle at base circle of virtual cylindr

**...**

SLOVENSKI STANDARD

SIST ISO 10300-1:2015

01-marec-2015

1DGRPHãþD

SIST ISO 10300-1:2002

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Calculation of load capacity of bevel gears - Part 1: Introduction and general influence

factors

Calcul de la capacité de charge des engrenages coniques - Partie 1: Introduction et

facteurs généraux d'influence

Ta slovenski standard je istoveten z: ISO 10300-1:2014

ICS:

21.200 Gonila Gears

SIST ISO 10300-1:2015 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST ISO 10300-1:2015

---------------------- Page: 2 ----------------------

SIST ISO 10300-1:2015

INTERNATIONAL ISO

STANDARD 10300-1

Second edition

2014-04-01

Calculation of load capacity of bevel

gears —

Part 1:

Introduction and general influence

factors

Calcul de la capacité de charge des engrenages coniques —

Partie 1: Introduction et facteurs généraux d’influence

Reference number

ISO 10300-1:2014(E)

©

ISO 2014

---------------------- Page: 3 ----------------------

SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2014

All rights reserved. Unless otherwise specified, 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

Case postale 56 • CH-1211 Geneva 20

Tel. + 41 22 749 01 11

Fax + 41 22 749 09 47

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ii © ISO 2014 – All rights reserved

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Contents Page

Foreword .iv

Introduction .v

1 Scope . 1

2 Normative references . 1

3 Terms and definitions . 2

4 Symbols and units . 2

5 Application . 8

5.1 Calculation methods . 8

5.2 Safety factors . 9

5.3 Rating factors . 9

5.4 Further factors to be considered .10

5.5 Further influence factors in the basic formulae .11

6 External force and application factor, K .12

A

6.1 Nominal tangential force, torque, power.12

6.2 Variable load conditions .12

6.3 Application factor, K .

A 13

7 Dynamic factor, K .13

v

7.1 General .13

7.2 Design .14

7.3 Manufacturing .14

7.4 Transmission error .14

7.5 Dynamic response .15

7.6 Resonance .15

7.7 Calculation methods for K .

v 15

8 Face load factors, K , K .25

Hβ Fβ

8.1 General documents.25

8.2 Method A .25

8.3 Method B .25

8.4 Method C .26

9 Transverse load factors, K , K .27

Hα Fα

9.1 General comments .27

9.2 Method A .28

9.3 Method B .28

9.4 Method C .30

9.5 Running-in allowance, y .

α 31

Annex A (normative) Calculation of virtual cylindrical gears — Method B1 .35

Annex B (normative) Calculation of virtual cylindrical gears — Method B2 .47

Annex C (informative) Values for application factor, K .53

A

Annex D (informative) Contact patterns .54

Bibliography .58

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SIST ISO 10300-1:2015

ISO 10300-1:2014(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. www.iso.org/directives

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any

patent rights identified during the development of the document will be in the Introduction and/or on

the ISO list of patent declarations received. www.iso.org/patents

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the meaning of ISO specific terms and expressions related to conformity

assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers

to Trade (TBT) see the following URL: Foreword - Supplementary information

The committee responsible for this document is ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity

calculation.

This second edition cancels and replaces the first edition (ISO 10300-1:2001), which has been technically

revised.

ISO 10300 consists of the following parts, under the general title Calculation of load capacity of bevel

gears:

— Part 1: Introduction and general influence factors

— Part 2: Calculation of surface durability (pitting)

— Part 3: Calculation of tooth root strength

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Introduction

When ISO 10300:2001 (all parts, withdrawn) became due for (its first) revision, the opportunity was

taken to include hypoid gears, since previously the series only allowed for calculating the load capacity

of bevel gears without offset axes. The former structure is retained, i.e. three parts of the ISO 10300

series, together with ISO 6336-5, and it is intended to establish general principles and procedures for

rating of bevel gears. Moreover, ISO 10300 (all parts) is designed to facilitate the application of future

knowledge and developments, as well as the exchange of information gained from experience.

Several calculation methods, i.e. A, B and C, are specified, which stand for decreasing accuracy and

reliability from A to C because of simplifications implemented in formulae and factors. The approximate

methods in ISO 10300 (all parts) are used for preliminary estimates of gear capacity where the final

details of the gear design are not yet known. More detailed methods are intended for the recalculation

of the load capacity limits when all important gear data are given.

ISO 10300 (all parts) does not provide an upgraded calculation procedure as a method A, although it

would be available, such as finite element or boundary element methods combined with sophisticated

tooth contact analyses. The majority of Working Group 13 decided that neither is it sufficient for an

International Standard to simply refer to such a complex computer program, nor does it make sense to

explain it step by step in an International Standard.

On the other hand, by means of such a computer program, a new calculation procedure for bevel and

hypoid gears on the level of method B was developed and checked. It is part of the ISO 10300 series as

submethod B1. Besides, if the hypoid offset, a, is zero, method B1 becomes identical to the set of proven

formulae of the former version of ISO 10300 (all parts):2001.

In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, an annex, called: “Calculation

of virtual cylindrical gears — Method B2”, is included in this part of ISO 10300. Additionally, ISO 10300-2

is supplemented by a separate clause: “Gear flank rating formulae — Method B2”; regarding ISO 10300-3,

it was agreed that the former method B2, which uses the Lewis parabola to determine the critical section

in the root and not the 30° tangent at the tooth fillet as method B1 does, now be extended by the AGMA

methods for rating the strength of bevel gears and hypoid gears. It was necessary to present a new,

clearer structure of the three parts, which is illustrated in Figure 1 (of this part of ISO 10300). Note,

ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when method B2.

The procedures covered by ISO 10300 (all parts) are based on both testing and theoretical studies, but

it is possible that the results obtained from its rating calculations might not be in good agreement with

certain, previously accepted, gear calculation methods.

ISO 10300 (all parts) provides calculation procedures by which different gear designs can be compared.

It is neither meant to ensure the performance of assembled gear drive systems nor intended for use by

the average engineer. Rather, it is aimed at the experienced gear designer capable of selecting reasonable

values for the factors in these formulae, based on knowledge of similar designs and on awareness of the

effects of the items discussed.

NOTE Contrary to cylindrical gears, where the contact is usually linear, bevel gears are generally manufactured

with profile and lengthwise crowning: i.e. the tooth flanks are curved on all sides and the contact develops an

elliptical pressure surface. This is taken into consideration when determining the load factors by the fact that the

rectangular zone of action (in the case of spur and helical gears) is replaced by an inscribed parallelogram for

method B1 and an inscribed ellipse for method B2 (see Annex A for method B1 and Annex B for method B2). The

conditions for bevel gears, different from cylindrical gears in their contact, are thus taken into consideration by

the longitudinal and transverse load distribution factors.

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Key

a

One set of formulae for both, bevel and hypoid gears.

b

Separate sets of formulae for bevel and for hypoid gears.

Figure 1 — Structure of calculation methods in ISO 10300 (all parts)

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SIST ISO 10300-1:2015

INTERNATIONAL STANDARD ISO 10300-1:2014(E)

Calculation of load capacity of bevel gears —

Part 1:

Introduction and general influence factors

1 Scope

This part of ISO 10300 specifies the methods of calculation of the load capacity of bevel gears, the

formulae and symbols used for calculation, and the general factors influencing load conditions.

The formulae in ISO 10300 (all parts) are intended to establish uniformly acceptable methods for

calculating the pitting resistance and bending strength of straight, helical (skew), spiral bevel, Zerol and

hypoid gears. They are applicable equally to tapered depth and uniform depth teeth. Hereinafter, the

term “bevel gear” refers to all of these gear types; if not the case, the specific forms are identified.

The formulae take into account the known major factors influencing pitting on the tooth flank and

fractures in the tooth root. The rating formulae are not applicable to other types of gear tooth deterioration

such as plastic yielding, micropitting, case crushing, welding, and wear. The bending strength formulae

are applicable to fractures at the tooth fillet, but not to those on the active flank surfaces, to failures

of the gear rim or of the gear blank through the web and hub. Pitting resistance and bending strength

rating systems for a particular type of bevel gears can be established by selecting proper values for the

factors used in the general formulae. If necessary, the formulae allow for the inclusion of new factors at

a later date. Note, ISO 10300 (all parts) is not applicable to bevel gears which have an inadequate contact

pattern under load (see Annex D).

The rating system of ISO 10300 (all parts) is based on virtual cylindrical gears and restricted to bevel

gears whose virtual cylindrical gears have transverse contact ratios of ε < 2. Additionally, the given

vα

relations are valid for bevel gears of which the sum of profile shift coefficients of pinion and wheel is

zero (see ISO 23509).

WARNING — The user is cautioned that when the formulae are used for large average mean spiral

angles (β +β )/2 > 45°, for effective pressure angles α > 30° and/or for large face widths

m1 m2 e

b > 13 m , the calculated results of ISO 10300 (all parts) should be confirmed by experience.

mn

2 Normative references

The following documents, in whole or in part, are normatively referenced in this document and are

indispensable to its application. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

ISO 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry

ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials

ISO 10300-2:2014, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability

(pitting)

ISO 10300-3:2014, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength

ISO 17485, Bevel gears — ISO system of accuracy

ISO 23509:2006, Bevel and hypoid gear geometry

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

3 Terms and definitions

For the purposes of this part of ISO 10300, terms and definitions given in ISO 1122-1 and ISO 23509

apply.

4 Symbols and units

For the purposes of this document, the symbols given in ISO 701, ISO 17485 and ISO 23509 apply.

Table 1 contains symbols and their units which are used at more than one places of ISO 10300 (all parts).

Other symbols, especially those of auxiliary variables, which are used in equations following closely

after their definitions, are not listed in Table 1. Table 2 contains general subscripts used in ISO 10300

(all parts).

Table 1 — Symbols and units used in ISO 10300 (all parts)

Symbol Description or term Unit

a hypoid offset mm

a relative hypoid offset —

rel

a centre distance of virtual cylindrical gear pair mm

v

a centre distance of virtual cylindrical gear pair in normal section mm

vn

b face width mm

b relative base face width —

b

b calculated effective face width mm

ce

b effective face width (e.g. measured length of contact pattern) mm

eff

b face width of virtual cylindrical gears mm

v

b effective face width of virtual cylindrical gears mm

v,eff

c empirical parameter to determine the dynamic factor —

v

c mean value of mesh stiffness per unit face width N/(mm ⋅ µm)

γ

c mesh stiffness for average conditions N/(mm ⋅ µm)

γ0

c’ single stiffness N/(mm ⋅ µm)

c ’ single stiffness for average conditions N/(mm ⋅ µm)

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

d base diameter of virtual cylindrical gear in normal section mm

vbn

d root diameter of virtual cylindrical gear mm

vf

d reference diameter of virtual cylindrical gear in normal section mm

vn

e exponent for the distribution of the load peaks along the lines of contact —

f distance from the centre of the zone of action to a contact line mm

f maximum distance to middle contact line mm

max

f maximum distance to middle contact line at right side of contact pattern mm

maxB

f maximum distance to middle contact line at left side of contact pattern mm

max0

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

f single pitch deviation µm

pt

f effective pitch deviation µm

p,eff

g length of contact line (method B2) mm

c

g length of path of contact of virtual cylindrical gear in transverse section mm

vα

g relative length of action in normal section —

vαn

g relative length of action to point of load application (method B2) —

J

g relative length of action within the contact ellipse —

η

h mean addendum mm

am

h tool addendum mm

a0

h mean dedendum mm

fm

h dedendum of the basic rack profile mm

fP

h mean whole depth used for bevel spiral angle factor mm

m

h relative mean virtual dedendum —

vfm

h bending moment arm for tooth root stress (load application at tooth tip) mm

Fa

h load height from critical section (method B2) mm

N

′

k contact shift factor —

l length of contact line (method B1) mm

b

l theoretical length of contact line mm

b0

l theoretical length of middle contact line mm

bm

m outer transverse module mm

et

m mean normal module mm

mn

m mean transverse module mm

mt

m mass per unit face width reduced to the line of action of dynamically equiva-

red

kg/mm

lent cylindrical gears

m* relative individual gear mass per unit face width referred to line of action kg/mm

–1

n rotational speed min

–1

n resonance speed of pinion min

E1

p peak load N/mm

p transverse base pitch (method B2) mm

et

p maximum peak load N/mm

max

p* relative peak load for calculating the load sharing factor (method B1) —

p relative mean normal pitch —

mn

p relative mean normal base pitch —

nb

p transverse base pitch of virtual cylindrical gear (method B1) mm

vet

q exponent in the formula for lengthwise curvature factor —

q notch parameter —

s

r cutter radius mm

c0

r tooth fillet radius at the root in mean section mm

mf

r mean pitch radius mm

mpt

r mean transverse radius to point of load application (method B2) mm

my 0

r relative mean virtual tip radius —

va

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

r relative mean virtual pitch radius —

vn

s mean normal circular thickness mm

mn

s amount of protuberance at the tool mm

pr

s tooth root chord in calculation section mm

Fn

s one-half tooth thickness at critical section (method B2) mm

N

u gear ratio of bevel gear —

u gear ratio of virtual cylindrical gear —

v

v tangential speed at outer end (heel) of the reference cone m/s

et

v maximum pitch line velocity at operating pitch diameter m/s

et,max

v sliding velocity in the mean point P m/s

g

v sliding velocity parallel to the contact line m/s

g,par

v sliding velocity vertical to the contact line m/s

g,vert

v tangential speed at mid-face width of the reference cone m/s

mt

v sum of velocities in the mean point P m/s

Σ

v sum of velocities in profile direction m/s

Σh

v sum of velocities in lengthwise direction m/s

Σl

v sum of velocities vertical to the contact line m/s

Σ,vert

w angle of contact line relative to the root cone °

x profile shift coefficient —

hm

x thickness modification coefficient —

sm

x tooth strength factor (method B2) mm

N

x distance from mean section to point of load application mm

oo

y running-in allowance for pitch deviation related to the polished test piece µm

p

y location of point of load application for maximum bending stress on path of

J

mm

action (method B2)

y location of point of load application on path of action for maximum root

3

mm

stress

y running-in allowance for pitch error µm

α

z number of teeth —

z number of teeth of virtual cylindrical gear —

v

z number of teeth of virtual cylindrical gear in normal section —

vn

z number of blade groups of the cutter —

0

A auxiliary factor for calculating the dynamic factor K —

v-C

A* related area for calculating the load sharing factor Z mm

LS

A outer tooth thickness allowance mm

sne

B accuracy grade according to ISO 17485 —

C correction factor of tooth stiffness for non average conditions —

F

C correction factor for the length of contact lines —

lb

C , C , constants for determining lubricant film factors

ZL ZR

—

C

ZV

2

E modulus of elasticity, Young’s modulus N/mm

E, G, H auxiliary variables for tooth form factor (method B1) —

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

F auxiliary variable for mid-zone factor —

F nominal tangential force at mid-face width of the reference cone N

mt

F determinant tangential force at mid-face width of the reference cone N

mtH

F nominal normal force N

n

F nominal tangential force of virtual cylindrical gears N

vmt

HB Brinell hardness —

K constant; factor for calculating the dynamic factor K —

v─B

K dynamic factor —

v

K * preliminary dynamic factor for non-hypoid gears —

v

K application factor —

A

K lengthwise curvature factor for bending stress —

F0

K transverse load factor for bending stress —

Fα

K face load factor for bending stress —

Fβ

K transverse load factor for contact stress —

Hα

K * preliminary transverse load factor for contact stress for non-hypoid gears —

Hα

K face load factor for contact stress —

Hβ

K mounting factor —

Hβ-be

N reference speed related to resonance speed n —

E1

N number of load cycles —

L

P nominal power kW

Ra = CLA = AA arithmetic average roughness µm

R outer cone distance mm

e

R mean cone distance mm

m

R relative mean back cone distance —

mpt

Rz mean roughness µm

Rz mean roughness for gear pairs with relative curvature radius ρ = 10 mm µm

10 rel

S safety factor for bending stress (against breakage) —

F

S minimum safety factor for bending stress —

F,min

S safety factor for contact stress (against pitting) —

H

S minimum safety factor for contact stress —

H,min

T nominal torque of pinion and wheel Nm

1,2

W wheel mean slot width mm

m2

Y tooth form factor of pinion and wheel (method B2) —

1,2

Y stress concentration and stress correction factor (method B2) —

f

Y inertia factor (bending) —

i

Y root stress adjustment factor (method B2) —

A

Y bevel spiral angle factor —

BS

Y tooth form factor for load application at the tooth tip (method B1) —

Fa

Y combined tooth form factor for generated gears —

FS

Y bending strength geometry factor (method B2) —

J

Y load sharing factor (bending) —

LS

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SIST ISO 10300-1:2015

ISO 10300-1:2014(E)

Table 1 (continued)

Symbol Description or term Unit

Y life factor (bending) —

NT

Y relative surface condition factor —

R,Rel T

Y stress correction factor for load application at the tooth tip —

Sa

Y stress correction factor for dimensions of the standard test gear —

ST

Y size factor for tooth root stress —

X

Y relative notch sensitivity factor —

δ,rel T

Y contact ratio factor for bending (method B1) —

ε

Z inertia factor (pitting) —

i

Z speed factor —

v

Z contact stress adjustment factor (method B2) —

A

2 1/2

Z elasticity factor (N/mm )

E

Z face width factor —

FW

Z hypoid factor —

Hyp

Z pitting resistance geometry factor (method B2) —

I

**...**

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