ISO/TS 10300-20:2021
(Main)Calculation of load capacity of bevel gears — Part 20: Calculation of scuffing load capacity — Flash temperature method
Calculation of load capacity of bevel gears — Part 20: Calculation of scuffing load capacity — Flash temperature method
This document provides a calculation method for bevel and hypoid gears regarding scuffing based on experimental and theoretical investigation[7]. This calculation method is a flash temperature method. The formulae in this document are intended to establish uniformly acceptable methods for calculating scuffing resistance of straight, helical (skew), spiral bevel, Zerol and hypoid gears made of steel. 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. A calculation method of the scuffing load capacity of bevel and hypoid gears based on an integral temperature method is not available when this document is published. The formulae in this document are 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 20: Calcul de la capacité de charge au grippage — Méthode de la température-éclair
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TECHNICAL ISO/TS
SPECIFICATION 10300-20
First edition
2021-04
Calculation of load capacity of bevel
gears —
Part 20:
Calculation of scuffing load capacity —
Flash temperature method
Calcul de la capacité de charge des engrenages coniques —
Partie 20: Calcul de la capacité de charge au grippage — Méthode de
la température-éclair
Reference number
ISO/TS 10300-20:2021(E)
©
ISO 2021
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ISO/TS 10300-20:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021
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: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
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ISO/TS 10300-20:2021(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Virtual cylindrical gear . 4
5.1 General . 4
5.2 Local geometry parameters . 5
5.2.1 Transverse path of contact . 5
5.2.2 Length of contact lines . 6
5.2.3 Local equivalent radius of curvature, ρ .
rel,Y 8
5.2.4 Local load sharing factor, X .
LS,Y 8
6 Stresses and velocities . 9
6.1 Local modified contact stress, σ .
H,mod,Y 9
6.2 Sliding and sum of velocities .10
6.3 Local relative lubricating film thickness, λ .
z,Y 11
6.4 Local coefficient of friction, µ .
Y 14
7 Local contact temperature, θ .14
C,Y
7.1 General .14
7.2 Power losses influencing the bulk temperature.15
7.2.1 General.15
7.2.2 Method A .15
7.2.3 Method B .15
7.2.4 Method C .15
7.3 Bulk temperature, θ .
M 15
7.3.1 General.15
7.3.2 Method A .15
7.3.3 Method B .15
7.3.4 Tip relief factor, X .
CA 17
7.4 Local flash temperature, θ .
fl,Y 17
8 Permissible contact temperature .18
8.1 Limit temperature from scuffing test, θ .
S,DIN 18
8.2 Permissible temperature, θ .
SC 19
8.3 Permissible scuffing temperature, θ .
S,Y 20
9 Local safety factor, S .21
S,Y
Bibliography .22
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ISO/TS 10300-20:2021(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.
A list of all parts in the ISO 10300 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.
iv © ISO 2021 – All rights reserved
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ISO/TS 10300-20:2021(E)
Introduction
The ISO 10300 series consists of International Standards, Technical Specifications (TS) and Technical
Reports (TR) under the general title Calculation of load capacity of bevel gears (see Table 1).
— International Standards contain calculation methods that are based on widely accepted practices
and have been validated.
— TS contain calculation methods that are still subject to further development.
— TR contain data that is informative, such as example calculations.
The procedures specified in ISO 10300 parts 1 to 19 cover fatigue analyses for gear rating. The
procedures described in ISO 10300 parts 20 to 29 are predominantly related to the tribological
behaviour of the lubricated flank surface contact. ISO 10300 parts 30 to 39 include example calculations.
The ISO 10300 series allows the addition of new parts under appropriate numbers to reflect knowledge
gained in the future.
Requesting standardized calculations according to the ISO 10300 series without referring to specific
parts requires the use of only those parts that are currently designated as International Standards (see
Table 1 for listing). When requesting further calculations, the relevant part or parts of the ISO 10300
series need to be specified. Use of a Technical Specification as acceptance criteria for a specific design
need to be agreed in advance between manufacturer and purchaser.
Table 1 — Parts of ISO 10300 series (status as of DATE OF PUBLICATION)
Calculation of load capacity of bevel gears International Technical Technical
Standard Specification Report
a
Part 1: Introduction and general influence factors X
a
Part 2: Calculation of surface durability (pitting) X
a
Part 3: Calculation of tooth root strength X
Part 4 to 19: to be assigned
Part 20: Calculation of scuffing load capacity — Flash X
temperature method
Part 21 to 29: to be assigned
Part 30: ISO rating system for bevel and hypoid gears X
— Sample calculations
Part 32: ISO rating system for bevel and hypoid gears X
— Sample Calculations of scuffing load capacity
a
Under revision.
This document and the other parts of the ISO 10300 series provide a coherent system of procedures
for the calculation of the load capacity of bevel and hypoid gears. The ISO 10300 series is designed to
facilitate the application of future knowledge and developments, and also the exchange of information
gained from experience.
Design considerations to prevent fractures emanating from stress raisers in the tooth flank, tip
chipping and failures of the gear blank through the web or hub will need to be analysed by general
machine design methods.
Several methods for the calculation of load capacity, as well as for the calculation of various factors, are
permitted. The directions in the ISO 10300 series are thus complex, but also flexible.
Scuffing is a localized damage caused by solid-phase welding between sliding surfaces. It is accompanied
by transfer of metal from one surface to another due to welding and tearing. Scuffing can occur in
gear flanks that operate in the boundary-lubrication regime where the lubricant film is insufficient
to separate tooth surfaces and contact breaks through the oxide layers that normally protect the
[4]
surfaces and enables bare metal surfaces to weld together. Blok hypothesized that scuffing occurs
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ISO/TS 10300-20:2021(E)
when the maximum surface temperature in the contact reaches a critical value. The maximum contact
temperature is determined by the sum of the gear tooth bulk temperature and the local, instantaneous
flash temperature. Scuffing risk is determined by comparing the maximum contact temperature to the
critical temperature. The critical temperature is not only a function of the lubricant-metal-atmosphere
combination; but it depends also upon operating conditions and surface characteristics. Consequently,
the most reliable critical temperatures are determined from tests performed on actual gears, under
actual service loads, and in actual service environments.
vi © ISO 2021 – All rights reserved
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TECHNICAL SPECIFICATION ISO/TS 10300-20:2021(E)
Calculation of load capacity of bevel gears —
Part 20:
Calculation of scuffing load capacity — Flash
temperature method
WARNING — The user is cautioned that when the formulae are used for large average mean spiral
angles, (β + β )/2 > 45°, for effective pressure angles, α > 30° and/or for large face widths,
m1 m2 e
b > 13 m , the calculated results of the ISO 10300 series should be confirmed by experience.
mn
1 Scope
This document provides a calculation method for bevel and hypoid gears regarding scuffing based on
[7]
experimental and theoretical investigation . This calculation method is a flash temperature method.
The formulae in this document are intended to establish uniformly acceptable methods for calculating
scuffing resistance of straight, helical (skew), spiral bevel, Zerol and hypoid gears made of steel. 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.
A calculation method of the scuffing load capacity of bevel and hypoid gears based on an integral
temperature method is not available when this document is published.
The formulae in this document are based on virtual cylindrical gears and restricted to bevel gears
whose virtual cylindrical gears have transverse contact ratios of ε < 2. The results are valid within
vα
the range of the applied factors as specified in ISO 10300-1 (see ISO 6336-2). Additionally, the given
relations are valid for bevel gears of which the sum of profile shift coefficients of pinion and wheel is
zero (see ISO 23509).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 10300-1, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors
ISO 10300-2, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability (pitting)
ISO 14635-1, Gears — FZG test procedures — Part 1: FZG test method A/8,3/90 for relative scuffing load-
carrying capacity of oils
ISO 17485, Bevel gears — ISO system of accuracy
ISO 23509, Bevel and hypoid gear geometry
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
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ISO/TS 10300-20:2021(E)
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols
For the purposes of this document, the symbols and units given in ISO 10300-1, ISO 23509 and Table 2
apply. Table 3 lists the generally used subscripts.
Table 2 — Symbols and units
Symbol Description or term Unit
A* related area for calculating the load sharing factor X at contact point Y mm
Y LS
a auxiliary value mm
a reference centre distance mm
ref
B accuracy grade (ISO 17485 shall apply) —
0,5
B thermal contact coefficient N/(ms K)
M
b half of the Hertzian contact width mm
H
b auxiliary value 1/mm
Y
C tip relief μm
A
C effective tip relief μm
eff
C correction factor for the length of contact lines at contact point Y —
lb,Y
C surface roughness structure factor —
RS
C K
gradient of the permissible temperature function for X >10,
th
T
C thermal correction factor at contact point Y —
th,Y
C K
gradient of the permissible temperature function for X ≤10,
tn
T
C lubricating film thickness factor at contact point Y —
λ,Y
c specific heat per unit mass of pinion / wheel J/(kgK)
M
D rotating direction factor —
2
E' reduced modulus of elasticity N/mm
e exponent (ISO 10300-2 shall apply) —
e immersion depth mm
d
F nominal normal force at mean point P (ISO 10300-2 shall apply) N
n
F nominal tangential force of virtual cylindrical gears N
vmt
f meshing coordinate of middle contact line at contact point Y mm
m,Y
f meshing coordinate of root contact line at contact point Y mm
r,Y
f meshing coordinate of tip contact line at contact point Y mm
t,Y
G material parameter —
g length of tip path of contact of virtual cylindrical gear mm
va
g coordinate for transverse path of contact at contact point Y mm
Y
h lubricating film thickness at contact point Y μm
0,Y
[5], [6]
h' lubricating film thickness according to Ertl/Grubin at contact point Y μm
0,Y
i number of calculation points along the path of contact —
K face load factor for contact stress at contact point Y —
Hβ,Y
L thermal load factor —
Y
l length of contact line (Method B1) at contact point Y mm
b,Y
l theoretical length of contact line at contact point Y mm
b0,Y
M centre of path of contact —
Y
P load dependent power losses kW
VZP
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ISO/TS 10300-20:2021(E)
Table 2 (continued)
Symbol Description or term Unit
2
p Hertzian stress N/mm
H
*
p related peak load for calculating the load sharing factor (Method B1) at —
Y
contact point Y
S local safety factor regarding scuffing at contact point Y —
S,Y
s local sliding-rolling-ratio at contact point Y —
x,Y
T pinion torque of the test load stage Nm
1T
t contact exposure time s
C
U local velocity parameter at contact point Y —
Y
v sliding velocity in tooth lengthwise direction at the mean point m/s
gs
v sliding velocity at contact point Y m/s
g,Y
v sliding velocity in profile direction at contact point Y m/s
gh,Y
v sum of velocities at contact point Y m/s
Σ,Y
v sum of velocities in profile direction at contact point Y m/s
Σh,Y
v sum of velocities in lengthwise direction m/s
Σs
v sum of velocities vertical to the contact line at contact point Y m/s
Σ vert,Y
W local load parameter at contact point Y —
Y
w maximum line load along path of contact N/mm
max
w surface velocity vertical to the contact line m/s
tvert
w local surface velocity in profile direction at contact point Y m/s
t1,2,h,Y
w surface velocity in lengthwise direction m/s
t1,2s
w local surface velocity m/s
t1,2,Y
X tip relief factor —
CA
X running-in factor —
E
X lubricant factor —
L
X local load sharing factor at contact point Y —
LS,Y
X driving direction factor —
Q
X lubrication factor —
S
X temperature factor —
T
X relative material structure factor —
WrelT
X curvature factor at contact point Y —
Y
x coordinates of the ends of the contact line at contact point Y mm
1,2,Y
y coordinates of the ends of the contact line at contact point Y mm
1,2,Y
2 1/2
Z elasticity factor (ISO 10300-2 shall apply) (N/mm )
E
z auxiliary value at contact point Y mm
Y
2
α pressure-viscosity coefficient m /N
p,θ
α temperature coefficient of the dynamic viscosity 1/K
th
ε tip contact ratio —
a
ε root contact ratio —
f
ε virtual addendum contact ratio —
v
ε root transverse contact ratio of virtual cylindrical gears —
vf
ε virtual maximum addendum contact ratio —
vmax
2
η dynamic viscosity at bulk temperature N s/m
M
2
η dynamic viscosity at bulk temperature θ N s/m
θ1,2 1,2
θ local contact temperature at contact point Y °C
C,Y
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ISO/TS 10300-20:2021(E)
Table 2 (continued)
Symbol Description or term Unit
θ flash temperature at contact point Y °C
fl,Y
θ bulk temperature °C
M
θ limit temperature according to standard scuffing tests °C
S,DIN
θ permissible scuffing temperature °C
S
θ permissible temperature considering the influence of the contact tem- °C
S,C
perature
θ oil temperature °C
Oil
θ reference oil temperature °C
Oil,Ref
λ specific heat conductivity of the oil W/(mK)
λ specific heat conductivity of material W/(mK)
M
λ local relative lubricating film thickness at contact point Y —
z,Y
μ local coefficient of friction at contact point Y —
Y
3
ρ density of material kg/m
M
ρ local equivalent radius of curvature vertical to the contact line at point C mm
rel,C
ρ local equivalent radius of curvature vertical to the contact line at con- mm
rel,Y
tact point Y
ρ radius of relative profile curvature (Method B2) mm
t
2
σ contact stress at contact point Y N/mm
H,Y
2
σ modified contact stress at contact point Y N/mm
H,mod,Y
ω angle between the surface velocities in lengthwise and tooth profile direc- °
wt1,2,Y
tion at contact point Y
Table 3 — Generally used subscripts
Subscripts Description
0 tool
1 pinion
2 wheel
A, B, B1, B2, C value according to Method A, B, B1, B2 or C
D drive flank /drive side
C coast flank / coast side
T relative to standardized test gear dimensions
(1), (2) trials of interpolation
Y contact point variable
5 Virtual cylindrical gear
5.1 General
The calculation method in this document uses virtual cylindrical gears to determine relevant
parameters, see ISO 10300-1.
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ISO/TS 10300-20:2021(E)
5.2 Local geometry parameters
5.2.1 Transverse path of contact
For local calculation of the flash temperature, θ , along the transverse path of contact, the coordinate
fl,Y
g is introduced with its origin in the pitch point C, i.e. g (C)=0, as shown in Figure 1.
Y Y
Figure 1 — Transverse path of contact
Towards the pinion tip g is defined as positive and towards the pinion root it is defined as negative. In
Y
the boundary points A and E on the transverse path of contact g is determined by Formulae (1) and (2).
Y
gg()A =− (1)
Yva2
gg()E = (2)
Yva1
where
1
2 2 2 2
(3)
gg=+gd=−dd− sinsα +−dd −d innα
vvα av12avav1 bv1 12vetvavbv2 2 vet
( ) ( )
2
g is the length of path of contact of virtual cylindrical gear in transverse section;
vα
g is the length of tip path of contact;
va
α is the transverse pressure angle of virtual cylindrical gear;
vet
d is the reference diameter of virtual cylindrical gear;
v
d is the tip diameter of virtual cylindrical gear;
va
d is the base diameter of virtual cylindrical gear.
vb
Between the two boundary points the length of the transverse path of contact can be subdivided in
a number of sections i which are specified by the user. For bevel gears with mean spiral angle zero
(β = 0) calculations are not performed at the tip and root boundary points to avoid infinity values in
m
some of the following formulae. Formula (4) is used to calculate the coordinate g (Y) of a contact point
Y
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ISO/TS 10300-20:2021(E)
Y on the transvers path of contact using auxiliary variable k to exclude tip and root boundary points
s
for bevel gears with mean spiral angle zero (β = 0).
m
()12− kg
svα
gg()YA=()()+kg +Y∙ with Yi=…0 (4)
YY svα
i
where
k = 0 for bevel gears with β > 0;
s vb
k = 0,001 for bevel gears with β = 0.
s vb
NOTE In all following formulae, g is a function of Y (g = g (Y)).
Y Y Y
5.2.2 Length of contact lines
A general definition of the length of contact lines is shown in Figure 2.
Figure 2 — General definition of length of contact lines
Distance of the tip, f , middle, f ,and root, f , contact line in the zone of action can be calculated by
t,Y m,Y r,Y
using Formulae (5) to (7).
fg=−()gg/c2+ ∙ osβ (5)
mY, va2 vYα vb
ff=+p ∙ cosβ (6)
tY,,mY vetvb
ff=−p ∙ cosβ (7)
rY,,mY vetvb
where
β is the helix angle at base circle;
vb
p is the transverse base pitch.
vet
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ISO/TS 10300-20:2021(E)
If the absolute value of f , f , or f is larger than f , the contact line is outside the zone of action.
m,Y t,Y r,Y max
Therefore the length of contact line l (see Formula (13)) and l (see Formula (14)) is set to zero.
b,Y b0,Y
Otherwise, l and l are calculated with Formulae (8) to (15).
b,Y b0,Y
Coordinates of the ends of the contact line x ; y can be calculated with Formulae (8) to (12).
1,2,Y 1,2,Y
For bevel gears with β = 0:
vb
x =0 (8)
1,Y
xb= (9)
2,Yv,eff
For bevel gears with β > 0:
vb
b
1
v,eff
ffcostββ++an sintβ ++gb anγγ
()
YvbvbY vb vvα ,eff
2 2
x = ≥0 (10)
1,Y
tantγβ+ an
vb
b
1
v,eff
ffcostββ++an sintβ −−gb anγγ
()
YvbvbY vb vvα ,eff
2 2
x = ≤b (11)
2,Y v,eff
tantγβ+ an
vb
where
b is the effective face width;
v,eff
γ is the auxiliary angle for length of contact line calculation.
b
v,eff
yx=− tancββ++ffos tansββin + (12)
12,,YY12,, vb YvbvbY vb
2
x and y shall be calculated with f , f and f for three contact lines.
1,2,Y 1,2,Y m,Y t,Y r,Y
Length of contact line, l , shall be calculated with Formulae (13) to (15).
b,Y
ll=−1 C (13)
()
bY,,bY0 lb,Y
where
2 2
lx=−xy+− y (14)
() ()
bY01,,YY2,,12YY,
l is the theoretical length of contact line;
b0,Y
2
2
b
f
v,eff
Y
C =−11 − (15)
lb,Y
f b
max v
C is the correction factor for the length of contact lines;
lb,Y
b is the face width;
v
f is the maximum distance to middle contact line.
max
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ISO/TS 10300-20:2021(E)
5.2.3 Local equivalent radius of curvature, ρ
rel,Y
Local equivalent radius of curvature vertical to the contact line in the contact point Y, ρ , shall be
rel,Y
calculated with Formulae (16) and (17).
1
ρρ= (16)
relY, rel
2
X
Y
where
ρ is the local equivalent radius of curvature vertical to the contact line;
rel
tanα
vet
X = (17)
Y
()dg/s2 ∙ inαα+ (dg/s2 ∙ in − ))
vv1 et Y vv2 et Y
∙
d /2 d /2
vb1 vb2
X is the curvature factor.
Y
5.2.4 Local load sharing factor, X
LS,Y
Local load sharing factor, X , shall be calculated with Formulae (18) to (20).
LS,Y
*
A
mY,
X = (18)
LS,Y
* * *
AA++A
tY, mY, rY,
where
1
**
Ap= π ∙∙ l (19)
YY bY,
4
is the related area for calculating the local load sharing factor, X
*
LS,Y;
A
Y
e
w f
* Y Y
p ==10− ≥ (20)
Y
w f
max max
*
is the related peak load for calculating the local load sharing factor;
p
Y
e is the exponent.
The load distribution along the contact line is shown in Figure 3.
Figure 3 — Load distribution along the contact line through Y
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ISO/TS 10300-20:2021(E)
Local face load factor, K , for contact stress shall be calculated with Formulae (21) to (23).
Hβ,Y
a
KK=− ∙∙10()bz ≥ (21)
HYββ, HY Y
with auxiliary values
2 2
bx +x yy+ l
g
v,effY12,,Y 12,,YY bm,Y
vα
zM= Y =− +− g +−g ≤ (22)
[]
YY va2 Y
22 2 222
1 2
a= ; b = (23)
Y
K −1 l
Hβ bm,Y
where K is the face load factor.
Hβ
6 Stresses and velocities
6.1 Local modified contact stress, σ
...
TECHNICAL ISO/TS
SPECIFICATION 10300-20
First edition
Calculation of load capacity of bevel
gears —
Part 20:
Calculation of scuffing load capacity —
Flash temperature method
Calcul de la capacité de charge des engrenages coniques —
Partie 20: Calcul de la capacité de charge au grippage — Méthode de
la température-éclair
PROOF/ÉPREUVE
Reference number
ISO/TS 10300-20:2021(E)
©
ISO 2021
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ISO/TS 10300-20:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021
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: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii PROOF/ÉPREUVE © ISO 2021 – All rights reserved
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ISO/TS 10300-20:2021(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Virtual cylindrical gear . 4
5.1 General . 4
5.2 Local geometry parameters . 5
5.2.1 Transverse path of contact . 5
5.2.2 Length of contact lines . 6
5.2.3 Local equivalent radius of curvature, ρ .
rel,Y 8
5.2.4 Local load sharing factor, X .
LS,Y 8
6 Stresses and velocities . 9
6.1 Local modified contact stress, σ .
H,mod,Y 9
6.2 Sliding and sum of velocities .10
6.3 Local relative lubricating film thickness, λ .
z,Y 11
6.4 Local coefficient of friction, µ .
Y 14
7 Local contact temperature, θ .14
C,Y
7.1 General .14
7.2 Power losses influencing the bulk temperature.15
7.2.1 General.15
7.2.2 Method A .15
7.2.3 Method B .15
7.2.4 Method C .15
7.3 Bulk temperature .15
7.3.1 General.15
7.3.2 Method A .15
7.3.3 Method B .15
7.3.4 Tip relief factor, X .
CA 17
7.4 Local flash temperature, θ .
fl,Y 17
8 Permissible contact temperature .18
8.1 Limit temperature from scuffing test, θ .
S,DIN 18
8.2 Permissible temperature, θ .
SC 19
8.3 Permissible scuffing temperature, θ .
S,Y 20
9 Local safety factor, S .21
S,Y
Bibliography .22
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ISO/TS 10300-20:2021(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.
A list of all parts in the ISO 10300 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/TS 10300-20:2021(E)
Introduction
The ISO 10300 series consists of International Standards, Technical Specifications (TS) and Technical
Reports (TR) under the general title Calculation of load capacity of bevel gears (see Table 1).
— International Standards contain calculation methods that are based on widely accepted practices
and have been validated.
— TS contain calculation methods that are still subject to further development.
— TR contain data that is informative, such as example calculations.
The procedures specified in ISO 10300 parts 1 to 19 cover fatigue analyses for gear rating. The
procedures described in ISO 10300 parts 20 to 29 are predominantly related to the tribological
behaviour of the lubricated flank surface contact. ISO 10300 parts 30 to 39 include example calculations.
The ISO 10300 series allows the addition of new parts under appropriate numbers to reflect knowledge
gained in the future.
Requesting standardized calculations according to the ISO 10300 series without referring to specific
parts requires the use of only those parts that are currently designated as International Standards (see
Table 1 for listing). When requesting further calculations, the relevant part or parts of the ISO 10300
series need to be specified. Use of a Technical Specification as acceptance criteria for a specific design
need to be agreed in advance between manufacturer and purchaser.
Table 1 — Parts of ISO 10300 series (status as of DATE OF PUBLICATION)
Calculation of load capacity of bevel gears International Technical Technical
Standard Specification Report
a
Part 1: Introduction and general influence factors X
a
Part 2: Calculation of surface durability (pitting) X
a
Part 3: Calculation of tooth root strength X
Part 4 to 19: to be assigned
Part 20: Calculation of scuffing load capacity — Flash X
temperature method
Part 21 to 29: to be assigned
Part 30: ISO rating system for bevel and hypoid gears X
— Sample calculations
Part 32: ISO rating system for bevel and hypoid gears X
b
— Sample Calculations of scuffing load capacity
a
Under revision.
b
Under preparation.
This document and the other parts of the ISO 10300 series provide a coherent system of procedures
for the calculation of the load capacity of bevel and hypoid gears. The ISO 10300 series is designed to
facilitate the application of future knowledge and developments, and also the exchange of information
gained from experience.
Design considerations to prevent fractures emanating from stress raisers in the tooth flank, tip
chipping and failures of the gear blank through the web or hub will need to be analysed by general
machine design methods.
Several methods for the calculation of load capacity, as well as for the calculation of various factors, are
permitted. The directions in the ISO 10300 series are thus complex, but also flexible.
Scuffing is a localized damage caused by solid-phase welding between sliding surfaces. It is accompanied
by transfer of metal from one surface to another due to welding and tearing. Scuffing can occur in
gear flanks that operate in the boundary-lubrication regime where the lubricant film is insufficient
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ISO/TS 10300-20:2021(E)
to separate tooth surfaces and contact breaks through the oxide layers that normally protect the
[3]
surfaces and enables bare metal surfaces to weld together. Blok hypothesized that scuffing occurs
when the maximum surface temperature in the contact reaches a critical value. The maximum contact
temperature is determined by the sum of the gear tooth bulk temperature and the local, instantaneous
flash temperature. Scuffing risk is determined by comparing the maximum contact temperature to the
critical temperature. The critical temperature is not only a function of the lubricant-metal-atmosphere
combination; but it depends also upon operating conditions and surface characteristics. Consequently,
the most reliable critical temperatures are determined from tests performed on actual gears, under
actual service loads, and in actual service environments.
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TECHNICAL SPECIFICATION ISO/TS 10300-20:2021(E)
Calculation of load capacity of bevel gears —
Part 20:
Calculation of scuffing load capacity — Flash
temperature method
WARNING — The user is cautioned that when the formulae are used for large average mean
spiral angles ββ+ /2>°45 , for effective pressure angles α >°30 and/or for large face
()
m1 m2 e
widths bm>13⋅ , the calculated results of the ISO 10300 series should be confirmed by
mn
experience.
1 Scope
This document provides a calculation method for bevel and hypoid gears regarding scuffing based on
[6]
experimental and theoretical investigation . This calculation method is a flash temperature method.
The formulae in this document are intended to establish uniformly acceptable methods for calculating
scuffing resistance of straight, helical (skew), spiral bevel, Zerol and hypoid gears made of steel. 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.
A calculation method of the scuffing load capacity of bevel and hypoid gears based on an integral
temperature method is not available when this document is published.
The formulae in this document are based on virtual cylindrical gears and restricted to bevel gears
whose virtual cylindrical gears have transverse contact ratios of ε < 2. The results are valid within
vα
the range of the applied factors as specified in ISO 10300-1 (see ISO 6336-2). Additionally, the given
relations are valid for bevel gears of which the sum of profile shift coefficients of pinion and wheel is
zero (see ISO 23509).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 10300-1, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors
ISO 10300-2, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability (pitting)
ISO 14635-1, Gears — FZG test procedures — Part 1: FZG test method A/8,3/90 for relative scuffing load-
carrying capacity of oils
ISO 17485, Bevel gears — ISO system of accuracy
ISO 23509, Bevel and hypoid gear geometry
3 Terms and definitions
No terms and definitions are listed in this document.
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ISO/TS 10300-20:2021(E)
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols
For the purposes of this document, the symbols and units given in ISO 10300-1, ISO 23509 and Table 2
apply. Table 3 lists the generally used subscripts.
Table 2 — Symbols and units
Symbol Description or term Unit
A* related area for calculating the load sharing factor X at contact point Y mm
Y LS
a auxiliary value mm
a reference centre distance mm
ref
B accuracy grade (ISO 17485 shall apply) —
0,5
B thermal contact coefficient N/(ms K)
M
b half of the Hertzian contact width mm
H
b auxiliary value 1/mm
Y
C tip relief μm
A
C effective tip relief μm
eff
C correction factor for the length of contact lines at contact point Y —
lb,Y
C surface roughness structure factor —
RS
C K
gradient of the permissible temperature function for X >10,
th
T
C thermal correction factor at contact point Y —
th,Y
C K
gradient of the permissible temperature function for X ≤10,
tn
T
C lubricating film thickness factor at contact point Y —
λ,Y
c specific heat per unit mass of pinion / wheel J/(kgK)
M
D rotating direction factor —
2
E' reduced modulus of elasticity N/mm
e exponent (ISO 10300-2 shall apply) —
e immersion depth mm
d
F nominal normal force at mean point P (ISO 10300-2 shall apply) N
n
F nominal tangential force of virtual cylindrical gears N
vmt
f meshing coordinate of middle contact line at contact point Y mm
m,Y
f meshing coordinate of root contact line at contact point Y mm
r,Y
f meshing coordinate of tip contact line at contact point Y mm
t,Y
G material parameter —
g length of tip path of contact of virtual cylindrical gear mm
va
g coordinate for transverse path of contact at contact point Y mm
Y
h lubricating film thickness at contact point Y μm
0,Y
[4], [5]
h' lubricating film thickness according to Ertl/Grubin at contact point Y μm
0,Y
i number of calculation points along the path of contact —
K face load factor for contact stress at contact point Y —
Hβ,Y
L thermal load factor —
Y
l length of contact line (Method B1) at contact point Y mm
b,Y
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ISO/TS 10300-20:2021(E)
Table 2 (continued)
Symbol Description or term Unit
l theoretical length of contact line at contact point Y mm
b0,Y
M centre of path of contact —
Y
P load dependent power losses kW
VZP
2
p Hertzian stress N/mm
H
*
p related peak load for calculating the load sharing factor (Method B1) at —
Y
contact point Y
S local safety factor regarding scuffing at contact point Y —
S,Y
s local sliding-rolling-ratio at contact point Y —
x,Y
T pinion torque of the test load stage Nm
1T
t contact exposure time s
C
U local velocity parameter at contact point Y —
Y
v sliding velocity in tooth lengthwise direction at the mean point m/s
gs
v sliding velocity at contact point Y m/s
g,Y
v sliding velocity in profile direction at contact point Y m/s
gh,Y
v sum of velocities at contact point Y m/s
Σ,Y
v sum of velocities in profile direction at contact point Y m/s
Σh,Y
v sum of velocities in lengthwise direction m/s
Σs
v sum of velocities vertical to the contact line at contact point Y m/s
Σ vert,Y
W local load parameter at contact point Y —
Y
w maximum line load along path of contact N/mm
max
w surface velocity vertical to the contact line m/s
tvert
w local surface velocity in profile direction at contact point Y m/s
t1,2,h,Y
w surface velocity in lengthwise direction m/s
t1,2s
w local surface velocity m/s
t1,2,Y
X tip relief factor —
CA
X running-in factor —
E
X lubricant factor —
L
X local load sharing factor at contact point Y —
LS,Y
X driving direction factor —
Q
X lubrication factor —
S
X temperature factor —
T
X relative material structure factor —
WrelT
X curvature factor at contact point Y —
Y
x coordinates of the ends of the contact line at contact point Y mm
1,2,Y
y coordinates of the ends of the contact line at contact point Y mm
1,2,Y
2 1/2
Z elasticity factor (ISO 10300-2 shall apply) (N/mm )
E
z auxiliary value at contact point Y mm
Y
2
α pressure-viscosity coefficient m /N
p,θ
α temperature coefficient of the dynamic viscosity 1/K
th
ε tip contact ratio —
a
ε root contact ratio —
f
ε virtual addendum contact ratio —
v
ε root transverse contact ratio of virtual cylindrical gears —
vf
ε virtual maximum addendum contact ratio —
vmax
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ISO/TS 10300-20:2021(E)
Table 2 (continued)
Symbol Description or term Unit
2
η dynamic viscosity at bulk temperature N s/m
M
2
ηθ1,2 dynamic viscosity at bulk temperature θ N s/m
1,2
θ local contact temperature at contact point Y °C
C,Y
θ flash temperature at contact point Y °C
fl,Y
θ bulk temperature °C
M
θ limit temperature according to standard scuffing tests °C
S,DIN
θ permissible scuffing temperature °C
S
θ permissible temperature considering the influence of the contact tem- °C
S,C
perature
θ oil temperature °C
Oil
θ reference oil temperature °C
Oil,Ref
λ specific heat conductivity of the oil W/(mK)
λ specific heat conductivity of material W/(mK)
M
λ local relative lubricating film thickness at contact point Y —
z,Y
μ local coefficient of friction at contact point Y —
Y
3
ρ density of material kg/m
M
ρ local equivalent radius of curvature vertical to the contact line at point C mm
rel,C
ρ local equivalent radius of curvature vertical to the contact line at con- mm
rel,Y
tact point Y
ρ radius of relative profile curvature (Method B2) mm
t
2
σ contact stress at contact point Y N/mm
H,Y
2
σ modified contact stress at contact point Y N/mm
H,mod,Y
ω angle between the surface velocities in lengthwise and tooth profile direc- °
wt1,2,Y
tion at contact point Y
Table 3 — Generally used subscripts
Subscripts Description
0 tool
1 pinion
2 wheel
A, B, B1, B2, C value according to Method A, B, B1, B2 or C
D drive flank /drive side
C coast flank / coast side
T relative to standardized test gear dimensions
(1), (2) trials of interpolation
Y contact point variable
5 Virtual cylindrical gear
5.1 General
The calculation method in this document uses virtual cylindrical gears to determine relevant
parameters, see ISO 10300-1.
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ISO/TS 10300-20:2021(E)
5.2 Local geometry parameters
5.2.1 Transverse path of contact
For local calculation of the flash temperature, θ , along the transverse path of contact, the coordinate
fl,Y
g is introduced with its origin in the pitch point C, i.e. g (C)=0, as shown in Figure 1.
Y Y
Figure 1 — Transverse path of contact
Towards the pinion tip g is defined as positive and towards the pinion root it is defined as negative. In
Y
the boundary points A and E on the transverse path of contact g is determined by Formulae (1) and (2).
Y
gg()A =− (1)
Yva2
gg()E = (2)
Yva1
where
1
2 2 2 2
(3)
gg=+gd=−dd− sinsα +−dd −d innα
() ()
vvα av12ava1 vv12et va v2 vet
vb1 vb2
2
g is the length of path of contact of virtual cylindrical gear in transverse section;
vα
g is the length of tip path of contact;
va
α is the transverse pressure angle of virtual cylindrical gear;
vet
d is the reference diameter of virtual cylindrical gear;
v
d is the tip diameter of virtual cylindrical gear;
va
d is the base diameter of virtual cylindrical gear.
vb
Between the two boundary points the length of the transverse path of contact can be subdivided in
a number of sections i which are specified by the user. For bevel gears with mean spiral angle zero
(β = 0) calculations are not performed at the tip and root boundary points to avoid infinity values in
m
some of the following formulae. Formula (4) is used to calculate the coordinate g (Y) of a contact point
Y
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ISO/TS 10300-20:2021(E)
Y on the transvers path of contact using auxiliary variable k to exclude tip and root boundary points
s
for bevel gears with mean spiral angle zero (β = 0).
m
12− kg
()
svα
gg()YA= ()+kg +Y∙ with Y=…0 i (4)
()
YY svα
i
where
k = 0 for bevel gears with β > 0;
s vb
k = 0,001 for bevel gears with β = 0.
s vb
NOTE In all following formulae, g is a function of Y (g = g (Y)).
Y Y Y
5.2.2 Length of contact lines
A general definition of the length of contact lines is shown in Figure 2.
Figure 2 — General definition of length of contact lines
Distance of the tip, f , middle, f ,and root, f ,contact line in the zone of action can be calculated by
t,Y m,Y r,Y
using Formulae (5) to (7).
fg=−()gg/c2+ ∙ osβ (5)
mY, va2 vYα vb
ff=+p ∙ cosβ (6)
tY,,mY vetvb
ff=−p ∙ cosβ (7)
rY,,mY vetvb
where
β is the helix angle at base circle;
vb
p is the transverse base pitch.
vet
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ISO/TS 10300-20:2021(E)
If the absolute value of f , f , or f is larger than f , the contact line is outside the zone of action.
m,Y t,Y r,Y max
Therefore the length of contact line l (see Formula (13)) and l (see Formula (14)) is set to zero.
b,Y b0,Y
Otherwise, l and l are calculated with Formulae (8) to (15).
b,Y b0,Y
Coordinates of the ends of the contact line x ; y can be calculated with Formulae (8) to (12).
1,2,Y 1,2,Y
For bevel gears with β = 0:
vb
x =0 (8)
1,Y
xb= (9)
2,Yv,eff
For bevel gears with β > 0:
vb
b
1
ve, ff
ffcostββ++an sintβ ++gb anγγ
()
YvbvbY vb vvα ,eff
2 2
x = ≥0 (10)
1,Y
tantγβ+ an
vb
b
1
ve, ff
ffcostββ++an sintβ −−gb anγγ
()
YvbvbY vb vvα ,eff
2 2
x = ≤b (11)
2,Y ve, ff
tantγβ+ an
vb
where
b is the effective face width;
v,eff
γ is the auxiliary angle for length of contact line calculation.
b
ve, ff
yx=− tancββ++ffos tansββin + (12)
12,,YY12,, vb YvbvbY vb
2
x and y shall be calculated with f , f and f for three contact lines.
1,2,Y 1,2,Y m,Y t,Y r,Y
Length of contact line, l , shall be calculated with Formulae (13) to (15).
b,Y
ll=−1 C (13)
()
bY,,bY0 lb,Y
where
2 2
lx=−xy+− y (14)
() ()
bY01,,YY2,,12YY,
l is the theoretical length of contact line;
b0,Y
2
2
b
f
ve, ff
Y
C =−11 − (15)
lb,Y
f b
max v
C is the correction factor for the length of contact lines;
lb,Y
b is the face width;
v
f is the maximum distance to middle contact line.
max
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ISO/TS 10300-20:2021(E)
5.2.3 Local equivalent radius of curvature, ρ
rel,Y
Local equivalent radius of curvature vertical to the contact line in the contact point Y, ρ , shall be
rel,Y
calculated with Formulae (16) and (17).
1
ρρ= (16)
relY, rel
2
X
Y
where
ρ is the local equivalent radius of curvature vertical to the contact line;
rel
tanα
vet
X = (17)
Y
dg/s2 ∙ inαα+ dg/s2 ∙ in −
() ( ))
vv1 et Y vv2 et Y
∙
d /2 d /2
vb1 vb2
X is the curvature factor.
Y
5.2.4 Local load sharing factor, X
LS,Y
Local load sharing factor, X , shall be calculated with Formulae (18) to (20).
LS,Y
*
A
mY,
X = (18)
LS,Y
* * *
AA++A
tY, mY, rY,
where
1
**
Ap= π ∙∙ l (19)
YY bY,
4
is the related area for calculating the local load sharing factor, X
*
LS,Y;
A
Y
e
w f
Y Y
*
p ==10− ≥ (20)
Y
w f
max max
*
is the related peak load for calculating the local load sharing factor;
p
Y
e is the exponent.
The load distribution along the contact line is shown in Figure 3.
Figure 3 — Load distribution along the contact line through Y
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ISO/TS 10300-20:2021(E)
Local face load factor, K , for contact stress shall be calculated with Formulae (21) to (23).
Hβ,Y
a
KK=− ∙∙10()bz ≥ (21)
HYββ, HY Y
with auxiliary values
2 2
bx +x yy+ l
g
ve,,ff 12YY,,12YY, bm ,Y
v
...
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