ISO 10300-2:2023

INTERNATIONAL ISO
STANDARD 10300-2
Third edition
2023-08
Calculation of load capacity of bevel
gears —
Part 2:
Calculation of surface durability
(macropitting)
Calcul de la capacité de charge des engrenages coniques —
Partie 2: Calcul de la résistance à la pression superficielle (macro-
écaillage)
Reference number
ISO 10300-2:2023(E)
© ISO 2023

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ISO 10300-2:2023(E)
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© ISO 2023
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Published in Switzerland
ii
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ISO 10300-2:2023(E)
Contents Page
Foreword .iv
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, general subscripts and abbreviated terms . 2
5 Macropitting damage — General aspects . 6
5.1 Acceptable versus unacceptable macropitting . 6
5.2 Assessment requirements . 6
5.3 General rating procedure . 7
6 Gear flank rating formulae — Method B1 . 7
6.1 Contact stress formula . 7
6.2 Permissible contact stress . 8
6.3 Calculated safety factor for contact stress . 8
6.4 Contact stress factors . 9
6.4.1 Mid-zone factor, Z . 9
M-B
6.4.2 Load sharing factor, Z . 10
LS
6.5 Permissible contact stress factors . 11
6.5.1 Bevel gear factor, Z . 11
KP
6.5.2 Size factor, Z .12
X
6.5.3 Hypoid factor, Z .12
Hyp
7 Gear flank rating formulae — Method B2 .15
7.1 Contact stress formula .15
7.2 Permissible contact stress . 16
7.3 Calculated safety factor for contact stress . 16
7.4 Contact stress factors . 16
7.4.1 General . 16
7.4.2 Macropitting resistance geometry factor, Z . 17
I
7.4.3 Facewidth factor, Z .20
FW
7.4.4 Contact stress adjustment factor, Z . 20
A
8 Factors for contact stress and permissible contact stress common for method B1
and method B2 .21
8.1 Elasticity factor, Z . 21
E
8.2 Lubricant film influence factors, Z , Z , Z . 21
L v R
8.2.1 General . 21
8.2.2 Restrictions . 21
8.2.3 Method B . . 21
8.2.4 Method C (product of Z , Z and Z ) . 23
L v R
8.3 Work hardening factor, Z .23
W
8.3.1 General .23
8.3.2 Work hardening factor, Z : Method A . 23
W
8.3.3 Work hardening factor, Z : Method B . 24
W
8.4 Life factor, Z . 26
NT
8.4.1 General . 26
8.4.2 Method A . . . 27
8.4.3 Method B .28
Annex A (informative) Local calculation method for surface durability (macropitting) –
Method B1-localised .29
Bibliography .35
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ISO 10300-2:2023(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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use
of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed
patent rights in respect thereof. As of the date of publication of this document, ISO had not received
notice of (a) patent(s) which may be required to implement this document. However, implementers are
cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all
such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear
capacity calculation.
This third edition cancels and replaces the second edition (ISO 10300-2:2014), which has been
technically revised.
The main changes are as follows:
— Table 1 has been inserted;
— Table 2 has been inserted;
— the term “pitting” has been replaced by “macropitting”;
— bevel gear factor, Z , for the calculation of the nominal value of the contact stress has been removed;
K
instead, a new bevel gear factor, Z , has been introduced for the calculation of the permissible
KP
contact stress;
— Formula (37) for the calculation of the length of action considering adjacent teeth has been modified;
— subclause 8.3 — work hardening factor, Z , has been updated and method A added;
W
— Figure 2 — load distribution in the contact area has been updated as the symbol for exponent e has
been changed to e ;
LS
— Figure 6 — facewidth factor, Z has been removed;
FW
— Figure 7 — lubricant factor, Z , for mineral oils has been removed;
L
— Figure 8 — speed factor, Z has been removed;
V
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ISO 10300-2:2023(E)
— Figure 9 — roughness factor, Z has been removed;
R
— Figure 10 — work hardening factor, Z has been removed;
W
— former Annex A has been replaced by new Annex A describing a local calculation method for surface
durability (macropitting) – Method B1-localised.
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 10300-2:2023(E)
Introduction
When ISO 10300:2001 (all parts) 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.
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, a separate clause: “Gear
flank rating formulae — Method B2” has been included in this document, while the former method B
was renamed method B1. It became necessary to present a new, clearer structure of the three parts,
which is illustrated in ISO 10300-1:2023, Figure 1.
NOTE ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when to use
method B2.
This document deals with the failure of gear teeth by macropitting, a fatigue phenomenon. Two varieties
of macropitting are recognized, initial and destructive macropitting.
In applications employing low hardness steel or through hardened steel, initial macropitting
frequently occurs during early use and is not deemed serious. Initial macropitting is characterized by
small pits which do not extend over the entire facewidth or profile depth of the affected tooth. The
degree of acceptability of initial macropitting varies widely, depending on the gear application. Initial
macropitting occurs in localized overstressed areas and tends to redistribute the load by progressively
removing high contact spots. Generally, when the load has been redistributed, the macropitting stops.
In applications employing high hardness steel and case carburized steel, the variety of macropitting
that occurs is usually destructive. The formulae for macropitting resistance given in this document are
intended to assist in the design of bevel gears which stay free from destructive macropitting during
[5]
their design lives (for additional information, see ISO/TR 22849 ).
The basic formulae, first developed by Hertz for the contact pressure between two curved surfaces,
have been modified to consider the following four items: the load sharing between adjacent teeth,
the position of the centre of pressure on the tooth, the shape of the instantaneous area of contact and
the load concentration resulting from manufacturing uncertainties. The Hertzian contact pressure
serves as the theory for the assessment of surface durability with respect to macropitting. Although
all premises for a gear mesh are not satisfied by Hertzian relations, their use can be justified by the
fact that, for a gear material, the limits of the Hertzian pressure are determined on the basis of running
tests with gears, which include the additional influences in the analysis of the limit values. Therefore, if
the reference is within the application range, Hertzian pressure can be used to convert test gear data to
gears of various types and sizes.
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 ISO 10300-1:2023, 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 face and transverse load distribution factors.
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INTERNATIONAL STANDARD ISO 10300-2:2023(E)
Calculation of load capacity of bevel gears —
Part 2:
Calculation of surface durability (macropitting)
1 Scope
This document specifies the basic formulae for use in the determination of the surface load capacity
of straight and helical (skew), Zerol and spiral bevel gears including hypoid gears, and comprises all
the influences on surface durability for which quantitative assessments can be made. This document is
applicable to oil lubricated bevel gears, as long as sufficient lubricant is present in the mesh at all times.
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.
The formulae in this document are not directly applicable to the assessment of other types of gear tooth
surface damage, such as plastic yielding, scratching, scuffing or any other type not specified.
NOTE This document is not applicable to bevel gears which have an inadequate contact pattern under load.
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 facewidths b > 13 m , the
m1 m2 e mn
calculated results of this document should be confirmed by experience.
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 701, International gear notation — Symbols for geometrical data
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 10300-1, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence
factors
ISO 17485, Bevel gears — ISO system of accuracy
ISO 23509, Bevel and hypoid gear geometry
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1122-1 and ISO 23509 and the
following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
1
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ISO 10300-2:2023(E)
3.1
macropitting
material fatigue phenomenon of two meshing surfaces under load
3.2
nominal contact stress
σ
H0
contact stress calculated on the basis of the Hertzian theory at the critical point of load application for
error-free gears loaded by a constant nominal torque
3.3
contact stress
σ
H
determinant contact stress at the critical point of load application including the load factors which
consider static and dynamic loads and load distribution
3.4
allowable stress number (contact)
σ
H,lim
maximum contact stress of standardized test gears and determined at standardized operating
conditions, as specified in ISO 6336-5
3.5
permissible contact stress
σ
HP
maximum contact stress of the evaluated gear set including all influence factors
4 Symbols, general subscripts and abbreviated terms
For the purposes of this document, the symbols given in ISO 701, ISO 17485, ISO 23509 and the following
shall apply.
Table 1 — Symbols
Symbol Description or term Unit
A Auxiliary factor for calculating the dynamic factor K —
v-C
A* Related area for calculating the load sharing factor Z mm
LS
*
Area above the middle contact line mm
A
m
*
Area above the root contact line mm
A
r
*
Area above the tip contact line mm
A
t
b Facewidth mm
b Relative base facewidth —
b
C , C , Constants for determining lubricant film factors —
ZL ZR
C
ZV
d Outer pitch diameter mm
e
d Mean pitch diameter mm
m
d Reference diameter of virtual cylindrical gear mm
v
d Tip diameter of virtual cylindrical gear mm
va
d Base diameter of virtual cylindrical gear mm
vb
2
E Modulus of elasticity, Young’s modulus N/mm
e Exponent for the load distribution along the lines of contact —
LS
F Auxiliary variable for mid-zone factor —
F Nominal tangential force at mid-facewidth of the reference cone N
mt
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ISO 10300-2:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Description or term Unit
F Nominal normal force N
n
f Distance from the centre of the zone of action to a contact line mm
f Maximum distance to middle contact line mm
max
g Length of contact line (method B2) mm
c
g Length of path of contact of virtual cylindrical gear in transverse section mm
va
g Relative length of action in normal section —
van
g Relative length of action within the contact ellipse —
η
g Relative length of action at critical point in contact ellipse —
ηI
g Relative length of action considering adjacent teeth —
ηIΣ
HBW Brinell hardness —
K Dynamic factor —
v
K Application factor —
A
K Transverse load factor for contact stress —
Hα
K Face load factor for contact stress —
Hβ
k Positive integer —
k’ Contact shift factor —
l Length of contact line (method B1) mm
b
l Theoretical length of middle contact line mm
bm
m Outer transverse module mm
et
m Mean normal module mm
mn
N Number of load cycles —
L
p Peak load N/mm
p Maximum peak load N/mm
max
p* Relative peak load for calculating the load sharing factor (method B1) —
p Relative mean normal base pitch —
nb
Ra Centre line average (CLA) = AA arithmetic average roughness μm
R Relative mean back cone distance —
mpt
Rz Mean peak-to-valley roughness μm
Rz Equivalent roughness µm
H
Rz Mean roughness for gear pairs with relative curvature radius ρ = 10 mm μm
10 rel
r Relative mean virtual tip radius —
va
r Relative mean virtual pitch radius —
vn
S Safety factor for contact stress (against macropitting) —
H
S Minimum safety factor for contact stress —
H,min
u Gear ratio of bevel gear —
V Ratio of maximum load over the middle contact line and total load —
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-facewidth of the reference cone m/s
mt
v Circumferential velocity at the pitch line m/s
w
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
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ISO 10300-2:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Description or term Unit
v Sum of velocities in lengthwise direction m/s
Σs
v Sum of velocities vertical to the contact line m/s
Σ,vert
w Angle of contact line relative to the root cone °
w Surface velocity m/s
t
w Surface velocity in profile direction m/s
t,h
w Surface velocity in lengthwise direction m/s
t,s
w Surface velocity vertical to the contact line m/s
t,vert
X Intermediate value —
Z Inertia factor (macropitting) —
i
Z Speed factor —
v
Z Contact stress adjustment factor (method B2) —
A
2 1/2
Z Elasticity factor (N/mm )
E
Z Facewidth factor —
FW
Z Hypoid factor —
Hyp
Z Macropitting resistance geometry factor (method B2) —
I
Z Bevel gear factor (method B1) —
KP
Z Lubricant factor —
L
Z Load sharing factor (method B1) —
LS
Z Mid-zone factor —
M-B
Z Life factor (macropitting) —
NT
Z Roughness factor for contact stress —
R
Z Bevel slip factor —
S
Z Work hardening factor —
W
Z Size factor —
X
z Number of teeth —
z Number of teeth of virtual cylindrical gear —
v
α Normal pressure angle at point of load application (method B2) °
L
α Adjusted pressure angle (method B2) °
a
α Normal pressure angle at tooth tip °
an
α Effective pressure angle for drive side/coast side °
eD,C
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
β Inclination angle of contact line °
B
β Mean base spiral angle °
bm
β Mean spiral angle °
m
ε Load sharing ratio for macropitting (method B2) —
NI
ζ Pinion offset angle in root plane °
R
ζ Slip vertical to the contact line °
vert
λ Adjustment angle for contact angle of hypoid gears (method B2) °
λ Adjustment angle for virtual spiral angle of hypoid gears (method B2) °
r
3
ρ Density of gear material kg/mm
ρ Local equivalent radius of curvature vertical to contact line mm
rel
ρ Relative radius of profile curvature between pinion and wheel (method B2) —
t
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ISO 10300-2:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Description or term Unit
ρ Relative radius of curvature change —
Δred
ρ Relative radius of curvature difference between point of load application and —
Δ1,2
mean point
Σ Shaft angle °
2
σ Contact stress N/mm
H
2
σ Allowable stress number for contact stress N/mm
H,lim
2
σ Permissible contact stress N/mm
HP
v Poisson’s ratio —
2
v , v Nominal kinematic viscosity of the oil at 40 °C and 50 °C respectively mm /s
40 50
ω Angle between surface velocity in lengthwise and profile direction °
wt
ω Inclination angle of the sum of velocities vector results °
Σ
Table 2 — General 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
C Coast flank
T Relative to standardized test gear dimensions
(1), (2) Trials of interpolation
Table 3 — Abbreviated terms
Abbreviated term Material Type
St Wrought normalized low carbon steels
Normalized low carbon steels/cast steels
St (cast.) Cast steels
Black malleable cast iron
GTS (perl.)
(perlitic structure)
Cast iron materials Nodular cast iron
GGG (perl., bai., ferr.)
(perlitic, bainitic, ferritic structure)
GG Grey cast iron

V Through hardened wrought steels Carbon steels, alloy steels
V (cast) Through hardened cast steels Carbon steels, alloy steels
Eh Case-hardened wrought steels
Flame or induction hardened wrought or
IF
cast steels

NT (nitr.) Nitriding steels
Nitrided wrought steels/nitriding steels/
through hardening steels, nitrided
NV (nitr.) Through hardening steels

NV (nitrocar.) Wrought steels, nitrocarburized Through hardening steels
5
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ISO 10300-2:2023(E)
5 Macropitting damage — General aspects
5.1 Acceptable versus unacceptable macropitting
When limits of the surface durability of the meshing flanks are exceeded, particles break out of the
flank, thus leaving pits. This damage is called pitting, also known as macropitting. The extent, to which
such pits may be tolerated, in terms of their size and number, varies within wide limits which depend
largely on the field of application. In some fields, extensive macropitting is acceptable; in others, no
macropitting is acceptable. The descriptions in 5.2 and 5.3 are relevant to average working conditions
and give guidelines to distinguish between initial and destructive, and acceptable and unacceptable
macropitting varieties.
A linear or progressive increase in the total area of pits (linear or progressive macropitting) is generally
considered to be unacceptable. However, it is possible that the effective tooth bearing area is enlarged
by initial
...