SIST ISO 10300-2:2015
Calculation of load capacity of bevel gears - Part 2: Calculation of surface durability (pitting)
Calculation of load capacity of bevel gears - Part 2: Calculation of surface durability (pitting)
This part of ISO 10300 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 part of
ISO 10300 is applicable to oil lubricated bevel gears, as long as sufficient lubricant is present in the mesh
at all times.
The formulae in this part of ISO 10300 are based on virtual cylindrical gears and restricted to bevel
gears whose virtual cylindrical gears have transverse contact ratios of εvα < 2. The results are valid
within the range of the applied factors as specified in ISO 10300-1 (see ISO 6336-2[1]). 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).
The formulae in this part of ISO 10300 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.
WARNING — The user is cautioned that when the formulae are used for large average mean spiral
angles (βm1+βm2)/2 > 45°, for effective pressure angles αe > 30° and/or for large face widths
b > 13 mmn, the calculated results of ISO 10300 should be confirmed by experience.
Calcul de la capacité de charge des engrenages coniques - Partie 2: Calcul de la résistance à la pression superficielle (formation des piqûres)
Izračun nosilnosti stožčastih zobnikov - 2. del: Izračun obratovalne vzdržljivosti zobnih bokov (jamičenje)
Ta del standarda ISO 10300 določa osnovne formule, ki se uporabljajo pri določanju nosilnosti površine ravnih, valjastih (poševnih), Zerol in spiralnih stožčastih zobnikov, vključno s hipoidnimi zobniki, ter vključuje vse vplive na trajnost površine, za katero je mogoče opraviti količinske ocene. Ta del standarda ISO 10300 se uporablja za z oljem namazane stožčaste zobnike, pri čemer mora biti v mreži vedno dovolj maziva.
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. Rezultati so veljavni znotraj obsega uporabljenih faktorjev iz standarda ISO 10300-1 (glej ISO 6336-2[1]). Poleg tega
so navedena razmerja veljavna za stožčaste zobnike, pri katerih je vsota koeficientov profilnega premika zobatega kolesca in kolesa
nič (glej ISO 23509).
Formule iz tega dela standarda ISO 10300 se ne uporabljajo neposredno za oceno drugih vrst poškodb površin zobnikovih zob, kot so nastajanje plastičnih deformacij, prask, razjed ali katerih koli drugih poškodb, ki niso opredeljene.
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 potrdil z izkušnjami.
General Information
Relations
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 10300-2
Second edition
2014-04-01
Calculation of load capacity of bevel
gears —
Part 2:
Calculation of surface durability
(pitting)
Calcul de la capacité de charge des engrenages coniques —
Partie 2: Calcul de la résistance à la pression superficielle (formation
des piqûres)
Reference number
ISO 10300-2:2014(E)
©
ISO 2014
---------------------- Page: 1 ----------------------
ISO 10300-2:2014(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
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Published in Switzerland
ii © ISO 2014 – All rights reserved
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ISO 10300-2:2014(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, units and abbreviated terms . 2
5 Pitting damage — General aspects . 3
5.1 Acceptable versus unacceptable pitting . 3
5.2 Assessment requirements . 3
5.3 General rating procedure . 4
6 Gear flank rating formulae — Method B1 . 4
6.1 Contact stress formula. 4
6.2 Permissible contact stress . 6
6.3 Calculated safety factor for contact stress . 6
6.4 Contact stress factors . 6
6.5 Permissible contact stress factors .10
7 Gear flank rating formulae — Method B2 .13
7.1 Contact stress formula.13
7.2 Permissible contact stress .14
7.3 Calculated safety factor for contact stress .14
7.4 Contact stress factors .15
8 Factors for contact stress and permissible contact stress common for method B1 and
method B2 .20
8.1 Elasticity factor, Z .
E 20
8.2 Lubricant film influence factors, Z , Z , Z .
L v R 20
8.3 Work hardening factor, Z .
W 24
8.4 Life factor, Z .
NT 25
Annex A (informative) Bevel slip factor Z — Method B1 .28
S
Bibliography .30
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ISO 10300-2:2014(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 10300-2:2001), 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 10300-2:2014(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.
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, it was agreed to include a
separate clause: “Gear flank rating formulae — Method B2” in this part of ISO 10300, while the former
method B was renamed method B1. So, it became necessary to present a new, clearer structure of the
three parts, which is illustrated in ISO 10300-1:2014, Figure 1. Note, ISO 10300 (all parts) gives no
preferences in terms of when to use method B1 and when method B2.
This part of ISO 10300 deals with the failure of gear teeth by pitting, a fatigue phenomenon. Two varieties
of pitting are recognized, initial and destructive pitting.
In applications employing low hardness steel or through hardened steel, initial pitting frequently occurs
during early use and is not deemed serious. Initial pitting is characterized by small pits which do not
extend over the entire face width or profile depth of the affected tooth. The degree of acceptability
of initial pitting varies widely, depending on the gear application. Initial pitting 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 pitting stops.
In applications employing high hardness steel and case carburized steel, the variety of pitting that occurs
is usually destructive. The formulae for pitting resistance given in this part of ISO 10300 are intended to
assist in the design of bevel gears which stay free from destructive pitting during their design lives (for
[4]
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 pitting. 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 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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INTERNATIONAL STANDARD ISO 10300-2:2014(E)
Calculation of load capacity of bevel gears —
Part 2:
Calculation of surface durability (pitting)
1 Scope
This part of ISO 10300 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 part of
ISO 10300 is applicable to oil lubricated bevel gears, as long as sufficient lubricant is present in the mesh
at all times.
The formulae in this part of ISO 10300 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
vα
[1]
within 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).
The formulae in this part of ISO 10300 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.
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 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 10300-1:2014, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence
factors
ISO 10300-3, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength
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
(geometrical gear terms) and the following apply.
3.1
pitting
material fatigue phenomenon of two meshing surfaces under load
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ISO 10300-2:2014(E)
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
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, units and abbreviated terms
For the purposes of this document, the symbols and units given in ISO 10300-1:2014, Table 1 and Table 2,
as well as the following abbreviated terms, apply (see ISO 6336-5).
Table 1 — 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 (perlitic struc-
GTS (perl.)
ture)
Cast iron materials Nodular cast iron (perlitic, bainitic, ferritic
GGG (perl., bai., ferr.)
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
2 © ISO 2014 – All rights reserved
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ISO 10300-2:2014(E)
5 Pitting damage — General aspects
5.1 Acceptable versus unacceptable pitting
When limits of the surface durability of the meshing flanks are exceeded, particles break out of the flank,
thus leaving pits. 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
pitting is acceptable; in others, no pitting 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, pitting varieties.
A linear or progressive increase in the total area of pits (linear or progressive pitting) is generally
considered to be unacceptable. However, it is possible that the effective tooth bearing area is enlarged
by initial pitting, and the rate of pit generation subsequently decreases (degressive pitting), or even
ceases (arrested pitting), and then may be considered tolerable. Nevertheless, where there is dispute
over the acceptability of pitting the next subclause shall be determinant.
5.2 Assessment requirements
Pitting involving the formation of pits which increase linearly or progressively with time under
unchanged service conditions shall be unacceptable. Damage assessment shall include the entire active
area of all the tooth flanks. The number and size of newly developed pits in unhardened tooth flanks
shall be taken into consideration. Pits are frequently formed on just one, or only a few, of the surface
hardened gear tooth flanks. In such circumstances, assessment shall be centred on the flanks actually
pitted.
Teeth suspected of being especially at risk should be marked for critical examination if a quantitative
evaluation is required.
In special cases, it is possible that a first, rough assessment can be based on considerations of the entire
quantity of wear debris. But in critical cases, the condition of the flanks should be examined at least
6
three times. The first time, however, the examination should take place only after at least 10 cycles
of load. Depending on the results of previous examinations, further ones should be carried out after a
period of service.
When deterioration caused by pitting is such that it puts human life in danger, or poses a risk of other
grave consequences, the pitting shall not be tolerated. Due to stress concentration effects, a pit of 1 mm
in diameter near the fillet of a through hardened or case hardened gear tooth can become the origin of
a crack which could lead to tooth breakage; for this reason, such a pit shall be considered unacceptable
(for example, in aerospace transmissions).
Similar considerations should be taken into account in respect of turbine gears. In general, during the
10 11
long life (10 to 10 cycles) demanded of these gears, neither pitting nor unduly severe wear should
be considered acceptable as such damage could lead to unacceptable vibrations and excessive dynamic
loads. Appropriately generous safety factors should be included in the calculation: only a low probability
of failure shall be tolerated.
In contrast, pitting on the operating flanks may be tolerated for some slow speed industrial gears with
large teeth (e.g. module 25) made from low hardness steel, which can safely transmit the rated power for
10 years to 20 years. Individual pits can be up to 20 mm in diameter and 0,8 mm deep. The apparently
“destructive pitting”, which occurs during the first two or three years of service, normally slows down.
In such cases, the tooth flanks become smoothed and work hardened to the extent of increasing the
surface Brinell hardness number by 50 % or more. For such conditions, relatively low safety factors (in
some, less than 1) may be chosen, with a correspondingly higher probability of tooth surface damage.
However, a high safety factor against tooth breakage shall be chosen.
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ISO 10300-2:2014(E)
5.3 General rating procedure
There are two main methods for rating the surface durability of bevel and hypoid gears: method B1 and
method B2. They are provided in Clause 6 and Clause 7, while Clause 8 contains those influence factors
which are equal for both. Although methods B1 and B2 use the same basis of calculation, the calculation
procedure is unique to each method.
With both methods, the capability of a gear tooth to resist pitting shall be determined by the comparison
of the following stress values:
— contact stress σ , based on the geometry of the tooth, the accuracy of its manufacture, the rigidity
H
of the gear blanks, bearings and housing, and the operating torque, expressed by the contact stress
formula (see 6.1 and 7.1);
— permissible contact stress σ , based on the endurance limit for contact stress, σ , and the
HP H,lim
effect of the operating conditions under which the gears operate, expressed by the permissible
contact stress Formulae (14) and (22) (see 6.2 and 7.2).
The ratio of the permissible contact stress and the calculated contact stress is the safety factor S . The
H
value of the minimum safety factor for contact stress, S , should be 1,0. For further recommendations
H,min
on the choice of this safety factor and other minimum values, see ISO 10300-1.
It is recommended that the gear designer and customer agree on the value of the minimum safety factor.
6 Gear flank rating formulae — Method B1
6.1 Contact stress formula
The calculation of pitting resistance is based on the contact (Hertzian) stress, in which the load is
distributed along the lines of contact (see ISO 10300-1:2014, Annex A). Calculations are to be carried out
for pinion and wheel together; however, in case of hypoid gears separately for drive (suffix D) and coast
side flank (suffix C):
σσ=≤KK KK σ (1)
H-B1 H0-B1A vHβαHHP-B1
with load factors K , K , K , K as specified in ISO 10300-1.
A v Hβ Hα
4 © ISO 2014 – All rights reserved
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ISO 10300-2:2014(E)
The nominal value of the contact stress is given by:
F
n
σ = ZZ ZZ (2)
H0-B1 M-BLSE K
l ρ
bm rel
where F is the nominal normal force of the virtual cylindrical gear at mean point P:
n
F
mt1
F = (3)
n
coscαβos
nm1
with
= generated pressure angle for drive side in accordance with ISO 23509;
αα=
nnD
αα= = generated pressure angle for coast side in accordance with ISO 23509;
nnC
l is the length of contact line in the middle of the zone of action as specified in
bm
ISO 10300-1:2014, A.2.7;
ρ is the radius of relative curvature vertical to the contact line as specified in
rel
ISO 10300-1:2014, A.2.8;
Z is the mid-zone factor which accounts for the conversion of the contact stress deter-
M-B
mined at the mean point to the determinant position (see 6.4.1);
Z is the load sharing factor that considers the load sharing between two or more pairs of
LS
teeth (see 6.4.2);
Z is the elasticity factor which accounts for the influence of the material’s E-Module and
E
Poisson’s ratio (see 8.1);
Z is the bevel gear factor which accounts for the influence of the bevel gear geometry (see
K
6.4.3).
The determinant position of load application is:
a) the inner point of single tooth contact, if ε = 0;
vβ
b) the midpoint of the zone of action, if ε ≥ 1;
vβ
c) interpolation between a) and b), if 0 < ε < 1.
vβ
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ISO 10300-2:2014(E)
6.2 Permissible contact stress
The permissible contact stress shall be calculated separately for pinion (suffix 1) and wheel (suffix 2):
σσ= ZZ ZZ ZZ Z (4)
HP-B1H,lim NT XL vR WHyp
where
σ is the allowable stress number (contact), which accounts for material, heat treatment,
H,lim
and surface influence at test gear dimensions as specified in ISO 6336-5;
Z is the life factor (see 8.4), which accounts for the influence of required numbers of
NT
cycles of operation;
Z is the size factor (see 6.5.1), which accounts for the influence of the tooth size, given by
X
the module, on the permissible contact stress;
Z , Z , Z are the lubricant film factors (see 8.2) for the influence of the lubrication conditions;
L v R
Z is the work hardening factor (see 8.3), which considers the hardening of a softer wheel
W
running with a surface-hardened pinion;
Z is the hypoid factor (see 6.5.2), which accounts for the influence of lengthwise sliding
Hyp
onto the surface durability.
6.3 Calculated safety factor for contact stress
The calculated safety factor for contact stress shall be checked separately for pinion and wheel, if the
values of permissible contact stress are different:
σ
HP-B1
SS=> (5)
H-B1 H,min
σ
H-B1
where S is the minimum safety factor; see 5.2 of ISO 10300-1:2014 for recommended numerical
H,min
values for the minimum safety factor or the risk of failure (damage probability).
NOTE Formula (5) defines the relationship of the calculated safety factor, S , with respect to contact stress.
H
A safety factor related to the transferable torque is equal to the square of S .
H
6.4 Contact stress factors
6.4.1 Mid-zone factor, Z
M-B
The mid-zone factor, Z , considers the difference between the radius of relative curvature ρ at the
M-B rel
mean point and at the critical point of load application of the pinion. The radius ρ at the mean point
rel
P can directly be calculated from the data of the bevel gears in mesh (see ISO 10300-1:2014, Annex A).
For the conversion to the critical point of mesh, the corresponding virtual cylindrical gears are used.
Depending on the face contact ratio it can be the inner point of single contact B of the pinion (ε = 0)
vβ
or point M in the middle of the path of contact (ε ≥ 1) or a point interpolated between B and M for
vβ
0 < ε < 1 (see Figure 1). The comparison with the results of tooth contact analyses shows a good
vβ
approximation for bevel gear as well as for hypoid gear sets.
ATTENTION — For hypoid gears, the mid-zone factor should be determined for both, drive and
coast flank, separately.
6 © ISO 2014 – All rights reserved
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ISO 10300-2:2014(E)
The schematic view of a cylindrical gear set in transverse section shows the line of action being tan-
gent to both base circles d and d of pinion and wheel. The tip circles d and d intersect the
vb1 vb2 va2 va1
line of action in points A and E, which define the path of contact. In between there are pitch point C,
midpoint M and inner point of single contact B, for which different radii of profile curvature are speci-
fied: ρ , ρ , ρ , the basis for Formula (6)
C1,2 M1,2 B1,2
Figure 1 — Radii of curvature at midpoint M and inner point of single contact B of the pinion
for determination of the mid-zone factor, Z
M-B
The mid-zone factor, Z , is calculated by Formula (6):
M-B
tanα
vet
Z = (6)
M-B
2 2
d π d π
va1 va2
−−1 F ⋅ −−1 F
1 2
d z d z
vb1 v1 vb2 v2
The auxiliary factors F and F for the mid-zone factor are given in Table 2.
1 2
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ISO 10300-2:2014(E)
Table 2 — Factors for calculation of mid-zone factor, Z
M-B
Parameters F F
1 2
ε = 0 2 2 (ε - 1)
vβ vα
0 < ε < 1 2 + (ε − 2) ε 2 ε − 2 + (2 − ε ) ε
vβ vα vβ vα vα vβ
ε ≥ 1 ε ε
vβ vα vα
6.4.2 Load sharing factor, Z
LS
The load sharing factor, Z , accounts for load sharing between two or more pairs of teeth. That
LS
means this factor determines the maximum portion of the total load which affects one tooth. The load
distribution along each contact line in the zone of action is assumed to be elliptical. The area, A, of
each semi-ellipse (see Figure 2) represents the load on the respective contact line, and the sum of all
areas over all contact lines being simultaneously in mesh, represents the total load on the gear set.
Additionally, the distribution of the peak loads, p, over the line of action is assumed to follow a parabola
(exponent e). On this basis, the maximum load over the middle contact line divided by the total load is a
...
SLOVENSKI STANDARD
SIST ISO 10300-2:2015
01-marec-2015
1DGRPHãþD
SIST ISO 10300-2:2002
,]UDþXQQRVLOQRVWLVWRåþDVWLK]REQLNRYGHO ,]UDþXQREUDWRYDOQHY]GUåOMLYRVWL
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Calculation of load capacity of bevel gears - Part 2: Calculation of surface durability
(pitting)
Calcul de la capacité de charge des engrenages coniques - Partie 2: Calcul de la
résistance à la pression superficielle (formation des piqûres)
Ta slovenski standard je istoveten z: ISO 10300-2:2014
ICS:
21.200 Gonila Gears
SIST ISO 10300-2:2015 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 10300-2:2015
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SIST ISO 10300-2:2015
INTERNATIONAL ISO
STANDARD 10300-2
Second edition
2014-04-01
Calculation of load capacity of bevel
gears —
Part 2:
Calculation of surface durability
(pitting)
Calcul de la capacité de charge des engrenages coniques —
Partie 2: Calcul de la résistance à la pression superficielle (formation
des piqûres)
Reference number
ISO 10300-2:2014(E)
©
ISO 2014
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SIST ISO 10300-2:2015
ISO 10300-2:2014(E)
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SIST ISO 10300-2:2015
ISO 10300-2:2014(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, units and abbreviated terms . 2
5 Pitting damage — General aspects . 3
5.1 Acceptable versus unacceptable pitting . 3
5.2 Assessment requirements . 3
5.3 General rating procedure . 4
6 Gear flank rating formulae — Method B1 . 4
6.1 Contact stress formula. 4
6.2 Permissible contact stress . 6
6.3 Calculated safety factor for contact stress . 6
6.4 Contact stress factors . 6
6.5 Permissible contact stress factors .10
7 Gear flank rating formulae — Method B2 .13
7.1 Contact stress formula.13
7.2 Permissible contact stress .14
7.3 Calculated safety factor for contact stress .14
7.4 Contact stress factors .15
8 Factors for contact stress and permissible contact stress common for method B1 and
method B2 .20
8.1 Elasticity factor, Z .
E 20
8.2 Lubricant film influence factors, Z , Z , Z .
L v R 20
8.3 Work hardening factor, Z .
W 24
8.4 Life factor, Z .
NT 25
Annex A (informative) Bevel slip factor Z — Method B1 .28
S
Bibliography .30
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SIST ISO 10300-2:2015
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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
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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 10300-2:2001), 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 10300-2:2015
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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.
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, it was agreed to include a
separate clause: “Gear flank rating formulae — Method B2” in this part of ISO 10300, while the former
method B was renamed method B1. So, it became necessary to present a new, clearer structure of the
three parts, which is illustrated in ISO 10300-1:2014, Figure 1. Note, ISO 10300 (all parts) gives no
preferences in terms of when to use method B1 and when method B2.
This part of ISO 10300 deals with the failure of gear teeth by pitting, a fatigue phenomenon. Two varieties
of pitting are recognized, initial and destructive pitting.
In applications employing low hardness steel or through hardened steel, initial pitting frequently occurs
during early use and is not deemed serious. Initial pitting is characterized by small pits which do not
extend over the entire face width or profile depth of the affected tooth. The degree of acceptability
of initial pitting varies widely, depending on the gear application. Initial pitting 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 pitting stops.
In applications employing high hardness steel and case carburized steel, the variety of pitting that occurs
is usually destructive. The formulae for pitting resistance given in this part of ISO 10300 are intended to
assist in the design of bevel gears which stay free from destructive pitting during their design lives (for
[4]
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 pitting. 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 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 10300-2:2015
INTERNATIONAL STANDARD ISO 10300-2:2014(E)
Calculation of load capacity of bevel gears —
Part 2:
Calculation of surface durability (pitting)
1 Scope
This part of ISO 10300 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 part of
ISO 10300 is applicable to oil lubricated bevel gears, as long as sufficient lubricant is present in the mesh
at all times.
The formulae in this part of ISO 10300 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
vα
[1]
within 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).
The formulae in this part of ISO 10300 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.
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 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 10300-1:2014, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence
factors
ISO 10300-3, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength
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
(geometrical gear terms) and the following apply.
3.1
pitting
material fatigue phenomenon of two meshing surfaces under load
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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
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, units and abbreviated terms
For the purposes of this document, the symbols and units given in ISO 10300-1:2014, Table 1 and Table 2,
as well as the following abbreviated terms, apply (see ISO 6336-5).
Table 1 — 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 (perlitic struc-
GTS (perl.)
ture)
Cast iron materials Nodular cast iron (perlitic, bainitic, ferritic
GGG (perl., bai., ferr.)
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
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SIST ISO 10300-2:2015
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5 Pitting damage — General aspects
5.1 Acceptable versus unacceptable pitting
When limits of the surface durability of the meshing flanks are exceeded, particles break out of the flank,
thus leaving pits. 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
pitting is acceptable; in others, no pitting 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, pitting varieties.
A linear or progressive increase in the total area of pits (linear or progressive pitting) is generally
considered to be unacceptable. However, it is possible that the effective tooth bearing area is enlarged
by initial pitting, and the rate of pit generation subsequently decreases (degressive pitting), or even
ceases (arrested pitting), and then may be considered tolerable. Nevertheless, where there is dispute
over the acceptability of pitting the next subclause shall be determinant.
5.2 Assessment requirements
Pitting involving the formation of pits which increase linearly or progressively with time under
unchanged service conditions shall be unacceptable. Damage assessment shall include the entire active
area of all the tooth flanks. The number and size of newly developed pits in unhardened tooth flanks
shall be taken into consideration. Pits are frequently formed on just one, or only a few, of the surface
hardened gear tooth flanks. In such circumstances, assessment shall be centred on the flanks actually
pitted.
Teeth suspected of being especially at risk should be marked for critical examination if a quantitative
evaluation is required.
In special cases, it is possible that a first, rough assessment can be based on considerations of the entire
quantity of wear debris. But in critical cases, the condition of the flanks should be examined at least
6
three times. The first time, however, the examination should take place only after at least 10 cycles
of load. Depending on the results of previous examinations, further ones should be carried out after a
period of service.
When deterioration caused by pitting is such that it puts human life in danger, or poses a risk of other
grave consequences, the pitting shall not be tolerated. Due to stress concentration effects, a pit of 1 mm
in diameter near the fillet of a through hardened or case hardened gear tooth can become the origin of
a crack which could lead to tooth breakage; for this reason, such a pit shall be considered unacceptable
(for example, in aerospace transmissions).
Similar considerations should be taken into account in respect of turbine gears. In general, during the
10 11
long life (10 to 10 cycles) demanded of these gears, neither pitting nor unduly severe wear should
be considered acceptable as such damage could lead to unacceptable vibrations and excessive dynamic
loads. Appropriately generous safety factors should be included in the calculation: only a low probability
of failure shall be tolerated.
In contrast, pitting on the operating flanks may be tolerated for some slow speed industrial gears with
large teeth (e.g. module 25) made from low hardness steel, which can safely transmit the rated power for
10 years to 20 years. Individual pits can be up to 20 mm in diameter and 0,8 mm deep. The apparently
“destructive pitting”, which occurs during the first two or three years of service, normally slows down.
In such cases, the tooth flanks become smoothed and work hardened to the extent of increasing the
surface Brinell hardness number by 50 % or more. For such conditions, relatively low safety factors (in
some, less than 1) may be chosen, with a correspondingly higher probability of tooth surface damage.
However, a high safety factor against tooth breakage shall be chosen.
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5.3 General rating procedure
There are two main methods for rating the surface durability of bevel and hypoid gears: method B1 and
method B2. They are provided in Clause 6 and Clause 7, while Clause 8 contains those influence factors
which are equal for both. Although methods B1 and B2 use the same basis of calculation, the calculation
procedure is unique to each method.
With both methods, the capability of a gear tooth to resist pitting shall be determined by the comparison
of the following stress values:
— contact stress σ , based on the geometry of the tooth, the accuracy of its manufacture, the rigidity
H
of the gear blanks, bearings and housing, and the operating torque, expressed by the contact stress
formula (see 6.1 and 7.1);
— permissible contact stress σ , based on the endurance limit for contact stress, σ , and the
HP H,lim
effect of the operating conditions under which the gears operate, expressed by the permissible
contact stress Formulae (14) and (22) (see 6.2 and 7.2).
The ratio of the permissible contact stress and the calculated contact stress is the safety factor S . The
H
value of the minimum safety factor for contact stress, S , should be 1,0. For further recommendations
H,min
on the choice of this safety factor and other minimum values, see ISO 10300-1.
It is recommended that the gear designer and customer agree on the value of the minimum safety factor.
6 Gear flank rating formulae — Method B1
6.1 Contact stress formula
The calculation of pitting resistance is based on the contact (Hertzian) stress, in which the load is
distributed along the lines of contact (see ISO 10300-1:2014, Annex A). Calculations are to be carried out
for pinion and wheel together; however, in case of hypoid gears separately for drive (suffix D) and coast
side flank (suffix C):
σσ=≤KK KK σ (1)
H-B1 H0-B1A vHβαHHP-B1
with load factors K , K , K , K as specified in ISO 10300-1.
A v Hβ Hα
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The nominal value of the contact stress is given by:
F
n
σ = ZZ ZZ (2)
H0-B1 M-BLSE K
l ρ
bm rel
where F is the nominal normal force of the virtual cylindrical gear at mean point P:
n
F
mt1
F = (3)
n
coscαβos
nm1
with
= generated pressure angle for drive side in accordance with ISO 23509;
αα=
nnD
αα= = generated pressure angle for coast side in accordance with ISO 23509;
nnC
l is the length of contact line in the middle of the zone of action as specified in
bm
ISO 10300-1:2014, A.2.7;
ρ is the radius of relative curvature vertical to the contact line as specified in
rel
ISO 10300-1:2014, A.2.8;
Z is the mid-zone factor which accounts for the conversion of the contact stress deter-
M-B
mined at the mean point to the determinant position (see 6.4.1);
Z is the load sharing factor that considers the load sharing between two or more pairs of
LS
teeth (see 6.4.2);
Z is the elasticity factor which accounts for the influence of the material’s E-Module and
E
Poisson’s ratio (see 8.1);
Z is the bevel gear factor which accounts for the influence of the bevel gear geometry (see
K
6.4.3).
The determinant position of load application is:
a) the inner point of single tooth contact, if ε = 0;
vβ
b) the midpoint of the zone of action, if ε ≥ 1;
vβ
c) interpolation between a) and b), if 0 < ε < 1.
vβ
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ISO 10300-2:2014(E)
6.2 Permissible contact stress
The permissible contact stress shall be calculated separately for pinion (suffix 1) and wheel (suffix 2):
σσ= ZZ ZZ ZZ Z (4)
HP-B1H,lim NT XL vR WHyp
where
σ is the allowable stress number (contact), which accounts for material, heat treatment,
H,lim
and surface influence at test gear dimensions as specified in ISO 6336-5;
Z is the life factor (see 8.4), which accounts for the influence of required numbers of
NT
cycles of operation;
Z is the size factor (see 6.5.1), which accounts for the influence of the tooth size, given by
X
the module, on the permissible contact stress;
Z , Z , Z are the lubricant film factors (see 8.2) for the influence of the lubrication conditions;
L v R
Z is the work hardening factor (see 8.3), which considers the hardening of a softer wheel
W
running with a surface-hardened pinion;
Z is the hypoid factor (see 6.5.2), which accounts for the influence of lengthwise sliding
Hyp
onto the surface durability.
6.3 Calculated safety factor for contact stress
The calculated safety factor for contact stress shall be checked separately for pinion and wheel, if the
values of permissible contact stress are different:
σ
HP-B1
SS=> (5)
H-B1 H,min
σ
H-B1
where S is the minimum safety factor; see 5.2 of ISO 10300-1:2014 for recommended numerical
H,min
values for the minimum safety factor or the risk of failure (damage probability).
NOTE Formula (5) defines the relationship of the calculated safety factor, S , with respect to contact stress.
H
A safety factor related to the transferable torque is equal to the square of S .
H
6.4 Contact stress factors
6.4.1 Mid-zone factor, Z
M-B
The mid-zone factor, Z , considers the difference between the radius of relative curvature ρ at the
M-B rel
mean point and at the critical point of load application of the pinion. The radius ρ at the mean point
rel
P can directly be calculated from the data of the bevel gears in mesh (see ISO 10300-1:2014, Annex A).
For the conversion to the critical point of mesh, the corresponding virtual cylindrical gears are used.
Depending on the face contact ratio it can be the inner point of single contact B of the pinion (ε = 0)
vβ
or point M in the middle of the path of contact (ε ≥ 1) or a point interpolated between B and M for
vβ
0 < ε < 1 (see Figure 1). The comparison with the results of tooth contact analyses shows a good
vβ
approximation for bevel gear as well as for hypoid gear sets.
ATTENTION — For hypoid gears, the mid-zone factor should be determined for both, drive and
coast flank, separately.
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SIST ISO 10300-2:2015
ISO 10300-2:2014(E)
The schematic view of a cylindrical gear set in transverse section shows the line of action being tan-
gent to both base circles d and d of pinion and wheel. The tip circles d and d intersect the
vb1 vb2 va2 va1
line of action in points A and E, which define the path of contact. In between there are pitch point C,
midpoint M and inner point of single contact B, for which different radii of profile curvature are speci-
fied: ρ , ρ , ρ , the basis for Formula (6)
C1,2 M1,2 B1,2
Figure 1 — Radii of curvature at midpoint M and inner point of single contact B of the pinion
for determination of the mid-zone factor, Z
M-B
The mid-zone factor, Z , is calculated by Formula (6):
M-B
tanα
vet
Z = (6)
M-B
2 2
d π d π
va1 va2
−−1 F ⋅ −−1 F
1 2
d z d z
vb1 v1 vb2
...
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