ISO 10300-1:2023
(Main)Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors
Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors
This document specifies the methods of calculation of the load capacity of bevel gears, the formulae and symbols used for calculation, and the general factors influencing load conditions. The formulae in this document are intended to establish uniformly acceptable methods for calculating the load-carrying capacity of straight, helical (skew), spiral bevel, Zerol and hypoid gears. They are applicable equally to tapered depth and uniform depth teeth. Hereinafter, the term “bevel gear” refers to all of the gear types; if not, the specific forms are identified. The formulae in this document take into account the known major factors influencing load-carrying capacity. The rating formulae are only applicable to types of gear tooth deterioration, that are specifically addressed in the individual parts of the ISO 10300 series. Rating systems for a particular type of bevel gears can be established by selecting proper values for the factors used in the general formulae. NOTE This document is not applicable to bevel gears which have an inadequate contact pattern under load (see Annex D). The rating system of this document is based on virtual cylindrical gears and restricted to bevel gears whose virtual cylindrical gears have transverse contact ratios of εvα 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 facewidths b > 13 mmn, the calculated results of this document should be confirmed by experience.
Calcul de la capacité de charge des engrenages coniques — Partie 1: Introduction et facteurs généraux d'influence
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 10300-1
Third edition
2023-08
Calculation of load capacity of bevel
gears —
Part 1:
Introduction and general influence
factors
Calcul de la capacité de charge des engrenages coniques —
Partie 1: Introduction et facteurs généraux d'influence
Reference number
ISO 10300-1:2023(E)
© ISO 2023
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ISO 10300-1:2023(E)
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ISO 10300-1:2023(E)
Contents Page
Foreword .v
Introduction .vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols and general subscripts . .2
5 Application .6
5.1 Calculation methods . 6
5.1.1 General . 6
5.1.2 Method A . . . 6
5.1.3 Method B . . 6
5.1.4 Method C . 6
5.2 Safety factors . 7
5.3 Rating factors . 7
5.3.1 Testing . 7
5.3.2 Manufacturing tolerances . 7
5.3.3 Implied accuracy . 8
5.4 Further factors to be considered . 8
5.4.1 General . 8
5.4.2 Lubrication . 8
5.4.3 Misalignment . 8
5.4.4 Deflection . . 8
5.4.5 Materials and metallurgy . 8
5.4.6 Residual stress . 8
5.4.7 System dynamics . 9
5.4.8 Contact pattern . 9
5.4.9 Corrosion . 9
5.5 Further influence factors in the basic formulae . 9
6 External force and application factor, K .10
A
6.1 Nominal tangential force, torque, power . 10
6.2 Variable load conditions . 10
6.3 Application factor, K . 10
A
6.3.1 Application factor — General . . 10
6.3.2 Influences affecting external dynamic loads . 11
6.3.3 Establishment of application factors . 11
7 Dynamic factor, K .11
v
7.1 General . 11
7.2 Design . 11
7.3 Manufacturing .12
7.4 Transmission error .12
7.5 Dynamic response . 12
7.6 Resonance . 13
7.6.1 General .13
7.6.2 Gear blank resonance . . .13
7.7 Calculation methods for K .13
v
7.7.1 General comments .13
7.7.2 Method A, K . 14
v-A
7.7.3 Method B, K . 14
v-B
7.7.4 Method C, K . 18
v-C
8 Face load factors, K , K .20
Hβ Fβ
8.1 General comments .20
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ISO 10300-1:2023(E)
8.2 Method A . 20
8.3 Method B . 21
8.4 Method C . 21
8.4.1 Face load factor, K . 21
Hβ-C
8.4.2 Local face load factor, K . 21
Hβ,Y
8.4.3 Face load factor, K . 22
Fβ-C
8.4.4 Lengthwise curvature factor for bending strength, K . .22
F0
9 Transverse load factors, K , K .23
Hα Fα
9.1 General comments .23
9.2 Method A . 24
9.3 Method B . 24
9.3.1 Bevel gears having virtual cylindrical gears with contact ratio ε ≤ 2. 24
vγ
9.3.2 Bevel gears having virtual cylindrical gears with contact ratio ε > 2 . 24
vγ
9.4 Method C . 25
9.4.1 General comments .25
9.4.2 Assumptions . 25
9.4.3 Determination of the factors . 25
9.5 Running-in allowance, y .25
α
Annex A (normative) Calculation of virtual cylindrical gears — Method B1.27
Annex B (normative) Calculation of virtual cylindrical gears — Method B2 .43
Annex C (informative) Values for application factor, K .49
A
Annex D (informative) Contact patterns .50
Bibliography .54
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ISO 10300-1:2023(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
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electrotechnical standardization.
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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
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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 10300-1:2014), which has been
technically revised.
The main changes are as follows:
— Table 1 has been inserted in which only symbols and units used in this document are provided;
— Table 2 has been inserted;
— subclause 9.1 — boundary conditions for the calculation of the transverse load factors method B
have been rearranged;
— Figure 3 — nomogram for the determination of the resonance speed, n , for the mating solid steel
E1
pinion/solid wheel, with c = 20 N/(mm · μm) (for bevel gears without offset only) has been removed;
γ
— Figure 4 — dynamic factor, K , has been removed;
v-C
— Figure 5 — transverse load factors, K and K has been removed;
Hα-B Fα-B
— Figure 6 — running-in allowance, y , of gear pairs with a tangential speed of v > 10 m/s has been
α mt2
removed;
— Figure 7 — running-in allowance, y , of gear pairs with a tangential speed of v ≤ 10 m/s has been
α mt2
removed;
— Figure A.6 — transverse path of contact has been newly inserted;
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ISO 10300-1:2023(E)
— Figure A.7 — general definition of length of contact lines for local geometry data has been newly
inserted.
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 10300-1:2023(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.
Several calculation methods, i.e. A, B and C, are specified, which stand for decreasing accuracy and
reliability from A to C because of simplifications implemented in formulae and factors. The approximate
methods in ISO 10300 (all parts) are used for preliminary estimates of gear capacity where the final
details of the gear design are not yet known. More detailed methods are intended for the recalculation
of the load capacity limits when all important gear data are given.
ISO 10300 (all parts) does not provide an upgraded calculation procedure as a method A, although it
would be available, such as finite element or boundary element methods combined with sophisticated
tooth contact analyses.
On the other hand, by means of such a computer program, a new calculation procedure for bevel and
hypoid gears on the level of method B was developed and checked. It is part of the ISO 10300 series as
submethod B1. Besides, if the hypoid offset, a, is zero, method B1 becomes identical to the set of proven
formulae of the former version of ISO 10300:2001 (all parts).
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, Annex B has been included
in this document. Additionally, ISO 10300-2 is supplemented by a separate clause: “Gear flank rating
formulae — Method B2”; as for ISO 10300-3, the former method B2, which uses the Lewis parabola to
determine the critical section in the root and not the 30° tangent at the tooth fillet as method B1 does,
is now extended by the AGMA methods for rating the strength of bevel gears and hypoid gears. It was
necessary to present a new, clearer structure of the three parts, which is illustrated in Figure 1.
NOTE ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when to use
method B2.
The procedures covered by ISO 10300 (all parts) are based on both testing and theoretical studies.
ISO 10300 (all parts) provides calculation procedures by which different gear designs can be compared.
It is not meant to ensure the performance of assembled gear drive systems. It is intended for use by
the experienced gear designer capable of selecting reasonable values for the factors in these formulae,
based on knowledge of similar designs and on awareness of the effects of the items discussed.
NOTE Contrary to cylindrical gears, where the contact is usually linear, bevel gears are generally
manufactured with profile and lengthwise crowning, i.e. the tooth flanks are curved on all sides and the contact
develops an elliptical pressure surface. This is taken into consideration when determining the load factors by
the fact that the rectangular zone of action (in the case of spur and helical gears) is replaced by an inscribed
parallelogram for method B1 and an inscribed ellipse for method B2 (see Annex A for method B1 and Annex B for
method B2). The conditions for bevel gears, different from cylindrical gears in their contact, are thus taken into
consideration by the face and transverse load distribution factors.
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ISO 10300-1:2023(E)
a
One set of formulae for both, bevel and hypoid gears.
b
Separate sets of formulae for bevel and for hypoid gears.
Figure 1 — Structure of calculation methods in ISO 10300 (all parts)
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INTERNATIONAL STANDARD ISO 10300-1:2023(E)
Calculation of load capacity of bevel gears —
Part 1:
Introduction and general influence factors
1 Scope
This document specifies the methods of calculation of the load capacity of bevel gears, the formulae and
symbols used for calculation, and the general factors influencing load conditions.
The formulae in this document are intended to establish uniformly acceptable methods for calculating
the load-carrying capacity of straight, helical (skew), spiral bevel, Zerol and hypoid gears. They are
applicable equally to tapered depth and uniform depth teeth. Hereinafter, the term “bevel gear” refers
to all of the gear types; if not, the specific forms are identified.
The formulae in this document take into account the known major factors influencing load-carrying
capacity. The rating formulae are only applicable to types of gear tooth deterioration, that are
specifically addressed in the individual parts of the ISO 10300 series. Rating systems for a particular
type of bevel gears can be established by selecting proper values for the factors used in the general
formulae.
NOTE This document is not applicable to bevel gears which have an inadequate contact pattern under load
(see Annex D).
The rating system of this document is based on virtual cylindrical gears and restricted to bevel gears
whose virtual cylindrical gears have transverse contact ratios of ε < 2. Additionally, for bevel gears
vα
the sum of profile shift coefficients of pinion and wheel is zero (see ISO 23509).
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 6336-6, Calculation of load capacity of spur and helical gears — Part 6: Calculation of service life under
variable load
ISO 10300-2, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability
(macropitting)
ISO 10300-3, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength
ISO 17485, Bevel gears — ISO system of accuracy
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ISO 10300-1:2023(E)
ISO 23509:2016, 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 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/
4 Symbols and general subscripts
For the purposes of this document, the symbols given in ISO 701, ISO 17485, ISO 23509, and the following
shall apply. See Tables 1 and 2.
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
a Hypoid offset mm
a Relative hypoid offset —
rel
a Centre distance of virtual cylindrical gear pair mm
v
a Relative centre distance of virtual cylindrical gear pair in normal section —
vn
B Accuracy grade according to ISO 17485 —
b Facewidth mm
b Calculated effective facewidth mm
ce
b Effective facewidth (e.g. measured length of contact pattern) mm
eff
b Facewidth of virtual cylindrical gears mm
v
b Effective facewidth of virtual cylindrical gears mm
v,eff
b Relative facewidth of virtual cylindrical gear —
v,rel
C Correction factor of tooth stiffness for non-average conditions —
F
C Correction factor for the length of contact lines —
lb
c Empirical parameter to determine the dynamic factor —
v
c Mean value of mesh stiffness per unit facewidth N/(mm⋅μm)
γ
c Mesh stiffness for average conditions N/(mm⋅μm)
γ0
c' Single stiffness N/(mm⋅μm)
c ' Single stiffness for average conditions N/(mm⋅μm)
0
d Outer pitch diameter mm
e
d Mean pitch diameter mm
m
d Tolerance diameter according to ISO 17485 mm
T
d Reference diameter of virtual cylindrical gear mm
v
d Tip diameter of virtual cylindrical gear mm
va
d Tip diameter of virtual cylindrical gear in normal section mm
van
d Base diameter of virtual cylindrical gear mm
vb
d Base diameter of virtual cylindrical gear in normal section mm
vbn
d Root diameter of virtual cylindrical gear mm
vf
d Reference diameter of virtual cylindrical gear in normal section mm
vn
2
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ISO 10300-1:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Description or term Unit
2
E Modulus of elasticity, Young’s modulus N/mm
e Exponent for the load distribution along the lines of contact —
LS
F Nominal tangential force at mid-facewidth of the reference cone N
mt
F Determinant tangential force at mid-facewidth of the reference cone N
mtH
F Nominal tangential force of virtual cylindrical gears N
vmt
f Distance from the centre of the zone of action to a contact line mm
f Distance of the middle contact line in the zone of action mm
m
f Distance of the middle contact line in the zone of action for a contact point Y mm
m,Y
f Maximum distance to middle contact line mm
max
f Maximum distance to middle contact line at right side of contact pattern mm
maxB
f Maximum distance to middle contact line at left side of contact pattern mm
max0
f Single pitch deviation μm
pt
f Effective pitch deviation μm
p,eff
f Distance of the root contact line in the zone of action mm
r
f Distance of the root contact line in the zone of action for a contact point Y mm
r,Y
f Distance of the tip contact line in the zone of action mm
t
f Distance of the tip contact line in the zone of action for a contact point Y mm
t,Y
g Length of path of contact mm
va
g Length of path of contact of virtual cylindrical gear in transverse section mm
vα
g Relative length of action in normal section —
vαn
g Relative length of action fro
...
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