ISO 10300-3:2014

INTERNATIONAL ISO
STANDARD 10300-3
Second edition
2014-04-01
Calculation of load capacity of bevel
gears —
Part 3:
Calculation of tooth root strength
Calcul de la capacité de charge des engrenages coniques —
Partie 3: Calcul de la résistance du pied de dent
Reference number
©
ISO 2014
© ISO 2014
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ii © ISO 2014 – All rights reserved

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 General rating procedure . 2
6 Gear tooth rating formulae — Method B1 . 3
6.1 Tooth root stress formula . 3
6.2 Permissible tooth root stress . 4
6.3 Calculated safety factor . 5
6.4 Tooth root stress factors . 5
6.5 Permissible tooth root stress factors .13
7 Gear tooth rating formulae — Method B2 .17
7.1 Tooth root stress formula .17
7.2 Permissible tooth root stress .17
7.3 Calculated safety factor .18
7.4 Tooth root stress factors .18
7.5 Permissible tooth root stress factors .36
8 Factors for permissible tooth root stress common for method B1 and method B2 .36
8.1 Size factor, Y .36
X
8.2 Life factor, Y .38
NT
Bibliography .41
Foreword
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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 10300-3:2001), 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

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When ISO 10300:2001 (all parts, withdrawn) became due for (its first) revision, the opportunity was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 tooth rating formulae — Method B2” in this part of ISO 10300, while the former
methods B and B1 were combined into one method, i.e. 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.
Failure of gear teeth by breakage can be brought about in many ways; severe instantaneous overloads,
excessive pitting, case crushing and bending fatigue are a few. The strength ratings determined by the
formulae in this part of ISO 10300 are based on cantilever projection theory modified to consider the
following:
— compressive stress at the tooth roots caused by the radial component of the tooth load;
— non-uniform moment distribution of the load, resulting from the inclined contact lines on the teeth
of spiral bevel gears;
— stress concentration at the tooth root fillet;
— load sharing between adjacent contacting teeth;
— lack of smoothness due to a low contact ratio.
The formulae are used to determine a load rating, which prevents tooth root fracture during the design
life of the bevel gear. Nevertheless, if there is insufficient material under the teeth (in the rim), a fracture
can occur from the root through the rim of the gear blank or to the bore (a type of failure not covered
by this part of ISO 10300). Moreover, it is possible that special applications require additional blank
material to support the load.
Surface distress (pitting or wear) can limit the strength rating, either due to stress concentration
around large sharp cornered pits, or due to wear steps on the tooth surface. Neither of these effects is
considered in this part of ISO 10300.
In most cases, the maximum tensile stress at the tooth root (arising from bending at the root when the
load is applied to the tooth flank) can be used as a determinant criterion for the assessment of the tooth
root strength. If the permissible stress number is exceeded, the teeth can break.
When calculating the tooth root stresses of straight bevel gears, this part of ISO 10300 starts from the
assumption that the load is applied at the tooth tip of the virtual cylindrical gear. The load is subsequently
converted to the outer point of single tooth contact. The procedure thus corresponds to method C for the
[1]
tooth root stress of cylindrical gears (see ISO 6336-3 ).
For spiral bevel and hypoid gears with a high face contact ratio of ε > 1 (method B1) or with a modified
vβ
contact ratio of ε > 2 (method B2), the midpoint in the zone of action is regarded as the critical point
vγ
of load application.
The breakage of a tooth generally means the end of a gear’s life. It is often the case that all gear teeth are
destroyed as a consequence of the breakage of a single tooth. A safety factor, S , against tooth breakage
F
higher than the safety factor against damage due to pitting is, therefore, generally to be preferred
(see ISO 10300-1).
INTERNATIONAL STANDARD ISO 10300-3:2014(E)
Calculation of load capacity of bevel gears —
Part 3:
Calculation of tooth root strength
1 Scope
This part of ISO 10300 specifies the fundamental formulae for use in the tooth root stress calculation
of straight and helical (skew), Zerol and spiral bevel gears including hypoid gears, with a minimum rim
thickness under the root of 3,5 m . All load influences on tooth root stress are included, insofar as
mn
they are the result of load transmitted by the gearing and able to be evaluated quantitatively. Stresses,
such as those caused by the shrink fitting of gear rims, which are superposed on stresses due to tooth
loading, are intended to be considered in the calculation of the tooth root stress, σ , or the permissible
F
tooth root stress σ . This part of ISO 10300 is not applicable in the assessment of the so-called flank
FP
breakage, a tooth internal fatigue fracture (TIFF).
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 also ISO 6336-3 ). Additionally,
the given relationships are valid for bevel gears, of which the sum of profile shift coefficients of pinion
and wheel is zero (see ISO 23509).
This part of ISO 10300 does not apply to stress levels above those permitted for 10 cycles, as stresses
in that range could exceed the elastic limit of the gear tooth.
Warning — The user is cautioned that when the formulae are used for large average mean spiral
angles (β + β )/2 > 45°, for effective pressure angles α > 30° and/or for large face widths
m1 m2 e
b > 13 m , the calculated results of ISO 10300 (all parts) should be confirmed by experience.
mn
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable to its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials
ISO 10300-1:2014, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence
factors
ISO 10300-2:2014, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability
(pitting)
ISO 23509:2006, 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
tooth root breakage
...