ISO/TS 6336-4:2019

Calculation of load capacity of spur and helical gears — Part 4: Calculation of tooth flank fracture load capacity

This document describes a procedure for the calculation of the tooth flank fracture load capacity of cylindrical spur and helical gears with external teeth. It is not intended to be used as a rating method in the design and certification process of a gearbox. The formulae specified are applicable for driving as well as for driven cylindrical gears while the tooth profiles are in accordance with the basic rack specified in ISO 53. They can also be used for teeth conjugate to other racks where the actual transverse contact ratio is less than εα = 2,5. The procedure was validated for case carburized[15] gears and the formulae of this document are only applicable to case carburized gears with specifications inside the following limits: — Hertzian stress: 500 N/mm2 ≤ pH ≤ 3 000 N/mm2; — Normal radius of relative curvature: 5 mm ≤ ρred ≤ 150 mm; — Case hardening depth at 550 HV in finished condition: 0,3 mm ≤ CHD ≤ 4,5 mm. This document is not applicable for the assessment of types of gear tooth damage other than tooth flank fracture.

Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale — Partie 4: Calcul de la capacité de charge de la rupture en flanc de dent

General Information

• Status: Published
• Publication Date: 29-Jan-2019
• ICS: 21.200 - Gears
• Technical Committee: ISO/TC 60/SC 2 - Gear capacity calculation
• Drafting Committee: ISO/TC 60/SC 2/WG 6 - Gear calculations
• Current Stage: 9093 - International Standard confirmed
• Completion Date: 23-Sep-2022

Standards Content (Sample)

TECHNICAL ISO/TS
SPECIFICATION 6336-4
First edition
2019-01
Corrected version
2019-07
Calculation of load capacity of spur
and helical gears —
Part 4:
Calculation of tooth flank fracture load
capacity
Calcul de la capacité de charge des engrenages cylindriques à
dentures droite et hélicoïdale —
Partie 4: Calcul de la capacité de charge de la rupture en flanc de dent
Reference number
ISO/TS 6336-4:2019(E)
ISO 2019
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ISO/TS 6336-4:2019(E)
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© ISO 2019

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ii © ISO 2019 – All rights reserved
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ISO/TS 6336-4:2019(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms, definitions, symbols and abbreviated terms ....................................................................................................... 1

3.1 Terms and definitions ....................................................................................................................................................................... 1

3.2 Symbols and abbreviated terms............................................................................................................................................... 2

3.3 Definition of local contact point, CP, and material depth, y ............................................................................. 3

4 Definition of tooth flank fracture ........................................................................................................................................................ 4

5 Basic formulae ........................................................................................................................................................................................................ 5

5.1 General ........................................................................................................................................................................................................... 5

5.2 Maximum material exposure, A ................................................................................................................................. 5

FF,max

5.3 Local material exposure, A (y) ......................................................................................................................................... 6

FF,CP

6 Local occurring equivalent stress, τ (y) .............................................................................................................................. 7

eff,CP

6.1 General ........................................................................................................................................................................................................... 7

6.2 Local equivalent stress without consideration of residual stresses, τ (y) .............................. 7

eff,L,CP

6.2.1 General...................................................................................................................................................................................... 7

6.2.2 Local normal radius of relative curvature, ρ .............................................................................. 8

red,CP

6.2.3 Reduced modulus of elasticity, E ..................................................................................................................... 8

6.2.4 Local Hertzian contact stress, p ............................................................................................................ 9

dyn,CP

6.3 Quasi-stationary residual stress, τ (y) ....................................................................................................................21

eff,RS

6.3.1 General...................................................................................................................................................................................21

6.3.2 Method A ..............................................................................................................................................................................21

6.3.3 Method B ..............................................................................................................................................................................21

6.4 Influence of the residual stresses on the local equivalent stress, ∆τ (y) .........................22

eff,L,RS,CP

7 Local material strength, τ (y)......................................................................................................................................................23

per,CP

7.1 General ........................................................................................................................................................................................................23

7.2 Hardness conversion factor K ......................................................................................................................................23

τ,per

7.3 Material factor K ................................................................................................................................................................23

material

7.4 Hardness depth profile, HV(y) ................................................................................................................................................25

7.4.1 General...................................................................................................................................................................................25

7.4.2 Method A ..............................................................................................................................................................................25

7.4.3 Method B ..............................................................................................................................................................................25

7.4.4 Method C1 ...........................................................................................................................................................................26

7.4.5 Method C2 ...........................................................................................................................................................................26

Annex A (informative) Calculation of local equivalent stress without consideration of

residual stresses, τ (y) .....................................................................................................................................................................28

eff,L,CP

Bibliography .............................................................................................................................................................................................................................29

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ISO/TS 6336-4:2019(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso

.org/iso/foreword .html.

This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear

capacity calculation.
A list of all parts in the ISO 6336 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.

This corrected version of ISO 6336-4:2019 incorporates the following corrections:

— mistakes in the formulae have been corrected.
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ISO/TS 6336-4:2019(E)
Introduction

The ISO 6336 series consists of International Standards, Technical Specifications (TS) and Technical

Reports (TR) under the general title Calculation of load capacity of spur and helical gears (see Table 1).

— International Standards contain calculation methods that are based on widely accepted practices

and have been validated.

— Technical Specifications (TS) contain calculation methods that are still subject to further

development.

— Technical Reports (TR) contain data that is informative, such as example calculations.

The procedures specified in ISO 6336-1 to ISO 6336-19 cover fatigue analyses for gear rating. The

procedures described in ISO 6336-20 to ISO 6336-29 are predominantly related to the tribological

behaviour of the lubricated flank surface contact. ISO 6336-30 to ISO 6336-39 include example

calculations. The ISO 6336 series allows the addition of new parts under appropriate numbers to reflect

knowledge gained in the future.

Requesting standardized calculations according to the ISO 6336 series without referring to specific

parts requires the use of only those parts that are currently designated as International Standards (see

Table 1 for listing). When requesting further calculations, the relevant part or parts of the ISO 6336

series need to be specified. Use of a Technical Specification as acceptance criteria for a specific designs

need to be agreed in advance between the manufacturer and the purchaser.
Table 1 — Parts of the ISO 6336 series (status as of DATE OF PUBLICATION)
International Technical Technical
Calculation of load capacity of spur and helical gears
Standard Specification Report
Part 1: Basic principles, introduction and general influ-
ence factors
Part 2: Calculation of surface durability (pitting) X
Part 3: Calculation of tooth bending strength X
Part 4: Calculation of tooth flank fracture load capacity X
Part 5: Strength and quality of materials X
Part 6: Calculation of service life under variable load X
Part 20: Calculation of scuffing load capacity (also
applicable to bevel and hypoid gears) — Flash tempera-
ture method
(replaces: ISO/TR 13989-1)
Part 21: Calculation of scuffing load capacity (also ap-
plicable to bevel and hypoid gears) — Integral tempera-
ture method
(replaces: ISO/TR 13989-2)
Part 22: Calculation of micropitting load capacity
(replaces: ISO/TR 15144-1)
Part 30: Calculation examples for the application of
ISO 6336 parts 1, 2, 3, 5
Part 31: Calculation examples of micropitting load capacity
(replaces: ISO/TR 15144-2)

This document provides principles for the calculation of the tooth flank fracture load capacity of

cylindrical involute spur and helical gears with external teeth. The method is based on theoretical and

experimental investigations (see References [9], [10], [12] and [15]) on case carburized test gears and

gears from different industrial applications.
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ISO/TS 6336-4:2019(E)

This document as a part of the ISO 6336 series includes a newly developed method for assessing the

risk of tooth flank fracture, which is still subject to further development. It is published in order to gain

a broader experience with the obtained results in various scopes of application. The knowledge gained

will serve for further development and refinement of this document.

Tooth flank fracture is characterized by a primary fatigue crack in the region of the active contact area,

initiated below the surface due to shear stresses caused by the flank contact. Failures due to tooth

flank fracture are reported from different industrial gear applications and have also been observed on

specially designed test gears for gear running tests. Tooth flank fracture is most often observed on case

carburized gears but failures are also known for nitrided and induction hardened gears. Most of the

observed tooth flank fractures occurred on the driven partner.

The basis for the calculation of the tooth flank fracture load capacity are sophisticated calculation

methods based on the shear stress intensity hypothesis (SIH, see References [13] and [16]) which

were transferred to a calculation method in closed form solution. With only a small set of parameters

concerning gear geometry, gear material and gear load condition, a calculation of the local material

exposure can be performed in order to calculate the tooth flank fracture load capacity.

It should also be understood that some aspects of this type of failure can be a complex interaction of

stress fluctuations and material inhomogeneities. As an example, the presence of retained austenite

in the carburized case can result in the transformation during service and its associated volumetric

change can cause a minute distortion of the teeth and loss of original contact quality thereby changing

the localised stress distribution. Another phenomenon is the development of localised “white etching

areas” (local work hardening) which ultimately develop into crack initiation and propagation. Clearly,

there is considerable research required to isolate these types of effects and the analysis of case histories

is paramount to the understanding of the subject.
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TECHNICAL SPECIFICATION ISO/TS 6336-4:2019(E)
Calculation of load capacity of spur and helical gears —
Part 4:
Calculation of tooth flank fracture load capacity
1 Scope

This document describes a procedure for the calculation of the tooth flank fracture load capacity of

cylindrical spur and helical gears with external teeth.

It is not intended to be used as a rating method in the design and certification process of a gearbox.

The formulae specified are applicable for driving as well as for driven cylindrical gears while the

tooth profiles are in accordance with the basic rack specified in ISO 53. They can also be used for teeth

conjugate to other racks where the actual transverse contact ratio is less than ε = 2,5. The procedure

[15]

was validated for case carburized gears and the formulae of this document are only applicable to

case carburized gears with specifications inside the following limits:
2 2
— Hertzian stress: 500 N/mm ≤ p ≤ 3 000 N/mm ;
— Normal radius of relative curvature: 5 mm ≤ ρ ≤ 150 mm;
red
— Case hardening depth at 550 HV in finished condition: 0,3 mm ≤ CHD ≤ 4,5 mm.

This document is not applicable for the assessment of types of gear tooth damage other than tooth flank

fracture.
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 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry

ISO 1328-1, Cylindrical gears — ISO system of flank tolerance classification — Part 1: Definitions and

allowable values of deviations relevant to flanks of gear teeth

ISO 6336-1, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction

and general influence factors

ISO 6336-2, Calculation of load capacity of spur and helical gears — Part 2: Calculation of surface durability

(pitting)

ISO 21771, Gears — Cylindrical involute gears and gear pairs — Concepts and geometry

3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 1122-1, ISO 6336-1 and

ISO 6336-2 apply.
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ISO/TS 6336-4:2019(E)

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at http: //www .iso .org/obp
— IEC Electropedia: available at https: //www .electropedia .org/
3.2 Symbols and abbreviated terms

The symbols and abbreviated terms used in this document and their units are given in Table 2. The

conversions of the units are included in the given formulae.
Table 2 — Symbols, abbreviated terms and units
Symbol Description Unit
A Tolerance class which shall be according to ISO 1328-1 —
A ( y) Local material exposure at considered contact point —
FF,CP
A Maximum material exposure —
FF,max
b Face width mm
b* Tooth width coordinate for contact point CP mm
b Half of the Hertzian contact width mm
b Half of the Hertzian contact width at contact point CP mm
H,CP
C Auxiliary constant mm
c Material exposure calibration factor —
CHD Case hardening depth at 550 HV mm
Considered local contact point CP (all parameters with index CP are defined as
CP —
local values)
d Tip diameter of pinion mm
d Tip diameter of wheel mm
d Base diameter of pinion mm
d Base diameter of wheel mm
d Diameter of pinion at the contact point CP mm
CP1
d Diameter of wheel at the contact point CP mm
CP2
E Modulus of elasticity of pinion N/mm
E Modulus of elasticity of wheel N/mm
E Reduced modulus of elasticity N/mm

End of active profile (for driving pinion: contact point E, for driving wheel: con-

EAP —
tact point A)
F (Nominal) Transverse tangential load at reference cylinder per mesh N
g Length of the path of contact mm

g Parameter on the path of contact (distance of local contact point CP from point A) mm

HV Hardness HV
HV Core hardness HV
core
HV Surface hardness HV
surface
K Application factor —
K Transverse load factor —
K Face load factor —
K Material factor —
material
K Dynamic factor —
K Mesh load factor —
K Hardness conversion factor —
τ,per
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ISO/TS 6336-4:2019(E)
Table 2 (continued)
Symbol Description Unit
p Hertzian contact stress including the load factors, K N/mm
dyn
p Local Hertzian contact stress at the contact point, CP N/mm
dyn,CP
p Transverse base pitch mm
p Nominal Hertzian contact stress N/mm
r Local contact radius mm
R Tensile strength of the gear material (see ISO 6336-5). N/mm
Start of active profile (for driving pinion: contact point A, for driving wheel:
SAP —
contact point E)
SIH Shear stress intensity hypothesis —
Chordal tooth thickness in transverse section at the diameter corresponding to
s mm
t,B−D
the middle between B and D on the line of action
X Local buttressing factor —
but,CP
X Local load sharing factor —

y Material depth (all parameters depending on y or ( y) are defined as local values) mm

y y-coordinate, where HV( y) = HV mm
Core Core
y y-coordinate of the maximum hardness mm
HV,max
2 0,5
Z Elasticity factor (N/mm )
∆τ ( y) Influence of the residual stresses on the local equivalent stress N/mm
eff,L,RS,CP
α Transverse pressure angle °
α Working pressure angle °
β Base helix angle °
ε Transverse contact ratio —
ε Overlap ratio —
ρ Local transverse radius of curvature on the pinion mm
t1,CP
ρ Local transverse radius of curvature on the wheel mm
t2,CP
ρ Local normal radius of relative curvature mm
red,CP
ρ Local transverse radius of relative curvature at the contact point CP mm
red,t,CP
σ ( y) Tangential component of the residual stress N/mm
σ Maximum residual stress N/mm
RS,max
ν Poisson's ratio of the pinion —
ν Poisson's ratio of the wheel —
τ ( y) Local equivalent stress N/mm
eff,CP
τ ( y) Local equivalent stress without consideration of residual stresses N/mm
eff,L,CP
τ ( y) Quasi-stationary residual stress N/mm
eff,RS
τ ( y) Local material shear strength N/mm
per,CP
3.3 Definition of local contact point, CP, and material depth, y

The calculation of the tooth flank fracture load capacity is carried out for defined local contact points,

CP, in the area of the active tooth flank. Each local contact point, CP, is specified by the tooth width

coordinate, b*, and the tooth height coordinate, r , (which is the local contact radius). For a specific

contact point, CP, the material depth y is orientated normal to the tooth flank surface in the material

and can be defined according to Figure 1. For calculation, a reasonable division of the contact area in

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ISO/TS 6336-4:2019(E)

order to define single calculation points shall be performed. Influences of tooth flank modifications on

the pressure distribution shall be appropriately considered.

NOTE All parameters depending on y respectively ( y) are defined as local values in the considered local

contact point, CP.
Key
1 area of active tooth flank

Figure 1 — Definition of local contact point, CP, and material depth, y, depending on tooth width,

b*, and contact radius, r
4 Definition of tooth flank fracture

Tooth flank fracture is characterized by a primary fatigue crack in the region of the active contact area,

initiated below the surface due to shear stresses caused by the flank contact. Failures due to tooth

flank fracture are reported from different industrial gear applications and have also been observed

on specially designed test gears for gear running tests (images of tooth flank fractures can be found in

Reference [9]). Tooth flank fracture is most often observed on case carburized gears but failures are

also known for nitrided and induction hardened gears. Tooth flank fracture is sometimes also referred

as subsurface-initiated bending fatigue crack, sub-surface fatigue or tooth flank breakage. The main

failure characteristics are:

— tooth fracture is due to a crack located in the active flank area, often at approximately half the

height of the tooth;

— primary crack initiation is at a considerable depth below the surface of the loaded gear flank,

typically at or below the case-core interface;

— the primary crack starter is often but not always associated with a small non-metallic inclusion;

— the primary crack propagates from the initial crack starter in both directions — towards the surface

of the loaded flank and into the core towards the opposite tooth root section;

— due to the high hardness in the case, the crack propagation towards the surface is smaller than

through the core;
— the angle between primary crack and flank surface is approximate 40° to 50°;

— due to the inner primary crack, secondary and subsequent cracks may occur which originate from

the surface;

— the crack propagation rate rapidly increases as soon as the primary crack has reached the surface

of the loaded gear flank;
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ISO/TS 6336-4:2019(E)

— the final breakage of the tooth is due to forced rupture; typically developing according to local

bending stress;

— the fractured surfaces show typical fatigue characteristics with a crack lens around the initiation

point and a residual zone of forced rupture;

— in many cases (but not all), no indications of surface related failures such as pitting or micropitting

are observed on the gear flanks.

Due to these characteristics the failure type of tooth flank fracture can be clearly differentiated from

the classical tooth root fatigue failure that is caused by tooth bending stresses in the tooth root area

and also from classical pitting damage that is initiated at or close to the flank surface and characterized

by shell-shaped material breakouts from the loaded flank surface. Furthermore, tooth flank fracture

may occur at loads below the rated allowable loads for pitting and bending strength as well as on gears,

which have completely fulfilled all the requirements regarding gear material, heat treatment and gear

quality according to existing standards. Failures due to tooth flank fracture occur typically in excess of

10 load cycles pointing out the fatigue character of this failure type.
5 Basic formulae
5.1 General

The calculation method for tooth flank fracture load capacity is based on a local comparison of the

total occurring stresses (load induced stresses and residual stresses) and the material strength for

each considered point of contact and over the material depth. For the herein presented procedure, the

occurring stresses are expressed by the local equivalent stress, τ (y), and the material strength

eff,CP

is described by the local material shear strength, τ (y). The calculation of τ (y) and τ (y)

per,CP eff,CP per,CP

is performed with help of an approximate calculation approach in closed form. This approach was

numerically matched with sophisticated calculation methods based on the SIH (see References

[10],[12],[13] and [16]) and was verified by experimental investigations and experiences from industrial

application.

The quotient of the local equivalent stress, τ (y), and the local material shear strength, τ (y),

eff,CP per,CP

is expressed as a local material exposure, A (y). The local material exposure, A (y), should be

FF,CP FF,CP

calculated for discrete contact points, CP, in the contact area along the tooth width and tooth height

and in each considered material depth, y (Method A). If there is no detailed information about the local

Hertzian contact stress calculated with a 3D load distribution program, the Hertzian contact stress

and the resulting material exposure can also be determined with the formulae according to Method B

for some specified points of contact which shall be chosen based upon a reasonable distribution of the

contact area. Influences of tooth flank modifications on the pressure distribution shall be appropriately

considered.
5.2 Maximum material exposure, A
FF,max

A is the maximum calculated local material exposure, A (y), for all analysed contact points, CP,

FF,max FF,CP

over the material depth, y, where y is equal to or greater than half of the Hertzian contact width, b .

H,CP

The material depth, y, should be chosen to ensure the maximum material exposure, A , is captured.

FF,max
 
AA= max y (1)
FF ,, max FF CP
 
with
yb≥ (2)
HC, P
where
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ISO/TS 6336-4:2019(E)
A is the maximum material exposure;
FF,max

A (y) is the local material exposure in the material depth, y, for the contact point, CP;

FF,CP
b is half of the Hertzian contact width at the contact point, CP.
H,CP
dynC, P
b =⋅4 ρ ⋅ (3)
H,CP redC, P
where
p is the local Hertzian contact stress at the contact point CP;
dyn,CP
ρ is the local normal radius of relative curvature at the contact point CP;
red,CP
E is the reduced modulus of elasticity.
[15]

It has been observed from experimental investigations on case carburized gears that a maximum

material exposure A ≥ 0,8 can lead to tooth flank fractures in the case of a constant input torque.

FF,max
Currently, there is no experience to
...