IEC TS 61400-4-1:2026

IEC TS 61400-4-1 ®
Edition 1.0 2026-02
TECHNICAL
SPECIFICATION
Wind energy generation systems -
Part 4-1: Reliability assessment of drivetrain components in wind turbines
ICS 27.180  ISBN 978-2-8327-1018-0

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CONTENTS
FOREWORD . 3
INTRODUCTION . 5
1 Scope . 6
2 Normative references . 6
3 Terms, definitions, abbreviated terms, units and conventions . 7
3.1 Terms and definitions . 7
3.2 Abbreviated terms and units . 8
4 System reliability analysis model . 10
4.1 General . 10
4.2 Failure mode identification, classification, and system element assignment . 10
5 Component reliability analysis models . 12
5.1 Individual failure modes. 12
5.2 Gear reliability calculation . 12
5.2.1 General. 12
5.2.2 Estimation of service life for defined failure probabilities . 12
5.2.3 Extrapolation of failure probabilities to the design life . 16
5.3 Rolling bearing reliability calculation . 17
5.4 Shaft reliability calculation . 18
Annex A (informative) Example reliability calculations . 20
A.1 General . 20
A.2 Example system reliability model . 20
A.2.1 Identification of components . 20
A.2.2 Identification of system elements . 20
A.2.3 Classification and selection of system elements . 21
A.2.4 Arrangement of reliability model and calculation of system reliability . 21
A.2.5 Example system assumptions. 21
A.3 Example gear tooth surface durability (pitting) reliability calculation . 22
A.3.1 Example gear assumptions . 22
A.3.2 Estimation of service life for defined failure probabilities . 22
A.3.3 Extrapolation of failure probabilities to the design life . 25
A.4 Example gear tooth bending strength reliability calculation. 26
A.4.1 Example gear assumptions . 26
A.4.2 Estimation of service life for defined failure probabilities . 26
A.4.3 Extrapolation of failure probabilities to the design life . 28
A.5 Example rolling bearing contact fatigue reliability calculation . 29
A.6 Example shaft fatigue fracture reliability calculation . 29
A.6.1 Example shaft assumptions . 29
A.6.2 Estimation of life for the nominal failure probability . 29
A.6.3 Extrapolation of service life for 10% failure probability . 30
A.7 Example system reliability calculation . 31
Annex B (informative) Application of the Weibull distribution to rolling bearing fatigue
life . 32
Bibliography . 35

Figure 1 – Calculated design versus apparent failure probability . 5
Figure 2 – Example of a system elements tree. 11
Figure 3 – Service-life calculation for a 50 % failure probability (top) from a scaled LRD
(bottom) . 13
Figure 4 – S-N curve for different failure probabilities (Hein et al. 2018) . 15
Figure A.1 – Functional elements . 20
Figure A.2 – System elements . 21
Figure A.3 – Service-life calculation with 1 % failure probability S-N curve (bottom) and
failure probability (top) . 24
Figure A.4 – Lognormal fit for gear pitting failure probability. 25
Figure A.5 – Lognormal fit for gear bending failure probability . 28
Figure B.1 – Evaluation of identical data by 2- and 3-parameter Weibull distributions . 32
Figure B.2 – Estimation of Weibull parameter γ by 3-parameter Weibull evaluation . 33
Figure B.3 – Evaluation of identical data by five test scenarios . 34

Table 1 – Failure probability conversion factors for permissible gear stresses . 15
Table A.1 – Simplified LRD . 22
Table A.2 – Contact stress for each load bin . 22
Table A.3 – Number of cycles for each load bin . 23
Table A.4 – Number of cycles for each load bin . 23
Table A.5 – Damage for each load bin . 24
Table A.6 – Damage sum, lifetime margin factor, and lifetime . 24
Table A.7 – Bending stress for each load bin . 26
Table A.8 – Number of cycles for each load bin . 27
Table A.9 – Number of cycles for each load bin . 27
Table A.10 – Damage for each load bin . 27
Table A.11 – Damage sum, lifetime margin factor, and lifetime . 27
Table A.12 – Torsional stress for each load bin . 29
Table A.13 – Number of cycles for each load bin . 30
Table B.1 – Effect of test scenario on L and Weibull parameters β and η . 34
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
Wind energy generation systems -
Part 4-1: Reliability assessment of drivetrain components in wind turbines

FOREWORD
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shall not be held responsible for identifying any or all such patent rights.
IEC TS 61400-4-1 has been prepared by IEC technical committee 88: Wind energy generation
systems. It is a Technical Specification.
The text of this Technical Specification is based on the following documents:
Draft Report on voting
88/1124/DTS 88/1147/RVDTS
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this Technical Specification is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
A list of all parts of the IEC 61400 series, published under the general title Wind energy
generation systems, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
– reconfirmed,
– withdrawn, or
– revised.
INTRODUCTION
Gearboxes historically have been and still are a large contributor to wind turbine operating
expenses and downtime. IEC 61400-4 describes requirements for the specification, design, and
verification of gearboxes in wind turbines. This Technical Specification (TS) accompanies
IEC 61400-4 and describes a method for the calculation of the design reliability of gearboxes
for wind turbines.
The method enables comparison of the calculated reliability of gearbox designs as a function
of time. It allows gearbox suppliers, wind turbine manufacturers, wind plant owners, and others
to compare different gearbox designs on equal terms. For example, the design reliability can
be compared between different gearbox designs for the same load conditions or for the same
gearbox in different load conditions. Wind turbine manufacturers and operators can also use
the information for defining field service and repair strategies.
Currently, that occur in the field have a standardized or generally accepted calculation method
(Hovgaard 2015). Therefore, as illustrated in Figure 1, there is a difference between the
calculated failure probability and apparent failure probability observed in the field.

Figure 1 – Calculated design versus apparent failure probability
The method described in this document can accommodate additional failure modes in the future,
as long these modes are calculable according to a standardized method and are time related.
Figure 1 also indicates how the inclusion of additional failure modes might reduce the gap
between calculated and apparent failure probability in the future. Further information can be
found in Strasser et al. (2015).

1 Scope
This part of IEC 61400 specifies a method to calculate the design reliability of wind turbines
gearboxes covered by IEC 61400-4, based upon failure modes where standardized calculation
methods are publicly available.
Currently, not all failure mechanisms that occur in the field have accepted theoretical models.
Therefore, the method only provides a quantitative assessment method of the failure
mechanisms that can be described with accepted mathematical models for the complete
gearbox, stages (functional units), field replaceable units, and individual components.
For the calculable failure mechanisms, it is possible to compare the reliability between different
gearbox designs within the limitations of the theoretical models. The use of field-based
statistical parameters can improve the accuracy of the calculated reliability.
The calculated design reliability can provide information for the lifecycle management strategy.
However, this document does not provide trade-off decisions between higher design reliability
and maintenance strategies (e.g. preventive or predictive maintenance). This document does
not consider repairable system analysis.
Due to the lack of accepted theoretical models for some failure modes, the model can currently
not predict the apparent failure probability in the field.
Neither this document nor IEC 61400-4 specify a minimum value of design reliability.
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.
IEC 61400-4, Wind energy generation systems - Part 4: Design requirements for wind turbine
gearboxes
IEC 61400-8, Wind energy generation systems - Part 8: Design of wind turbine structural
components
ISO 6336-2:2019, Calculation of load capacity of spur and helical gears - Part 2: Calculation of
surface durability (pitting)
ISO 6336-3:2019, Calculation of load capacity of spur and helical gears - Part 3: Calculation of
tooth bending strength
ISO 6336-5:2016, 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 16281, Rolling bearings - Methods for calculating the modified reference rating life for
universally loaded bearings
DIN 743 (all parts), Shafts and axles, calculations of load capacity
3 Terms, definitions, abbreviated terms, units and conventions
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
– IEC Electropedia: available at http://www.electropedia.org/
– ISO Online browsing platform: available at http://www.iso.org/obp
3.1.1
apparent failure probability
failure probability observed in the field, including all failure modes, whether they are considered
in the calculated system reliability as described in this document or not
3.1.2
component
part in the gearbox system comprising one or more functional elements
EXAMPLE Gear wheel.
3.1.3
failure mode
manner in which a failure occurs
EXAMPLE Gear tooth root bending fatigue fracture.
3.1.4
failure probability
F(t)
unreliability function
probability that the time to failure is lower or equal to the time, t
3.1.5
failure probability density function
derivative of the distribution function, which describes the amount of failures as a function of
time
3.1.6
field replaceable unit
individual component or gearbox subassembly that can be replaced with relatively low cost and
effort, considerably less so than a complete gearbox replacement
EXAMPLE In typical wind turbine gearboxes, the high-speed shaft and bearings are considered as field replaceable
units.
3.1.7
functional element
element of a component providing a specific function
EXAMPLE Gear tooth.
Note 1 to entry: A component can have several functional elements.
3.1.8
reliability
probability that a product does not fail during a defined period of time under given functional
and environmental conditions
Note 1 to entry: The term probability takes into consideration that various failure events can be caused by
coincidental, stochastically distributed causes and that the probability can only be described quantitively. See
Bertsche (2008).
3.1.9
reliability function
R(t)
survival probability
probability of survival until time, t
3.1.10
system element
unique combination of a failure mode with a functional element of a component
EXAMPLE Gear tooth root bending fatigue fracture of the sun pinion.
3.1.11
system element reliability function
R (t)
SE
failure behaviour of a system element
3.1.12
system reliability function
R (t)
S
failure behaviour of the complete system, calculated from the system element failure behaviours
and Boolean system theory
3.2 Abbreviated terms and units
This document uses equations and relationships from several engineering specialties. As a
result, there are, in some cases, conflicting definitions for the same symbol. All the symbols
used in the document are nevertheless listed, but, if there is ambiguity, the specific definition
is presented in the clause where they are used in equations, graphs, or text.
F(t) failure probability %
f conversion factor for tooth root bending strength for failure –
F1
probability, F
f conversion factor for pitting strength for failure probability, F –
H1
f failure free time factor –
tB
i load bin index –
j system element index –
L lifetime where failure of F % of the elements is expected h
F
L bearing rating life for 10 % failure probability (i.e. 90 % reliability) h
L bearing combined modified reference rating life for 10 % failure h
10mr
probability (i.e. 90 % reliability)
N number of shaft load cycles for endurance strength according to –
D
DIN 743 series
N number of gear load cycles for endurance limit according to –
L ref
ISO 6336-6
N allowable number of load cycles for tooth root bending strength for –
FF,i
failure probability, F, and load bin, i
N allowable number of load cycles for pitting strength for failure –
HF,i
probability, F, and load bin, i
N allowable number of load cycles for shaft fatigue fracture for failure –
SF,i
probability, F, and load bin, i
n number of cycles for load bin, i –
i
n shaft rotational speed r/min
R
n relative shaft rotational speed for load bin, i –
rel,i
p material S-N curve slope exponent –
R(t) reliability function –
R (t) system element reliability function for element, j –
SE,j
R (t) system reliability function –
S
S lifetime margin factor for bending strength for failure probability, F –
LFF
S lifetime margin factor for pitting strength for failure probability, F –
LHF
s relative standard distribution for bending strength for failure %
F50 %
probability, F
s relative standard distribution for pitting strength for failure %
H50 %
probability, F
T relative torque for load bin, i –
rel,i
t time h
t design life, typically 175 000 h for a 20-year design life h
d
t tooth root bending strength service life h
sF
t pitting strength service life h
sH
t relative time for load bin, i %
rel,i
U critical damage sum –
crit
U damage sum for gear tooth root bending strength for failure –
FF
probability, F
U damage for gear tooth root bending strength for failure probability, –
FF,i
F, and for load bin, i
U damage sum for gear pitting strength for failure probability, F
HF
U damage for gear pitting strength for failure probability, F, and for –
HF,i
load bin, i
U damage sum for shaft fatigue fracture for failure probability, F
SF
Z quantile of the standard normal distribution for failure probability, –
F
F
Weibull shape parameter –
β
γ Weibull location parameter h
η Weibull characteristic life or scale parameter h
σ lognormal distribution standard deviation h
σ shaft endurance strength according to DIN 743 series MPa
ADK
σ shaft fatigue strength for each load bin MPa
ANK,i
σ gear tooth root stress for load bin, i MPa
F,i
σ gear tooth root bending stress limit for failure probability, F MPa
FPF
σ gear tooth contact stress for load bin, i MPa
H,i
σ gear tooth pitting stress limit for failure probability, F MPa
HPF
DIN Deutsches Institut für Normung
FVA Forschungsvereinigung Antriebstechnik
IEC International Electrotechnical Commission
ISO International Organization for Standardization
LRD load revolution distribution
VDMA Verband Deutscher Maschinen- und Anlagenbau
4 System reliability analysis model
4.1 General
This document specifies a Boolean approximation for calculating the system reliability function,
R (t), of the gearbox. The gearbox elements are represented as a series of blocks, each of
S
them representing the probability of a gearbox element failing in one calculable failure mode.
The approach makes the following assumptions:
– The gear elements currently considered in the model do not have any redundancies.
Therefore, the reliability elements are arranged in sequential blocks. This indicates that the
model considers the gearbox as failed if any of the individual elements fail. In particular, the
individual elements of a planetary gear system are not considered redundant or have
parallel paths.
– All individual elements within the gearbox are assumed to be independent.
NOTE Several other approaches for reliability analysis exist. Standardizing one method for wind turbine drivetrains
improves the opportunities to share data between different stakeholders (e.g., operators, manufacturers of wind
turbines or gearboxes) and thereby accelerates the validation of the analysis against field data and enriches the
model with empirical data.
Within these assumptions, the system reliability function, R (t), is calculated as the product of
S
the system element reliability functions, R (t)
,
SE j
R (t) = R (t)
S ∏ SE,j
(1)
∀j
If a system is comprised of multiple identical components, the reliability of each component
shall be considered in Formula (1).
An example of a system reliability calculation is described in Annex A.
4.2 Failure mode identification, classification, and system element assignment
For analysing system reliability, the gearbox system is structured according to its sub-systems,
components, functional elements, and failure modes. A system element is a unique combination
of a failure mode of a functional element of a component. The structured system can be
illustrated as a system element tree as outlined with dashed lines in Figure 2, with an example
system element "pitting on sun pinion gear teeth".
Figure 2 – Example of a system elements tree
All relevant failure modes are categorized as A1, A2, B or C as described in IEC 61400-4.
IEC 61400-4 recommends that all failure modes be identified by the critical system analysis
(e.g. failure mode and effects analysis) and failure risks mitigated by analysis or the verification
plan. The present reliability calculation method includes only the A1 failure modes described
in 5.1.
The failure modes should be described in accordance with standardized definitions. ISO 15243
provides failure mode definitions for rolling bearings and ISO 10825-1 and ISO/TR 10825-2
provide failure mode definitions for gears.
NOTE Describing the failure modes in accordance with standards supports the comparison of calculated reliability
with field data if the field data follow the same definitions. A calibration of the calculation model by means of field
data can be considered to improve calculation model accuracy.
5 Component reliability analysis models
5.1 Individual failure modes
The design reliability calculation shall include all category A1 failure modes described in
IEC 61400-4 for which a life can be estimated by means of a standardized calculation method,
currently including:
– gear tooth surface durability (pitting) according to ISO 6336-2:2019;
– gear tooth bending strength according to ISO 6336-3:2019;
– bearing rolling contact fatigue according to ISO 16281;
– shaft fracture according to DIN 743 series or IEC 61400-8.
The calculation methodology and assumptions for each failure mode shall be documented.
The methodology described herein can be expanded to include additional unique failure modes
that demonstrate a similarly standardized life calculation or are supported by empirical data.
Plain bearings are designed such that no fatigue failure is expected during the design life.
Hence, they are currently not considered in the reliability model.
5.2 Gear reliability calculation
5.2.1 General
The failure probability for gears is calculated for surface durability (pitting) and tooth root fatigue
fracture failure modes using the same methodology. The calculation procedure can also be
applied to any failure mode for which an S-N curve and corresponding statistical distribution
function are available. The basic principle is the damage accumulation according to Miner.
The gear reliability calculation is conducted in two parts: estimation of the service life for defined
failure probabilities as described in 5.2.2, followed by extrapolation of those service life
estimates to very low failure probabilities typical for wind turbine gearboxes as described
in 5.2.3. This extrapolated failure probability is then used to estimate the gear system element
reliability, R (t), at or even below the design life, t .
SE d
5.2.2 Estimation of service life for defined failure probabilities
The first part of the calculation estimates the service life of a gear wheel for a defined set of
failure probabilities, F, from 0,1 % to 99,9 % in accordance with the service-life calculations
described in ISO 6336-6. The load spectrum is determined as described in ISO 6336-6:2019,
4.1 based on the specified gearbox loads. The result is represented by an LRD. The stress
spectrum and the service life are calculated according to ISO 6336-6:2019, 4.2. The S-N curves
for different failure probabilities are determined based on FVA project 304 (Stahl et al. 1999).
These S-N curves include the translation of the failure probability from a single tooth to the
entire gear wheel.
Figure 3 illustrates an example of the service life estimation procedure. The example shows a
design LRD for 20 years, which has a failure probability below 1 %. The design LRD leads to a
damage sum less than 1, so it can be scaled in time until the damage sum equals 1. The scaled
LRD results in a failure probability of 50 %. The resulting scaling factor in time is designated as
the lifetime margin factor for failure probability, F. With this calculation, one point in the failure
probability progression over time, F(t), is determined.
Figure 3 – Service-life calculation for a 50 % failure probability (top)
from a scaled LRD (bottom)
The calculation consists of the following steps. The damage sums, U and U , for an LRD
HF FF
representing the design life for the S-N curve for a given failure probability, F, are
UU=
∑
HF H,Fi
(2)
∀i
UU=
∑
FF F,Fi
(3)
∀i
The damages for each load bin, U and U , are determined from the ratio of the number of
HF,i FF,i
cycles in each load bin, n , to the number of allowable cycles in each load bin, N and N
i HF,i FF,i
n
i
U =
(4)
H,Fi
N
H,Fi
n
i
U =
(5)
F,Fi
N
F,Fi
where
p

σ
HPF
(6)
N = N 
HFi, L ref

σ
H,i

p

σ
FPF
(7)
NN=

FFi, L ref

σ
F,i

and N and p are material parameters. The lifetime margin factors, S and S , are
L ref LHF LFF
U
crit
S =
(8)
LHF
U
HF
U
crit
S =
(9)
LFF
U
FF
The critical damage sum, U , is assumed to be 1. Multiplying the lifetime margin factors with
crit
the design lifetime, t , yields the service lives, t and t
d sH sF
t = tS
(10)
sH d LHF
t = tS
(11)
sF d LFF
The S-N curves for tooth surface durability and tooth bending strength can be derived for
different failure probabilities using appropriate statistical methods applied to suitable fatigue
test data. Comprehensive fatigue test data for tooth surface durability and tooth bending
strength derived from test gears in FVA project 304 (Stahl et al. 1999) can be described by a
standard normal distribution in the endurance range. Figure 4 shows S-N curves for different
failure probabilities, F, and their failure probability density functions.
NOTE 1 For purely illustrative purposes, the strength values are shown as normal distributions even though the
S-N curves are plotted on a logarithmically scaled diagram.
NOTE 2 For purely illustrative purposes, the endurance limit is shown as a horizontal line, whereas ISO 6336-2 and
ISO 6336-3 also define a slope in the endurance region.
Figure 4 – S-N curve for different failure probabilities (Hein et al. 2018)
According to FVA project 304 (Stahl et al. 1999), the relative standard deviation (standard
deviation as a percent of mean) for 50 % failure probability is s = 3,4 % for tooth bending
F50%
endurance strength of case carburized, shot blasted or shot peened gears and s = 3,5 %
H50%
for surface durability endurance strength of case carburized gears. Based on these standard
deviations, FVA project 304 yields factors to convert the stress limit from 50 % to 1 % failure
probability for case carburized gears. In a similar way, FVA projects 615 yields conversion
factors for nitrided gears. Table 1 lists these conversion factors.
Table 1 – Failure probability conversion factors for permissible gear stresses
Material processing Surface Root bending Source
durability strength
(endurance) (endurance)
f f
H1% F1%
Case carburized 0,92 0,86 FVA project 304
(Stahl et al. 1999)
Case carburized with controlled shot 0,92 0,92 FVA project 304
blasting or shot peening of root fillet (Stahl et al. 1999)
Nitrided 0,88 0,86 FVA project 615/III
(Hoja et al. 2024)
ISO 6336-5:2016 provides stress limits for 1 % failure probability. These stress limits can be
converted to 50 % failure probability by
σ
HP1%
σ =
(12)
HP50%
f
H1%
σ
FP1%
σ =
(13)
FP50%
f
F1%
Stress limits for different failure probabilities can be calculated by means of the median, the
relative standard deviation, and the quantile of the standard normal distribution for either pitting
or tooth root strength
σ σ 1+sZ
(14)
( )
HPFFHP50% H50%
σ σ 1+sZ
(15)
( )
FPF FP50% F50% F
where
−1
Z 2 erf 2Ft( )−1 (16)
( )
F
-1
NOTE erf is the inverse Gaussian error function.
Repeating the calculation procedure for several S-N curves with different failure probabilities,
F, ranging from 0,1 % to 99,9 % gives the service life estimation shown in Figure 3. The service
life should be estimated with at least 12 steps of 0,1 %, 1 %, 2 %, 5 %, 10 %, 30 %, 50 %, 70 %,
90 %, 95 %, 98 %, and 99,9 % to achieve sufficient convergence for the lognormal curve fitting
and extrapolation of failure probabilities to the design life described in 5.2.3.
5.2.3 Extrapolation of failure probabilities to the design life
A wind turbine gear component with safety factors according to IEC 61400-4 typically has a
failure probability, F, much lower than 0,1% at typical design lifetimes (e.g. 20 years). The
second part of the gear reliability calculation extrapolates the failure probabilities, F(t),
from 5.2.2 to or even below the design life, t , to determine the gear system element reliability,
d
R (t).
SE
A lognormal function should be fit to extrapolate the service life estimates from the higher failure
probabilities of 0,1 % to 99,9 % (see Bertsche (2008) and VDMA 23904) to the failure
probability at the design life, F(t ). The mean, 𝜇𝜇, and the standard deviation, σ, of the lognormal
d
function should be obtained using a numerical regression method such as maximum likelihood
estimation or rank regression (least squares). The system element reliability based on the
lognormal function is
(lnτμ− )
t
−
1 2
(17)
2σ
R t 1− e dτ
( )
SE, j
∫
τσ 2π
=
=
=
=
Other distribution functions such as Weibull can be used if proven by test data.
5.3 Rolling bearing reliability calculation
The relevant failure modes for rolling bearings in wind turbine gearboxes are described in
IEC 61400-4. Of these modes, only rolling bearing contact fatigue is considered in the reliability
calculation because it is the only one that has a standardized calculation model. However, it is
not advisable to select or optimize a rolling bearing arrangement based on a calculated
theoretical reliability alone, because the actual bearing reliability in service is also dependent
on minimum load, rolling element slip, lubricant, lubricant supply, and heat dissipation.
For values of t below L , the rolling bearing fatigue life is usually described by a 3-parameter
Weibull distribution (see also Annex B). The theoretical reliability value for a 3-parameter
Weibull distribution is
β
t−γ
−

(18)
η

R (te) =
SE, j
ISO/TR 1281-2 provides values for the Weibull shape parameter of β = 1,5 and a lower limit for
the Weibull location parameter of γ = 0,05 × L , which are also used for the calculation of the
life modification factor for reliability specified in ISO 281. This estimation of the Weibull location
parameter, γ , was chosen to be deliberately conservative, so the actual reliability of a rolling
bearing will be generally higher than calculated.
Using the specified values of β and γ from ISO/TR 1281-2 and the bearing rating life
requirements from IEC 61400-4, η can be calculated as
1− 0,05
ηL ≈×4,259 L
10mr 10mr
1 (19)
1,5
−−ln(1 0,1)
which yields
1 if t ≤×0,05 L

10mr

1,5


1,5
R t = −ln(0,90) 
( ) t (20)
 
SE, j
− −0,05


0,95 L
10mr


e if tL>×0,05
10mr

for the theoretical reliability value of a bearing where L is the modified reference rating life
10mr
calculated for a failure probability of 10 % in accordance with ISO 16281 and IEC 61400-4.
IEC 61400-4 limits the ratio of modified reference rating life, L , to the nominal reference
10mr
rating life, L . This limitation should not be applied for the reliability analysis described in this
10r
document unless experience from operation of similar gearboxes indicates otherwise. The
operating conditions of the bearing as specified in IEC 61400-4 can have a significant influence
on the calculated bearing life and failure probability.
=
5.4 Shaft reliability calculation
Shafts can include features where local stress is concentrated because of notch effects. In
general, only the feature with the lowest load reserve is considered for the reliability calculation.
The fatigue calculation for shafts yields a damage sum, U , for the design life, t , based on S-N
S d
curves for a given failure probability, F. The reference lifetime, L , for failure probability
F
F(L ) = F % is
F
t
d
L =
(21)
F
U
SF
where the damage sum, U , is
SF
n
i
U =
SF ∑ (22)
N
SF ,i
∀i
The allowable number of load cycles, N , for any fatigue strength, σ , is calculated using
SF,i ANK,i
the S-N curve
p

σ
ADK
(23)
N = N 
S,Fi D

σ
ANK,i

where the slope of S-N curve, p, depends on the stresses and loading as follows:
– For load bins above the endurance strength (σ > σ ):
ANK,i ADK
• p = 5 for mainly bending loads;
• p = 8 for mainly torsional loads.
– For load bins below the endurance strength (σ < σ ):
ANK,i ADK
• p = (2×5) − 1 = 9 for mainly bending loads;
• p = (2×8) − 1 = 15 for mainly torsional loads, according to Miner-Haibach
(Haibach 2006).
Thus, all load bins contribute to the damage sum.
The calculated reliability of a shaft, R (t), is determined using a 3-parameter Weibull
SE
distribution. These parameters are the Weibull shape parameter, β, characteristic lifetime, η, for
failure probability F(η) = 63,2 % and location parameter, γ, which in fatigue analysis is often
interpreted as the time-to-first failure. The Weibull location parameter, γ, and characteristic
lifetime, η, are calculated from L , while the Weibull shape parameter, β, is a value that is
F
assumed to be 1,5 in this document. Deviations from this value shall be documented but should
be between 1,1 and 1,9 as described in Bertsche (2008). If the component lifetime, L , is given
F
for any other failure probability F(L ) = F %, the lifetime L is calculated as
F 10
L
F
L =
  ln 1− F
γγ ( ) (24)
β
+−1
 
LL ln 1− 0,1
( )
10 10
 
The nominal S-N curve for shafts is determined for a failure probability of F = 2,5 %
(i.e. a reliability 97,5 %).
The location parameter, γ, is defined as γ = f L . Substituting into Formula (24) yields
tB 10
L
F
L =
ln(1− F )
(25)
β
ff+ 1−
( )
tB tB
ln 1− 0,1
( )
For shafts, the failure free time factor, f , should be between 0,7 and 0,9 as described in
tB
Bertsche (2008). This document uses 0,7 for shafts and any deviations shall be documented.
The Weibull scale parameter, η, for failure probability F(η) = 63,2 % is then calculated as
L −γ L − fL
F tB 10
F
η
(26)
ββ
−−ln 1 FF−−ln 1
( ) ( )
The reliability R (t) for a given design life, t , is calculated as
SE d
1 if t ≤γ


β
R t =
( ) t−γ (27)

SE, j
−


η

etif >γ

In typical wind turbine gearbox designs, the safety values for shafts are very
...