Railway applications - Axle design method

This Technical Report gives guidance for:
- the use of Finite Element Method (FEM) to supplement the axle calculation defined in relevant standards for wheelset calculation and to deteremine in particular conditions for fitting transitions and groves;
- determination of fatigue limits consistent with the FEM procedure;
- validation of the fatigue limit of the blasted axles and unpainted axles.
It contains a proposal of a method for the analysis of in service load measurements to be applied in the fatigue assessment of axles.

Bahnanwendungen - Konstruktionsverfahren von Radsatzwellen

Applications ferroviaires - Méthode de conception des essieux

Le présent document décrit l'état des connaissances acquises dans le cadre du projet EURAXLES en ce qui concerne la conception des essieux-axes, ainsi que les autres éléments à prendre en compte.
Il a pour objet de :
- définir les charges à prendre en compte ;
- décrire la méthode de calcul des contraintes selon la méthode des éléments finis, ainsi que les processus de validation associés ;
- spécifier les contraintes maximales admissibles à utiliser pour les calculs, ainsi que les coefficients de sécurité à appliquer.
Le présent Rapport technique est applicable aux :
- essieux montés définis dans l'EN 13261 ;
- autres conceptions d'essieux-axes rencontrées sur les matériels roulants particuliers, par exemple les essieux-axes équipés de roues indépendantes, à écartement variable ou empruntant le réseau ferroviaire urbain, etc.
Le présent document n'a pas pour objet de remplacer l'EN 13103 1 et la CEN/TS 13103-2, mais de décrire une méthode complémentaire aux méthodes actuelles.

Železniške naprave - Metoda načrtovanja osi

General Information

Status
Published
Public Enquiry End Date
22-Jan-2020
Publication Date
06-Apr-2020
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
06-Apr-2020
Due Date
11-Jun-2020
Completion Date
07-Apr-2020

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SLOVENSKI STANDARD
SIST-TP CEN/TR 17469:2020
01-junij-2020
Železniške naprave - Metoda načrtovanja osi
Railway applications - Axle design method
Bahnanwendungen - Konstruktionsverfahren von Radsatzwellen
Applications ferroviaires - Méthode de conception des essieux
Ta slovenski standard je istoveten z: CEN/TR 17469:2020
ICS:
45.040 Materiali in deli za železniško Materials and components
tehniko for railway engineering
SIST-TP CEN/TR 17469:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN/TR 17469:2020
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SIST-TP CEN/TR 17469:2020
CEN/TR 17469
TECHNICAL REPORT
RAPPORT TECHNIQUE
March 2020
TECHNISCHER BERICHT
ICS 45.040
English Version
Railway applications - Axle design method

Applications ferroviaires - Méthode de conception des Bahnanwendungen - Konstruktionsverfahren von

essieux Radsatzwellen

This Technical Report was approved by CEN on 24 February 2020. It has been drawn up by the Technical Committee CEN/TC

256.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2020 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 17469:2020 E

worldwide for CEN national Members.
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CEN/TR 17469:2020 (E)
Contents Page

European foreword ....................................................................................................................................................... 4

Introduction .................................................................................................................................................................... 5

1 Scope .................................................................................................................................................................... 9

2 Normative references .................................................................................................................................... 9

3 Terms, definitions, symbols and abbreviations ................................................................................... 9

3.1 Terms and definitions ................................................................................................................................... 9

3.2 Symbols and abbreviations ......................................................................................................................... 9

4 Loads ................................................................................................................................................................. 11

4.1 Reliability analysis based on the Stress Strength Interference Analysis method ................ 11

4.2 Fatigue load analysis method .................................................................................................................. 13

4.2.1 General ............................................................................................................................................................. 13

4.2.2 Load signals processing and Fatigue-Equivalent-Load .................................................................. 13

4.2.3 Method to generate the distribution of in-service load severities ............................................. 19

4.3 Fatigue reliability assessment of a railway passenger coach axle ............................................. 23

4.3.1 Load measurements .................................................................................................................................... 23

4.3.2 Load spectra classification and generation and distribution of load severity....................... 27

4.3.3 Estimation of the probability of a crack initiation ........................................................................... 31

5 Modelling ......................................................................................................................................................... 33

5.1 General ............................................................................................................................................................. 33

5.2 Stress concentration factors .................................................................................................................... 33

5.3 Length of the transition ............................................................................................................................. 36

5.4 Numerical modelling of axles .................................................................................................................. 38

5.4.1 Development of numerical models and validation .......................................................................... 38

5.4.2 Analysis of mounted components .......................................................................................................... 42

5.4.3 Modelling recommendations ................................................................................................................... 43

5.5 Axle calculation method ............................................................................................................................ 44

6 Fatigue limits ................................................................................................................................................. 45

6.1 Testing method principals ........................................................................................................................ 45

6.1.1 F1 tests ............................................................................................................................................................. 45

6.1.2 F4 tests ............................................................................................................................................................. 46

6.1.3 Fatigue limit estimation ............................................................................................................................. 46

6.2 Test plan .......................................................................................................................................................... 47

6.3 Axle body fatigue limit results ................................................................................................................. 51

6.3.1 F1 standard surface – transitions and groves (EA4T axles) ......................................................... 51

6.3.2 F1 Blasted surface – transitions (EA4T axles) ................................................................................... 52

6.3.3 F1 Standard surface – transitions (EA1N axles) ................................................................................ 53

6.3.4 F1 Corroded surfaces – transitions of unpainted axles .................................................................. 54

6.4 Axle press-fit seat fatigue limits (F4) .................................................................................................... 55

6.4.1 Diameter ratio = 1,12 (EA4T axles) ....................................................................................................... 55

6.4.2 Diameter ratio = 1,08 (EA4T) .................................................................................................................. 56

7 Safety factors.................................................................................................................................................. 57

7.1 Aims and problem statement................................................................................................................... 57

7.2 Probabilistic fatigue assessment ............................................................................................................ 60

7.2.1 Failure probability under constant amplitude stress ..................................................................... 60

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7.2.2 Fatigue damage under VA loading .......................................................................................................... 60

7.2.3 Bignonnet method ........................................................................................................................................ 61

7.3 Input data for probabilistic fatigue assessment of railway axles ................................................ 62

7.3.1 Definitions of reference S-N diagrams .................................................................................................. 62

7.3.2 Miner Index at failure.................................................................................................................................. 63

7.3.3 Target reliability and failure rate for railway axles ........................................................................ 66

7.4 Probabilistic fatigue damage calculations for railway axles ........................................................ 66

7.4.1 Format for the calculations ....................................................................................................................... 66

7.4.2 Montecarlo simulations .............................................................................................................................. 67

7.4.3 Stress spectra ................................................................................................................................................. 67

7.5 Results .............................................................................................................................................................. 68

7.5.1 General ............................................................................................................................................................. 68

7.5.2 Safety factor and reliability under constant amplitude stress ..................................................... 69

7.5.3 Safety factor for damage calculations ................................................................................................... 70

8 Conclusions of Euraxles Project .............................................................................................................. 71

9 Recommendations of CEN TC256/SC2/WG11 .................................................................................... 75

Annex A (informative) Application example of the axle calculation method ...................................... 76

A.1 General ............................................................................................................................................................. 76

A.2 General descriptions ................................................................................................................................... 76

A.3 Load distribution .......................................................................................................................................... 77

A.4 Results according to EN 13103-1 ............................................................................................................ 78

A.5 Design of EURAXLES method .................................................................................................................... 80

A.6 Comparison of results ................................................................................................................................. 82

Bibliography ................................................................................................................................................................. 83

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European foreword

This document (CEN/TR 17469:2020) has been prepared by Technical Committee CEN/TC 256 “Railway

applications”, the secretariat of which is held by DIN.

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

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

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Introduction

The first railway accident due to the fatigue failure of an axle occurred on 1842, May 8th, in France, near

Meudon, on the Versailles-Paris line.

In those days, the fatigue phenomenon was unknown. This failure initiated numerous studies including

German Engineer August WOHLER works on wheelset failures at the end of XIX century.

In the middle of XX century, M. KAMMERER, an engineer working for French railways, established the

bases for the calculation of wheelset axles.

At international level, the report ORE B136 RP11 « Calculation of fret wagon and passenger coaches’

wheelset axles » was edited in April 1979, using in particular the French approach.

This document allowed editing on 1994, July 1st of UIC leaflet 515-3 «Railway rolling stock – Bogie –

Running gears – Axle calculation method».

The first edition of the European Standards about design of axles occurs on April 2001 (EN 13103 for

non-powered axles for powered axles).

The ongoing European standardization has allowed the merging of EN 13103 in only one standard

(EN 13103-1 Railway applications – Wheelsets and bogies – Part 1: Design method for axles with external

journals) and the creation of a new Technical Specification about internal journal (CEN/TS 13103-2

Railway applications – Wheelsets and bogies – Part 2: Design method for axles with internal journals).

All these documents, including M. KAMMERER’s work up to EN 13103-1 and CEN/TS 13103-2, use the

beam theory calculation method. The stresses taken into account are then the nominal stresses. The

fatigue limit is determined from full scale tests in which nominal stresses are taken into account.

Concentration factors are defined from tests to consider the local geometry and to increase the nominal

stress locally. The method is quite simple, with no need of sophisticated calculations or dedicated

software.

On another hand, in the middle of XX century, the need in mechanics to have a tool to calculate

complicated parts lead to the development of the finite element method.

Along with the theoretical study of this method, the use of new mathematical objects and the growth of

calculation capacities of computers, the finite element method raised to a large and common use in

design.

The stresses then calculated are local stresses, and not anymore nominal stresses, and the fatigue limit

to be applied with this methodology are based on local stresses.

In the Euraxles project, the objective was to propose the use of a new assessment method based on load

measurements, finite element method, experimental fatigue limit and new safety concept for the design

of axles in particular for axle designs requiring more complex geometries. This design procedure is

different from today’s proven methods given by the EN standards and not in a status to substitute them.

Nevertheless, it was considered interesting to gather the Euraxles project results inside this Technical

Report. The content should be considered as partial and only for informative uses at this stage. For

example, the reliability of the input data, the variability of parameters, boundary conditions and the

confidence in the partial results should be assessed at full extent.

Where relevant, CEN TC256/SC2/WG11 comments and responses to preliminary enquiry inside the

community were inserted for additional use for the reader, as Observations of CEN/TC 256/SC 2/WG 11.

Besides, a general recommendation of use has been drafted by WG11 members in chapter 9.

This new method is described in this Technical Report in order to allow the possibility for wheelset

designers to apply it and to collect return of experience for further improvement.

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Work Program summary

Clause 4 deals with the definition of a new fatigue design method which enables to assess the in-service

reliability of axles with regards to fatigue failure. The proposed approach, based on the “Stress Strength

Interference Analysis” (SSIA) and the “Fatigue-Equivalent-Load” (FEL) methods, aims at estimating the

probability of axles’ fatigue failure by characterizing the variability of in-service loads and the scatter of

the axles fatigue strength.

First of all, the main lines of the SSIA method are recalled. This method aims at evaluating the in-service

reliability of components for their design or their homologation. In the second part, the fatigue load

analysis method that is proposed for railway axles is described. It starts with a post-processing of an axle

load measurement: from a time signal of forces applied to both wheels fitted on the axle, fatigue cycles of

bending moment applied to the axle are identified and transformed into a cyclic equivalent load, Meq,

which is a measurement of the severity of the initial variable load. Then, virtual but realistic load spectra

are generated, thanks to a classification operation followed by a random draw of elementary load data

that considers the operation and maintenance conditions of the axle. All the spectra are then analysed

with the FEL method in order to build the distribution of in-service load severities. This distribution gives

a picture of the stress to which the axles are submitted. In the third and last part, the methods are applied

to real data of SNCF. Sensitivity analyses are performed in order to quantify the effect on Meq of variations

of parameters and to verify the convergence and robustness of the process. Finally, results obtained for

a passenger coach are given. The comparison between the distribution of load severities and the

normative load, defined as according to standards EN 13103-1, shows that, for the studied axle, the

normative load is very conservative. Finally, using the axles fatigue limits identified on full-scale tests, a

Stress Strength Interference Analysis is performed to calculate the probability of failure of the axle.

Figure 1 — Flowchart for load analysis and reliability assessment
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Clause 5 concerns the mechanical modelling of an axle and defines a procedure to obtain local stresses

from the applied loads.

The characteristics of the finite element models to be applied to railway axles are analysed in terms of

element definition, convergence analysis, boundary conditions. A parametric analysis was performed to

assess the applicability of the models. The numerical models generated were validated through the

comparison with experimental results coming from full scale fatigue tests. Finally, a methodology to

design axles using modelling tools as a complement to current European norms is proposed looking for

a compromise between the computational effort and the results obtained.
Figure 2 — Flowchart for modelling

The main scope of Clause 6 is to provide the fatigue limits for standard steel grades considering also the

effect of surface conditions that may be different from the normal newly machined axles, like surface

corrosion that can appear during the service or surface blasting as a method to improve paint adhesion.

The areas of the axles considered were the free body transitions or groves and the wheel seats where at

high bending rates relative micro slips take place generating the so called fretting fatigue phenomena.

The paper provides in the conclusions a comparison with the fatigue limits that are today included in the

European Standards.

Another aspect that is treated in this work is the stress concentration effect that takes place along the

transitions where the body fatigue limit is verified. These parameters were measured by strain gauges

during each test and used inside the Euraxle project to validate their estimation through FE model

calculation.
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Figure 3 — Full-scale and small-scale fatigue tests
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CEN/TR 17469:2020 (E)
1 Scope

This document presents the stage of knowledge resulting from the Euraxles project about the design of

the axle, and further steps to be taken.
It is the support:
- to define the loads to be taken into account;

- to describe the stress calculation method using finite elements and the validation processes associated;

- to specify the maximum permissible stresses to be assumed in calculations and the safety factors to be

used.
This technical report is applicable for:
- wheelset Axles defined in EN 13261 as “pure wheelset”;

- other axle designs such as those encountered in particular rolling stocks e.g. with independent wheels,

variable gauges, urban rail…

This document has not for aim to replace EN 13103-1 and CEN/TS 13103-2 but to present a

complementary method to the existing ones.
2 Normative references
There are no normative references in this document.
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
No terms and definitions are listed in this document.

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 https://www.iso.org/obp/ui
3.2 Symbols and abbreviations
FEL fatigue equivalent load method
SSIA Stress Strength Interference Analysis
KMR Consequent Miner Rule
FEM Finite Element Method
Nomenclature is given in Table 1.
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Table 1 — Nomenclature
Y (t), Y (t) lateral force applied to both wheels
1 2
Q (t), Q (t) vertical force applied to both wheels
1 2
P1, P2 Vertical loads applied on the journals
C Minimum transition length
min
F Fatigue load
F Fatigue equivalent load

F Severe representative load that can be defined for test and simulation validation

x, y, z Longitudinal, axial, vertical direction of wheelset reference axis
Bending moment applied to the y-section of the axle in the x direction (train
M (y)
circulation direction)

M Bending moment applied to the most critical section of the axle in the x direction

Equivalent bending moment applied to the most critical section of the axle in the

x,eq
x direction
M Normative bending moment
x,EN
MR Resultant bending moment
P Probability
P Probability of failure
P Probability of having a more severe load than F
n n
E Young modulus
K Stress correction factor
Kt Stress concentration factor
K Fatigue stress concentration factor
K Stress concentration factor based on strain measurements
t,s
D Total fatigue damage
d Partial damage generated by the ith class of a load spectrum
n Occurrence of the ith class of a load spectrum
N Number of cycles for a crack initiation for the ith class of a load spectrum
CV Coefficient of variation for the X variable
m Slope of the S-N diagram when using a one single slope curve
k Slope of the S-N diagram for S > S
k’ Slope of the S-N diagram for S < S
N number of cycle for the knee of the S-N diagram
S Stress load
S stress amplitude for the knee of the S-N diagram
K total mileage of an axle
ref
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σ Allowable fatigue stress
σ Calculated dynamic stress
σ Von Mises stress
σ Hydrostatic stress
τ Shear stress
σ Principal stress
ε Principal strain
σn Nominal stress
D/d Diameter ratio (diameter of wheel seat divided diameter of nearby body)
D Outer diameter of hub
d Diameter of the axle shaft
Maximum value of the radius of the transition r
max
F1 Full scale axle body fatigue limit
F4 Full scale axle seat fatigue limit
4 Loads

4.1 Reliability analysis based on the Stress Strength Interference Analysis method

Fatigue is known to be a damage phenomenon which is very dispersive. The sources of variability are

linked to the material properties that depend on its composition but also on the manufacturing process,

the geometry of the structure, loads, usages, environment, etc. To ensure safety, margins applied to the

specified loads and the prescribed fatigue limits, associated to a stress calculation method were defined

in standards EN 13103-1 [21] for the design and validation of railway axles. They were established in the

past decades, based on experience of railway experts and experimental and modelling works. Today, they

enable to guaranty a high level of safety for the European railway sector, as feedback from operation

shows. But, to gain competitiveness, it can be very useful to measure the available margins in order to

ensure that when a new design or a new technology is introduced, the level of safety is maintained.

For that reason, it would be beneficial to switch little by little from conservative approaches towards

reliability approaches. Maximalist approaches ensure safe designs by defining safety factors that make

the load specifications more severe and underestimate the allowable fatigue limits. The consequence is

that optimized solutions can’t be found. Moreover, when a significant change occurs in the system, it is

difficult to evaluate its impact on reliability. In reliable approaches, the aim is to have a “just necessary”

design associated to a target probability of failure. For safety critical components, the probability of

−5 −8

failure during the lifetime generally vary from 10 to 10 . In the example given in [4] on an automotive

engine part, the target probability is 10-6. For railway safety applications, if one considers that the

−6 −7

number of accidents due to mechanical failures is rather small, a target between 10 and 10 sounds

reasonable.
−6 −7

Observations of CEN/TC 256/SC 2/WG 11: The target value quoted (10 to 10 ) is a failure rate per

axle during its whole life. It is approximately in line with the 10 failure rate per operational hour defined

in the CSM (EU regulation 402/2013) for technical systems for which a functional failure with immediate

disastrous consequences is assumed.
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Reliability approaches have been developed for many years in various industries. The methods always

consist in characterizing the variabilities of the system to be designed and in calculating its probability of

failure by propagating the uncertainties in a deterministic modelling, as shown in Figure 4.

Figure 4 — Reliability approaches

The SSIA (Stress Strength Interference Analysis) is one of the reliability methods. It is widely used in

industries, due to its simplicity. Within this approach, only two global parameters are used to characterize

the variability of the problem: the load severity - referred to as STRESS - and the component strength -

referred to as STRENGTH. These two parameters are chosen so as to be comparable (for instance, local

stresses vs fatigue limits). Once the distributions of the Stress and the Strength are identified and

modelled, a probability of failure can be easily calculated, by means of analytical expressions or numerical

resolutions, as explained for example in [1][2][3][4]. The SSIA is therefore often used in the validation

process of a new component. But it is even more powerful in the design process: from a pre-defined target

probability of failure Pf, for a given distribution of Stress, the Strength distribution (mean value and

scatter) can be specified. Let’s notice that there is not a unique solution to this problem, as shown in

Figure 5.
a) SSIA for the validation process b) SSIA for the design process
Figure 5 — SSIA approach

To apply the SSIA approach, it is necessary to characterize both distributions. The distribution of Strength

can be identified thanks to laboratory fatigue tests. To have a good estimation of its distribution and not

only its mean value, a sufficient number of tests is necessary. In the Euraxles project, new tests were

performed for steel grades EA1N and EA4T. They are described in [17] and in Clause 4 of the report. For

the Stress distribution, measurements of loads shall be carried out in various operating conditions in

order to capture the variability of the behaviour of the component, as described in 4.2.3. Using

complementary information on the variability of usages from an axle to another, a distribution of in-

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service load severity S can be generated. Accordingly, a representative and severe load can be defined as

a specification to be used in the
...

SLOVENSKI STANDARD
kSIST-TP FprCEN/TR 17469:2020
01-januar-2020
Železniške naprave - Metoda načrtovanja osi
Railway applications - Axle design method
Bahnanwendungen - Konstruktionsverfahren von Radsatzwellen
Applications ferroviaires - Méthode de conception des essieux
Ta slovenski standard je istoveten z: FprCEN/TR 17469
ICS:
45.040 Materiali in deli za železniško Materials and components
tehniko for railway engineering
kSIST-TP FprCEN/TR 17469:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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kSIST-TP FprCEN/TR 17469:2020
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kSIST-TP FprCEN/TR 17469:2020
FINAL DRAFT
TECHNICAL REPORT
FprCEN/TR 17469
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
October 2019
ICS
English Version
Railway applications - Axle design method

Applications ferroviaires - Méthode de conception des Bahnanwendungen - Konstruktionsverfahren von

essieux Radsatzwellen

This draft Technical Report is submitted to CEN members for Vote. It has been drawn up by the Technical Committee CEN/TC

256.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.

Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are

aware and to provide supporting documentation.

Warning : This document is not a Technical Report. It is distributed for review and comments. It is subject to change without

notice and shall not be referred to as a Technical Report.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. FprCEN/TR 17469:2019 E

worldwide for CEN national Members.
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kSIST-TP FprCEN/TR 17469:2020
FprCEN/TR 17469:2019 (E)
Contents

European foreword ....................................................................................................................................................... 4

Introduction .................................................................................................................................................................... 5

1 Scope .................................................................................................................................................................... 9

2 Normative references .................................................................................................................................... 9

3 Terms, definitions, symbols and abbreviations ................................................................................... 9

3.1 Terms and definitions ................................................................................................................................... 9

3.2 Symbols and abbreviations ......................................................................................................................... 9

4 Loads ................................................................................................................................................................. 11

4.1 Reliability analysis based on the Stress Strength Interference Analysis method ................ 11

4.2 Fatigue load analysis method .................................................................................................................. 13

4.2.1 General ............................................................................................................................................................. 13

4.2.2 Load signals processing and Fatigue-Equivalent-Load .................................................................. 13

4.2.3 Method to generate the distribution of in-service load severities ............................................. 19

4.3 Fatigue reliability assessment of a railway passenger coach axle ............................................. 22

4.3.1 Load measurements .................................................................................................................................... 22

4.3.2 Load spectra classification and generation and distribution of load severity....................... 26

4.3.3 Estimation of the probability of a crack initiation ........................................................................... 30

5 Modelling ......................................................................................................................................................... 32

5.1 General ............................................................................................................................................................. 32

5.2 Stress concentration factors .................................................................................................................... 32

5.3 Length of the transition ............................................................................................................................. 35

5.4 Numerical modelling of axles .................................................................................................................. 37

5.4.1 Development of numerical models and validation .......................................................................... 37

5.4.2 Analysis of mounted components .......................................................................................................... 40

5.4.3 Modelling recommendations ................................................................................................................... 41

5.5 Axle calculation method ............................................................................................................................ 42

6 Fatigue limits ................................................................................................................................................. 43

6.1 Testing method principals ........................................................................................................................ 43

6.1.1 F1 tests ............................................................................................................................................................. 43

6.1.2 F4 tests ............................................................................................................................................................. 44

6.1.3 Fatigue limit estimation ............................................................................................................................. 44

6.2 Test plan .......................................................................................................................................................... 45

6.3 Axle body fatigue limit results ................................................................................................................. 49

6.3.1 F1 standard surface – transitions and groves (EA4T axles) ......................................................... 49

6.3.2 F1 Blasted surface – transitions (EA4T axles) ................................................................................... 50

6.3.3 F1 Standard surface – transitions (EA1N axles) ................................................................................ 51

6.3.4 F1 Corroded surfaces – transitions of unpainted axles .................................................................. 52

6.4 Axle press-fit seat fatigue limits (F4) .................................................................................................... 53

6.4.1 Diameter ratio = 1,12 (EA4T axles) ....................................................................................................... 53

6.4.2 Diameter ratio = 1,08 (EA4T) .................................................................................................................. 54

7 Safety factors.................................................................................................................................................. 55

7.1 Aims and problem statement................................................................................................................... 55

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7.2 Probabilistic fatigue assessment ............................................................................................................ 57

7.2.1 Failure probability under constant amplitude stress ..................................................................... 57

7.2.2 Fatigue damage under VA loading .......................................................................................................... 58

7.2.3 Bignonnet method ........................................................................................................................................ 59

7.3 Input data for probabilistic fatigue assessment of railway axles ................................................ 60

7.3.1 Definitions of reference S-N diagrams .................................................................................................. 60

7.3.2 Miner Index at failure.................................................................................................................................. 62

7.3.3 Target reliability and failure rate for railway axles ........................................................................ 63

7.4 Probabilistic fatigue damage calculations for railway axles ........................................................ 64

7.4.1 Format for the calculations ....................................................................................................................... 64

7.4.2 Montecarlo simulations .............................................................................................................................. 65

7.4.3 Stress spectra ................................................................................................................................................. 65

7.5 Results .............................................................................................................................................................. 66

7.5.1 General ............................................................................................................................................................. 66

7.5.2 Safety factor and reliability under constant amplitude stress ..................................................... 67

7.5.3 Safety factor for damage calculations ................................................................................................... 68

8 Conclusions of Euraxles Project .............................................................................................................. 69

9 Recommendations of CEN TC256/SC2/WG11 .................................................................................... 73

Annex A (informative) Application example of the axle calculation method ...................................... 74

A.1 General ............................................................................................................................................................. 74

A.2 General descriptions ................................................................................................................................... 74

A.3 Load distribution .......................................................................................................................................... 75

A.4 Results according to EN 13103-1 ............................................................................................................ 76

A.5 Design of EURAXLES method .................................................................................................................... 77

A.6 Comparison of results ................................................................................................................................. 79

Bibliography ................................................................................................................................................................. 80

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European foreword

This document (FprCEN/TR 17469:2019) has been prepared by Technical Committee CEN/TC 256

“Railway applications”, the secretariat of which is held by DIN.
This document is currently submitted to the Vote on TR.
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Introduction

The first railway accident due to the fatigue failure of an axle occurred on 1842, May 8th, in France, near

Meudon, on the Versailles-Paris line.

In those days, the fatigue phenomenon was unknown. This failure initiated numerous studies including

German Engineer August WOHLER works on wheelset failures at the end of XIXth century.

In the middle of XXth century, M. KAMMERER, an engineer working for French railways, established the

bases for the calculation of wheelset axles.

At international level, the report ORE B136 RP11 « Calculation of fret wagon and passenger coaches’

wheelset axles » was edited in April 1979, using in particular the French approach.

This document allowed editing on 1994, July 1st of UIC leaflet 515-3 « Railway rolling stock – Bogie –

Running gears – Axle calculation method».

The first edition of the European Standards about design of axles occurs on April 2001 (EN 13103 for

non-powered axles for powered axles).

The ongoing European standardization has allowed the merging of EN 13103 in only one standard

(EN 13103-1 Railway applications – Wheelsets and bogies – Part 1: Design method for axles with external

journals) and the creation of a new Technical Specification about internal journal (prTS13103-2 Railway

applications – Wheelsets and bogies – Part 2: Design method for axles with internal journals).

All these documents, including M. KAMMERER’s work up to EN 13103−1 and prTS 13103−2, use the beam

theory calculation method. The stresses taken into account are then the nominal stresses. The fatigue

limit is determined from full scale tests in which nominal stresses are taken into account. Concentration

factors are defined from tests to consider the local geometry and to increase the nominal stress locally.

The method is quite simple, with no need of sophisticated calculations or dedicated software.

On another hand, in the middle of XXth century, the need in mechanics to have a tool to calculate

complicated parts lead to the development of the finite element method.

Along with the theoretical study of this method, the use of new mathematical objects and the growth of

calculation capacities of computers, the finite element method raised to a large and common use in

design.

The stresses then calculated are local stresses, and not anymore nominal stresses, and the fatigue limit

to be applied with this methodology are based on local stresses.

In the Euraxles project, the objective was to propose the use of a new assessment method based on load

measurements, finite element method, experimental fatigue limit and new safety concept for the design

of axles in particular for axle designs requiring more complex geometries. This design procedure is

different from today’s proven methods given by the EN standards and not in a status to substitute them.

Nevertheless, it was considered interesting to gather the Euraxles project results inside this Technical

Report. The content should be considered as partial and only for informative uses at this stage. For example,

the reliability of the input data, the variability of parameters, boundary conditions and the confidence in the

partial results should be assessed at full extent.

Where relevant, CEN TC256/SC2/WG11 comments and responses to preliminary enquiry inside the

community were inserted for additional use for the reader, as Observations of CEN/TC 256/SC 2/WG 11.

Besides, a general recommendation of use has been drafted by WG11 members in chapter 9.

This new method is described in this Technical Report in order to allow the possibility for wheelset

designers to apply it and to collect return of experience for further improvement.

Work Program summary
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Clause 3 deals with the definition of a new fatigue design method which enables to assess the in-service

reliability of axles with regards to fatigue failure. The proposed approach, based on the “Stress Strength

Interference Analysis” (SSIA) and the “Fatigue-Equivalent-Load” (FEL) methods, aims at estimating the

probability of axles’ fatigue failure by characterizing the variability of in-service loads and the scatter of

the axles fatigue strength.

First of all, the main lines of the SSIA method are recalled. This method aims at evaluating the in-service

reliability of components for their design or their homologation. In the second part, the fatigue load

analysis method that is proposed for railway axles is described. It starts with a post-processing of an axle

load measurement: from a time signal of forces applied to both wheels fitted on the axle, fatigue cycles of

bending moment applied to the axle are identified and transformed into a cyclic equivalent load, Meq,

which is a measurement of the severity of the initial variable load. Then, virtual but realistic load spectra

are generated, thanks to a classification operation followed by a random draw of elementary load data

that considers the operation and maintenance conditions of the axle. All the spectra are then analysed

with the FEL method in order to build the distribution of in-service load severities. This distribution gives

a picture of the stress to which the axles are submitted. In the third and last part, the methods are applied

to real data of SNCF. Sensitivity analyses are performed in order to quantify the effect on Meq of variations

of parameters and to verify the convergence and robustness of the process. Finally, results obtained for

a passenger coach are given. The comparison between the distribution of load severities and the

normative load, defined as according to standards EN 13103-1, shows that, for the studied axle, the

normative load is very conservative. Finally, using the axles fatigue limits identified on full-scale tests, a

Stress Strength Interference Analysis is performed to calculate the probability of failure of the axle.

Figure 1 — Flowchart for load analysis and reliability assessment

Clause 4 concerns the mechanical modelling of an axle and defines a procedure to obtain local stresses

from the applied loads.
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The characteristics of the finite element models to be applied to railway axles are analysed in terms of

element definition, convergence analysis, boundary conditions. A parametric analysis was performed to

assess the applicability of the models. The numerical models generated were validated through the

comparison with experimental results coming from full scale fatigue tests. Finally, a methodology to

design axles using modelling tools as a complement to current European norms is proposed looking for

a compromise between the computational effort and the results obtained.
Figure 2 — Flowchart for modelling

The main scope of Clause 5 is to provide the fatigue limits for standard steel grades considering also the

effect of surface conditions that may be different from the normal newly machined axles, like surface

corrosion that can appear during the service or surface blasting as a method to improve paint adhesion.

The areas of the axles considered were the free body transitions or groves and the wheel seats where at

high bending rates relative micro slips take place generating the so called fretting fatigue phenomena.

The paper provides in the conclusions a comparison with the fatigue limits that are today included in the

European Standards.

Another aspect that is treated in this work is the stress concentration effect that takes place along the

transitions where the body fatigue limit is verified. These parameters were measured by strain gauges

during each test and used inside the Euraxle project to validate their estimation through FE model

calculation.
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Figure 3 — Full-scale and small-scale fatigue tests
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1 Scope

This document presents the stage of knowledge resulting from the Euraxles project about the design of

the axle, and further steps to be taken.
It is the support:
- to define the loads to be taken into account;

- to describe the stress calculation method using finite elements and the validation processes associated;

- to specify the maximum permissible stresses to be assumed in calculations and the safety factors to be

used.
This technical report is applicable for:
- wheelset Axles defined in EN 13261 as “pure wheelset”;

- other axle designs such as those encountered in particular rolling stocks e.g. with independent wheels,

variable gauges, urban rail…

This document has not for aim to replace EN 13103-1 and prTS 13103-2 but to present a complementary

method to the existing ones.
2 Normative references
There are no normative references in this document.
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
No terms and definitions are listed in this document.

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
3.2 Symbols and abbreviations
FEL fatigue equivalent load method
SSIA Stress Strength Interference Analysis
KMR Consequent Miner Rule
FEM Finite Element Method
Nomenclature is given in Table 1.
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Table 1 — Nomenclature
Y (t), Y (t) lateral force applied to both wheels
1 2
Q (t), Q (t) vertical force applied to both wheels
1 2
P1, P2 Vertical loads applied on the journals
C Minimum transition length
min
F Fatigue load
F Fatigue equivalent load

F Severe representative load that can be defined for test and simulation validation

x, y, z Longitudinal, axial, vertical direction of wheelset reference axis
Bending moment applied to the y-section of the axle in the x direction (train
M (y)
circulation direction)

M Bending moment applied to the most critical section of the axle in the x direction

Equivalent bending moment applied to the most critical section of the axle in the

x,eq
x direction
M Normative bending moment
x,EN
MR Resultant bending moment
P Probability
P Probability of failure
P Probability of having a more severe load than F
n n
E Young modulus
K Stress correction factor
Kt Stress concentration factor
K Fatigue stress concentration factor
K Stress concentration factor based on strain measurements
t,s
D Total fatigue damage
d Partial damage generated by the ith class of a load spectrum
n Occurrence of the ith class of a load spectrum
N Number of cycles for a crack initiation for the ith class of a load spectrum
CV Coefficient of variation for the X variable
m Slope of the S-N diagram when using a one single slope curve
k Slope of the S-N diagram for S > S
k’ Slope of the S-N diagram for S < S
N number of cycle for the knee of the S-N diagram
S Stress load
S stress amplitude for the knee of the S-N diagram
K total mileage of an axle
ref
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σ Allowable fatigue stress
σ Calculated dynamic stress
σ Von Mises stress
σ Hydrostatic stress
τ Shear stress
σ Principal stress
ε Principal strain
σn Nominal stress
D/d Diameter ratio (diameter of wheel seat divided diameter of nearby body)
D Outer diameter of hub
d Diameter of the axle shaft
Maximum value of the radius of the transition r
max
F1 Full scale axle body fatigue limit
F4 Full scale axle seat fatigue limit
4 Loads

4.1 Reliability analysis based on the Stress Strength Interference Analysis method

Fatigue is known to be a damage phenomenon which is very dispersive. The sources of variability are

linked to the material properties that depend on its composition but also on the manufacturing process,

the geometry of the structure, loads, usages, environment, etc. To ensure safety, margins applied to the

specified loads and the prescribed fatigue limits, associated to a stress calculation method were defined

in standards EN 13103-1 [21] for the design and validation of railway axles. They were established in the

past decades, based on experience of railway experts and experimental and modelling works. Today, they

enable to guaranty a high level of safety for the European railway sector, as feedback from operation

shows. But, to gain competitiveness, it can be very useful to measure the available margins in order to

ensure that when a new design or a new technology is introduced, the level of safety is maintained.

For that reason, it would be beneficial to switch little by little from conservative approaches towards

reliability approaches. Maximalist approaches ensure safe designs by defining safety factors that make

the load specifications more severe and underestimate the allowable fatigue limits. The consequence is

that optimized solutions can’t be found. Moreover, when a significant change occurs in the system, it is

difficult to evaluate its impact on reliability. In reliable approaches, the aim is to have a “just necessary”

design associated to a target probability of failure. For safety critical components, the probability of

−5 −8

failure during the lifetime generally vary from 10 to 10 . In the example given in [4] on an automotive

engine part, the target probability is 10-6. For railway safety applications, if one considers that the

−6 −7

number of accidents due to mechanical failures is rather small, a target between 10 and 10 sounds

reasonable.
−6 −7

Observations of CEN/TC 256/SC 2/WG 11: The target value quoted (10 to 10 ) is a failure rate per axle

during its whole life. It is approximately in line with the 10 failure rate per operational hour defined in

the CSM (EU regulation 402/2013) for technical systems for which a functional failure with immediate

disastrous consequences is assumed.
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Reliability approaches have been developed for many years in various industries. The methods always

consist in characterizing the variabilities of the system to be designed and in calculating its probability of

failure by propagating the uncertainties in a deterministic modelling, as shown in Figure 4.

Figure 4 — Reliability approaches

The SSIA (Stress Strength Interference Analysis) is one of the reliability methods. It is widely used in

industries, due to its simplicity. Within this approach, only two global parameters are used to characterize

the variability of the problem: the load severity - referred to as STRESS - and the component strength -

referred to as STRENGTH. These two parameters are chosen so as to be comparable (for instance, local

stresses vs fatigue limits). Once the distributions of the Stress and the Strength are identified and

modelled, a probability of failure can be easily calculated, by means of analytical expressions or numerical

resolutions, as explained for example in [1][2][3][4]. The SSIA is therefore often used in the validation

process of a new component. But it is even more powerful in the design process: from a pre-defined target

probability of failure Pf, for a given distribution of Stress, the Strength distribution (mean value and

scatter) can be specified. Let’s notice that there is not a unique solution to this problem, as shown in

Figure 5.
a) SSIA for the validation process b) SSIA for the design process
Figure 5 — SSIA approach

To apply the SSIA approach, it is necessary to characterize both distributions. The distribution of Strength

can be identified thanks to laboratory fatigue tests. To have a good estimation of its distribution and not

only its mean value, a sufficient number of tests is necessary. In the Euraxles project, new tests were

performed for steel grades EA1N and EA4T. They are described in [17] and in Clause 4 of the report. For

the Stress distribution, measurements of loads shall be carried out in various operating conditions in

order to capture the variability of the behaviour of the component, as described in 4.2.3. Using

complementary information
...

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