EN 13103-1:2017+A1:2022

Railway applications - Wheelsets and bogies - Part 1: Design method for axles with external journals

This European Standard:
— defines the forces and moments to be taken into account with reference to masses, traction and braking conditions;
— gives the stress calculation method for axles with outside axle journals;
— specifies the maximum permissible stresses to be assumed in calculations for steel grade EA1N, EA1T and EA4T defined in EN 13261:2020;
— describes the method for determination of the maximum permissible stresses for other steel grades;
— determines the diameters for the various sections of the axle and recommends the preferred shapes and transitions to ensure adequate service performance.
This European Standard is applicable for:
— axles defined in EN 13261:2020
— powered and non-powered axles and
— all track gauges3.
The powered axle design method of this European Standard applies to:
— solid and hollow powered axles for railway rolling stock;
— solid and hollow non-powered axles of motor bogies;
— solid and hollow non-powered axles of locomotives.
The non-powered axle design method of this standard applies to solid and hollow axles of railway rolling stock used for the transportation of passengers and freight that are not considered in the list above.
This European Standard is applicable to axles fitted to rolling stock intended to run under normal European conditions. Before using this European Standard, if there is any doubt as to whether the railway operating conditions are normal, it is necessary to determine whether an additional design factor has to be applied to the maximum permissible stresses. The calculation of wheelset axles for special applications (e.g. tamping/lining/levelling machines) may be made according to this European Standard only for the load cases of free-rolling and rolling in train formation. This European Standard does not apply to the loads induced by the vehicles in their working mode. They are calculated separately.
This method can be used for light rail and tramway applications.

Bahnanwendungen - Radsätze und Drehgestelle - Teil 1: Konstruktionsleitfaden für außengelagerte Radsatzwellen

Diese Europäische Norm:
—   legt die Kräfte und Momente fest, die aufgrund der Massenwirkungen sowie der Antriebs  und Bremsbedingungen zu berücksichtigen sind;
—   gibt das Verfahren zur Spannungsberechnung außengelagerter Radsatzwellen an;
—   !legt die höchstzulässigen Spannungen für die Stahlgüten EA1N, EA1T und EA4T nach EN 13261:2020 fest, die in die Berechnung einzusetzen sind";
—   beschreibt die Vorgehensweise zur Ermittlung der höchstzulässigen Spannungen für andere Stähle;
—   ermöglicht die Berechnung der Durchmesser der verschiedenen Wellenabschnitte und gibt Empfehlungen zu den bevorzugten Formen und Übergängen, um ein sicheres Betriebsverhalten zu erreichen.
Diese Europäische Norm ist anwendbar für:
—   !Radsatzwellen nach EN 13261:2020";
—   Treibrad  und Laufradsatzwellen;
—   alle Spurweiten3).
Das in der vorliegenden Norm beschriebene Konstruktionsverfahren für Treibradsatzwellen gilt für:
—   Treibradsatzwellen (Voll  oder Hohlwellen) von Schienenfahrzeugen;
—   Laufradsatzwellen (Voll  oder Hohlwellen) von Motordrehgestellen;
—   Laufradsatzwellen (Voll  oder Hohlwellen) von Lokomotiven.
Das in der vorliegenden Europäischen Norm beschriebene Konstruktionsverfahren für Laufradsatzwellen gilt für Voll  oder Hohlwellen von Schienenfahrzeugen, die für den Transport von Fahrgästen oder Gütern bestimmt sind und nicht in der vorstehenden Liste aufgeführt sind.
Diese Europäische Norm gilt für Radsatzwellen von Fahrzeugen, die für den Einsatz unter üblichen in Europa herrschenden Betriebsbedingungen vorgesehen sind. Wenn Zweifel bestehen, ob normale Betriebsbedingungen vorherrschen, ist es notwendig, vor Anwendung dieser Europäischen Norm zu entscheiden, ob ein zusätzlicher Sicherheitsfaktor für die maximal zulässigen Spannungen angewendet werden muss. Die Anwendung dieser Europäischen Norm auf die Berechnung von Radsätzen für besondere Anwendungsfälle (z. B. Gleisstopf , Nivellier  und Richtmaschinen) darf nur für Lastfälle von Einzelfahrzeugen außerhalb des Arbeitsmodus erfolgen und für Fahrzeuge, die in einen Zug eingestellt werden. Diese Europäische Norm gilt nicht für Arbeitslastfälle. Solche werden separat berechnet.
Dieses Verfahren kann für Stadt  und Straßenbahnen verwendet werden.

Applications ferroviaires - Essieux montés et bogies - Partie 1: Méthode de conception des essieux-axes avec fusées extérieures

Železniške naprave - Kolesne dvojice in podstavni vozički - 1. del: Metoda za načrtovanje gredi z zunanjim uležajenjem (vključuje dopolnilo A1)

Ta evropski standard:
– določa sile in momente, ki jih je treba upoštevati glede na mase, pogoje vleke in zaviranja;
– podaja metodo izračuna napetosti za gredi z zunanjim uležajenjem;
– določa največje dovoljene napetosti, ki se predpostavijo pri izračunih za razrede jekla EA1N, EA1T in EA4T, opredeljene v standardu EN 13261;
– opisuje metodo za določanje največjih dovoljenih napetosti za druge razrede jekla;
– določa premere za različne odseke gredi ter priporoča prednostne oblike in prehode za zagotovitev ustrezne delovne učinkovitosti.
Ta evropski standard se uporablja za:
– gredi, določene v standardu EN 13261
– pogonske in nepogonske gredi in
– vse tirne širine3.
Način oblikovanja pogonskih gredi pri tem evropskem standardu velja za:
– trdne in votle pogonske gredi za tirna vozila;
– trdne in votle nepogonske gredi motornih podstavnih vozičkov;
– trdne in votle nepogonske gredi lokomotiv.
Metoda zasnove nepogonskih gredi tega standarda velja za trdne in votle gredi železniških tirnih vozil za prevoz potnikov in tovora, ki niso vključeni v zgornji seznam.
Ta evropski standard se uporablja za gredi, pritrjene na tirna vozila, namenjena za uporabo pod običajnimi evropskimi pogoji. Če obstaja kakršen koli dvom v zvezi s tem, ali so pogoji delovanja železnice običajni, je treba pred uporabo tega evropskega standarda ugotoviti, ali je treba za največje dovoljene napetosti uporabiti dodaten konstrukcijski dejavnik. Izračun gredi kolesnih dvojic za posebne uporabe (npr. stroji za gramoziranje/oblaganje/izenačevanje) se na podlagi tega evropskega standarda lahko izvede le za proste in vodene primere obremenitve pri sestavi vlaka. Ta evropski standard se ne uporablja za obremenitve, ki jih povzročajo vozila v svojem delovnem načinu. Te se izračunajo ločeno.
To metodo je mogoče uporabiti za lahka železniška vozila in tramvaje.

General Information

• Status: Published
• Publication Date: 20-Dec-2022
• ICS: 45.040 - Materials and components for railway engineering
• Technical Committee: CEN/TC 256 - Railway applications
• Drafting Committee: CEN/TC 256/SC 2/WG 11 - Wheels - Wheelsets
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 21-Dec-2022
• Due Date: 29-Jun-2021
• Completion Date: 21-Dec-2022
• Directive: 2016/797/EU - Directive (EU) 2016/797 of the European Parliament and of the Council of 11 May 2016 on the interoperability of the rail system within the European Union (Text with EEA relevance)
• Mandate: M/483 - Mandate for programming and standardisation addressed to the European standardisation bodies under directive 2008/57/EC in the field of the interoperability of the rail system within the European Union
• Mandate: M/591 - Standardisation request to the European Committee for Standardisation and the European Committee for Electrotechnical Standardisation as regards railway products in support of Directive (EU) 2016/797
• Ref Project: SIST EN 13103-1:2018+A1:2023 - Railway applications - Wheelsets and bogies - Part 1: Design method for axles with external journals

Relations

• Merged From: EN 13103-1:2017 - Railway applications - Wheelsets and bogies - Part 1: Design method for axles with external journals
• Effective Date: 19-Jan-2023
• Merged From: EN 13103-1:2017/FprA1 - Railway applications - Wheelsets and bogies - Part 1: Design method for axles with external journals
• Effective Date: 18-Jan-2023

Overview

EN 13103-1:2017+A1:2022 - published by CEN - is the European design standard for railway axles with external journals used in wheelsets and bogies. It defines the forces and moments to consider, gives a stress calculation method for axles with outside journals, sets maximum permissible stresses for specified steel grades, and prescribes geometric sizing guidance (diameters, transitions and preferred shapes). The document includes Amendment 1 (2022) and supports vehicle interoperability requirements under Directive 2008/57/EC.

Key topics and technical requirements

• Load definitions: Specifies forces and moments from masses, braking, traction and curving effects. Loads reference vehicle masses per EN 15663.
• Stress calculation method: Nominal stress calculation for axles with external journals using beam‑theory-based approaches and correction coefficients validated by fatigue tests.
• Maximum permissible stresses: Prescribes stress limits for steel grades EA1N, EA1T and EA4T (as defined in EN 13261:2020) and provides a method to determine permissible stresses for other steel grades.
• Geometry and sizing: Rules for determining journal diameters, axle body diameters, wheel seats and transitions to ensure fatigue life and service performance.
• Powered and non-powered axles: Design method covers solid and hollow powered axles, and solid/hollow non‑powered axles for motor bogies, locomotives and general rolling stock.
• Fatigue testing and validation: Includes Annex D (normative) describing procedures for full‑scale fatigue limit determination; Annexes provide calculation sheets, tilting vehicle load factors and guidance for reduced‑gauge applications.
• Scope limits: Applicable to axles intended for normal European operating conditions; special operating conditions may require additional design factors. The method can also be used for light rail and tramway applications.

Practical applications

• Designing and verifying wheelset axles and bogie components for passenger and freight rolling stock.
• Structural stress and fatigue assessments for powered axles, axle bores and wheel seats.
• Selecting and validating axle material properties (EA1N, EA1T, EA4T or other steels) and establishing manufacturing geometry to meet service life expectations.
• Engineering checks for new vehicle designs, retrofit projects, or certification to European interoperability requirements.

Who uses this standard

• Rolling stock designers and mechanical engineers
• Bogie and wheelset manufacturers
• Railway vehicle technical approval bodies and homologation teams
• Maintenance engineers performing axle life assessment or replacement planning
• Test laboratories performing axle fatigue testing

Related standards

• EN 13261:2020 (Axles - product requirements)
• EN 13260:2020 (Wheelsets - product requirements)
• EN 15663:2017+A1:2018 (Vehicle reference masses)
• EN 15313:2016 (In‑service wheelset operation requirements)

EN 13103-1:2017+A1:2022 is the reference design method for safe, fatigue‑resistant axle design and is essential for compliance, manufacture and long‑term performance of railway wheelsets and bogies.

Standards Content (Sample)

SLOVENSKI STANDARD
01-marec-2023
Železniške naprave - Kolesne dvojice in podstavni vozički - 1. del: Metoda za
načrtovanje gredi z zunanjim uležajenjem (vključuje dopolnilo A1)
Railway applications - Wheelsets and bogies - Part 1: Design method for axles with
external journals
Bahnanwendungen - Radsätze und Drehgestelle - Teil 1: Konstruktionsleitfaden für
außengelagerte Radsatzwellen
Applications ferroviaires - Essieux montés et bogies - Partie 1: Méthode de conception
des essieux-axes avec fusées extérieures
Ta slovenski standard je istoveten z: EN 13103-1:2017+A1:2022
ICS:
45.040 Materiali in deli za železniško Materials and components
tehniko for railway engineering
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN 13103-1:2017+A1
EUROPEAN STANDARD
NORME EUROPÉENNE
December 2022
EUROPÄISCHE NORM
ICS 45.040 Supersedes EN 13103-1:2017
English Version
Railway applications - Wheelsets and bogies - Part 1:
Design method for axles with external journals
Applications ferroviaires - Essieux montés et bogies - Bahnanwendungen - Radsätze und Drehgestelle - Teil
Partie 1: Méthode de conception des essieux-axes avec 1: Konstruktionsleitfaden für außengelagerte
fusées extérieures Radsatzwellen
This European Standard was approved by CEN on 11 September 2017 and includes Amendment 1 approved by CEN on 29
August 2022.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

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, Türkiye 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
© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13103-1:2017+A1:2022 E
worldwide for CEN national Members.

Contents Page
Foreword . 4
Introduction . 5
1 European scope . 6
2 Normative references . 7
3 Terms and definitions . 7
4 Symbols and abbreviations . 8
5 tab General . 10
6 Forces and moments to be taken into consideration. 10
6.1 Types of forces . 10
6.2 Effects due to masses in motion . 10
6.3 Effects due to braking . 16
6.4 Effects due to curving and wheel geometry. 20
6.5 Influence of traction . 20
6.6 Calculation of the resultant moment . 21
7 Determination of geometric characteristics of the various parts of the axle . 22
7.1 Stresses in the various sections of the axle . 22
7.2 Determination of the diameter of journals and axle bodies . 25
7.3 Determination of the diameter of the various seats from the diameter of the axle body
or from the journals . 25
7.3.1 tab General . 25
7.3.2 Transition between collar bearing surface and wheel seat . 28
7.3.3 Wheel seat in the absence of an adjacent seat . 28
7.3.4 Case of two adjacent wheel seats . 29
7.3.5 Case of two non-adjacent wheel seats . 30
8 Maximum permissible stresses . 30
8.1 tab General . 30
8.2 tab Steel grade EA1N and EA1T. 31
8.3 tab Steel grades other than EA1N and EA1T . 32
8.3.1 tab General . 32
8.3.2 Steel grade EA4T . 33
8.3.3 Other steel grades . 35
Annex A (informative) Model of axle calculation sheet. 36
Annex B (informative) Procedure for calculating the load coefficient for tilting vehicles. 38
Annex C (informative) Values of forces to take into consideration for wheelsets for reduced
gauge track (metric or close to a metre) . 40
Annex D (normative) Method for determination of full-scale fatigue limits for new materials . 41
D.1 Scope . 41
D.2 General requirements for test pieces . 41
D.3 General requirements for test apparatus . 41
D.4 Axle body fatigue limit ("F1") . 41
D.4.1 Geometry . 41
D.4.2 Verification of the applied stress . 42
D.4.3 End of test criterion . 43
D.4.4 Determination of the fatigue limit . 43
D.5 Axle bore fatigue limit ("F2") . 43
D.5.1 Geometry . 43
D.5.2 Verification of the applied stress . 44
D.5.3 End of test criterion . 44
D.5.4 Determination of the fatigue limit . 44
D.6 Wheel seat fatigue limit ("F3 and F4") . 44
D.6.1 Geometry . 44
D.6.2 Verification of the applied stress . 46
D.6.3 End of test criterion . 46
D.6.4 Determination of the fatigue limit . 46
D.7 Content of the test report. 47
Bibliography . 48

Foreword
This document (EN 13103-1:2017+A1:2022) has been prepared by Technical Committee CEN/TC 256
"Railway applications", the secretariat of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, by June 2023 at the latest, and all conflicting national standards shall
be withdrawn no later than June 2023.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights or similar rights.Attention is drawn to the possibility that some of the elements of this
document may be the subject of patent rights or similar rights. CEN and/or CENELEC shall not be held
responsible for identifying all or some of these patent rights.
This document includes Amendment 1 approved by the CEN on 29 August 2022.
This document will supersede !EN 13103-1:2017".
The start and end of the text added or modified by the amendment are indicated in the text with ! and "
respectively.
This document has been prepared in the context of a standardization request given to CEN by the
European Commission and the European Free Trade Association, and supports essential requirements of
Directive 2008/57/EC.
For the relationship with Directive 2008/57/EC, see informative Annex ZA, which forms an integral part
of this document.
The user should address any feedback or questions regarding this document to their country's national
standards organisation. A comprehensive list of these organisations can be found on the CEN website.
According to the CEN/CENELEC Internal Regulations, the national standards organisations of the
following countries are required to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, the Czech Republic, Denmark, Estonia, Finland, the Former Yugoslav Republic of
Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg,
Malta, the Netherlands, Norway, Poland, Portugal, the Republic of Serbia, Romania, Slovakia, Slovenia,
Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Introduction
Railway axles were among the first train components to give rise to fatigue problems.
Many years ago, specific methods were developed in order to design these axles. They were based on a
feedback process from the service behaviour of axles combined with the examination of failures and on
fatigue tests conducted in the laboratory, so as to characterize and optimize the design and materials
used for axles.
A European working group under the aegis of UIC started to harmonize these methods at the beginning
of the 1970s. This led to an ORE document applicable to the design of trailer stock axles, subsequently
incorporated into national standards (French, German, Italian). It was consequently converted into a UIC
leaflet.
The method for this standard is based on the calculation of nominal stresses using beam theory. It was
developed at a time when the calculation method per finished item had yet to be established. Fatigue limit
values were obtained from tests, and the level of stress on the test pieces was calculated using beam
theory. In addition, fatigue correlation coefficients were determined in the same way, using the
experimental results from test pieces of different diameters and transition radii.
The following three elements:
— calculation method;
— correction coefficient values;
— fatigue limit values;
are closely linked, with the values of the two latter parameters being dependent on the calculation
method.
The bibliography lists the relevant documents used for reference purposes. The method described
therein is largely based on conventional loadings (now deduced from the definition of the masses
declined in EN 15663). The outcome is validated by many years of operations on the various railway
systems.
This standard is based largely on this method which has been improved and its scope enlarged.
In order to simplify the maintenance of axle design standardization, it was decided to merge two previous
documents EN 13103 and EN 13104 into a single standard, in the form of this document.
Furthermore, this standard makes reference to mass standard EN 15663 to define the loads used in the
calculations.
UIC: Union Internationale des Chemins de fer.
ORE: Office de Recherches et d'Essais de l'UIC.
1 European scope
This European standard:
— defines the forces and moments to be taken into account with reference to masses, traction and
braking conditions;
— gives the stress calculation method for axles with outside axle journals;
— !specifies the maximum permissible stresses to be assumed in calculations for steel grades EA1N,
EA1T and EA4T defined in EN 13261:2020";
— describes the method for determination of the maximum permissible stresses for other steel grades;
— determines the diameters for the various sections of the axle and recommends the preferred shapes
and transitions to ensure adequate service performance.
This European Standard applies to:
— !axles defined in EN 13261:2020";
— powered and non-powered axles;
— all track gauges .
The design method for powered axles described in this European Standard applies to:
— solid or hollow powered axles for railway vehicles;
— solid or hollow non-powered axles for motor bogies;
— solid or hollow non-powered axles for locomotives.
The design method for non-powered axles described in this European Standard applies to solid or hollow
axles for railway vehicles intended for the transportation of passengers or freight and which do not
appear in the preceding list.
This European Standard is applicable to axles fitted to rolling stock intended to run under normal
European conditions. Before using this European Standard, if there is any doubt as to whether the railway
operating conditions are normal, it is necessary to determine whether an additional design factor has to
be applied to the maximum permissible stresses. The calculation of wheelsets for special applications
(e.g. tamping/lining/levelling machines) may be made according to this European Standard only for the
load cases of free-running and running in train formation. This European Standard does not apply to
workload cases. They are calculated separately.
This method may be used for light rail and tramway applications.

If the gauge is not standard, certain formulae need to be adapted.
2 Normative references
The following documents are referenced in a normative manner, in part or in full, in this document, and
are indispensable for its application. For dated references, only the cited edition applies. For undated
references, the last edition of the reference document applies (including any amendments).
!EN 13260:2020", Railway applications — Wheelsets and bogies — Wheelsets — Product requirements
!EN 13261:2020", Railway applications- Wheelsets and bogies - Axles - Product requirements
!EN 15313:2016", Railway applications - In-service wheelset operation requirements - In-service and off-
vehicle wheelset maintenance
!EN 15663:2017+A1:2018", Railway applications - Vehicle reference masses
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
Powered axle
the following axles are considered as powered axles:
— solid or hollow powered axles for railway vehicles;
— solid or hollow non-powered axles for motor bogies;
— solid or hollow non-powered axles for locomotives
3.2
non-powered axle
a solid or hollow axle used for railway vehicles intended for the transportation of passengers or freight
and that is not considered as a powered axle as defined in paragraph 3.1
3.3
technical specification
a document describing the specific parameters and/or requirements of the product in addition to the
requirements of this standard
3.4
Guiding axle
!axle of the first (i.e. leading) bogie of a coach used at the head of a reversible trainset. If an axle can be
used in both positions (guiding or non-guiding), it is to be considered as a guiding axle"
4 Symbols and abbreviations
For the purposes of this European Standard, the symbols and abbreviations in Table 1 apply.
Table 1
Symbol Unit Description
m kg Mass on journals (including bearings and axle boxes)
m kg Wheelset mass and masses on the wheelset between wheel rolling circles. A
definition will be included in the current revision of EN 13262 (brake disc, gear
etc.)
m + m kg For the wheelset considered, proportion of the mass of the vehicle on the rails
1 2
g m/s Acceleration due to gravity
m m g
1 2
P N
Half the vertical force per wheelset on the rail
m g
P N
Vertical static force per journal when the wheelset is loaded symmetrically
P N Vertical force on the more heavily-loaded journal
P N Vertical force on the less heavily-loaded journal
P’ N Proportion of P braked by any mechanical braking system
Y N Wheel/rail horizontal force perpendicular to the rail on the side of the more
heavily- loaded journal
Y N Wheel/rail horizontal force perpendicular to the rail on the side of the less
heavily-loaded journal
H N Force balancing forces Y and Y
1 2
Q N Vertical reaction on the wheel situated on the side of the more heavily-loaded
journal
Q N Vertical reaction on the wheel situated on the side of the less heavily-loaded
journal
Forces exerted by the masses of the unsprung elements situated between the
F N
i
two wheels (brake disc(s) etc.)
Maximum force input of the brake shoes of the same shoeholder on one wheel
F N
f
or interface force of the pads on one disc
M Nmm Bending moment due to the masses in motion
x
M’ , M’ Nmm Bending moments due to braking
x z
M’ Nmm Torsional moment due to braking
y
M’’ , M’’ Nmm Bending moments due to traction
x z
M’’ Nmm Torsional moment due to traction
y
MX, MZ Nmm Sum of bending moments
MY Nmm Sum of torsional moments
Symbol Unit Description
MR Nmm Resultant moment
2b mm Distance between vertical force input points on axle journals
2s mm Distance between wheel rolling circles
Height above the axle centreline of vehicle centre of gravity of masses carried by
h mm
the wheelset
y mm Distance between the rolling circle of one wheel and force Fi
i
Abscissa for any section of the axle calculated from the section subject to force
y mm
P1
Average friction coefficient between the wheel and the brake shoe or between
Γ
the brake pads and the disc
σ N/mm Stress calculated in one section
K  Fatigue stress correction factor
R mm Nominal wheel radius (Nominal wheel diameter / 2)
R mm Application radius of the braking force
b
d mm Diameter for one section of the axle
d’ mm Bore diameter of a hollow axle
dm mm Diameter used for determining K
r mm Radius of transition fillet or groove used to determine K
S  Safety coefficient
G  Centre of gravity
2 7
R N/mm Fatigue limit under rotating bending up to 10 cycles for smooth test pieces
fL
2 7
R N/mm Fatigue limit under rotating bending up to 10 cycles for notched test pieces
fE
a m/s Unbalanced transverse acceleration
q
f  Thrust factor
q
5 11.2.3.1\tab General
The major phases for the design of an axle are:
a) definition of the forces to be taken into account and calculation of the moments on the various
sections of the axle;
b) selection of the diameters of the axle body and journals and - on the basis of these diameters -
calculation of the diameters for the other parts of the axle;
c) the options taken are verified in the following manner:
— stress calculation for each section;
— comparison of these stresses with the maximum permissible stresses.
The maximum permissible stresses are mainly defined by:
— the steel grade;
— whether the axle is solid or hollow.
— the type of drive transmission.
An example of a data sheet with all these phases is given in Annex A.
6 Forces and moments to be taken into consideration
6.1 Types of forces
Three types of forces are to be taken into consideration as a function:
— of the masses in motion;
— of the braking system.
— of traction.
6.2 Effects due to masses in motion
The forces generated by masses in motion are concentrated along the vertical symmetry plane (y, z) (see
Figure 1) intersecting the axle centreline.
Figure 1 — Definition of axes and moments caused by masses in motion
The bending moment M is due to the vertical forces parallel to the Z axis.
x
Without any other requirement in the technical specification, Table 2 defines the masses (m + m ) to take
1 2
into account for the main types of rolling stock. For certain specific applications, e.g. suburban vehicles,
alternative mass definitions are required, in accordance with the specific operating conditions.
!Table 2 — Masses to take into account for the main types of rolling stock
Type of rolling stock units Mass (m + m )
1 2
Freight wagons In-service design mass + normal design payload
(maximum payload)
Powered coaches with no accommodation for
passengers, luggage or post In-service design mass and the normal design
payload are defined in Standard EN
15663:2017+A1:2018
Coaches and powered coaches including 1 – High-speed or main line vehicles
accommodation for passengers, luggage or post:
In-service design mass is defined in Standard EN
15663:2017+A1:2018.
 High speed or long distance trains
The normal design payload is defined in Standard
EN 15663:2017+A1:2018, where standing
passengers shall be considered as:
² ²
- 160 kg/m (2 passengers per m ) in the areas
accessible to standing passengers and in the
restaurant compartments
Coaches and powered coaches including 1 – High-speed or main line vehicles
accommodation for passengers, luggage or post:
In-service design mass is defined in Standard EN
15663:2017+A1:2018.
 Passenger vehicles other than high speed or
long distance
The normal design payload is defined in Standard
EN 15663:2017+A1:2018, where standing
passengers shall be considered as:
² ²
- 210 kg/m (3 passengers per m ) in the corridor
areas;
² ²
- 350 kg/m (5 passengers per m ) on platforms;
² ²
the value of 280 kg/m (4 passengers per m )
st
may be used in specific cases (e.g. the 1 class
compartment) as described in the technical
specification
"
The bending moment Mx in every section is calculated from the forces P1, P2, Q1, Q2, Y1, Y2 and Fi
indicated in Figure 2. It corresponds to the most unfavourable load case for the axle, i.e.:
— asymmetric distribution of forces;
— the direction of the forces Fi due to the masses of the unsprung components selected in such a
manner that their effect on bending is added to that due to the vertical forces;
— the value of the forces Fi results from multiplying the mass of each unsprung component by 1 g.
Wheel rejected
G centre of gravity of vehicle
Figure — Forces to calculate the bending moment
Table 3 shows the values of the forces calculated from m1.
The formulae coefficient values are applicable to standard gauge axles and classical suspension. For very
different gauges, a metric gauge for example, or a new system of suspension, a tilting system for example,
other values shall be considered (see Annexes B and C).
Table 3 — Formulae to calculate forces
For any non-guiding non-powered axle
P  (0,625 0,075h /b)mg
1 1 1
P  (0,6250,075h /b)mg
2 1 1
Y  0,30mg
1 1
Y  0,15mg
2 1
H Y Y  0,15mg
1 2 1
For guiding axle and any powered axle
P  (0,625 0,0875h /b)mg
1 1 1
P  (0,6250,0875h /b)mg
2 1 1
Y  0,35mg
1 1
Y  0,175mg
2 1
H Y Y  0,175mg
1 2 1
For all axles
Q  PbsPbsY Y R F2sy 
1 1 2 1 2 i i
i
2s
     
Q  P bs P bs  Y Y R F y 
2 2 1 1 2 i i i
2s
Table 4 shows the formulae to calculate Mx for each zone of the axle and the general outline of variations
along the axle.
Table 4 — Forces to calculate the bending moment
Zone of the axle Mx a
Between loading plane and
M Py
x 1
running surface
Figure 3a
Between running surfaces
M PyQ (ybs)YR F (ybsy )
x 1 1 1 i i i
Fi: force(s) on the left of the section considered
Figure 3b
General outline of Mx variation

Figure 3c
a For a non-symmetric axle, the calculations shall be carried out after applying the load alternately
to the two journals to determine the worst-case scenario.
6.3 Effects due to braking
Braking generates moments that can be represented by three components: M’x, M’y, M’z (see Figure 4).

Figure 4 — Moments due to braking
— the bending component M’x is due to the vertical forces parallel to the z axis;
— the bending component M’z is due to the horizontal forces parallel to the x axis;
— the torsional component M’y is directed along the axle centreline (y axis); it is due to the forces
applied tangentially to the wheels.
The components M’x, M’y and M’z are shown in Table 5 for each method of braking.
If several methods of braking are superimposed, the values corresponding to each method shall be added.
For example, forces and moments due to electric or regenerative braking shall be considered.
NOTE If other methods of braking are used, the forces and moments to be taken into account can be obtained
on the basis of the same principles as those shown in Table 5. Special attention should be paid to the calculation of
the component M’x, which is to be added directly to the component Mx representing masses in motion.
!Table 5 — Formulae for the calculation of moments due to braking
Components Braking configuration
M'x, M'z, M'y
Friction brake blocks on both sides of Friction brake block on one side only of
each wheel each wheel
Between loading Between running Between loading Between running
plane and plane and running
surfaces surfaces
running surface surface
M'x = 0,3Ff Γ y M'x = 0,3Ff Γ (b − s) M'x = Ff Γ y M'x = Ff Γ (b − s)

a, b a, b b b
M'x
Figure 5a
Figure 5b
M'z = M'z = M'z =
M'z = Ff (1 + Γ) y
Ff (0,3 + Γ) y Ff (0,3 + Γ) (b − s) Ff (1 + Γ) (b − s)

a, b a, b b b
M'z
Figure 5c
Figure 5d
M'y = 0 M'y = 0,3 P' R M'y = 0 M'y = 0,3 P' R
M'y
c d c d
Components Braking configuration
M'x, M'z, M'y
f
Two brake discs mounted on the axle Two brake discs attached to the wheel hub
Between Between Between discs Between loading Between running
loading running plane and running surfaces
plane and surfaces surface
running and disc
surface
M'x =
M'x = Ff Γ y M'x = Ff Γ y M'x = Ff Γ (b − s + yi)
Ff Γ (b − s + yi)
b b b b
M'x
Figure 5e
Figure 5f
M'z =
R R R
b b b
R y
b
y
R R R
M'z = Ff Γ (b − s) M'z = Ff Γ M'z = Ff Γ (b − s)
R
Ff Γ
b b b b
M'z
Figure 5g
Figure 5h
M'y = 0 M'y = 0 M'y = 0,3 P' R
M'y = 0,3 P' R
M'y
d, e
d, e
Components Braking configuration
M'x, M'z, M'y
One brake disc mounted on the axle One brake disc attached to the wheel hub f
st
Between first Between disc and Between 1 loading Between running
nd
loading plane and second loading plane plane and running surface and 2
disc surface loading plane
M'x = M'x = M'x = M'x =
     
bs y bsy  bs y bs y
i i i i
 
y 2by y 2b y
2b 2b 2b 2b
Ff Γ FfΓ Ff Γ Ff Γ
b b b b
M'x
Figure 5j
Figure 5i
st
Between loading Between 1 loading Between running
Between running
nd
planes and plane and running surface and 2
surfaces
running surface surface loading plane
M'z = M'z = M'z =
1 R
b
1 R 1 R y 1 R
b b b
y
2 R
M'z = Ff Γ
2 R 2 R 2 R
Ff Γ Ff Γ (b − s) Ff Γ (b − s)
b b b b
M'z
Figure 5k
Figure 5l
st
Between loading Between 1 loading Between running
Between running
nd
planes and plane and running surface and 2
surfaces
running surface surface loading plane

M'y = 0 M'y = 0,3 P'R M'y = 0 M'y = 0,3 P'R

M'y
d, e d, e
Components Braking configuration
M'x, M'z, M'y
a The coefficient 0,3 results from experiments which established the possible differences between the applied
forces of two blocks on each wheel.
b Unless other values are justified:
• For brake blocks:
  0,1
° for cast iron blocks;
  0,17
° for all blocks with low-friction coefficient excluding cast iron;
  0,25
° for all blocks with high-friction coefficient excluding cast iron.
• for brake pads:
  0,35
° .
c This value was obtained from experimental tests and corresponds to a braking force difference between the
two wheels producing a force difference tangential to the wheels and equates to 0,3 P'. It includes the torsional
moment as specified in 6.3.
d P' is the proportion of P braked with the method of braking considered.
e Conventionally, the torsional moment between running surfaces equates to 0,3 P'R. It includes the torsional
moment due to braking and the torsional moment defined in 6.4.
f When the disc is mounted on the wheel web, then yi = 0.
"
6.4 Effects due to curving and wheel geometry
For an unbraked wheelset, a torsional moment of M’y is equal to 0,2 PR is used to account for possible
differences in wheel diameters and the effect of passing through curves.
For a braked wheelset, these effects are included in the effects due to braking.
6.5 Influence of traction
Forces exerted on the axles by the engine torque transmission under stable grip conditions, may generally
''
M
x
be disregarded. Indeed, calculation and experience has shown that they produce bending moments
''
''
M
M
y
z
and , and torsional moments , below those due to braking, and that they are not applied at the
same time as the latter.
The design of the axle should also take into account the instantaneous drop in traction, for example in
cases of an overload due to short-circuits. The short-circuit torque shall be considered as a static load
case.
!When the traction control systems are used to regulate the power of traction at the grip limit, the
controlled oscillations that may result around the mid traction torque range shall be taken into
consideration to determine the amplitude of the torsional torque My’’".
For certain applications, when the start-up torque is very high and start-ups are very frequent, the
calculation shall be done as follows:
a) once under normal conditions defined previously in 6.2, 6.3 and 6.4;
b) and again under the following conditions:
1) influence of the masses on movement given in Table 6;
2) influence of the start-up torque.
The influence of the conditions defined in b 1) and b 2) shall be combined.
The most severe conditions between a) and b) shall be considered for calculating the axle.
Table 6 — Formulae to calculate the influence of masses on movement
P  0,55m g
1 1
P  0,55m g
2 1
Y  0,10m g
Start-up forces
1 1
Y  0,05mg
2 1
H  0,05m g
6.6 Calculation of the resultant moment
In every section, the maximum stresses are calculated (see the following NOTE) from the resultant
moment MR which is equal to:
2 2 2
MR MX MY MZ
where MX, MY and MZ are the sums of the various components due to masses in motion and braking:
4)
MX = Mx + ∑M’x
4)
MY = ∑M’y
4)
MZ = ∑M’z
d
NOTE At a point on the outer surface of a solid cylinder (also in the case of a hollow one) with diameter , the
components MX, MY and MZ generate:
— a normal stress for MX and MZ;
— a shear stress for MY.
The normal stress has the following value (bending of beams with a circular section):
2 2
32 MX MZ
 
n
d
The value of the shear stress is the following (torsion of beams with a circular section):
16MY
 
t
d
 
1 2
As a result, the two principal stresses and are obtained as:
2 2
2 2
    4
    4
n n t
n n t
 
 
2 2
' ''
' ' '' ''
M M
M M M M
y y
x z x z
The values for , , can be replaced with , and respectively if the moments due to traction
exceed the moments due to braking.
Since the normal stress has a much higher absolute value (10 to 20 times) than the shear stress, the
 
1 2
diameter of the largest Mohr's circle is selected ( in this case) as a check of the value assumed for
d.
2 2 2 2 2
      4   MX MZ MY
1 2 n t
d
As a result, the definition of a resultant moment is:
2 2 2
MR MX MY MZ
7 Determination of geometric characteristics of the various parts of the axle
7.1 Stresses in the various sections of the axle
On any section of the axle with d as diameter, the stress to be taken into account is the following:
K32MR
 
d
— for a solid axle (see Figure 6a):
— for a hollow axle (see Figure 6b):
K32MRd
 
4 '4
 (d d )
— on the outer surface:
'
K32MRd
 
4 '4
 (d d )
— in the bore:
In the case of a conical wheel seat, the stress is calculated for the section where the resultant moment is
the highest and the diameter of this section is taken to be equal to the lower diameter of the wheel seat.

Figure 6a Figure 6b
Figure 6 — Axle geometric parameters
In a cylindrical part, on the surface of a solid or hollow axle, and in the bore of a hollow axle, the coefficient
K is equal to 1. On the other hand, each change of section produces stress concentrations for which the
maximum value is:
K is a fatigue stress correction factor (i.e. it takes account of the geometry)
— at the bottom of a transition between two adjacent cylindrical parts with different diameters;
— at the groove bottom;
— at the intersection of the transition radii when the transition length is short (see Note 2 of 7.3.3).
The fatigue stress correction factor K used to calculate this increment is shown in the nomograms in
Figure 7 (transition between two cylindrical parts) and in Figure 8 (groove bottom). It is obtained from
the two ratios:
D
r
d
d
and
with
r groove radius or transition fillet radius
d is the diameter of the cylindrical part in which the stress concentration is calculated;
D is the diameter of the other cylindrical part.

Figure 7 — Fatigue stress correction factor K as a function of D/d and r/d (at the bottom of the
transition between two cylindrical parts)
K
Figure 8 — Fatigue stress correction factor K as a function
D/d r /d
of and (groove bottom)
When a wheel, a brake disc, a gearwheel or a bearing has an interference fit (hot or cold) on a seat, D is
to be assumed to be equal to the diameter of the hub or the bearing ring (see Figures 9a, 9b and 9c). For
D
a collar or deflector or cross-bar, is assumed to be equal to the diameter of the bearing seat, since the
interference fit of these parts is very small.

Figure 9a Figure 9b Figure 9c
Figure 9 — Wheel seats — Definition of parameter D
The design shall be verified for the minimum section diameters including a maintenance re-profiling
allowance.
7.2 Determination of the diameter of journals and axle bodies
In selecting the diameters of the journals and axle body, reference should be made initially to existing
sizes of associated components (e.g. bearings).
The maximum stresses in the axle should then be calculated using the following formulae:
K32MR
 
d
— for a solid axle:
K32MRd
 
4 4
d d' 
— for a hollow axle:
The selection of diameters is then verified as shown in Clause 8, the calculated stresses being compared
to the maximum permissible stresses. A very shallow groove (0,1 mm to 0,2 mm) shall be provided so
that the end of the inner bearing ring does not cause any notch effect on the journal (see Figure 10).
7.3 Determination of the diameter of the various seats from the diameter of the axle
body or from the journals
7.3.1 11.2.3.1\tab General
In order to standardise, whenever possible, the diameter of the collar bearing surface (d2) should be 30
mm greater than that of the journal (d1). The transition between the journal and the collar bearing
surface is then provided as specified in Figure 10 and Figure 13.
Dimensions in millimetres
Wheel rejected
1 journal
2 collar bearing surface
3 wheel seat
X p = 0,1 to 0,2
1) Variant when a is too large for maintaining the depth p with a single radius of 40 mm, see Figure 13
Figure 10 — Recommended transition areas between:
journal and collar bearing surface ― collar bearing surface and wheel seat
Wheel rejected
Key cylindrical part of the bearing ring bore
b overlap ≥ 0, considering all possible tolerances
c bearing ring
Figure 11 — Detail A of Figure 10

Wheel rejected
Key wheel hub
b overlap ≥ 0, considering all possible tolerances; the conditions associated with maintenance shall be taken
into consideration
Figure 12 — Detail B of Figure 10
!In the case of a chamfer on the external edge of the wheel seat, the length of the chamfer is included in
the overlap. This overlap criterion also applies to the chamfered seats of the brake discs and gears."
Dimensions in millimetres
Wheel rejected
Key bottom of cylindrical groove
Figure 13 — Recommended transition between journal and collar bearing surface
7.3.2 Transition between collar bearing surface and wheel seat
In order to standardize, whenever possible, this transition should have only a single radius of 25 mm.
If this value cannot be met, the highest possible value should be selected so as to minimize the stress
concentration on this area.
7.3.3 Wheel seat in the absence of an adjacent seat
The diameter of the wheel seat in the wear limit state shall be at least 1,12 times the diameter of the body.
It is recommended that the diameter of the wheel seat in the new condition is at least 1,15 times the
diameter of the body.
The transition between these two areas should be provided in such a way that the stress concentration
remains at the lowest possible level.
The lengths of the wheel seat and of the wheel hub are selected so that the latter slightly overlaps the
wheel seat, especially on the axle body side. The design shall ensure that, at the maintenance limit, there
is an overlap including all worst
...