EN 15302:2021

Railway applications - Wheel-rail contact geometry parameters - Definitions and methods for evaluation

This document establishes definitions and evaluation methods for wheel-rail contact geometry parameters influencing the vehicle running dynamic behaviour:
-   the rolling radius difference between the two wheels of a wheelset (Δr-function) which serves as a basis for all further calculations;
-   the equivalent conicity function from which are derived:
-   a single equivalent conicity value for a specified amplitude which is relevant for the assessment of vehicle running stability on straight track and in very large radius curves according to EN 14363;
-   the nonlinearity parameter which characterizes the shape of this function and is related to the vehicle behaviour particularly in the speed range close to the running stability limit;
-   the rolling radii coefficient which is used to describe the theoretical radial steering capability of a wheelset in a curved track.
Additional information is given about the relationship between the contact angles of the two wheels of a wheelset (Δtanγ-function) and about the roll angle parameter.
NOTE   Out of the presented parameters only those related to the contact angle are relevant for independently rotating wheels of wheel pairs.
Descriptions of possible calculation methods are included in this document. Test case calculations are provided to achieve comparable results and to check the proper implementation of the described algorithms.
To validate alternative methods not described in this document acceptance criteria are given for the equivalent conicity function. This includes reference profiles, profile combinations, tolerances and reference results with tolerance limits.
This document also includes minimum requirements for the measurement of wheel and rail profiles as well as of the parameters needed for the transformation into a common coordinate system of right- and left-hand profiles.
This document does not define limits for the wheel-rail contact geometry parameters and gives no tolerances for the rail profile and the wheel profile to achieve acceptable results.
For the application of this document some general recommendations are given.

Bahnanwendungen - Parameter der Rad-Schiene Kontaktgeometrie - Definitionen und Berechnungsmethoden

In diesem Dokument werden Definitionen und Auswertemethoden für die Rad-Schiene-Berührgeometrieparameter angegeben, die das dynamische Fahrverhalten der Fahrzeuge beeinflussen:
-   die Rollradiendifferenz der beiden Räder eines Radsatzes (Δr-Funktion), die als Basis für alle weiteren Berechnungen dient;
-   die Funktion der äquivalenten Konizität, aus der ermittelt werden:
-   ein einzelner Konizitätswert für eine konkrete Amplitude, die für die Beurteilung der Fahrstabilität eines Fahrzeuges nach EN 14363 im geraden Gleis und in Gleisbögen mit sehr großen Gleisbogenhalbmessern relevant ist;
-   der Nichtlinearitätsparameter, der die Form der Funktion charakterisiert und mit dem Fahrzeugverhalten insbesondere im Geschwindigkeitsbereich um die Stabilitätsgrenze herum in Beziehung steht;
-   der Rollradienkoeffizient, der benutzt wird, um das theoretische Radialstellungsvermögen eines Radsatzes im Gleisbogen zu beschreiben.
Außerdem werden Informationen über die Beziehung zwischen den Berührwinkeln der beiden Räder eines Radsatzes (Δtanγ -Funktion) und über den Wankwinkelparameter gegeben.
ANMERKUNG   Von den genannten Parametern sind für Radpaare mit unabhängig voneinander rotierenden Rädern nur diejenigen relevant, die mit dem Berührwinkel in Beziehung stehen.
Dieses Dokument enthält Beschreibungen möglicher Berechnungsmethoden. Es werden Testrechenfälle bereitgestellt, um die Vergleichbarkeit der Ergebnisse zu erzielen und die korrekte Implementierung der beschriebenen Algorithmen zu überprüfen.
Zur Validierung alternativer Methoden, die nicht in diesem Dokument beschrieben werden, werden Akzeptanzkriterien für die Funktion der äquivalenten Konizität angegeben. Dazu gehören Referenzprofile, Profilkombinationen, Toleranzen und Referenzergebnisse mit Toleranzgrenzen.
Dieses Dokument enthält auch Mindestanforderungen an die Messung von Rad- und Schienenprofilen sowie an die Parameter, die für die Transformation in ein gemeinsames Koordinatensystem der rechten und linken Profile benötigt werden.
In diesem Dokument werden keine Grenzwerte für die Rad-Schiene-Berührgeometrieparameter und keine Toleranzen für Schienen- und Radprofile zur Gewährleistung akzeptabler Ergebnisse angegeben.
Bezüglich der Anwendung dieses Dokuments werden einige allgemeine Empfehlungen gegeben.

Applications ferroviaires - Paramètres géométriques du contact roue-rail - Définitions et méthodes de determination

Le présent document établit les définitions et les méthodes d'évaluation relatives aux paramètres géométriques du contact roue-rail, qui influencent le comportement dynamique des véhicules ferroviaires :
- la différence de rayon de roulement entre les deux roues d'un essieu (fonction Δr) qui sert de base à tous les calculs ;
- la fonction de conicité équivalente à partir de laquelle sont dérivées :
-- une valeur de conicité équivalente unique pour une amplitude spécifique, qui sera pertinente pour l'évaluation de la stabilité dynamique du véhicule sur voie en alignement et en courbes de très grand rayon conformément à l'EN 14363 ;
-- le paramètre de non-linéarité qui caractérise la forme de cette fonction et qui est lié au comportement du véhicule, particulièrement dans la plage de vitesses proches de la limite de stabilité dynamique ;
- le coefficient des rayons de roulement qui est utilisé pour décrire la capacité de guidage radial théorique d'un essieu dans une voie en courbe.
Le présent document fournit également des informations concernant la relation entre les angles de contact des deux roues d'un essieu (fonction Δtanγ) et le paramètre d'angle de roulis.
NOTE Parmi les paramètres décrits, seuls ceux liés à l'angle de contact sont pertinents pour les paires de roues à rotation indépendante.
Le présent document fournit également des descriptions des différentes méthodes de calcul possibles. Des calculs sur des cas type sont fournis afin d'obtenir des résultats comparables et de vérifier la mise en œuvre adéquate des algorithmes décrits.
Pour valider d'autres méthodes qui ne sont pas décrites dans le présent document, des critères d'acceptation sont donnés pour la fonction de conicité équivalente (profils de référence, combinaisons de profils, tolérances et résultats de référence avec limites de tolérance).
Le présent document spécifie également les exigences minimales pour la mesure des profils de roue et de rail, ainsi que les paramètres nécessaires à la déduction d'un système de coordonnées commun pour les profils droit et gauche.
Le présent document ne définit pas de limites pour les paramètres géométriques du contact roue-rail, ni de tolérances pour les profils de rail et de roue afin d'obtenir des résultats acceptables.
Pour l'application du présent document, des recommandations générales sont données.

Železniške naprave - Geometrijski parametri stika kolo-tirnica - Definicije in metode vrednotenja

General Information

• Status: Published
• Publication Date: 05-Oct-2021
• Withdrawal Date: 29-Apr-2022
• ICS: 17.040.20 - Properties of surfaces
• ICS: 45.060.01 - Railway rolling stock in general
• Technical Committee: CEN/TC 256 - Railway applications
• Drafting Committee: CEN/TC 256/WG 10 - Vehicle/Track Interaction
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 06-Oct-2021
• Due Date: 24-Mar-2020
• Completion Date: 06-Oct-2021
• Directive: 2008/57/EC - Directive 2008/57/EC of the European Parliament and of the Council of 17 June 2008 on the interoperability of the rail system within the Community (Recast)
• 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 15302:2021 - Railway Applications - Wheel-rail contact geometry parameters - Definitions and methods for evaluation

Relations

• Replaces: EN 15302:2008+A1:2010 - Railway applications - Method for determining the equivalent conicity
• Effective Date: 15-Feb-2017

Overview

EN 15302:2021 (EN 15302:2021) is a CEN European standard for railway applications that defines wheel‑rail contact geometry parameters and the methods to evaluate them. It specifies how to derive key contact functions from measured wheel and rail profiles - notably the rolling radius difference (Δr‑function) and the equivalent conicity function - and provides test cases, reference profiles and acceptance criteria to validate calculation methods and software implementations.

Key topics and technical requirements

• Rolling radius difference (Δr‑function): Basis for subsequent calculations; describes the rolling radius difference between the two wheels of a wheelset.
• Equivalent conicity: Derived from the Δr function; the standard defines how to obtain a single equivalent conicity value for a specified amplitude used in vehicle running stability assessments (refer to EN 14363).
• Nonlinearity parameter: Characterizes the shape of the equivalent conicity function and is related to vehicle behaviour near the running stability limit.
• Rolling radii coefficient: Describes the theoretical radial steering capability of a wheelset in curves; point E definition and calculation method are included.
• Contact angles and roll angle: Relationship between wheel contact angles (Δtanγ‑function) and roll angle parameter is described. Note: angle‑related parameters apply to independently rotating wheel pairs.
• Measurement and data processing requirements: Minimum requirements for wheel and rail profile measurement, uncertainty considerations, and transformation of left/right profiles into a common coordinate system.
• Validation and test cases: Normative reference profiles, numerical reference results, tolerances and test case calculations are provided to ensure reproducible implementation and software verification.
• Scope limits: The document gives no acceptance limits for contact parameters or profile tolerances; it focuses on definitions, methods and validation rather than prescriptive limits.

Practical applications and users

This standard is intended for professionals involved in:

• Vehicle dynamics and running behaviour analysis
• Wheelset design and maintenance engineering
• Track geometry and rail profile assessment
• Measurement system vendors and test laboratories validating calculation software
• Infrastructure managers and operators assessing wheel‑rail interaction and stability

Use cases include calculating equivalent conicity for stability evaluation (EN 14363 workflows), assessing steering behaviour on curves, validating data processing algorithms, and ensuring consistent interpretation of wheel/rail profile measurements.

Related standards

• EN 14363 (vehicle running stability and ride dynamics assessments)
• Other CEN railway standards on wheel and rail profiling and measurement (see national implementations of EN 15302:2021)

This standard is a technical reference for consistent, validated determination of wheel‑rail contact geometry parameters used in railway vehicle dynamics, maintenance decision making, and software verification.

Standards Content (Sample)

SLOVENSKI STANDARD
01-december-2021
Nadomešča:
SIST EN 15302:2008+A1:2010
Železniške naprave - Geometrijski parametri stika kolo-tirnica - Definicije in
metode vrednotenja
Railway Applications - Wheel-rail contact geometry parameters - Definitions and
methods for evaluation
Bahnanwendungen - Parameter der Rad-Schiene-Berührgeometrie - Definitionen und
Auswertemethoden
Applications ferroviaires - Paramètres géométriques du contact roue-rail - Définitions et
méthodes de détermination
Ta slovenski standard je istoveten z: EN 15302:2021
ICS:
45.060.01 Železniška vozila na splošno Railway rolling stock in
general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN 15302
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2021
EUROPÄISCHE NORM
ICS 17.040.20; 45.060.01 Supersedes EN 15302:2008+A1:2010
English Version
Railway applications - Wheel-rail contact geometry
parameters - Definitions and methods for evaluation
Applications ferroviaires - Paramètres géométriques Bahnanwendungen - Parameter der Rad-Schiene
du contact roue-rail - Définitions et méthodes de Kontaktgeometrie - Definitionen und
détermination Berechnungsmethoden
This European Standard was approved by CEN on 2 August 2021.

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, 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
© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 15302:2021 E
worldwide for CEN national Members.

Contents Page
European foreword . 7
Introduction . 8
1 Scope . 9
2 Normative references . 9
3 Terms and definitions . 10
4 Symbols and abbreviations . 11
5 Overview of the process for determining contact parameters . 12
6 Description of wheel and rail profiles . 12
6.1 General . 12
6.2 Uncertainty of the measuring systems . 14
7 Plausibility check and processing of measured wheel and rail profiles . 15
8 Determining the wheel-rail contact positions and contact functions . 16
8.1 General . 16
8.2 Determining the rolling radius difference function . 16
8.3 Other wheel-rail contact geometry functions . 17
9 Determining the equivalent conicity and the related nonlinearity parameter . 17
9.1 Background to equivalent conicity . 17
9.1.1 Mathematical description of the kinematic lateral wheelset motion . 17
9.1.2 Determining the wavelength of a coned wheelset . 18
9.2 Determining the equivalent conicity . 19
9.3 Determining the nonlinearity parameter . 19
10 Determining the rolling radii coefficient . 20
10.1 Background and definition . 20
10.2 Determining point E for the calculation of the rolling radii coefficient . 22
11 Other wheel-rail contact parameters . 23
12 Testing of calculation software for contact geometry parameters . 24
12.1 Overview . 24
12.2 Validation of the calculation algorithms . 24
12.3 Assessment of the smoothing process . 24
13 Assessment of the complete process for determination of wheel-rail contact
parameters . 28
13.1 General . 28
13.2 Reproducibility of contact parameter determination based on rail profile
measurement . 28
13.2.1 Manual rail profile measuring devices . 28
13.2.2 Vehicle based rail profile measuring systems . 29
13.3 Reproducibility of contact parameter determination based on wheel profile
measurement . 30
13.3.1 Manual wheel profile measuring devices . 30
13.3.2 Ground based wheel profile measuring systems . 30
Annex A (informative) Example of presentation of contact geometry functions . 32
Annex B (informative) Derivation of the kinematic equation of wheelset motion . 33
Annex C (informative) Determination of the lateral peak displacements . 36
Annex D (informative) Method for determining the wavelength of the wheelset motion by
two-step integration of the nonlinear differential equation . 38
D.1 General . 38
D.2 Step 1 . 38
D.3 Step 2 . 38
Annex E (informative) Method for determining the wavelength of the wheelset motion by
direct integration of the nonlinear differential equation . 40
Annex F (informative) Method for determining the equivalent conicity by linear regression
of the Δr function . 41
F.1 General . 41
F.2 Concerns regarding the method . 41
Annex G (informative) Method for determining linearization parameters by harmonic
linearization . 43
G.1 General . 43
G.2 Concerns regarding the method . 44
Annex H (informative) Handling of special cases of the Δr function . 45
Annex I (normative) Reference profiles for testing . 48
I.1 General . 48
I.2 Wheel A . 49
I.2.1 Drawing . 49
I.2.2 Analytic definition . 49
I.2.3 Cartesian coordinates . 50
I.3 Wheel B . 52
I.3.1 Drawing . 52
I.3.2 Analytic definition . 52
I.3.3 Cartesian coordinates . 53
I.4 Wheel C . 55
I.4.1 Drawing . 55
I.4.2 Analytic definition . 55
I.4.3 Cartesian coordinates . 56
I.5 Wheel H . 58
I.5.1 Drawing . 58
I.5.2 Analytic definition . 58
I.5.3 Cartesian coordinates . 59
I.6 Wheel I . 61
I.6.1 Drawing . 61
I.6.2 Analytic definition . 61
I.6.3 Cartesian coordinates . 62
I.7 Rail A . 64
I.7.1 Drawing . 64
I.7.2 Analytic definition . 64
I.7.3 Cartesian coordinates . 65
Annex J (normative) Calculation results with reference profiles . 67
J.1 General . 67
J.2 Wheel A/Rail A . 68
J.2.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 68
J.2.2 Numerical values for Δr function . 69
J.2.3 Numerical values for tanγ function . 70
e
J.3 Wheel B/Rail A . 72
J.3.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 72
J.3.2 Numerical values for Δr function . 73
J.3.3 Numerical values for tanγ function . 74
e
J.4 Wheel C/Rail A . 76
J.4.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 76
J.4.2 Numerical values for Δr function . 77
J.4.3 Numerical values for tanγ function . 79
e
J.5 Wheel H/Rail A . 81
J.5.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 81
J.5.2 Numerical values for Δr function . 82
J.5.3 Numerical values for tanγ function . 83
e
J.6 Wheel I/Rail A . 85
J.6.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 85
J.6.2 Numerical values for Δr function . 86
J.6.3 Numerical values for tanγ function . 87
e
J.7 Modified Wheel A (−2 mm on left wheel diameter)/Rail A . 89
J.7.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 89
J.7.2 Numerical values for Δr function . 90
J.7.3 Numerical values for tanγ function . 91
e
J.8 Modified Wheel B (−2 mm on left wheel diameter)/Rail A . 93
J.8.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 93
J.8.2 Numerical values for Δr function . 94
J.8.3 Numerical values for tanγ function . 95
e
J.9 Modified Wheel H (−2 mm on left wheel diameter)/Rail A . 97
J.9.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 97
J.9.2 Numerical values for Δr function . 98
J.9.3 Numerical values for tanγ function . 99
e
J.10 Modified Wheel I (−2 mm on left wheel diameter)/Rail A . 101
J.10.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 101
J.10.2 Numerical values for Δr function . 102
J.10.3 Numerical values for tanγ function . 103
e
J.11 (Right Wheel A – Left Wheel B)/Rail A . 105
J.11.1 Representation of contact points, diagrams of Δr, Δtanγ, tanγ functions and
e
representation of kinematic rolling movement of the wheelset on track . 105
J.11.2 Numerical values for Δr function . 106
J.11.3 Numerical values for tanγ function . 107
e
Annex K (normative) Tolerances on equivalent conicity for testing calculations . 109
K.1 General . 109
K.2 Wheel A/Rail A . 110
K.2.1 Diagram . 110
K.2.2 Numerical values . 111
K.3 Wheel B/Rail A . 113
K.3.1 Diagram . 113
K.3.2 Numerical values . 114
K.4 Wheel C/Rail A . 116
K.4.1 Diagram . 116
K.4.2 Numerical values . 117
K.5 Wheel H/Rail A . 119
K.5.1 Diagram . 119
K.5.2 Numerical values . 120
K.6 Wheel I/Rail A . 122
K.6.1 Diagram . 122
K.6.2 Numerical values . 123
K.7 Modified Wheel A (−2 mm on left wheel diameter)/Rail A . 125
K.7.1 Diagram . 125
K.7.2 Numerical values . 126
K.8 Modified Wheel B (−2 mm on left wheel diameter)/Rail A . 128
K.8.1 Diagram . 128
K.8.2 Numerical values . 129
K.9 Modified Wheel H (−2 mm on left wheel diameter)/Rail A . 131
K.9.1 Diagram . 131
K.9.2 Numerical values . 132
K.10 Modified Wheel I (−2 mm on left wheel diameter)/Rail A . 134
K.10.1 Diagram . 134
K.10.2 Numerical values . 135
K.11 (Right Wheel A – Left Wheel B)/Rail A . 137
K.11.1 Diagram . 137
K.11.2 Numerical values . 138
Bibliography . 140

European foreword
This document (EN 15302:2021) 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, at the latest by April 2022, and conflicting national standards shall be
withdrawn at the latest by April 2022.
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.
This document supersedes EN 15302:2008+A1:2010.
The main changes with respect to the previous edition are listed below:
— Extension of the Scope;
— Introduction of new wheel-rail contact geometry parameters (rolling radii coefficient, nonlinearity
parameter);
— Additional methods for evaluation of equivalent conicity;
— Improvement of the description of the reference profiles;
— Additional reference wheel profile C;
— Reference results based on analytical solutions;
— Hints for plausibility checking of measured profiles;
— Revised assessment of the smoothing process;
— New assessment of the complete process.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association.
Any feedback and questions on this document should be directed to the users’ national standards body.
A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: 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 the United
Kingdom.
Introduction
This document is based on the UIC Code 519 OR submitted to CEN by the International Union of Railways
(UIC) and which has been revised by CEN/TC 256/WG 10 “Vehicle/Track Interaction”.
The wheel-rail contact geometry is fundamental for explaining the dynamic running behaviour of a
railway vehicle, as well as the quasi-static behaviour in curves. Among the parameters which influence
the dynamic behaviour of a rail vehicle, the equivalent conicity plays an essential role since it allows for
the satisfactory characterization of the wheel-rail contact geometry on tangent track and on very large-
radius curves. A wheelset describes a waveform while running on a track. Klingel’s theory, valid for
massless wheelsets with conical profiles, states that the waveform is sinusoidal and its wavelength
depends on the cone angle of the wheel profile.
Real wheel profiles are not pure cones, but have changing cone angles across the tread, leading to a
nonlinear dependency of the rolling radius difference on the lateral movement of the wheelset on the
track. The wavelength of the wheelset movement according to the nonlinear kinematic equations of
motion may be calculated by solving numerically this formula or by specific methods for linearization of
the rolling radius difference function. Equivalent conicity is evaluated by comparison of this wavelength
with the equivalent wavelength of a conical wheelset according to Klingel's formula or by calculating the
conicity from the linearized rolling radius difference function.
It is important to have a clear specification for the evaluation of wheel-rail contact geometry parameters,
which are used in European and national standards and documents (legal and technical).
The objective is to ensure that the results for the determined parameters are consistent. However, it is
possible to use different evaluation procedures to those given in this document, provided that the
procedure used leads to the determination of wheel-rail contact parameters in accordance with the
calculation results using the reference profiles specified in Annex I. A validation process is given in this
document to be used in order to determine whether or not an evaluation procedure can achieve the
specified reference results.
Technical background will be given in a Technical Report published after the publication of this
document.
1 Scope
This document establishes definitions and evaluation methods for wheel-rail contact geometry
parameters influencing the vehicle running dynamic behaviour:
— the rolling radius difference between the two wheels of a wheelset (Δr-function) which serves as a
basis for all further calculations;
— the equivalent conicity function from which are derived:
— a single equivalent conicity value for a specified amplitude which is relevant for the assessment
of vehicle running stability on straight track and in very large radius curves according to
EN 14363;
— the nonlinearity parameter which characterizes the shape of this function and is related to the
vehicle behaviour particularly in the speed range close to the running stability limit;
— the rolling radii coefficient which is used to describe the theoretical radial steering capability of a
wheelset in a curved track.
Additional information is given about the relationship between the contact angles of the two wheels of a
wheelset (Δtanγ-function) and about the roll angle parameter.
NOTE Out of the presented parameters only those related to the contact angle are relevant for independently
rotating wheels of wheel pairs.
Descriptions of possible calculation methods are included in this document. Test case calculations are
provided to achieve comparable results and to check the proper implementation of the described
algorithms.
To validate alternative methods not described in this document acceptance criteria are given for the
equivalent conicity function. This includes reference profiles, profile combinations, tolerances and
reference results with tolerance limits.
This document also includes minimum requirements for the measurement of wheel and rail profiles as
well as of the parameters needed for the transformation into a common coordinate system of right- and
left-hand profiles.
This document does not define limits for the wheel-rail contact geometry parameters and gives no
tolerances for the rail profile and the wheel profile to achieve acceptable results.
For the application of this document some general recommendations are given.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
EN 13231-2:2020, Railway applications — Track — Acceptance of works — Part 2: Acceptance of
reprofiling rails in plain line, switches, crossings and expansion devices
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at https://www.electropedia.org/
— ISO Online browsing platform: available at https://www.iso.org/obp
NOTE This document uses the standard European notation for numeric values with “comma” (,) as the decimal
point and “space” ( ) as the thousands delimiter. Thus, for example 2,5 is to be understood as two and one-half and
1 500 as one thousand five hundred.
3.1
equivalent conicity
tangent of the cone angle of a wheelset with coned wheels whose kinematic movement has the same
wavelength as the given wheelset for a certain amplitude of the lateral wheelset movement
3.2
nonlinearity parameter
local slope of the equivalent conicity function between two specified wheelset displacement amplitudes
3.3
radial steering index
ratio between the curve radius negotiable without longitudinal creepage and the actual curve radius of
the track section to describe the radial steering capability of a wheelset in a track section
3.4
rolling radii coefficient
relationship describing the capability of a wheel-rail contact geometry to provide the rolling radii
difference needed for a wheelset to negotiate an actual curve without longitudinal creepage and flange
contact
Note 1 to entry: This parameter is related to the radial steering index.
3.5
uncertainty
refer to the definition of expanded uncertainty with a coverage factor equal to 2 as defined in
ISO/IEC Guide 98-3:2008-09 (JCGM/WG1/100)
Note 1 to entry: The uncertainty as defined corresponds to a confidence level of about 95 % of a normal
distribution.
3.6
reproducibility
degree of agreement between the values of successive measurements of the same parameter made under
varying conditions using the same measurement and interpretation methods
4 Symbols and abbreviations
For the purposes of this document, the following symbols apply.
2b nominal contact point spacing (defined as 1 500 mm for standard gauge)
A
tread datum position; location on the wheel tread, 70 mm (for standard gauge) from the
D
internal face of the wheel
x displacement of the wheelset in the longitudinal direction of the track
y displacement of the wheelset in the lateral direction of the track (at top of rail level)
Ψ angle of the wheelset movement in the x-y-plane
ds curve length of the path corresponding to the angle dΨ
V speed of forward movement of the vehicle
R local radius of the wheelset path
WS
r mean rolling-radius of both wheels
r radius of the wheels when the wheelset is centred on the track
r rolling-radius of the right-hand wheel
r rolling-radius of the left-hand wheel
Δr difference of the rolling-radius between right-hand and left-hand wheels
y lateral displacement where Δr = 0
em
y minimum value of lateral displacements
emin
y maximum value of lateral displacements
emax
ˆ
y amplitude of the wave
λ wavelength of the wheelset movement
γ contact angle; angle between the tangent at the wheel-rail contact point and the track plane
Δtanγ difference of the tangents of the contact angles between right-hand and left-hand wheels
tanγ equivalent conicity
e
N nonlinearity parameter
P
Δr rolling radius difference available for kinematic rolling (rolling without slip)
E
R minimum curve radius for kinematic rolling
E
q radial steering index
E
ρ rolling radii coefficient
E
ε contact angle parameter
e
φ roll angle of the wheelset around the longitudinal axis
σ roll angle parameter
e
σ standard deviation of random profile errors
err
NOTE Some additional symbols not included in the list above are explained in the section where they are used.
5 Overview of the process for determining contact parameters
Figure 1 gives an overview of the process for determining the contact parameters described in this
document. The figure also shows the clauses of this standard where more information on particular steps
of the process is given, including possible options.

Figure 1 — Process of contact geometry parameter determination
6 Description of wheel and rail profiles
6.1 General
The determination of wheel-rail contact geometry parameters requires knowledge of the shapes of the
wheel and rail profiles to be assessed as well as their relative position including:
— wheel back-to-back distance,
— wheel diameters, if relevant,
— track gauge,
— profile orientation in relation to the track plane (rail inclination, wheel inclination due to axle
bending).
NOTE 1 If there is significant difference in wheel diameter (more than 2 mm) the resulting roll effect may need
to be included if not covered by the measuring system.
NOTE 2 The bending of the axle under the load generally is relevant. Therefore, the measurements are usually
made for representative load conditions near to the contact point.
In case of measuring systems which are not able to include the wheel inclination due to axle bending, the
orientation may be determined by other methods such as static calculations. In some cases, it may be
possible to use already known bending angles representative for the vehicle considered.
When the profiles are determined by measurement, special-purpose devices can be used, such as wheel
and rail profile measuring devices or automatic measuring systems carried aboard special railbound
vehicles for rail profiles or ground based systems for wheel profiles.
The measurement devices shall be able to provide the profile coordinates with a maximum 0,5 mm
spacing along the arc of the profile.
NOTE 3 In areas with high profile curvature, a lower spacing may be required in order to get an accurate profile
shape.
It shall be reported whether the profiles were measured in the loaded or unloaded condition.
NOTE 4 For freight vehicles contact geometry is potentially more significantly influenced by the load. Therefore,
if the equivalent conicity is to be used to investigate running behaviour, the contact geometry is sometimes
considered in empty and laden condition.
When theoretical profiles are used the inclination shall be considered.
Independent of the source of the profiles (theoretical or measured), the two rails of the railway track shall
be referred to a track-related coordinate system oriented such that the x-axis is longitudinal to the track,
the y-axis tangential to the upper surface of the rail heads and the z-axis perpendicular to both axes,
see Figure 2. The two wheels of the wheelset shall be referred to a single coordinate system with axes
oriented in analogous directions.
NOTE 5 The relative position and orientation of the two profiles is relevant. Therefore, the use of a measuring
system with a single profile measuring head without reference between the two sides can lead to large uncertainties
of the calculated contact parameters.

Key
1 Track-related coordinate system
2 Top of rail level
Figure 2 — Track-related coordinate system (consistent with EN 13848-1)
It is recommended to provide the input data (theoretical or measured) related to the following coordinate
systems.
For the rails the origin of the coordinate system is defined so that y = 0 at the middle of the measured
track gauge and z = 0 at the top of the rails.
For the wheels the origin of the coordinate system is defined so that y = 0 at the middle of the wheel back
to back distance and z = 0 at D for both wheels. Any significant wheel diameter difference shall be
included as an offset in the rolling radius difference function, see 8.2.
The wheel and rail profiles shall be characterized such that:
— for the rail, the profile is defined not only on the top but also on the inner side (gauge face) at least
down to 14 mm below the top of the rail,
— for the wheel, the profile is defined not only on the wheel tread but also on the outer part and in the
area of the wheel flange root down to at least 10 mm below D ,
— any significant radius difference between the two wheels of a wheelset (measured at the tread datum
positions of the profiles) is taken into account.
The numerical resolution of the profile data shall be consistent with the evaluation process (smoothing
and calculation). If profile data are given with low numerical resolution, the shape may become step-like
with repeated samples of identical amplitude and jumps which are much larger than in reality. This will
lead to unrealistic results for the contact parameters. It is therefore recommended to provide profile data
−3
with a high numerical resolution (number of digits), e.g. with 1·10 mm. This is clearly beyond the
precision of the measurement system but prevents problems in the calculation of contact geometry
parameters.
For the following steps in the procedure the profile coordinates shall be provided sorted along the arc, in
order to give a continuous profile.
6.2 Uncertainty of the measuring systems
The uncertainty of the measuring system shall be quanti
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