SIST EN 15302:2021
(Main)Railway Applications - Wheel-rail contact geometry parameters - Definitions and methods for evaluation
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-Berührgeometrie - Definitionen und Auswertemethoden
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 gemäß 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 détermination
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
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 15302:2021
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
SIST EN 15302:2021 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN 15302:2021
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SIST EN 15302:2021
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.
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SIST EN 15302:2021
EN 15302:2021 (E)
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
2
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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
3
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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
4
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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
5
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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
6
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SIST EN 15302:2021
EN 15302:2021 (E)
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, P
...
SLOVENSKI STANDARD
oSIST prEN 15302:2019
01-februar-2019
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: prEN 15302
ICS:
45.060.01 Železniška vozila na splošno Railway rolling stock in
general
oSIST prEN 15302:2019 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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oSIST prEN 15302:2019
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oSIST prEN 15302:2019
DRAFT
EUROPEAN STANDARD
prEN 15302
NORME EUROPÉENNE
EUROPÄISCHE NORM
December 2018
ICS 17.040.20; 45.060.01 Will supersede 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 Berührgeometrie - Definitionen und
détermination Auswertemethoden
This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee
CEN/TC 256.
If this draft becomes a European Standard, 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.
This draft European Standard was established by CEN 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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, 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 European Standard. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 15302:2018 E
worldwide for CEN national Members.
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oSIST prEN 15302:2019
prEN 15302:2018 (E)
Contents Page
European foreword . 6
Introduction . 7
1 Scope . 8
2 Normative references . 8
3 Terms and definitions . 8
4 Symbols and abbreviations . 9
5 Overview of the process for determining contact parameters . 10
6 Description of wheel and rail profiles . 11
6.1 General . 11
6.2 Uncertainty of the measuring systems . 13
7 Plausibility check and processing of measured wheel and rail profiles . 13
8 Determining the wheel-rail contact positions and contact functions . 14
8.1 General . 14
8.2 Determining the rolling radius difference function . 15
8.3 Other wheel-rail contact geometry functions . 15
9 Determining the equivalent conicity and the related nonlinearity parameter . 16
9.1 Background to equivalent conicity . 16
9.1.1 Mathematical description of the kinematic lateral wheelset motion . 16
9.1.2 Determining the wavelength of a coned wheelset . 17
9.2 Determining the equivalent conicity . 17
9.3 Determining the nonlinearity parameter . 18
10 Determining the rolling radii coefficient . 19
10.1 Background and definition . 19
10.2 Determining point E for the calculation of the rolling radii coefficient . 21
11 Other wheel-rail contact parameters . 22
12 Testing of calculation software for contact geometry parameters . 22
12.1 Overview . 22
12.2 Validation of the calculation algorithms . 22
12.3 Assessment of the smoothing process . 23
13 Assessment of the complete process for determination of wheel-rail contact
parameters . 25
13.1 General . 25
13.2 Reproducibility of contact parameter determination based on rail profile
measurement . 25
13.2.1 Manual rail profile measuring devices . 25
13.2.2 Vehicle based rail profile measuring systems . 26
13.3 Reproducibility of contact parameter determination based on wheel profile
measurement . 27
13.3.1 Manual wheel profile measuring devices . 27
13.3.2 Ground based wheel profile measuring systems . 27
Annex A (informative) Example of presentation of contact geometry functions . 29
2
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Annex B (informative) Derivation of the kinematic equation of wheelset motion . 30
Annex C (informative) Determination of the lateral peak displacements . 33
Annex D (informative) Method for determining the wavelength of the wheelset motion by
two-step integration of the nonlinear differential equation . 35
D.1 General . 35
D.2 Step 1 . 35
D.3 Step 2 . 35
Annex E (informative) Method for determining the wavelength of the wheelset motion by
direct integration of the nonlinear differential equation . 37
Annex F (informative) Method for determining the equivalent conicity by linear regression
of the Δr function . 38
F.1 General . 38
F.2 Concerns regarding the method . 38
Annex G (informative) Method for determining linearization parameters by harmonic
linearization . 40
G.1 General . 40
G.2 Concerns regarding the method . 41
Annex H (informative) Handling of special cases of the Δr function . 42
Annex I (normative) Reference profiles for testing . 45
I.1 General . 45
I.2 Wheel A . 45
I.2.1 Drawing . 45
I.2.2 Analytic definition . 45
I.2.3 Cartesian coordinates . 46
I.3 Wheel B . 47
I.3.1 Drawing . 47
I.3.2 Analytic definition . 47
I.3.3 Cartesian coordinates . 48
I.4 Wheel C . 50
I.4.1 Drawing . 50
I.4.2 Analytic definition . 50
I.4.3 Cartesian coordinates . 50
I.5 Wheel H . 52
I.5.1 Drawing . 52
I.5.2 Analytic definition . 52
I.5.3 Cartesian coordinates . 53
I.6 Wheel I . 54
I.6.1 Drawing . 54
I.6.2 Analytic definition . 54
I.6.3 Cartesian coordinates . 55
I.7 Rail A . 57
I.7.1 Drawing . 57
I.7.2 Analytic definition . 57
I.7.3 Cartesian coordinates . 58
Annex J (normative) Calculation results with reference profiles . 60
J.1 General . 60
J.2 Wheel A/Rail A . 61
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 . 61
3
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J.2.2 Numerical values for Δr function . 62
J.2.3 Numerical values for tanγ function . 63
e
J.3 Wheel B/Rail A . 65
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 . 65
J.3.2 Numerical values for Δr function . 66
J.3.3 Numerical values for tanγ function . 67
e
J.4 Wheel C/Rail A . 69
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 . 69
J.4.2 Numerical values for Δr function . 70
J.4.3 Numerical values for tanγ function . 72
e
J.5 Wheel H/Rail A . 74
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 . 74
J.5.2 Numerical values for Δr function . 75
J.5.3 Numerical values for tanγ function . 76
e
J.6 Wheel I/Rail A . 78
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 . 78
J.6.2 Numerical values for Δr function . 79
J.6.3 Numerical values for tanγ function . 80
e
J.7 Modified Wheel A (−2 mm on left wheel diameter)/Rail A . 82
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 . 82
J.7.2 Numerical values for Δr function . 83
J.7.3 Numerical values for tanγ function . 84
e
J.8 Modified Wheel B (−2 mm on left wheel diameter)/Rail A . 86
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 . 86
J.8.2 Numerical values for Δr function . 87
J.8.3 Numerical values for tanγ function . 88
e
J.9 Modified Wheel H (−2 mm on left wheel diameter)/Rail A . 90
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 . 90
J.9.2 Numerical values for Δr function . 91
J.9.3 Numerical values for tanγ function . 92
e
J.10 Modified Wheel I (−2 mm on left wheel diameter)/Rail A . 94
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 . 94
J.10.2 Numerical values for Δr function . 95
J.10.3 Numerical values for tanγ function . 96
e
J.11 (Right Wheel A – Left Wheel B)/Rail A . 98
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 . 98
J.11.2 Numerical values for Δr function . 99
J.11.3 Numerical values for tanγ function . 100
e
Annex K (normative) Tolerances on equivalent conicity for testing calculations . 102
K.1 General . 102
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K.2 Wheel A/Rail A . 103
K.2.1 Diagram . 103
K.2.2 Numerical values . 104
K.3 Wheel B/Rail A . 106
K.3.1 Diagram . 106
K.3.2 Numerical values . 107
K.4 Wheel C/Rail A . 109
K.4.1 Diagram . 109
K.4.2 Numerical values . 110
K.5 Wheel H/Rail A . 112
K.5.1 Diagram . 112
K.5.2 Numerical values . 113
K.6 Wheel I/Rail A . 115
K.6.1 Diagram . 115
K.6.2 Numerical values . 116
K.7 Modified Wheel A (−2 mm on left wheel diameter)/Rail A . 118
K.7.1 Diagram . 118
K.7.2 Numerical values . 119
K.8 Modified Wheel B (−2 mm on left wheel diameter)/Rail A . 121
K.8.1 Diagram . 121
K.8.2 Numerical values . 122
K.9 Modified Wheel H (−2 mm on left wheel diameter)/Rail A . 124
K.9.1 Diagram . 124
K.9.2 Numerical values . 125
K.10 Modified Wheel I (−2 mm on left wheel diameter)/Rail A . 127
K.10.1 Diagram . 127
K.10.2 Numerical values . 128
K.11 (Right Wheel A – Left Wheel B)/Rail A . 130
K.11.1 Diagram . 130
K.11.2 Numerical values . 131
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of Directive 2008/57/EC aimed to be covered . 133
Bibliography . 135
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European foreword
This document (prEN 15302:2018) 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 CEN Enquiry.
This document will supersede EN 15302:2008+A1:2010.
This document has been prepared under a standardization request given to CEN by the European
Commission and the European Free Trade Association, and supports essential requirements of
EU Directive 2008/57/EC.
For relationship with EU Directive 2008/57/EC, see informative Annex ZA, which is an integral part of
this document.
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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 profi
...
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