CEN/TR 17792:2022
(Main)Railway Applications - Wheel-rail contact geometry parameters - Technical report and background information about EN 15302
Railway Applications - Wheel-rail contact geometry parameters - Technical report and background information about EN 15302
This document provides background information regarding the changes from EN 15302:2008+A1:2010 to the revised version dated 2021, including the reasons for decisions and additional explanation and guidance that is not appropriate in the standard.
The range of equivalent conicity results obtained with different software tools is described. The additional wheel-rail contact parameters, rolling radii coefficient and nonlinearity parameter, are explained. More information is also provided on the different calculation methods and the updated reference profiles for the assessment. The influence of simplifications used in determination of equivalent conicity is discussed.
To provide more information on the importance of considering the complete measurement and calculation process, methods for plausibility checks, eliminating outliers and assessing the uncertainty and repeatability of measurements are included as well as assessments of the smoothing process.
Guidance is given on fields of application of the wheel-rail contact parameters, on the selection of appropriate reference profiles (choice of reference rail profile and rail inclination for assessing wheel profiles and vice versa) and on handling special cases.
As some references in EN 14363 to wheel-rail contact test conditions have caused difficulties in understanding, clarifications issued by ERA are mentioned.
Interpretation of equivalent conicity results, using tools such as conicity maps, is discussed and various approximations such as ‘quick conicity’ assessments are also described.
Information is included on possible additional wheel-rail contact parameters, not yet ready for standardization, but where further experience is needed.
NOTE In this document the commonly used term “wheel-rail contact geometry” is used as a synonym for the more precise term “wheelset-track contact geometry”.
Bahnanwendungen - Rad-Schiene-Berührgeometrieparameter - Technischer Bericht und Hintergrundinformationen zur EN 15302
Applications ferroviaires - Paramètres géométriques du contact roue-rail - Rapport technique et informations générales sur l’EN 15302:2021
Železniške naprave - Geometrijski parametri stika kolo-tirnica - Tehnično poročilo in temeljne informacije o standardu EN 15302
To tehnično poročilo vsebuje temeljne informacije v zvezi s spremembami iz standarda EN 15302:2008+A1:2010 v revidirani različici iz leta 2021, vključno z razlogi za odločitve ter dodatnim pojasnilom in smernicami, ki v standardu niso primerni.
Opisan je razpon rezultatov ekvivalentne konicitete, pridobljenih z različnimi programskimi orodji. Pojasnjeni so dodatni parametri stika kolo-tirnica, koeficient kotalnega radija in parameter nelinearnosti. Podane so tudi dodatne informacije o različnih računskih metodah in posodobljenih referenčnih profilih za ocenjevanje. Obravnavan je vpliv poenostavitev, uporabljenih pri določanju ekvivalentne konicitete.
Za zagotovitev dodatnih informacij v zvezi s tem, kako pomembno je upoštevati celoten postopek merjenja in izračuna, so vključene metode za preverjanje verodostojnosti, odpravljanje osamelcev ter ocenjevanje negotovosti in ponovljivosti meritev, vključno z ocenami postopka izravnave.
Podane so smernice o področjih uporabe parametrov stika kolo-tirnica, o izbiri ustreznih referenčnih profilov (izbira referenčnega profila tirnice in nagiba tirnice za ocenjevanje profilov koles oz. obratno) ter o obravnavi posebnih primerov.
Ker so nekateri sklici na preskusne pogoje stika kolo-tirnica v standardu EN 14363 povzročili težave pri razumevanju, so navedena pojasnila, ki jih je izdala Evropska agencija za železniški promet (ERA).
Obravnavana je interpretacija rezultatov ekvivalentne konicitete z uporabo orodij, kot so zemljevidi konicitete, opisani pa so tudi različni približki, kot so ocene »hitre konicitete«.
Vključene so informacije o morebitnih dodatnih parametrih stika kolo-tirnica, ki še niso pripravljeni za standardizacijo, vendar so v zvezi s tem potrebne dodatne izkušnje.
OPOMBA: Splošno uporabljen izraz »geometrija stika kolo-tirnica« se v tem dokumentu uporablja kot sopomenka za natančnejši izraz »geometrija stika kolesna dvojica-tirnica«.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-april-2022
Železniške naprave - Geometrijski parametri stika kolo-tirnica - Tehnično poročilo
in temeljne informacije o standardu EN 15302
Railway Applications - Wheel-rail contact geometry parameters - Technical report and
background information about EN 15302
Bahnanwendungen - Rad-Schiene-Berührgeometrieparameter - Technischer Bericht und
Hintergrundinformationen zur EN 15302
Applications ferroviaires - Paramètres géométriques du contact roue-rail - Rapport
technique et informations générales sur l’EN 15302:2021
Ta slovenski standard je istoveten z: CEN/TR 17792:2022
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.
CEN/TR 17792
TECHNICAL REPORT
RAPPORT TECHNIQUE
February 2022
TECHNISCHER BERICHT
ICS 17.040.20; 45.060.01
English Version
Railway Applications - Wheel-rail contact geometry
parameters - Technical report and background
information about EN 15302
Applications ferroviaires - Paramètres géométriques Bahnanwendungen - Rad-Schiene-
du contact roue-rail - Rapport technique et Berührgeometrieparameter - Technischer Bericht und
informations générales sur l'EN 15302:2021 Hintergrundinformationen zur EN 15302
This Technical Report was approved by CEN on 10 January 2022. It has been drawn up by the Technical Committee CEN/TC 256.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 17792:2022 E
worldwide for CEN national Members.
Contents Page
European foreword . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 5
4 Overview of the most important changes made to EN 15302 . 6
4.1 List of main changes . 6
4.2 Additional wheel-rail contact geometry parameters . 6
4.2.1 Rolling radii coefficient . 6
4.2.2 Nonlinearity parameter . 6
4.3 Methods for evaluation of equivalent conicity . 7
4.4 Assessment of the smoothing process . 7
4.5 New assessment of the complete process . 8
5 Technical background to and justification of changes in the revised EN 15302 . 8
5.1 Equivalent conicity . 8
5.1.1 Review of equivalent conicity results obtained with different software tools . 8
5.1.2 Comparison with multibody system simulation results .11
5.1.3 Influence of discretisation step size of the rolling radius difference function .14
5.2 Rolling radii coefficient .15
5.2.1 Background .15
5.2.2 Current method .17
5.3 Nonlinearity parameter .20
5.4 Calculation of equivalent conicity by two-step integration .22
5.5 Calculation of equivalent conicity by direct integration of the kinematic equation of
motion .23
5.6 Calculation of equivalent conicity by harmonic linearization .23
5.7 Updated reference profiles and results based on analytical solutions .25
5.8 Revised assessment of the smoothing process .27
5.9 Example for uncertainty assessment of the complete process .27
5.10 Influence of simplifications .31
5.10.1 General .31
5.10.2 Wheelset roll movement (rotation around the longitudinal axis) .31
5.10.3 Contact elasticity of wheel and rail .36
6 Guidance for the application of the wheel-rail contact parameters given in EN 15302
....................................................................................................................................................................39
6.1 Fields of application – Overview .39
6.2 General guidelines .39
6.3 Selection of appropriate reference profiles for assessment of rail head profiles
and/or wheel profiles .40
6.3.1 General .40
6.3.2 British Rail Research Survey .40
6.3.3 Reference profiles in the DynoTRAIN project.40
6.3.4 Assessment of design wheel profiles and design rail profiles .42
6.4 Development of equivalent conicity of wheelsets over mileage .43
6.5 Assessment of the contact geometry of a line .45
6.5.1 Methods for determining averaged contact geometry parameters .45
6.5.2 Assessment of a line for different wheel profiles . 46
6.6 Rolling radii coefficient and radial steering index . 48
6.7 Nonlinearity parameter . 51
6.8 Equivalent conicity in wheel-rail maintenance and interface with TSIs . 53
6.8.1 General . 53
6.8.2 Equivalent conicity that a vehicle was designed and tested for . 53
6.8.3 Equivalent conicity as parameter in wheel profile maintenance regimes . 53
6.9 Clarification of wheel-rail contact test conditions according to EN 14363 . 54
6.10 Application of Contact angle parameter and Roll angle parameter . 55
7 Alternative contact parameters not handled in the standard . 55
7.1 Difference of contact angles and gravitational stiffness . 55
7.2 Contact Concentration Index . 56
8 Approximation of equivalent conicity by simple alternative methods. 60
8.1 Background . 60
8.2 British Rail Research investigations . 60
8.2.1 Initial BRR work in 1980s. 60
8.2.2 BRR further work in 1990s . 63
8.3 Investigations on Quick conicity using DynoTRAIN data . 66
8.3.1 DynoTRAIN project data collection . 66
8.3.2 Investigations on rail data . 67
8.3.3 Investigations on wheel data . 73
8.3.4 Combined assessment – track and wheelset . 75
8.3.5 Next Steps . 75
8.4 Ongoing development of Gradient Index Profile (GIP) . 76
8.4.1 Definition of GIP . 76
8.4.2 Comparison between equivalent conicity and GIP combined . 77
9 Development and usage of the so called conicity maps . 77
10 Plausibility check of measured profiles and elimination of outliers . 79
10.1 Introduction . 79
10.2 Profile area to be covered. 79
10.3 Spacing of points on the profile . 79
10.4 Elimination of outliers . 80
11 Examples for validation of profile measuring systems . 81
11.1 General . 81
11.2 Evaluations of rail profile measuring systems . 81
11.3 Evaluations of ground-based wheel profile measuring systems . 83
12 Effect of wheel diameter differences on the running behaviour . 84
Bibliography . 85
European foreword
This document (CEN/TR 17792:2022) has been prepared by Technical Committee CEN/TC 256 “Railway
applications”, the secretariat of which is held by DIN.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document has been prepared under a Standardization Request 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.
1 Scope
This document provides background information regarding the changes from EN 15302:2008+A1:2010
to the revised version dated 2021, including the reasons for decisions and additional explanation and
guidance that is not appropriate in the standard.
The range of equivalent conicity results obtained with different software tools is described. The
additional wheel-rail contact parameters, rolling radii coefficient and nonlinearity parameter, are
explained. More information is also provided on the different calculation methods and the updated
reference profiles for the assessment. The influence of simplifications used in determination of equivalent
conicity is discussed.
To provide more information on the importance of considering the complete measurement and
calculation process, methods for plausibility checks, eliminating outliers and assessing the uncertainty
and repeatability of measurements are included as well as assessments of the smoothing process.
Guidance is given on fields of application of the wheel-rail contact parameters, on the selection of
appropriate reference profiles (choice of reference rail profile and rail inclination for assessing wheel
profiles and vice versa) and on handling special cases.
As some references in EN 14363 to wheel-rail contact test conditions have caused difficulties in
understanding, clarifications issued by ERA are mentioned.
Interpretation of equivalent conicity results, using tools such as conicity maps, is discussed and various
approximations such as ‘quick conicity’ assessments are also described.
Information is included on possible additional wheel-rail contact parameters, not yet ready for
standardization, but where further experience is needed.
NOTE In this document the commonly used term “wheel-rail contact geometry” is used as a synonym for the
more precise term “wheelset-track contact geometry”.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
4 Overview of the most important changes made to EN 15302
4.1 List of main changes
The list below provides an overview of the main changes introduced in the revised EN 15302:
— extension of the Scope;
— introduction of new wheel-rail contact geometry parameters (rolling radii coefficient, nonlinearity
parameter);
— improvement of the description of the methods for evaluation of equivalent conicity including the
determination of the lateral peak displacements;
— introduction of additional methods for evaluation of equivalent conicity;
— improvement of the description of the reference profiles;
— introduction of the additional reference wheel profile C;
— reference results based on analytical solutions;
— hints for plausibility checking of measured wheel and rail profiles;
— revised assessment of the profile smoothing process;
— new assessment of the complete process for determination of wheel-rail contact parameters.
In this Technical Report the ideas behind the mentioned changes and a more detailed explanation are
given where necessary.
4.2 Additional wheel-rail contact geometry parameters
4.2.1 Rolling radii coefficient
In addition to the now well-established parameter “equivalent conicity”, which describes the contact
geometry in straight track and in curves with very large radii based on a simplified model of the run of
the wheelset, an additional parameter for the guiding behaviour of the wheelset in curves with small and
very small radii is defined. This parameter, the so-called rolling radii coefficient, is intended to describe
the capability of achieving a radial position of a wheelset in the curve. Details are given in 5.2 and 6.6.
4.2.2 Nonlinearity parameter
Equivalent conicity is traditionally used to assess the wheel-rail contact geometry in regard to running
stability. However, the equivalent conicity as a linearized parameter does not consider the nonlinearity
of wheel-rail contact geometry. One value of equivalent conicity is usually used to characterize the wheel-
rail contact geometry: the equivalent conicity value for a wheelset displacement amplitude of 3 mm.
However, the same value of equivalent conicity for a wheelset displacement amplitude of 3 mm can arise
from a large number of very different contact geometries, see Figure 1.
Figure 1 — Possible equivalent conicity functions determined from a set of wheel-rail contact
geometries with the same equivalent conicity value for a wheelset displacement amplitude of
3 mm.
Simulation studies [1] and [2] demonstrated, that the vehicle’s dynamic behaviour at the stability limit
depends on the overall properties of the wheel-rail contact geometry; therefore, also on the overall shape
of the equivalent conicity function for a range of wheelset displacements inside of the clearance between
wheelset and track (i.e. before flange contact).
A second parameter called nonlinearity parameter is proposed in [2] to enhance the characterization of
the wheel-rail contact geometry. This parameter represents the slope of the conicity function between
the wheelset amplitudes of 2 mm and 4 mm. The nonlinearity parameter does not replace the equivalent
conicity as used for the characterization of wheel-rail contact geometry regarding the stability. It should
be understood as additional information complementing the equivalent conicity. While the equivalent
conicity value for a wheelset amplitude of 3 mm represents a “level parameter” for the assessment of
contact geometry regarding the instability limit according to EN 14363, the nonlinearity parameter has
to be understood as a “performance parameter”, characterizing the vehicle performance at the stability
limit as well as the sensitivity of vehicles to the lateral excitation by track irregularity. Details are given
in 5.3 and 6.7.
4.3 Methods for evaluation of equivalent conicity
The description of all evaluation methods was largely improved. All calculation steps are now explained.
In particular, the two-step integration method was clarified (see 5.4 for details), and a description of the
direct integration of the differential equation has been added (see 5.5 for details).
Moreover, it is pointed out that the linear regression and the harmonic linearization (see 5.6 for details)
are approximations, which may give good results but have to be used with care.
Harmonic linearization has been developed in the 1970s to determine linearization parameters required
for linearized calculations of railway vehicle dynamics. As the method is usually available in simulation
tools, it is also used for the determination of equivalent conicity of measured profiles of wheels and rails.
It was thus decided to include this method in the current revision of the standard EN 15302.
4.4 Assessment of the smoothing process
As in the former versions of EN 15302, the effects of profile errors originating from the profile
measurement still have to be assessed. However, the definition of the errors to be used for the assessment
is revised and updated according to the performance of current measuring systems as well as of the
increased available computation power. Further, new quality numbers for the equivalent conicity and the
rolling radii coefficient are introduced describing the ability of the tested smoothing algorithms to deal
with measuring errors. Hence it can be checked if the smoothing process meets the requirements taking
the measuring accuracy of the used profile measuring system into account.
More details are provided in 5.8.
4.5 New assessment of the complete process
According to EN ISO 10012:2003 (Measurement management systems - Requirement for measurement
processes and measuring equipment), an effective measurement management system ensures that
measuring equipment and measurement processes are fit for their intended use and is important in
achieving product quality objectives and managing the risk of incorrect measurement results.
An important part in/of the measurement management system is the metrological confirmation including
estimation of measurement uncertainty. The commonly used method for the estimation of measurement
uncertainty is described in ISO/IEC Guide 98-3:2008 - Guide to the expression of uncertainty in
measurement (GUM: 1995). A measurement cannot be properly interpreted without knowledge of its
uncertainty.
Corresponding to these standards a new assessment method for the complete process of wheel-rail
contact parameter determination (including measurement and calculation) is introduced in EN 15302. In
5.9 of this Technical Report an example is given for the possibility of estimation of measurement
uncertainty applied to the wheel-rail contact parameters derived from measured rail profiles.
The different methods applied today for assessment of measuring uncertainty are at least as strict as the
requirements used when the current limit values for wheel-rail contact parameters were established. The
limit values already include a margin for measuring uncertainty and no additional adjustment of the
result or the limit value shall be made.
5 Technical background to and justification of changes in the revised EN 15302
5.1 Equivalent conicity
5.1.1 Review of equivalent conicity results obtained with different software tools
In the beginning of the revision of EN 15302 a benchmark comparison of currently used calculation
methods for equivalent conicity tan γ was carried out in order to check the tolerances given in the
e
Standard against the methods. The test included all combinations of the reference wheel profiles with the
reference rail profile A as defined in the EN 15302:2008+A1:2010 as well as a selected wheel-rail
combination representing the special case described in B.3 of that document (hollow worn wheel profile).
The tan γ functions have been calculated for the following methods:
e
— direct integration of the differential equation of lateral wheelset motion;
— harmonic linearization;
— two-step integration as described in EN 15302:2008+A1:2010, Annex B;
— linear regression as described in EN 15302:2008+A1:2010, Annex C;
— analytical solution (where applicable).
In some cases, the methods are applied also accounting for the elasticity in the wheel-rail contact (non-
elliptical contact patches) and/or the effect of the axle's roll angle around the axis longitudinal to the
track due to the lateral shift of the wheelset. All the tested methods are implemented in at least two
different software tools. In total the calculation results listed in Table 1 have been provided for the
benchmark.
Table 1 — Available results for equivalent conicity
Identifier Method Roll angle Elastic contact
considered
DB Netz Direct Integration No No
ITCF (DMA) Direct Integration No No
ALSTOM Two-step Integration No No
SNCF (Klingel) Direct Integration No No
SNCF (Ann. C) Linear Regression No No
SNCF (SIMPACK) Direct Integration ? No
Siemens (integ.) Direct Integration No No
Siemens (Ann. B) Two-step Integration No No
Siemens (Ann. C) Linear Regression No No
Siemens (harmonic) Harmonic Linearization No No
Siemens (RSGEO) Harmonic Linearization Yes No
Siemens (SIMPACK integ.) Direct Integration No Yes
Siemens (SIMPACK harm.) Harmonic Linearization No Yes
DB Systemtechnik Two-step Integration No No
IIR (ETQ) Linear Regression Yes No
IIR (Vampire) Linear Regression Yes No
NR Two-step Integration No No
The calculation results of the different methods are shown in the following Figures together with the
reference results and the respective tolerances according to EN 15302:2008+A1:2010, Annex F. Figure 2
contains the results for the symmetrical cases (identical profiles and identical wheel diameters at left-
and right-hand side) whereas Figure 3 provides the graphs for the cases with a wheel diameter difference
of 2 mm and Figure 4 for the asymmetrical wheel profiles. The analytical solutions are not plotted here
because they are nearly identical to the related original reference results.
Figure 2 — Calculation results for equivalent conicity of various calculation methods
(reference profiles in nominal condition)
Figure 3 — Calculation results for equivalent conicity of various calculation methods
(wheel diameter difference of 2 mm applied)
a) Comparison of equivalent conicity b) Comparison of equivalent conicity
wheels A+B worn wheel
Figure 4 — Calculation results for equivalent conicity of various calculation methods
(asymmetrical wheel profiles)
Except for the wheel-rail combination representing the special case described in B.3 (right diagram in
Figure 4), the comparisons show good agreement of the different methods and also confirm that the
tolerance bands for the equivalent conicity as given in EN 15302 are practical. There are only a few
methods providing results partly outside the tolerances, mainly for large lateral wheelset amplitudes
where the contact position is at or close to the wheel flange. As the practical meaning of equivalent
conicity values for this range of lateral wheelset amplitudes is very limited (see also below) it was decided
to restrict the normative range for which a new calculation method shall be tested against the reference
results to amplitudes of 1 mm to 6 mm.
The performed investigation showed also the high importance of a unique definition of the lateral
wheelset displacement. In the beginning, for some methods the lateral wheelset displacement was
measured at the centre of gravity of the wheelset. In combination with the consideration of the roll
movement around the longitudinal axis this resulted in significant deviations of the equivalent conicity
functions. Therefore, the revised EN 15302 contains a clear statement now: “the lateral displacement of
the wheelset as used in this document is considered at the top of rail level”.
The large scatter of conicity results for the special case with the hollow worn wheel, see the right diagram
of Figure 4, showed that there is a need for more information on how to deal with such cases. Therefore,
a new Annex H has been added to EN 15302 explaining the possible existence of multiple solutions. It is
also important to understand that the negative values of equivalent conicity shown by some calculation
tools have no physical meaning.
5.1.2 Comparison with multibody system simulation results
In order to find out up to which lateral displacement the obtained kinematic wheelset movement
provides a physically reasonable assessment, multibody system (MBS) simulations have been performed
and the resulting wavelengths of the lateral wheelset motion have been compared with the wavelengths
of the respective kinematic wheelset trajectory. The dynamic solutions for the lateral wheelset motion
are found by means of simulations of a single vertically loaded wheelset with a soft primary suspension
moving along straight track. Starting with an initial lateral displacement the lateral wheelset trajectory is
calculated and analysed. The equivalent conicity is calculated based on the changing wavelength
according to Klingel's formula and plotted against the related wheelset amplitude, see Figure 5.
Figure 5 — Determination of equivalent conicity by means of MBS simulation
By varying the input parameters speed, primary stiffness (in the range below 2e6 N/m) and wheel-rail
friction coefficient a wide range of amplitudes has been covered. In the following Figures the resulting
conicity values (coloured markers) are compared to an example of the kinematic solution (solid line) for
all the reference cases of EN 15302.
a) wheel A/rail A b) wheel B/rail A
c) wheel H/rail A d) wheel I/rail A
Figure 6 — Comparison of kinetic and kinematic solutions for equivalent conicity
(reference profiles in nominal condition)
a) wheel A (ΔD = 2 mm)/rail A b) wheel B (ΔD = 2 mm)/rail A
c) wheel H (ΔD = 2 mm)/rail A d) wheel I (ΔD = 2 mm)/rail A
Figure 7 — Comparison of kinetic and kinematic solutions for equivalent conicity
(wheel diameter difference of 2 mm applied)
a) wheels AB/rail A b) S1002–1425/60 E1, 1:40, 1435
Figure 8 — Comparison of kinetic and kinematic solutions for equivalent conicity
(asymmetrical case of EN 15302 and combination of wheel profile S1002 with rail profile 60E1)
It can be concluded for the selected parameters that the MBS simulation of the wheelset movement gives
very similar results to the kinematic solutions. In most cases the wavelength is a bit longer leading to
slightly lower equivalent conicity values. However, in some cases of large amplitudes (covering large
contact angles) or big jumps of the contact point positions no dynamic solution for the harmonic wheelset
oscillation was found. This confirms the chosen range of amplitudes (1 mm to 6 mm) for testing
calculation tools for equivalent conicity.
5.1.3 Influence of discretisation step size of the rolling radius difference function
Another question raised during the work on the revision of EN 15302 is related to the influence of
different discretisation step sizes of the rolling radius difference function Δr(y) on the equivalent conicity.
In addition to the results shown above some workgroup members provided conicity results for different
sampling rates of the Δr-function varying between 0,01 mm and 0,2 mm. Based on these results
(presented in Figure 9) it can be concluded that the step size used for Δr(y) may be important if only a
single conicity value at a wheelset amplitude y close to a jump in the conicity function is considered.
A
Nevertheless, for practical applications it is sufficient to use a step size of 0,2 mm as long as only the
equivalent conicity is of interest. However, for the determination of the rolling radii coefficient a
maximum step size of 0,1 mm is required.
a) Comparison of equivalent conicity b) Comparison of equivalent conicity
wheel A/rail A wheel B/rail A
c) Comparison of equivalent conicity d) Comparison of equivalent conicity
wheel H/rail A wheel I/rail A
Figure 9 — Influence of the discretisation of the Δr-function on equivalent conicity
5.2 Rolling radii coefficient
5.2.1 Background
The many years of experience of many railways have confirmed the importance of recording and
assessing wheel-rail contact geometry, especially for high-speed traffic. The procedure for determining
the parameters and functions of contact geometry in straight lines and in curves with very large radii has
been regulated by the UIC 519 [21] and incorporated in European Standard EN 15302. The UIC 518 [22],
which deals with the running test specifications for vehicle homologations, specifies the requirements for
the contact geometry parameters. At this time these requirements related exclusively to straight lines
and curves with very large radii. Therefore, the goal was to define a relevant parameter based on a
simplified model for the guidance behaviour of the wheelset in curves with small and very small radii.
This parameter shall describe the capability of achieving a radial position for a wheelset in the curve.
The influence of the contact geometry on the dynamic behaviour of a vehicle in curves with small and
very small radii has been studied several times in the literature. Running through curves was also a
subject of both the theoretical and experimental investigations of ORE B 176. One of the essential
conclusions of these investigations is the recognition and confirmation that not only the adhesion
coefficients but also the contact geometry significantly influences the running behaviour of a vehicle in
curves. The theoretical considerations were presented in ORE B 176/DT 292, Part 1 [19]. The results of
the experimental investigations were documented in ORE B 176/DT 292, Part 5 [20].
The statement in [19] “. the continuous measurement of the rail profile geometry and thus of the wheel-
rail contact is currently not possible .” corresponded to the then state of the art in the field of recording
rail profiles. Modern measurement technology now makes it possible to record the rail profiles from
measuring vehicles at very short intervals and at reasonable speeds of the measuring vehicle. Thus,
extensive new measurement results are available that have been further processed and assessed.
The evaluation of the contact geometry in straight lines and in curves with very large radii according to
UIC 519 [21] provides the parameters and functions:
— equivalent conicity;
— ∆r function;
— Σtanγ function;
— position of the contact points on the wheel and on the rail.
These parameters and functions also form the basis of the analysis of the contact geometry in curves with
small and very small radii. The equivalent conicity has only a relevance for such vehicles which, due to
the design of the running gear, allow for sinusoidal running in curves with smaller radii.
The aim of an optimal, track friendly vehicle design should be to pass through a curve with the lowest
possible wheel-rail forces and thus to minimize wear and rail fatigue. The profile shape of the wheels
which is based on a conical profile, so that the wheelset corresponds to a double cone, allows for pure
kinematic rolling in the curve. This wheelset rolling in the curve is characterized by the so-called radial
position of the wheelset which is corresponding to an angle of attack = 0. There are three types of
wheelset position in the track:
— over-radial steering of the wheelset;
— under-radial steering of the wheelset;
— radial steering of the wheelset (angle of attack = 0).
The different wheelset positions are influenced not only by the contact geometry parameters but also by
the vehicle suspension design and the wheel-rail friction conditions. For example, lubrication of the flange
contact on the outer rail may reduce the effectiveness of radial steering.
ORE B 176/DT 292, Part 5 [20] defines parameters describing the capability of achieving a radial position
o oo
of the wheelset which are obtained from the points O, A , A of the Δr function, see Figure 10.
Figure 10 — Definition of parameters for running in curves based on the Δr function
5.2.2 Current method
A free wheelset runs optimally through a curve if it can pass purely rolling without any sliding movement.
The two relevant requirements for this are:
1) Movement of the wheelset on the so-called kinematic rolling line
The trajectory corresponds to the lateral offset of the wheelset at which the rolling radius difference Δr
amounts to
2b
A
∆r= r
R
with:
— 2b . nominal contact point spacing (1 500 mm for standard gauge);
A
— r . radius of the wheel when the wheelset is centred on the track;
— R . curve radius.
2) One-point contact on the outer wheel
The functions Δr = f(y) and Σtanγ = f(y) of a wheel-rail profile combination are very important for the
contact geometry in curves. An ideal contact geometry from the point of view of the general curving
behaviour is present for a given wheel-rail-profile combination if the Δr and Σtanγ functions provide:
— a smooth continuous function;
— no offset at the central wheelset position in the track;
— no asymmetry with respect to the direction of the curve.
If there is a discontinuity in the Δr function which represents a real two-point contact, such a contact
geometry is considered to be less than optimum since two-point contact occurs in the small radius curves,
which increases in particular the guiding forces and thus also the wheel and rail wear.
The Δr function is the starting point for the evaluation of the contact conditions in curves. Essential values
of this function are marked by the following points in Figure 10:
Point O - kinematic rolling position
The point O on the Δr function represents the lateral offset in which the wheelset in the curve can roll
purely kinematically in a radial position.
o
Point A
o
The point A denotes the bottom contact point of a pronounced discontinuity, which represents a two-
o
point contact. The contact point corresponding to A is always on the tread of the wheel.
oo
Point A
oo
The point A denotes the upper contact point of a pronounced discontinuity, which represents a two-
oo
point contact. The contact point corresponding to A is always on the wheel flange.
Point E
o
The point E lies on the Δr function at the lateral displacement y = y - 1 mm. The definition of this point
E A
was made under the assumption that with 1 mm margin before the discontinuity point an ideal
positioning of the wheelset (radial position) is possible. The margin permits the generation of steering
forces to overcome the longitudinal forces in the suspension for a constrained wheelset.
Border between the wheel flange and the tread
o
In case there is no pronounced discontinuity before flange contact is reached then the point A is defined
as the last point before |Δr| = 10 mm when starting at y = 0.
The described points are used to determine the following parameters:
Parameters d and e of the function Δr = f (y)
E E
The parameter d is the distance between the points O and E with respect to the y-coordinate. The
E
parameter e represents the distance of point E from point O with respect to Δr. Both parameters have
E
already been described in [20]. In the present method the distance d is reduced by 1 mm (d becomes d ).
E
o o
Thus, the ordinate value e is read not at the point A but at the wheelset lateral displacement y = (y -
1 A
1 mm) at the point E (e becomes e ).
1 E
o
Parameter q
A
o o
The quotient q is the kinematically negotiable curve radius at the point A normalized with the nominal
A
radius of the examined curve:
R
o
A
q =
o
A
R
with
2b
A
— Rr= … radius of the kinematically negotiable curve corresponding to the rolling radius
o
A
∆r
o
A
o
difference of point A ;
— R … radius of the examined curve.
Radial steering index q
E
The radial steering index according to UIC 518 [22] and EN 14363 [23] is the kinematically negotiable
curve radius at point E normalized with the radius of the examined curve:
R
E
q =
E
R
with
a) R radius of the kinematically negotiable curve corresponding to the rolling radius difference of
E
point E;
b) R radius of the examined curve.
That means that
c) if q ≤ 1 radial steering is possible; and
E
d) if q > 1 radial steering is not possible but flange contact will occur before a rolling radius difference
E
Δr, big enough for the curve in question, is achieved.
Rolling radii coefficient ρ
E
The rolling radii coefficient was introduced in the revised EN 15302 to allow for a clearer understanding
of the practical meaning. It is defined as:
R R
ρ∆−=11⋅ r−
EE
R rb⋅ 2
E 0A
which means
e) if ρ ≥ 0 radial steering is possible; and
E
f) if ρ < 0 radial steering is not possible, but flange contact will occur before a rolling radius difference
E
Δr, big enough for the curve in question, is achieved.
The rolling radii coefficient can also be obtained from the radial steering index:
ρ − 1
E
q
E
=
=
5.3 Nonlinearity parameter
Equivalent conicity is traditionally used to assess the contact geometry wheelset/track in regard to
running stability. However, the equivalent conicity as a linearized parameter does not consider the
nonlinearity of wheel-rail contact geometry.
An important difference of a nonlinear dynamic system compared to a linearized system is a possible
coexistence of multiple solutions depending on system parameters. To visualize the multiplicity of
solutions, bifurcation diagrams are used. For railway vehicles, a bifurcation diagram usually displays the
amplitude of wheelset lateral oscillation versus speed. Investigations in [1] and [2] as well as comparisons
with other publications resulted in the conclusion, that there is an interrelationship between the shape
of the bifurcation diagram of a railway vehicle and the contact nonlinearity represented by the equivalent
conicity as a function of wheelset displacement amplitude. This relationship can be seen in Figure 11 for
three different vehicles and two different contact geometries wheelset-track. Both examples of wheel-
rail contact geometry represent the same equivalent conicity for 3 mm amplitude, but different values for
other wheelset amplitudes.
a) equivalent conicity function b) bifurcation diagram vehicle 1
c) bifurcation diagram vehicle
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.
Loading comments...