In this paper, nonlinear dynamics of a railway wheelset is investigated during kinematic oscillations. Based on the nonlinear differential equations, the notion of nonlinearity factor is introduced, which expresses the effect of the vibration amplitude on the frequency of the oscillations. The analytical formula of this nonlinearity factor is derived from the local geometry of the rail and wheel profiles. The results are compared to the ones obtained from the rolling radius difference (RRD) function.

References

References
1.
Wickens
,
A. H.
,
1999
, “
The Dynamics of Railway Vehicle—From Stephenson to Carter
,”
Proc. Inst. Mech. Eng.
,
212
(
3
), pp.
209
217
.
2.
Wickens
,
A. H.
,
2006
, “
A History of Railway Vehicle Dynamics
,”
Handbook of Railway Vehicle Dynamics
,
S.
Iwnicki
, ed.,
CRC Press
, Boca Raton, FL.
3.
Reynolds
,
O.
,
1875
, “
On Rolling Friction
,”
Philos. Trans. R. Soc.
,
166
, pp.
155
–174.
4.
Carter
,
F. W.
,
1926
, “
On the Action of a Locomotive Driving Wheel
,”
Proc. R. Soc.
,
112
(
760
), pp.
151
157
.
5.
Iwnicki
,
S.
,
2003
, “
Simulation of Wheel-Rail Contact Forces
,”
Fatigue Fract. Eng. Mater. Struct.
,
26
(
10
), pp.
887
900
.
6.
Ayasse
,
J.-B.
, and
Chollet
,
H.
,
2006
, “
Wheel-Rail Contact
,”
Handbook of Railway Vehicle Dynamics
,
S.
Iwnicki
, ed.,
CRC Press
, Boca Raton, FL.
7.
Wickens
,
A. H.
,
2003
,
Fundamentals of Rail Vehicle Dynamics: Guidance and Stability
.
Swets and Zeitlinger
,
Lisse, The Netherlands
.
8.
Wickens
,
A. H.
,
1965
, “
The Dynamic Stability of Railway Vehicle Wheelsets and Bogies Having Profiled Wheels
,”
Int. J. Solids Struct.
,
1
(
3
), pp.
319
341
.
9.
Stichel
,
S.
,
2002
, “
Limit Cycle Behaviour and Chaotic Motions of Two-Axle Freight Wagons With Friction Damping
,”
Multibody Syst. Dyn.
,
8
(
3
), pp.
243
255
.
10.
Kumar
,
S.
,
Kim
,
J. S.
,
Rao
,
D. L. P.
, and
Qian
,
L.
,
1983
, “
Effect of Kinematic Oscillation on Tractive Characteristics of Steel Wheel on Rail
,”
J. Eng. Ind.
,
105
(
2
), pp.
61
63
.
11.
Szabo
,
Z.
, and
Lorant
,
G.
,
2000
, “
Parametric Excitation of a Single Railway Wheelset
,”
Veh. Syst. Dyn.
,
33
, pp.
49
55
.
12.
UIC
,
2004
, “
Method for Determining the Equivalent Conicity
,” International Union of Railways, Paris, UIC Code 519.
13.
EN
,
2008
, “
Railway Applications—Method for Determining the Equivalent Conicity
,” European Committee for Standardisation, Brussels, UK, Standard No. EN 15302.
14.
Klingel
,
J.
,
1883
, “
Über den Lauf von Eisenbahnwagen auf gerader Bahn
,”
Organ Fortschr. Eisenbahnwes.
,
38
, pp.
113
123
.
15.
Heumann
,
H.
,
1937
, “
Lauf der Drehgestell-Radsatze in der Geraden
,”
Organ Fortschr. Eisenbahnwes.
,
92
, pp.
149
173
.
16.
Joly
,
R.
,
1970
, “
Etude de la stabilite transversale d'un vehicule ferroviaire
,”
Rev. Fr. Mec.
,
36
, pp.
5
26
.
17.
Meijaard
,
J. P.
,
2014
, “
Kinematic Analysis of a Wheelset as an Aid to Understanding and Modifying the Postcritical Behaviour
,”
8th European Nonlinear Dynamics Conference (ENOC 2014)
, Vienna, Austria, pp.
1
2
.
18.
Schwab
,
A. L.
, and
Meijaard
,
J. P.
,
2002
, “
Two Special Finite Elements for Modelling Rolling Contact in a Multibody Environment
,”
1st Asian Conference on Multibody Dynamics
, Iwaki, Japan, pp.
386
391
.
19.
Antali
,
M.
,
Stepan
,
G.
, and
Hogan
,
J.
,
2015
, “
Kinematic Oscillations of Railway Wheelsets
,”
Multibody Syst. Dyn.
,
34
(
3
), pp.
259
274
.
20.
de Pater
,
A. D.
,
1988
, “
The Geometrical Contact Between Track and Wheelset
,”
Veh. Syst. Dyn.
,
17
(
3
), pp.
127
140
.
21.
Gu-ang
,
Y.
, and
de Pater
,
A. D.
,
1992
, “
The Determination of the Nonlinear Motion of a Railway Vehicle
,”
Veh. Syst. Dyn.
,
20
, pp.
225
239
.
22.
Alonso
,
A.
,
Gimenez
,
J. G.
, and
Garcia
,
M.
,
2015
, “
Analytical Methodology to Solve the Geometric Wheel-Rail Contact Problem Taking Into Account the Wheelset Yaw Angle
,”
24st IAVSD Symposium
, Graz, Austira, pp.
1
9
.
23.
Strogatz
,
S. H.
,
1994
,
Nonlinear Dynamics and Chaos
,
Perseus Books
, Reading, MA.
24.
Guckenheimer
,
J.
, and
Holmes
,
P.
,
1983
,
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
,
Springer
,
Berlin
.
25.
Wiggins
,
S.
,
2003
,
Introduction to Applied Nonlinear Dynamical Systems and Chaos
,
2nd ed.
,
Springer
,
Berlin
.
26.
Antali
,
M.
, and
Stepan
,
G.
,
2014
, “
Nonlinear Kinematic Oscillations of Railway Wheelsets of General Surface Geometry
,”
Proc. Appl. Math. Mech.
,
14
(
1
), pp.
303
304
.
27.
Polach
,
O.
,
2009
, “
Characteristic Parameters of Nonlinear Wheel/Rail Contact Geometry
,”
21st IAVSD Symposium
, Stockholm, Sweden, pp.
1
12
.
28.
Mazzola
,
L.
,
Alfi
,
S.
,
Braghin
,
F.
, and
Bruni
,
S.
,
2010
, “
Limit Wheel Profile for Hunting Instability of Railway Vehicles
,”
Non-Smooth Problems in Vehicle Systems Dynamics
,
P.
Grove Thomsen
and
H.
True
, eds.,
Springer
,
Berlin
, pp.
41
52
.
29.
True
,
H.
,
2007
, “
Zur aquivalenten konizitat
,”
ZEVrail Glasers Annalen
,
Tagungsband SFT
,
Graz, Austria
, Vol.
131
, pp.
290
298
.
30.
Jordan
,
D. W.
, and
Smith
,
P.
,
2007
,
Nonlinear Ordinary Differential Equations
,
4th ed.
,
Oxford University Press
, Oxford, UK.
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