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Research Papers

On the Nonlinear Kinematic Oscillations of Railway Wheelsets

[+] Author and Article Information
Mate Antali

Department of Applied Mechanics,
Budapest University of
Technology and Economics,
Budapest 1111, Hungary
e-mail: antali@mm.bme.hu

Gabor Stepan

Department of Applied Mechanics,
Budapest University of
Technology and Economics,
Budapest 1111, Hungary
e-mail: stepan@mm.bme.hu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 12, 2015; final manuscript received February 25, 2016; published online May 12, 2016. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 11(5), 051020 (May 12, 2016) (10 pages) Paper No: CND-15-1436; doi: 10.1115/1.4033034 History: Received December 12, 2015; Revised February 25, 2016

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.

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References

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Carter, F. W. , 1926, “ On the Action of a Locomotive Driving Wheel,” Proc. R. Soc., 112(760), pp. 151–157. [CrossRef]
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Figures

Grahic Jump Location
Fig. 1

Parameters of the system in the central position of the wheelset. The parameters of the local geometry at the nominal contact point (h, Rw, Rr and the curvature derivatives) can be calculated from the profile curves cw and cr.

Grahic Jump Location
Fig. 2

Three classes of profiles. Left panel: conical wheel with square rail. Middle panel: profiles with constant curvatures. Right panel: profiles with varying curvatures. In case of curved profiles, the necessary parameters of the local geometry are listed (see Table 1).

Grahic Jump Location
Fig. 3

Variables describing the motion of the wheelset. The sequence of the rotations by the Euler angles ψ, ϑ, and φ are determined by Eq. (7).

Grahic Jump Location
Fig. 4

Sketch of phase portraits of the oscillating system described by different variables which are connected by the transformations Eqs. (27) and (30). For a chosen trajectory, also the amplitudes ψ¯ and ψ¯* are denoted.

Grahic Jump Location
Fig. 5

Kinematic oscillation of the wheelset. In the figure, the special positions are denoted where the axle of the wheelset lays either in the horizontal (ϑ = 0) or in the vertical (ψ = 0) plane.

Grahic Jump Location
Fig. 6

Kinematic oscillation based on the analytical result (35) in the case of β > 0. In this case, the frequency increases with the increasing amplitude of the oscillation.

Grahic Jump Location
Fig. 7

Kinematic oscillation based on the analytical result (35) in the case of β < 0. In this case, the frequency decreases with the increasing amplitude of the oscillation.

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