Keywords: track, asymmetric wheelset, steady-state interaction, Green's function, parametric resonance.

This paper presents an analysis of the steady state interaction between an asymmetric wheelset and track arising from the parametric excitation of sleepers. This issue is typical for many kinds of driven wheelset that have an asymmetric distribution of the inertia, as the driving gear is assembled on the axle close by a wheel. The track model consists of two uncoupled rails, each of them resting on discretely equidistant supports. The rails are considered as infinite Timoshenko beams. The model of the periodic support has two three-direction Kelvin-Voigt systems for the rail pad and the ballast, and a mixed Kelvin-Voigt-Maxwell system for the subgrade. Also, the inertia of the sleeper and the ballast block are introduced. In fact, the sleeper and the ballast block are rigid bodies with three and one degrees of freedom, respectively. The theoretical results obtained by means of this support model show a good agreement with the results from the measurements for an extended frequency range, particularly at low frequencies (0-50 Hz) and at the pinned-pinned resonance frequency. The driven wheelset of a locomotive is used for modelling. The wheelset is considered as a uniform Timoshenko beam with attached rigid bodies for wheels, axle boxes and driving gear. Upon neglecting the gyroscopic effect, the bending modes are taken into account and included in the response of each wheel. The contact between wheels and rails is considered as linear Hertzian contact. The equations of motion are solved by means of the Green's function method. The asymmetric wheelset-track steady-state interaction is dominated by the parametric resonance that occurs when the passing frequency meets the frequency of the rigid mode of vibration of the wheelset on the track. Also, the corresponding 1/2 and 1/3 sub-harmonic parametric resonances occur at velocities of 1/2 and 1/3 of the parametric excitation velocity. The dynamic contact force is higher at the 'heavy' wheel, due to the inertia asymmetric distribution. The spectrum of the difference between the dynamic components of the contact forces exhibits a peak in the pinned-pinned resonance range, and its magnitude increases with velocity. In fact, when the wheelset works in the traction behaviour, the contact force difference triggers torsion vibration of the axle and contributes to the formation of the short-pitch rail corrugation.

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