Vehicle–track interaction at high frequencies – Modelling of a flexible rotating wheelset in non-inertial reference frames

Vehicle–track interaction in the mid- and high-frequency range has become an important issue for rolling-stock manufacturers, railway operators and administrations. Previous modelling approaches have been focused on the development of flexible wheelset–track systems based on the assumption that the unsprung masses are decoupled from the high-frequency dynamic behaviour of carbody and bogies. In this respect, the available flexible wheelset models account for gyroscopic and inertial effects due to the main rotation but are, in general, developed from the viewpoint of inertial spaces and consequently restricted to the study of tangent layouts. The aim of this paper is to present the formulation of a flexible rotating wheelset derived within the framework of a non-inertial vehicle moving reference frame. This brings a double advantage; on the one hand, the formulation is not restricted to tangent tracks, but is also suitable for the study of transition curves and curve negotiation. On the other hand, the use of a vehicle moving reference frame allows the introduction of the hypothesis of small displacement for the degrees of freedom of the wheelset. This hypothesis is not applied to the pitch angle, as it is associated with the main axis of rotation. In addition, unlike previous flexible wheelset models that only consider the rotation around the main axis, all the degrees of freedom will be considered when developing the dynamic equations of motion. Results for the proposed model will be presented and the influence of the inertial and gyroscopic terms not taken into account in previous derived formulations will be evaluated.