Wheel-rail dynamics with closely conformal contact Part 1: Dynamic modelling and stability analysis

Observations on the Vancouver mass transit system suggest that noise, vibration and corrugation of the rail appear to be associated with close conformity between the transverse profiles of the wheel and rail. To investigate this, a dynamic model of the wheel and rail under conditions of close conformity has been developed. Previous work has suggested that motion of the wheel could be neglected, so the model comprises two subsystems: (a) the rail and its supports, and (b) the contact between wheel and rail. A dynamic model of a continuously supported rail is presented, which is consistent with similar models in the literature. Conformal contact has been represented in two ways: (a) as a single highly eccentric elliptical contact, and (b) as a two-point contact. Novel ‘rolling contact mechanics’ have been incorporated in both these models. The complete system is closed: oscillations of the rail give rise to fluctuating contact forces, which in turn excite the rail. A linear stability analysis of the system shows it to be stable under all conditions examined, thus precluding the possibility of self-excited oscillations occurring on a perfectly smooth rail. The model can then be used to investigate the forced response to existing roughness on the railhead, which is the subject of a companion paper (1).