Continuous and Discontinuous Modelling of the Contact between Wheel Flange and Rail

In this paper some aspects of the dynamics of a single railway wheelset are studied. The behaviour of a railway vehicle with respect to the lateral motion is to a large extent determined by the interaction between the wheels and the rails. The relations which determine the forces in the contact zones are non-linear because of the complex geometry of the contact between wheel and rail [1] and the non-linearity of the creep law [2]. Over a period of about a century, the dynamics of railway vehicles has been the subject of a considerable number of studies; but in relatively recent times, it was found that chaotic motions can occur at high speeds [3,4,5,6]. In particular the influence of flange contact was investigated by Meijaard [7], and Knudsen and others [8]. In the former study, the contact between wheels and flanges was modelled discontinuously, where it was assumed that a partially elastic impact occurred when the flange came in contact with the rail. A direct transition to chaotic motion was found at the critical speed, which did not conform to any of the known routes to chaos for continuous systems, though it resembled an intermittent transition. On the other hand, in the work of Knudsen, the contact was modelled by a stiff spring and on close examination a period doubling route to chaos was found in a narrow region.