The Role of Non-Linearities in the Dynamics of a Single Railway Wheelset.

This paper presents the results of the analytical and semi-analytical investigation of a single railway wheelset. The non-linearities appear in the expression of the creep force law and in the flange contact model. Smoothing process is used to obtain a sufficiently smooth (C 4 ) creep force law. Above a certain critical speed, the stationary motion of the wheelset loses its stability. The methods of Hopf bifurcation theory provide the parameter domains where unstable periodic motions appear around the stable stationary motion, and also those domains where stable periodic motions exist above the critical speed. The amplitudes of these periodic motions are calculated in closed form and are checked by numerical simulation. In case of great amplitude increments for small speed variation, the non-linearity related to the flange contact becomes much more important than the non-linearity of the creep force law. By means of a linear creep force law and a flange contact modelled by a spring with dead band, almost one dimensional Poincare maps are constructed and presented on a realistic parameter domain. These maps describe and explain the often chaotic wheelset behaviour in a small range of the speed just above its critical value. Computer algebra is involved because of the complexity of the equations of motion.