On the problems of non-smooth railway vehicle dynamics

Railway vehicle dynamics is inherently a problem of nonlinear dynamics. The unavoidable nonlinearities stem from the rail/wheel contact geometry and the stress/strain velocity relation in the rail/wheel contact surface. In addition motion delimiters and dry friction contact between elements in the construction create discontinuities in the mathematical dynamic model. The stick/slip of dry friction can be modelled as a discontinuity or be smoothed whereby discontinuities of higher order spatial derivatives are introduced. Higher order discontinuities are also introduced through the rail/wheel contact relation. These discontinuities create problems for the advanced equation solvers that are needed for the numerical investigation of the nonlinear dynamic problem. The results of the integration of the dynamic system will depend on the correct choice and application of the solver. In the worst case the solver will deliver resulting dynamics, which is qualitatively wrong. In this presentation we shall use various examples to demonstrate how the numerical problems are solved and reliable dynamic results obtained. The emphasis will be on the numerical aspects rather than the modelling and the dynamics of the models.