Modelling of Tram-Track Interaction

The paper deals with numerical model of a tram moving on the track. The rail is modelled as elastically supported continuous beam with lumped masses. A vehicle is approximated as a discrete system consisting of three rigid masses connected with linear elastic springs. Dissipation mechanisms in the system are modelled with the linear dashpots. Two basic assumptions that are used are: a) the Euler-Bernoulli beam theory and b) the separation of the wheel from the rail is not permitted. The system of differential equations of motion is solved by an implicit version of step by step method based on the direct integration technique. The algorithm is conceived on the first order predictor - (re)corrector method. The contact condition is modelled by the force method. Results of the calculations are compared with the results of measurement on the tram track. Numerical predictions for displacements and accelerations are in good agreement with the experimental findings