A new method for the solution of the normal contact problem in the dynamic simulation of railway vehicles

Due to requirements related to computational efficiency, in the majority of railway dynamic simulators the Hertz theory is used for solving the normal problem in wheel/rail contact. This theory is based on a large number of assumptions. Particularly noteworthy is the assumed simplification that the undeformed distance between the bodies in contact can be assimilated by a quadratic function. There are many situations in which the undeformed distance cannot be represented by this kind of function. As such, the results obtained with Hertz theory in these cases are not accurate.

In this paper, a new method for solving the normal problem that overcomes the above-mentioned limitation is presented. First, the exactness of the new method is tested with Hertzian cases. The results obtained are almost exact. Second, the results calculated with the new method in more general cases are compared with the ones obtained with the variational method of Kalker (more exact but computationally less efficient).