Computation of Common Normal between a wheelset and rail is a key problem in simulation of wheel/rail interaction. Such an algorithm must be robust and efficient. In this work, computation of location of the common normal is formulated as an optimization problem. This framework has the advantage of being able to use optimization techniques for determination of location of common normal as an alternative Newton method. The numerical results obtained using Trust-Region Method are presented.

Simulations are playing an important role to predict derailment, switching, wheel climbing and curving in the study of dynamics of railroad vehicles. For a successful simulation, a robust and efficient approach for computation of all common normal between wheel and rail surface is needed. In a previous work, the authors had devised an approach based on sign distant function to compute all common normal between a pair of wheel and surface. As part of this approach, two major computational tasks were formulated. They were computation of cauchy index around a cell (a closed curve) and computation of the zero’s of the gradient of the signed distance function. In this study, a bookkeeping technique is devised to compute the cauchy index more efficiently. Also the performance of trust region method as a solver for a set of nonlinear equation is compared to Newton’s method.