On Quasi-Newton Method Applied To 2D Wheel-Rail Contact Models

Reliable and proficient numerical methods are required to determine the contact points between wheel and rail. This paper presents the use of Quasi-Newton method for determining the solution of a reduced number of non-linear wheel-rail contact geometry equations that arise as a result of the interaction of wheel and rail on the track.
A novel two dimensional (2D) wheel-rail contact model is developed by using the wheel-rail contact co-ordinates to calculate the wheel-rail normal contact forces without approximating the contact angle. The simulated results are stored in a lookup table and accessed during the simulation of the bogie dynamic behaviour thus reducing the computational time. The reduced number of non-linear wheel-rail contact geometry equations and employment of Quasi-Newton method enable the proposed 2D wheel-rail contact model to be used for fast and real time simulations of complex and non-linear wheel-rail contact mechanics.