Numerical Procedure for Solving the Non-Linear Equations of the Geometrical Contact between Wheelset and Track (Revised)

摘要

In 1988, De Pater has derived the exact and approximate geometrical compatibility equations for a wheelset moving along a straight track. On the base of his so-called first-order theory the authors drew up a computer program which for the symmetrical case can be employed to obtain numerical solutions of the approximate equations, which are still strongly non-linear, by the Newton-Raphson method. The program has been applied to calculate the possible contact positions between the wheelset and the track for given values of the rolling and yaw angles. It turns out that in certain cases there exist two contact points. A searching method is used for finding such positions. A comparison with the results published by Hobbs in 1975 shows good agreement.