The Stationary Motion of a One-Axle Vehicle Along a Circular Curve with Real Rail and Wheel Profiles

Abstract

In this paper, we present a theory on the stationary motion of a one-axle railway vehicle along a circular curve in the presence of single- or double-point contact. The rail and the wheel profiles may be either stylized or real and as an example we take the profile combination UIC60 1:40 S1002. The mathematical model of the system is based on De Pater's first-order theory [1]. The geometrical contact problem between wheel and rail is solved by using a modified Newton-Raphson procedure. Both the cases with and without friction are considered. When friction is present, the non-linear Kalker creep law [6, 7] is used to describe the physical contact. For various values of the friction coefficient, the cant angle and the curvature of the track, the contact forces are presented as functions of the velocity parameter C v = V 2 / V 2 eq, where V is the velocity of the vehicle and V eq is the equilibrium velocity of the frictionless case. For the case of stylized profiles in which both the wheel treads and the wheel flanges are conical, and the rail cross sections are circular, we have determined the velocity range with single point contact in dependence on the friction coefficient, the conicity of the tread, the curvature of the track and the cant angle.