Study of the effect of the spiral geometry on wheel/rail contact forces

Abstract

Spiral sections are used in the construction of railroad tracks in order to achieve a smooth change in the curvature. In order to satisfy the kinematic conditions at the position, velocity, and acceleration levels in railroad vehicle dynamics computational algorithms based on the constraint contact formulations; third-order derivatives of the wheel/rail contact constraint functions with respect to the wheel and rail geometric surface parameters must be evaluated. Discontinuities in these higher derivatives can produce jumps in the wheel/rail contact forces at the spiral entries and exits. This paper develops a simple procedure that can be applied online to ensure that the curvature and its derivative of the rail space curve are continuous at the spiral entries and exits. Because continuity of the space curve geometric variables does not ensure continuity of these variables on the rail surface, the effect of the proposed procedure on the contact forces is examined. The constraint and elastic wheel/rail contact formulations are first reviewed in order to show the degree of continuity required and the basic kinematic conditions used to search online for the wheel/rail contact points. The rigid track geometry is described using the absolute nodal coordinate formulation (ANCF), which employs a geometric description that ensures the continuity of the position and gradient vectors at the track nodes. In order to ensure the continuity of the curvature vector and its derivative at the intersection of the spirals with the tangent and curve segments, a set of linear conditions are developed and solved online, allowing for implicit elimination of track nodal variables. These conditions are not considered as kinematic constraints imposed on the system motion since they are mainly used to improve the rigid track geometric description and do not involve the system generalized coordinates or their time derivatives. The procedure described in this investigation does not require making changes in the description of the track geometry and does not require the use of higher order derivatives of the track node angles in order to achieve the desired degree of continuity. Because higher degree of continuity achieved for the rail space curve does not ensure a similar degree of continuity on the surface where the wheel/rail contact occurs; the effect of the change of the degree of continuity of the space curve at the spiral entries and exits on the rail surface geometry is also discussed in this paper. The results presented in this study show that the proposed procedure can lead to improvement in the wheel/rail contact force results in some simulation scenarios. The results, obtained using the proposed procedure, are compared with the results obtained using local mesh refinements.