Investigation of the finite element method for computing wheel/rail contact forces in steady curving

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Virginia Polytechnic Institute and State University


The understanding of rail vehicle steady-state and dynamic curving has increased substantially in the last few years. Contemporary curving models include such nonlinear effects as two-point contact, creep force saturation, and rail flexibility. The usual approximation concerning the contact geometry is that the Iocalized wheel and rail curvatures at the center of the contact patch are constant throughout the contact patch. This approximation allows computation of contact stresses using Hertzian theory, and it allows the computation of contact patch forces using one of Kalker’s theories.

In vehicle curving, contact usually occurs at or near the wheel flange, where the wheel/rail contact geometry is non·Hertzian. Furthermore, after being in service for some time, the wheel and rail profiles provide non·Hertzian geometry due to wear. Both of these effects tend to invalidate the assumption of Hertzian contact geometry in the contact region.

This work uses a generic wheelset model which is the basic component of any rail vehicle model. The wheel/rail interaction is modelled using the finite element method. The wheel is generated as a surface of revolution of its tread profile, and the rail is generated as an extrusion of the rail head profile. Three—dimensional contact elements are used to characterize the wheel/rail interface. A simple stick/slip friction model is used wherein relative motion is permitted if the tangential force exceeds the adhesion limit, and no relative motion occurs otherwise.

The results show that the finite element method was successfully used to solve the static contact problem. Both Hertzian and non-Hertzian contact problems were anaIyzed correctly. However, the application of the finite element method to the rolling contact problem was not completely successful. The finite element method results for tangential contact forces were about 25 percent lower than forces predicted by Kalker’s theory. Recommendations for extending the analysis to solve the rolling contact problem are made. The report includes a derivation of the wheelset steadystate equations of motion, as well as a solution algorithm for the nonlinear, algebraic equations.