# Graduate School in Nonlinear Science

```
MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark

```

A FAST, APPROXIMATE METHOD TO CALCULATE NORMAL AND TANGENTIAL CONTACT PROBLEMS FOR WHEEL AND RAIL

by Jerzy Piotrowski
Faculty of Automobiles and Heavy Machines Engineering
Warsaw University of Technology
Warsaw, Poland

MIDIT-seminar 422

Thursday November 5, 1998, 14.00 h
at MIDIT, IMM Building 305, room 027

Abstract: A fast, approximate method to calculate contact between wheel and rail will be presented. The normal contact is calculated in one step. To calculate creep forces the FASTSIM algorithm has been implemented to non-elliptical contact region obtained by normal contact calculation. Results are compared with solutions obtained with the program CONTACT by Kalker. The performance of the method, according to numerous comparisons with the program CONTACT, is very good as far as the normal contact is concerned. Creep forces calculated with the approximate method + FASTSIM are reasonable when compared with solutions from the program CONTACT.

In many practical cases the contact area between wheel and rail is curved as it is spread over a curved section of profiles. For weakly curved contact area the methods of contact mechanics employing the half-space assumption for elasticity are used which neglect contact area curvature. Even for moderately curved contact area these methods are employed to obtain some approximation to the exact solution - which is presently not available.

It is proposed to calculate normal problem for weakly curved contact with the forementioned method but to take into account curvature of the area while calculating creep forces during rolling. To this end so-called non-dimensional rigid slip should be calculated directly for each point of the contact area using the profile data.

A derivation of the rigid slip is given which does not use the notion of the spin creepage, which is a global quantity related to so-called point of geometrical contact.

The influence of contanct curvature on creep force is presented on three examples. The first example is a steel roller rolling in the groove. The next two examples refer to railway wheel/rail. The creep forces for the last two examples have been compared with those calculated in a usual manner when one neglects the curvature of the contact area. The differences in creep forces for considered two approaches can be significant, which may be important for modelling rail vehicle-track interaction.

A demonstration computer program will be presented which allows submitting any (including drawn by hand) profile and separation data. The solution is presented graphically and shows the contact area and the distribution of tangential stresses. This program demonstrates reliability and speed of the approximate method for calculating normal contact and creep forces.