Simplified solution for elliptical-contact problem with wear

摘要

The problem in which rigid and elastic half-spaces make sliding contact in an elliptical region is considered. The model employs the Archard law of wear in which the rate of material removal is proportional to pressure and speed of sliding. The approximate solution was developed based on the representation of the normal surface displacement due to the wear in any time moment by a polynomial function. The problem is reduced to the system of four non-linear equations with unknown rigid body displacement, the semi-axes of the contact ellipse and the ratio of the contact pressure in the contact area centre to the average contact pressure. The equations are solved numerically. Graphs are included to facilitate the numerical calculations and to illustrate the results obtained.