Dissipative function of coulomb friction on elliptical contact area

Abstract

The problem of calculation of the moduli of the resultant vector and the basic moment of the forces of the dry rolling friction of a solid body against a rough plane surface in the presence of spinning around a vertical axis is solved in quadratures. The elementary forces of sliding friction are directed opposite to the points of the elliptical contact area fulfilling plane motion. The friction coefficient is accepted to be independent of velocity. The proposed method of computing the resultant vector and the basic moment of friction forces on the elliptical contact area makes it possible to find with a preset accuracy the forces and the friction torque in the contact problems by using numerical procedures. In particular, it is used to determine the tangential forces arising during the motion of a rail vehicle. With increasing vertical load on the wheels, the contact spot area in which the friction forces of sliding play the main role becomes larger. The proposed method can also be used with some modifications, e.g., by introducing a corrective factor, to calculate the contact spots having a configuration different from elliptical but restricted by a closed curve.