The Influence of Elastic Deformation upon the Motion of a Ball Rolling between Two Surfaces

Abstract

When a ball rolls between two surfaces, in general, a tangential contact force and a relative angular velocity of spin are present at each point of contact. Both these actions give rise to tangential frictional tractions transmitted across the contact surface which are shown to result in a velocity of creep of the ball in a direction perpendicular to the nominal rolling path. The magnitude of the creep velocity depends critically upon the magnitudes of the tangential force and the velocity of spin. If these actions are small there is negligible slip between the contacting surfaces and the creep motion is predominantly a function of the elastic properties of the materials. At larger spin velocities slip extends over a greater proportion of the contact area and the creep is influenced by the frictional properties of the surfaces. Creep measurements have been made over a wide range of conditions of rolling. The results are reduced to non-dimensional form, in terms of two parameters expressing the effect of tangential forces and spin respectively. The resistance to rolling has been measured and is shown to control the axis about which the ball rolls. The detailed mechanism of the rolling process is discussed.