The Effect of a Tangential Contact Force Upon the Rolling Motion of an Elastic Sphere on a Plane

Abstract

Abstract The motion and deformation of an elastic sphere rolling on an elastic plane under a normal contact pressure N have been studied for the case where a tangential force T is also sustained at the point of contact. Provided that T < μN (μ = coefficient of friction), the sphere rolls without sliding but exhibits a small velocity relative to the plane, termed “creep.” Following the work of Mindlin and Poritsky, it is shown that creep arises from slip over part of the area of contact, and further, that this slip takes place toward the trailing edge of the contact area. On the assumption of a locked region in which no slip occurs, of circular shape, tangential to the circle of contact at its leading point, surface tractions are found which satisfy the condition of no slip within the locked region and are approximately consistent with the laws of friction in the slip region. The variation of creep velocity with tangential force is thereby determined. Experimental measurements of the creep of a steel ball rolling on a flat steel surface are in reasonable agreement with the theoretical results.