Rolling friction of a viscous sphere on a hard plane

¹ Moscow State University, Physics Department - Moscow 119899, Russia
² Humboldt-Universität zu Berlin, Institut für Physik Invalidenstraße 110, D-10115 Berlin, Germany

Received: 12 February 1998
Accepted: 15 April 1998

Abstract

A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of the sphere material. The relation obtained refers to the case when the deformation of the sphere ξ is small, the velocity of the sphere V is much less than the speed of sound in the material and when the characteristic time is much larger than the dissipative relaxation times of the viscoelastic material. To our knowledge this is the first “first-principle” expression of the rolling friction coefficient which does not contain empirical parameters.