Rolling friction of a viscous sphere on a hard plane

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 $\xi$ is small, the velocity of the sphere $V$ is much less than the speed of sound in the material and when the characteristic time $\xi /V$ 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.

6 pages, 2 figures

References in corpus (2)

• A model for collisions in granular gases
• Coefficient of normal restitution of viscous particles and cooling rate of granular gases

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