Rolling friction of a viscous sphere on a hard plane

TL;DR

This paper derives a fundamental, parameter-free expression for the rolling friction coefficient of a viscoelastic sphere on a hard plane, linking it to material properties under specific conditions.

Contribution

It provides the first first-principle continuum-mechanics formula for rolling friction of a viscoelastic sphere without empirical parameters.

Findings

Derived a parameter-free expression for rolling friction coefficient.

Linked friction to viscous and elastic constants of the sphere.

Applicable under small deformation and low velocity conditions.

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.