Rolling friction for hard cylinder and sphere on viscoelastic solid

TL;DR

This paper presents a theoretical and experimental study of rolling friction for cylinders and spheres on viscoelastic solids, highlighting the non-linear dependence on load and velocity, and proposes using friction measurements to characterize viscoelastic properties.

Contribution

The paper provides a new theoretical model for rolling friction on viscoelastic solids and validates it with experiments, extending understanding of frictional behavior in rubber-like materials.

Findings

Rolling friction coefficient depends non-linearly on load and velocity.

Theoretical results agree with Hunter's exact solution for a single relaxation time.

Experimental data align well with the theoretical model, suggesting new ways to measure viscoelastic properties.

Abstract

We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute an useful way to determine the viscoelastic modulus of rubber-like materials.