Rolling Friction: Comparison of Analytical Theory with Exact Numerical Results

We study the contact mechanics of a smooth hard cylinder rolling on a flat surface of a linear viscoelastic solid. Using the measured viscoelastic modulus of unfilled and filled (with carbon black) nitrile rubber, we compare numerically exact results for the rolling friction with the prediction of a simple analytical theory. For the unfilled rubber, the two theories agree perfectly while some small difference exists for the filled rubber. The rolling friction coefficient depends nonlinearly on the normal load and the rolling velocity.