Periodic Rolling and Bumping

Abstract

We consider a sphere that rolls down an inclined corrugation of identical, frictional circular cylinders in contact. We assume that the motion is a periodic succession of rolling and bumping that results in a velocity that is, on average, steady. We use balances of force and moment and impulse and momentum change to calculate the instantaneous and average velocities, the tangential and normal contact forces, and their ratio in rolling regimes that involve no sliding, some sliding and a transition between these at contact. We compare the predictions for the steady average velocity versus the inclination for different sphere to cylinders radii ratio and the predictions for the angle of inclination versus the radii ratio for stopping, initiation of sliding and loss of contact with the results of numerical simulations.