Contribution of rolling resistance to the drag coefficient of short-span cylinders freely rolling on a rough inclined surface

Abstract: This study examines the contribution of rolling resistance to the drag coefficient of finite-span cylinders rolling freely without slipping on a rough inclined surface in a quiescent fluid. Experiments are performed to obtain the variation of the time-mean drag coefficient against the varied roughness of the panel. The total drag is decomposed into a fluid drag and drag due to rolling resistance. The fluid drag is estimated by combining the predictions of lubrication theory for the gap-dependent drag with numerical simulations for the wake drag. This model provides reasonable predictions of the drag coefficient for small roughness. However, we show that the fluid drag underestimates the measured drag coefficient, particularly for large surface roughness. We propose that this larger drag is due to the added effects of rolling resistance. Rolling resistance is modelled as a resistive torque that opposes the cylinder's motion. We show that the rolling resistance coefficient can be predicted using the non-dimensional peak roughness of the panel. Additionally, the rolling resistance coefficient increases with the cylinder's non-dimensional downslope velocity. Finally, an empirical relationship between rolling resistance, peak roughness, and downslope velocity is obtained. Keywords: lubrication theory, surface roughness, rolling resistance, short-span cylinders