Theory of Rolling Friction for Spheres

A theory of rolling friction featuring the importance of elastic hysteresis losses is presented. A simple model of retarded elasticity is chosen to represent the physical properties of the material. A prediction resulting from the theory is that the coefficient of friction for a relatively hard sphere rolling on a softer base material should vary with speed so as to go through a maximum. This relationship resembles closely the variation of mechanical loss with frequency. The results are not restricted to rolling but also apply to well-lubricated sliding where shearing forces have been minimized. Although the theory is developed for a material with idealized physical properties, it nevertheless affords a basis for comparing real materials and for predicting their frictional properties in cases where deformation losses are predominant.