Friction-Force Model for a Ball with Predisplacement of Rolling on a Rough Surface

A study was conducted to propose a model of friction forces for a ball taking into account the predisplacement effect. The model represented the elastic displacement of one body of the friction pair with respect to another under the action of a tangential force. It disappeared with elimination of the indicated external force. It was established that the direct proportionality between the displacing force and the displacement existed only at the initial stage of displacement in the sliding, rolling and spinning friction. Additional relations for the static and dynamic components of the rolling-friction torque and the similar components of the spinning-friction torque were introduced in which the predisplacement effect (PDE) was taken into account in the equations of the ball motion with sliding and spinning friction.