Use of Hypocycloidal Motion in the Study of Rolling Friction

摘要

The paper proposes a device for finding the coefficient of rolling friction using a sphere in contact with the inner surface of a ring that rotates about a horizontal axis. The motion of the ball is characterized by the fact that for a stipulated rotation speed of the ring the centre of the ball executes a damped oscillatory motion and at equilibrium the centre of the ball is situated on different vertical than the one the centre of the ring is positioned. It is assumed that this feature is produced by the rolling friction torque that is proportional with the normal pressing force and the nonlinear differential equation of motion is obtained for the intended dynamic model. By the integration of the equation of motion there are confirmed the oscillatory motion of the ball and the eccentric equilibrium position and it is found a dependency of equilibrium position on the coefficient of rolling friction.