Upon the relationship between rolling friction and sliding friction

Abstract

Whereas for sliding friction the Amonton-Coulomb law clearly states the proportionality between the friction force and the normal force, the rolling friction torque and normal force dependency is assumed linear in some references and nonlinear in others. The coefficient of rolling friction can be obtained using various pendula, based on the assumption of linear dependence between the rolling friction torque and normal force. The theoretical models lead to a linear decrease of angular amplitude (confirmed experimentally for the dry sliding friction case) while the experimental damping of amplitude is nonlinear for any of the employed pendula. The basis for finding the rolling friction coefficient is the equality between the theoretical and experimental slopes of the decreasing angular amplitude of the pendulum. Due to this nonlinearity, the value of the coefficient of rolling friction depends on the launching amplitude of the pendulum. In the present paper the equation of motion of the evolvent pendulum is obtained based on the hypothesis that the dependency of resistant torque on normal force is a power law. Experimental tests performed with the new heavy pendulum have confirmed a nonlinear, exponential attenuation of angular amplitude. Thus, finding the coefficient of rolling friction for the least favourable situation was aimed. This happens when the launching amplitude of the pendulum has the highest possible value and occurs when the ratio between the tangential force and the normal force equals the coefficient of sliding friction. A technique is proposed for obtaining the critical value of the coefficient of rolling friction.