Validation of Nonlinear Dependence of Rolling Friction Moment on the Normal Force for Elastic Materials

Analogous to the Amonton-Coulomb relation, which states the linear dependency between the dynamic sliding friction and the normal reaction, the rolling friction moment is commonly accepted as proportional to the normal reaction in a concentrated point contact. This hypothesis persists since it gives simple dynamic models and also due to difficulties met in experimental estimations of the rolling friction torques. Recent theoretical studies proved that this dependency is nonlinear even for elastic materials. A special rotor is designed, with an adjustable position for the center of mass but with constant mass and constant axial inertia moment. The pure rolling motion of the rotor on an inclined controlled small slope is studied. The angular acceleration of motion is theoretically deduced, assuming that the rolling friction torque is proportional to the normal force raised at a certain power. The deduced theoretical dynamic model evidences the influence of the eccentricity of the rotor upon the acceleration. For the particular case of linear dependency-the exponent of the power equal to one, the law of motion is independent of the configuration of the rotor. Experimental tests were made using the rotor constructed according to the theoretical model. For two positions of the center of mass, the experimental law of motion on the inclined plane is established by a non-contact method and the two different laws obtained to validate the nonlinear dependence rolling friction torque-normal force. The paper validates in an experimental manner the considered nonlinear assumption. The experimental tests concerning the microtopography of the contacting surfaces reveal that the hypothesis required by Hertzian theory, namely smooth contacting surfaces, is not satisfied. Thus, the distribution of pressure on the contact area does not obey the Hertzian semi-ellipsoidal distribution and further experimental tests are required for quantitative findings on the rolling friction torque-normal force relationship.