Modeling of Velocity-Dependent Rolling Friction in Linear Microball Bearings

Earlier experimental results showed the dependence of rolling friction on the relative velocity in microfabricated linear microball bearings. In this paper a viscoelastic model is proposed to elucidate the observed phenomenon. Inspired by the work of Poschel et al., we model the bearing groove, on which a microball rolls, as a continuum of mass-spring-damper elements. Given a rolling velocity, the penetration depth of the ball into the groove plane is determined through an implicit equation of force balance and can be solved for by the fixed-point iteration algorithm. The mechanical power required to actuate the continuum of mass-spring-dampers is then calculated, from which the rolling resistance (friction) is derived. The agreement of numerical results with experimental ones shows that the proposed model is able to capture essential characteristics of ball-groove interactions in the bearings.