Measurement and Modeling of Dynamic Rolling Friction in Linear Microball Bearings

In prior work of the authors and co-workers, a vision-based system was developed for characterizing the tribological behavior of silicon-micromachined linear microball bearings. Plain difference methods introduce amplitude and/or phase distortion in computing the derivative signals (e.g., velocity and acceleration) based on the position snapshots. In this paper frequency-dependent amplitude and phase compensation algorithms are developed for both the forward difference and the central difference methods to retrieve without distortion the friction and the relative velocity between bearing elements. Processing of experimental data with these techniques reveals nonlinear, viscous frictional behavior in the bearing. A viscoelastic model based on a continuum of mass-spring-damper elements is then proposed for the ball-groove interaction. Numerical results show that this model captures the nonlinear velocity dependence of the rolling friction observed in experiments.