Analysis of part motion on a longitudinally vibrating plate

We analyze the dynamics of part motion for a novel type of planar parts feeder consisting of a longitudinally vibrating flat plate and a part placed on its surface. For each vibration cycle, the plate's velocity is held positive (forward motion) for a longer time than it is held negative (backward motion). This type of asymmetric vibration combined with the nonlinear nature of Coulomb friction causes the part to accelerate along a straight line to a terminal velocity called the "feed rate". The average force exerted by the plate on the part is shown to be proportional to the latter's deviation from the feed rate. In other words, the part behaves as if it were immersed in a forward moving viscous fluid. Expressions for the feed rate and viscosity constants are derived with respect to various physical and control parameters. Rigid-body dynamic simulation results are shown to be in good agreement with the analysis.