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