Integrated Force Shaping and Optimized Mechanical Design in Underactuated Linear Vibratory Feeders

This study proposes a method to improve the feeding speed in an underactuated and flexible linear vibratory feeder through the simultaneous synthesis of the optimal excitation forces and the tuning of the mechanical design. The target is to increase the flow of the parts by ensuring uniform displacements along the tray with the prescribed throw angle, despite the relevant tray flexibility. First, a multi-DOF (degrees of freedom) analytical model of the underactuated feeder is formulated in term of actuated and unactuated coordinates. Hence, the subspace of allowable motion is computed, to highlight the relation between the achievable displacements and the physical parameters of the system (mass, stiffness and force distribution matrices and excitation frequency). Then, such subspace is optimized through dynamic structural modification where parametric sensitivities are adopted to select the structural modifications that enable to reduce the actuation effort. Once the mechanical design has been optimized, the optimal harmonic forces are computed through an ad-hoc inverse dynamics algorithm, defined “force shaping”. Finally, a multibody model developed in MSC Adams is used to evaluate the flow of the parts over the feeder. The improved mechanical design of the system together with the shaped forces evidence the improved system performances with reduced actuation forces.