Inverse structural modification for improving the design of harmonic excitation forces in underactuated vibration generators

In this paper a novel method to shape the harmonic excitation forces in underactuated vibrating systems is proposed. The idea is to handle simultaneously the optimal design of both the feedforward harmonic forces exerted by the actuators, and the inertial and elastic parameters of the mechanical system. The theory is developed with reference to a general linear-time-invariant underactuated vibrating system with sparse input matrix. The method is validated through the model of a simplified linear vibratory feeder often employed in packaging lines to convey parts. A uniform flow of the products obtained through a uniform vertical displacement of the flexible tray, is required. The feeder is actuated by three independent harmonic forces. Lumped masses and springs, as well as the amplitude of the harmonic forces, are the design variables aimed at compensating for the tray flexibility. The method outperforms the typical heuristic approaches used in this kind of applications and here adopted as benchmarks.