Stability and self-balancing characteristic of an internal drive vibrating system with three unbalanced rotors

Abstract

A new internal drive mechanism with four rigid frames (RFs) driven by three unbalanced rotors (URs), is proposed to investigate the stability and the self-balancing characteristic of the corresponding system in the present work. Based on Lagrange's equation, the differential motion equations of a vibrating system are deduced. Using the average method and Hamilton's principle, the criterion of synchronization for three URs and the stability criterion of the system, are established analytically, respectively. In addition, a self-balancing condition is proposed to further determine the resonance region that can achieve zero amplitude of the outer rigid frame (ORF) in theory. Dynamic characteristics of the system, including the stable states, the self-balancing ability, and the corresponding motion types of the system in different resonant regions, are qualitatively discussed in numeric. The validity of theoretical analytical results is proved by simulations and experiments. It is shown that the reasonable working points of the system should be selected in this region that the sub-resonant region for the two key natural frequencies with single-equilibrium stable operation state, in order to meet the engineering requirements.