Synchronization investigation on space vibration system driven by two vibrators with arbitrary direction axes

Abstract

To reveal the more inclusive vibration synchronization mechanism, investigation is extended to space vibration system driven by two vibrators with arbitrary direction axes. Based on a reliable method for changing the relative rotation direction of vibrators, Lagrange dynamic equation is introduced to obtain vibration responses of the constructed model. Then the electromechanical coupling torque is analyzed through considering load generated by mechanical structure into two vibrators, and synchronization stability is explored by Lyapunov with Kronecker product theory. Next, some important numerical calculations are conducted to analyze synchronization characteristics further. Finally, corresponding experiments are organized to verify the reliability of theoretical and numerical analysis, and the feasibility of detection method through vibration testing displacements for phase differences (PDs) in unstable and stable states is discussed. Results indicate that in arbitrary space or plane patterns a better universality of this study is possessed whether or not identical rotation directions of two vibrators; the PDs can be accurately obtained from vibration displacements.