Spatial synchronization behavior of vibration system with tri-motor excitation

The existing research of vibration synchronization among multiple rotors is mainly concentrated on plane vibration system. In this paper, the synchronization mechanism of the spatial vibration system actuated with tri-motor rotating in identical direction is studied. Firstly, the dynamic model is established, and the motion differential equations are deduced via Lagrange formulation. Then, small parameter average method is applied to explore the synchronization condition; Lyapunov equation and Routh-Hurwitz criterion are introduced to analyze the synchronization stability. Finally, the influence of the system parameter on synchronization is discussed by numerical calculation, and the electromechanical coupling simulation based on Matlab/Simulink is given to confirm the reliability of the theoretical analysis. The research result indicates that the vibration synchronization is affected by the horizontal distance between two coaxial motors, the installation height and the masses of three eccentric rotors (ERs), but the influence of the horizontal distance between coaxial motor and noncoaxial motor on synchronization is small.