Analyses of synchronous motion characteristics for a two-rigid-body vibration system with three co-rotating eccentric rotors mounted on two different rigid bodies

Abstract

In this paper, the synchronous motion characteristics of a two-rigid-body vibration system with three vibrating motors installed on two different vibrating rigid bodies are investigated. First, differential equations of the system are deduced according to the Lagrange equation, and their steady-state solutions are obtained. Next, the synchronization theories of the system are obtained via the average method, and the stability conditions are deduced via the Lyapunov’s stability theory. The structural parameters of the system are brought into the theoretical derivation results. Finally, the theory and simulation are mutually verified by the electromechanical coupling simulation model. The results show that the system can implement stable synchronous motion when the system parameters satisfy the synchronization and stability conditions. In the resonance region (i.e., $k_{y2}=100000\mathrm{N}/\mathrm{m},k_{y1}\in \left[\mathrm{100000,2000000}\right]\mathrm{N}/\mathrm{m}$ or $k_{y2}=500000\mathrm{N}/\mathrm{m},k_{y1}\in \left[\mathrm{100000,2000000}\right]\mathrm{N}/\mathrm{m}$ ), the support spring stiffnesses $k_{y1}$ and $k_{y2}$ significantly affect the synchronous motion characteristics of the system. The phase differences $2{\alpha }_1$ and $2{\alpha }_2$ bifurcate in the regions R2, R5, and R6. However, the bifurcation phenomena have almost no effect on the steady-state responses. The parameters in the regions R3, R4, R7, and R8 are of great values in engineering applications.

Graphical Abstract