Theoretical studies of self-synchronous transmission mechanism in a far super-resonant vibrating system actuated with four central symmetry motors

Different from straight-line or circular synchronization motion, the elliptical screening trajectory among multiple exciters can effectively improve the material transport ability and separation efficiency of vibration system, when the drilling slurries are stuck into screen meshes. Therefore, the self-synchronous theory of vibration system driven by four exciters with circular symmetry arrangement is proposed in this paper. Firstly, the mathematical model of the mechanical device actuated with multi-rotor is established by Lagrangian method. Secondly, combining with integral average method and Routh–Hurwitz principle, the self-synchronization condition and stability criterion of achieving constant phase-difference motion are revealed. Subsequently, the influence of different structural parameters on the dynamical responses of the system is discussed quantitatively. Finally, the theoretical derivation and the numerical analysis related to the mechanical model are further verified by establishing electromechanical coupled simulation model in far super-resonance state. Meanwhile, the dynamical characteristics of performance parameters under different working conditions are explained, and the feasibility of circular symmetrical synchronization theory is proved. The research achievements not only provide a theoretical foundation for the design and optimization of new vibration machinery with elliptical trajectory, but also have important practical guidance significance for solving common problems in other material screening fields.