Theory of Frequency Captured of Eccentric Rotor by Vibration Environment with Same Direction

Aiming at the frequency synchronization phenomena of oscillating or rotating bodies, this paper proposes a novel solution to address the self-synchronization problem of vibration systems. An integral mean method with small parameters and periodic coefficient (IMM-SPPC) is proposed, which converts the relative motion of the electrically driven eccentric rotor and the vibration environment into a second-order periodic coefficient differential equation. Through the calculation of the equilibrium point of the second-order periodic coefficient differential equation and the study of its stability, the synchronization criterion and the stability criterion of the eccentric rotor and the vibration environment are deduced. The simulation results show the validity of the deduced synchronization criterion and stability criterion. The proposed IMM-SPPC provides a new way for studying vibration synchronization.