Self-synchronization theory of tri-motor excitation with double-frequency in far resonance system

Abstract

With the rapid development of petroleum exploitation industry, vibrating screen actuated with a single frequency is unsuitable to separate cuttings from drilling fluid, since it usually results in screen blocking. Hence, for solving the above-mentioned problem, tri-motor excitation with double-frequency in far resonance system is introduced. This paper aims to explore the self-synchronization mechanism of the proposed system. First, dynamic equation is established according to physical model of the system. Then, displacement response of the system in steady state is obtained with dynamic formulas. Subsequently, synchronous condition among the three exciters is determined by small parameters method, and criterion of synchronous stability among the three exciters is derived by Poincare-Lyapunov method. Finally, in light of the differential motion equation, Runge-Kutta principle is assigned to validate the reliability of self-synchronous theory and the stability of the double-frequency system. The results indicate that electromagnetic torques of low-frequency motors are dynamically antisymmetric in synchronous operation, and synchronous ability of the system is determined by the mass ratio among the rotors. In addition, stable phase difference among the rotors is significantly influenced by the structural parameters of the system. And this study will be helpful for the improvement of separation technology.