Synchronization and Stability of a Three Co-Rotating Rotor System Coupled with Springs in a Non-Resonance System

With the rapid development of horizontal drilling technology, the drilling fluid shale shaker (DFSS) features high capacity and high efficiency. Hence, a vibrating mechanism of a three co-rotating rotor system coupled with springs is proposed for designing large-sized and heavy-duty vibrating screens in petroleum drilling engineering. To master synchronization of the vibrating system, the dynamic equations of three corotating rotors coupled with springs are first developed based on Lagrange’s equations. Second, synchronous conditions of the system are derived based on the average method, and its stability criterion is obtained by adopting Hamilton’s principle. Furthermore, the influences of various factors, including positional parameters of three motors, stiffness coefficient of the springs and frequency ratio on synchronization behaviour, are numerically analysed in the steady state. Additionally, the Runge–Kutta algorithm with adaptive control is employed to build an electromagnetic coupling model, and the relationships between the synchronization state of the system and its mechanical-electrical coupling characteristics are investigated. Finally, an experimental prototype is designed to validate the theory and numerical analysis. The research result shows that the in-phase synchronization of three co-rotating rotors coupled with springs is easy to implement with the selection of a sufficiently large stiffness.