Synchronization behavior of triple-rotor-pendula system in a dual-super-far resonance system

Abstract

In this paper, a novel design for vibrating screens, called the triple-rotor-pendula system, is presented in a dual-super-far resonance system, which makes it possible to produce wanted vibrations with self-adjustable of the synchronization state between unbalanced rotors. To grasp the synchronization characteristics of the system, the dynamics equation of the triple-rotor-pendula system is primarily derived by adopting Lagrange’s equations. Next, the displacement responses of the system in steady state are obtained by Laplace’s transform method. Meanwhile, considering the average method with revised small parameter, the synchronization implement of the system is ascertained on condition that the absolute values of residual electromagnetism torques between two arbitrary motors are less than or equal to their load torque differences. Then, according to Routh–Hurwitz theorem and generalized Lyapunov equation, the criterion of synchronization stability of the system is obtained. Finally, the simulation computations confirm the results of analytical investigations, which show that the theoretical analysis for the synchronization behavior of the triple-rotor-pendula system is feasible. It can be known that the synchronization state of the system is influenced by mass ratio coefficients, structure parameters, rotating directions, and frequency ratios.