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

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.

Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems

The problem is motivated by observations of a rotor-pendula system, which derived from a new shale shaker. To grasp the dynamic characteristics of the shale shaker, the key research is exploring the synchronous mechanism for the system, since synchronous state between rotors is closely related to the dynamic characteristics of the system. In this paper, the dynamic equation of the rotor-pendula system is firstly derived by applying Lagrange’s equations. Through Laplace’s transformation method, the approximate responses of the system in synchronous state are obtained, which is determined coupling coefficients and synchronous state of the system. Then, the synchronous balance equation and the stability criterion of the system are obtained with Poincaré method on which stable phase difference and synchronous behavior can be ascertained. To verify the correctness of the theoretical analysis, numerical simulations are implemented by Runge–Kutta method, and it is shown that the synchronous behavior is determined by the geometry parameters, coupling coefficients, and rotor rotation direction.