For vibrating screen machinery, the granular block material can be quickly loosed and fully layered when entering the screening equipment if it is placed an exciting system with low frequency and large amplitude at the feeding end. A high frequency with small amplitude exciter is set near the discharging end. It can make the material appear high-frequency vibration and reduce the phenomenon more effectively that the granular material blocks the screen hole. Because of this, taking the elliptical vibrating screen system as our research object, the concept of compound nonlinear screening trajectories is proposed from the two times frequency vibrating synchronization system driven by three exciters. Firstly, the differential motion equation of the system is obtained by establishing the Laplace equations of the system. Then, by introducing small parameters and dimensionless time parameters, the first-order differential motion equations of the driving motor of the exciters are obtained, the second approximate motion equation of the system is obtained by applying the principle of the average method. Based on this, the criterion for the system to achieve the multi-frequency vibration synchronization state and the phase difference relations among the exciters at steady-state are drawn out by taking the two times frequency vibration synchronization as an example. Meanwhile, the stability criterion of the vibration synchronization state of the system is analyzed. Besides, the functional relation that the location and the rotational direction of the exciters influence on the phase difference of the exciters are given out. Finally, the correctness of the theoretical research is verified by experimental research; the prospect of engineering application of the system is discussed.

Introduction

Since the 1950s, Blehman has installed two inertial exciters driven by two motors on a single vibration body. He has found that two exciters can rotate in an asynchronous way when some conditions are met. Through theoretical analysis, he has explained the physical mechanism of vibration synchronization of the mechanical system, gradually formed the theory of vibration synchronization and self-synchronization of the mechanical system [1], [2]. The academic definition of synchronization in the sense of kinematics and dynamics is also given by Blekhman [3], [4]. Based on this theory, the synchronization machinery of traditional rigid transmission (e.g., gear transmission) and flexible transmission (e.g., chain or belt transmission) are gradually reduced, replaced by vibration synchronization equipment driven by two or more exciters. They enable the vibrating system to achieve linear motion trajectory, elliptical motion trajectory and other kinds of nonlinear trajectories through vibrating synchronization. Various motion trajectories of the body of the vibrating system mainly depend on the stable phase differences between the eccentric blocks of the exciters when the system operates at the steady-state. Usually, when the phase differences between the exciters are close to 0 degrees, the system obtains in-phase vibration synchronization.