Multi-frequency Vibration Synchronization and Stability of the Nonlinear Screening System

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.