Study on stability of self-synchronous far-resonant vibrating system of two eccentric rotors considering material impact

Abstract

The self-synchronizing far-resonant vibrating system of two eccentric rotors is widely used in petroleum, mining and food industries, and its motion stability is affected by material impact. However, the synchronous characteristics and stability of this kind of the system are studied rarely. Based on the background, a simplified mechanical model of the selfsynchronous vibrating system driven by two eccentric rotors considering material impact is proposed. Firstly, the differential equations of motion about the system in non-collision and collision phase are established by using Lagrange equation and the theorem of momentum. Then, the section of Poincare maps and linearization matrix at the fixed point are solved. Finally, the dynamic behavior of material and system is analyzed, and then the change characteristics of the phase difference of the two eccentric rotors are revealed by numerical simulation. It can be concluded that the motion forms of the system and the rules of abrupt change about the phase difference evolve from periodic variation into chaotic state with the mass ratio of material to vibrating body increasing.