Theoretical and numerical studies on stability of multiple eccentric rotors uniformly distributed along the circumference of two rigid bodies

This paper aims at studying synchronization, stability and motion characteristics of a new generalized dynamical model with two rigid bodies (RBs), driven by multiple eccentric rotors (ERs) uniformly distributed on the circumference of two different RBs. Using Lagrange's equation, the motion differential equations of the system are deduced. The generalized theoretical analytical expressions of the criteria for implementing synchronization and stable operation of multiple ERs are obtained. Based on the above theoretical results, and taking the present dynamical model with six ERs for example, numerical qualitative discussions are given to deeply reveal the stable states and motion characteristics of the system in different resonant regions. The simulations are further carried out quantitatively, which verifies the validity of the above theoretical and numerical qualitative results. It is shown that, in the sub-resonant state with respect to the natural frequency of the main vibrating system, the stable zero phase difference between arbitrary two ERs on each RB can be achieved, in this case, the relative circular motion of two RBs with anti-phase is realized. This paper can lay a foundation for designing some new types of large scale high-frequency vibrating ball mills with high supply power.

Automated summary

This paper studies a new generalized dynamical model driven by multiple eccentric rotors, and reveals the stable states and motion characteristics of the system in different resonant regions through qualitative and quantitative analysis.