Self-balance characteristics of the vibrating system with four split-driving vibrators

The isolation vibration design for a self-synchronous vibrating system is challenging because the realization of the system’s function depends on itself vibrating. We propose a method to solve the problem of vibrating isolation of the vibrating system, which is the realization of the self-balance function of the system from the perspective of self-synchronization. In the current study, a vibrating system with five rigid frames (RFs) driven by four vibrators is proposed to study its synchronization, stability, and self-balance characteristics. Utilizing the average method and Routh–Hurwitz stability criterion, the theoretical conditions of synchronization, stability, and self-balance of the system are obtained, respectively. Based on these three conditions, the stability and self-balance characteristics of the system in the different resonant regions are qualitatively analyzed in numeric, and the reasonable parameters matching principle of the system in realizing the synchronous stable operation with the function of self-balance is defined. A series of numerical simulations and experiments are further given to examine the correctness of the theoretical derivation and the rationality and practicability of the design of the mechanical system. The present work can be applied to the design of a new kind of vibrating machine, in which the working rigid frames can work with their circular motion trajectory, and the isolated rigid frame can remain stationary with around zero amplitude.