Double and triple-frequency synchronization and their stable states of the two co-rotating exciters in a vibrating mechanical system

摘要

In this paper the double and triple-frequency synchronization of the two co-rotating exciters, in a far super-resonant vibrating system, are analyzed by theory, numeric, simulation and experiment. The motion differential equations of the system are given firstly. The theoretical conditions of implementing double/triple-frequency synchronization, are deduced by introducing the asymptotic method and average method, and the stability conditions for the corresponding synchronous states are verified to satisfy Routh-Hurwitz criterion. Based on the theory results, the stable states of the system are qualitatively discussed in detail by numeric, which is further examined by the following simulations and experiments. It is shown that, the stability of the system is mainly determined by the stability ability coefficient (SAC) depending on a key dimensionless structural parameter (KDSP), and the KDSP is a ratio between the distance from rotational center of each exciter to centroid of the system and its equivalent rotational radius. Under the precondition of the two identical exciters, the phase difference between the two exciters for double/triple-frequency synchronization, is stabilized in the vicinity of zero when SAC is greater than zero; otherwise, it is stabilized in the neighborhood of Pi. The present work can provide a foundation for designing some new types of vibrating machines characterized by two frequencies.