Theoretical, numerical and experimental studies on multi-cycle synchronization of two pairs of reversed rotating exciters

Abstract

With the rapid development of science technology in vibration utilization engineering fields, more and more high demands are proposed to improve the functions and performances of machines, especially some new types of large scale vibrating equipments with linear motion driven by two different driving frequencies, designed by the multi-cycle synchronization theory of multiple exciters, have been the urgent desires for engineers and scholars. In the present work, taking a dynamical model driven by two pairs of reversed rotating exciters in a far super-resonant vibrating mechanical system for example, the multi-cycle synchronization and stability of the system are studied in detail by theory, numeric and experiment. Firstly the differential equations of motion of system are deduced by Lagrange equations. Introducing the asymptotic method, the theoretical conditions of implementing foundation frequency (1:1), double-frequency (1:2) and triple-frequency (1:3) synchronization among the two pairs of exciters, are obtained, as well as the stability conditions corresponding to the synchronous states based on the Routh-Hurwitz criterion. The synchronous stable regions of the system are numerically discussed. Simulations and experiments are carried out to further verify the feasibility of the used theory method and the obtained results. It is shown that, for the foundation frequency, double-frequency or triple-frequency synchronous states, under the precondition of satisfying the conditions of multi-cycle synchronization and stability, the phase differences among the two pairs of exciters, can be stabilized in the vicinity of zero of the Region II, in this case, the linear motion of the system with two different driving frequencies can be realized, which is of great significance in engineering.