Stability and motion characteristics in a vibrating system with five rigid frames driven by two counter-rotating exciters

Abstract

A new dynamical model with five rigid frames (RFs), driven by two counter-rotating exciters, is proposed to explore the synchronization, stability, and motion characteristics of the system in this paper. The motion differential equations and the corresponding responses of the system are given firstly. Using the average method, the average torque balance equations for the two exciters are deduced. According to the relationship between the difference of the dimensionless effective output electromagnetic torques for the two motors and the coupling torques of the system, the theory condition of realizing synchronization is obtained. Based on the Hamilton’s theory, the theory condition of stability of the system is deduced. The stability and motion characteristics of the system for different resonant regions are qualitatively discussed in numeric, including the stable phase difference of the two exciters, relative phase relationships among the five rigid frames, amplitude-frequency characteristics, stability coefficients, and the effective load torque between the two exciters. Simulations are carried out to further quantitatively validate the feasibility of the above theoretical and numerical qualitative results. It is shown that in engineering the reasonable working points of the system should be selected in Region II, only in this way, can the synchronous and stable relative linear motion of the system with the zero stable phase difference in vertical direction be realized, and in this case, the vibrations of the four inner rigid frames (IRFs) in the horizontal direction are compensated with each other, and the energy is also saved due to utilizing the resonant effect. Based on the present work, some new types of vibrating coolers/dryers or vibrating screening machines can be designed.