Stability Characteristics of a Vibrating System with Double Rigid Frames Driven by Four Co-Rotating Coupling Vibrators

Abstract

In this paper, a dynamic model is adopted to investigate the stability and response characteristics of a vibrating system driven by four vibrators placed on two different rigid frames (RFs). Using the equations of motion of the system derived, the conditions for synchronization and stable operation of the system are studied by the average method and Hamilton’s rules, respectively. Based on the theoretical results obtained, some factors are further studied concerning the stable phase differences (SPDs), the coefficients for ensuring stability, and the vibration amplitudes of the two RFs in different resonant regions. These serve to reveal the stability and response characteristics of the system that determine the ultimate function of the vibrating machine. Finally, numerical simulations are carried out to examine the validity of the theoretical methods and numerical qualitative results. Based on the results from the theory and simulation analyses, it is suggested that the working region of the system should be selected in the sub-resonant region corresponding to the natural frequency (NF) of the main vibrating system in the [Formula: see text]- and [Formula: see text]-directions. In this case, the ideal relative circular motion for two RFs with a well isolation effect can be achieved, and the energy is saved.