Synchronization and Stability of Two Pairs of Reversed Rotating Exciters Mounted on Two Different Rigid Frames

Usually, the synchronization studies of two or multiple exciters are focused on the single rigid frame (RF), but that mounted on different RFs is still a problem in engineering practice. This study attempts to solve this issue by considering a dynamical model with double RFs including two pairs of exciters, in which each pair of exciters is distributed on different RFs. The synchronous and stable states of the system in different resonant regions are discussed in detail in present work. First, the mathematical modeling of the system is carried out, and the relative motion differential equations of two RFs and their responses are achieved by using the transfer function method. Then, the theoretical conditions of implementing synchronization and stability of the system are derived. The coupling dynamic characteristics of the system, including frequency-amplitude relationships, coupling torques, stable phase differences, synchronization and stability abilities, and the phenomenon of the diversity of nonlinear system, are numerically investigated. Finally, simulations are performed by using the Runge-Kutta method to validate the theoretical and numerical characteristic analysis results. In the sub-resonant region with respect to the natural frequency with regard to the relative motion between two RFs, the stronger and more stable positive superposition of vibration amplitude between two RFs can be realized, which is the desire in engineering.