Synchronization phenomenon in a vibration system with three rigid frames driven by two co-rotating unbalanced rotors

In this paper, a vibration system is studied that consists of three rigid frames excited by two co-rotating unbalanced rotors mounted on different rigid frames. Synchronization phenomenon is analyzed theoretically and experimentally and selected motion characteristics of the system are revealed. Applying the Lagrange approach, the governing equation of motion is obtained first. Using the averaging method, the synchronization condition for the unbalanced rotors is obtained by considering the torques applied on the rotors. Using the Lyapunov stability theory, the stability condition for the system’s synchronous motion is derived. In order to analyze the selected motion characteristic of the vibration system, a series of numerical parametric studies is conducted, with the focus on the phase difference between the unbalanced rotors, motions of the rigid frames and the coupling torque in the system. The rotation frequency, mass ratio of the unbalanced rotors and stiffness of the coupling springs in the system are shown to affect the synchronization of the system. Finally, a series of experiments is carried out to validate the obtained theoretical results.