Synchronization of coaxial co-rotating tri-exciter with two torsional springs in far-resonance system

To propose a vibration system with coaxial elastic-coupled tri-exciters, which can achieve in-phase (the phase difference angle is close to 0°) synchronization and operate stably. Solving the problem of excitation force cancellation caused by the anti-phase synchronization (with a phase difference angle around 180°) of the eccentric rotors (ERs) of multiple exciters rotating in the same direction. Using the Lagrange equation, the system's dynamic equation is established. The average method is employed to derive the torque balance equations for the three ERs and the torque difference balance equations between ER 1 and 2, and ER 2 and 3. Synchronization and stability conditions are determined through the existence and stability of the zero solution of the torque difference balance equation, and the synchronization and stability indexes are calculated by numerical methods. The effects of parameters such as eccentric mass, eccentricity radius, screen mass and rotational speed of the ERs on synchronization and stability are discussed. Theoretical predictions are validated through simulations and experimental research. As the torsional stiffness of the coupling element changes, the synchronization state of the system is divided into near self-synchronization, asynchronous and coupled synchronization zones. With appropriate torsional stiffness, the system achieves nearly zero-phase difference angle synchronization in the coupled synchronization zone, and increased torsional stiffness enhances system stability. In the coupled synchronization state, even if only two of the three exciters are powered, the synchronization phase difference angle remains similar to that with all three exciters active. The coaxial elastic-coupled tri-exciter vibration system not only achieves in-phase synchronization of the three exciters and ensure high performance of vibration machines, but also achieves energy conservation simultaneously.