We study synchronization of two eccentric rotors (ERs) with common rotational axis in the vibration system of the far-resonant spatial motion. We deduce the dimensionless coupling equation of two ERs with applying the average method of small parameters. We convert the synchronization problem into the existence and stability of solving the zero solutions for the dimensionless coupling equations. By introducing the synchronization torque and the difference between the residual torques of two motors, we obtain the synchronization condition that two ERs achieve the synchronized motion. We derive the stability condition of the synchronized motion, which satisfies Routh-Hurwitz criterion. We discuss numerically the choosing motion feature of the vibration system, which indicates that the vibration system has two steady motion modes. The synchronization torque forces the phase difference to approachπwhen the structural parameters of the vibration system satisfy the condition of the spatial cone motion, and the synchronization torque drives the phase difference to approach zero when those satisfy the condition of the spatial circle motion. Finally, through the comparison and analysis of experimental data, the structural parameters of the vibration system satisfying the above two conditions can guarantee the synchronization stability for two ERs.

This paper studies synchronization of a class of even pairs and symmetrically distributed eccentric rotors in a vibration system of a single mass body. A vibration system driven by four ERs with circular distribution structure and the same rotating direction is adopted as the dynamic model. The motion differential equations of the system are established based on Lagrange equation. The angular velocity and the phase of each rotor are perturbed by the average value of the synchronous velocity. The state equation of the system is obtained by applying the averaging method. According to the necessary condition of the steady-state motion, the synchronization condition and the dimensionless coupling torques of the system are deduced. The stability condition of the synchronous motion is derived by applying Lyapunov indirect method. The distribution law of the steady-state phase difference is discussed qualitatively by the numerical analysis of the theoretical results. Then combined with the numerical results, five sets of experiments are carried out on the experimental machine, which includes the sub-resonant state and the super-resonant state. The experimental results show that this vibration system has two super-resonant motion states and one sub-resonant motion state. The experiment proves the correctness of the theory, which can provide theoretical guidance for the design of this kind of vibration machine.

In this work, the controlled synchronization of two nonidentical homodromy coupling exciters driven by inductor motors in a vibratory system is investigated. According to the previous works, using small parameter perturbation method deduces the conditions of implementing self-synchronous motion of two exciters. The shortage of self-synchronization method in design of vibratory system is found. The controlled synchronization method is proposed by employing sliding mode control and proportional–integral method on two inductor motors based on the master-slave control strategy to replace the self-synchronization. The stability of the controllers is proved by Lyapunov theorem. The performances of the control system are demonstrated by numerical simulation, which shows the controlled synchronization method is feasible. Additionally, the effects of various uncertainties including internal parameter perturbations and external disturbances on the control system are discussed, which indicate the proposed controllers have a good robustness.