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The unreasonable dynamic characteristics results in decrease of screening efficiency of the vibrating screen. However, the synchronous behavior of motors is key factor to determine dynamic characteristics of the screens. In this paper, two unbalanced rotors actuated with motors in a three-dimensional space are proposed. To understand the synchronous mechanism, the dynamic equation of the system is firstly confirmed based on Lagrangian formulation; meanwhile, synchronization condition of the system is calculated with average and small parameter method; then, synchronization stability of the system is explored by Lyapunov method; finally, some numerical simulations are given to validate the theoretical computations. It is found that, to implement the stable synchronous rotation between the rotors, the values of the parameter in this system must be satisfied by synchronous condition and synchronous stability; the synchronous state is determined by the rotation direction, the damping ratio, the frequency ratio, and the motor position; the system is a planar motion when the identical mass rotors oppositely actuated, but the system is a spatial motion in the other cases.

This work is a continuation and verification of the original literature by using experimental strategy. Based on the published paper, in order to avoid anti-phase synchronization with two co-rotating rotors system, a vibrating system with two co-rotating rotors installed with nonlinear springs have been proposed, and then, the synchronous condition and the synchronous criterion of the system are theoretically derived. From the analysis mentioned, it is shown that the synchronous state is mainly determined by the structural parameters of the coupling unit, coupling coefficients and positional parameters of the two exciters, etc. The main objective of the present work is to investigate the synchronous mechanism by experiments and simulations in this paper. Some simulation computations are firstly implemented to explain the synchronous mechanism of the system. Additionally, an experimental strategy with synchronous tests and dynamic characteristic tests of the vibrating system are carried out to validate the correctness of the simulation analysis. The simulations and experiments demonstrate that the nonlinear springs can overcome the difference of residual torques of the two motors to realize the synchronization of near zero phase difference under the condition of in-phase difference between two exciters. Finally, the error analysis results among the dynamic testing, synchronous testing results and simulations are discussed. This research can provide theoretical reference for designing large-sized and heavy-duty Vibrating Screens.

In-phase self-synchronization of two eccentric rotors with common rotational axis is hardly implemented in far-resonance system. In this article, a dual motor coaxially coupling with a torsion spring is proposed to obtain in-phase synchronization between the eccentric rotors. To explore the dynamic and synchronous characteristics of the proposed system, the mechanical model is first established with Lagrangian formulation. Second, the steady response of the system is calculated based on differential motion equations. Subsequently, the synchronous mechanism between the eccentric rotors is discussed by averaged small parameter method. Finally, some numerical computations are further implemented to verify correctness of theoretical analysis. The result shows that the synchronous state is determined by stiffness of torsion spring, masses of eccentric rotors, and distance between the motors. When axial distance between the motor is smaller, “critical stiffness of in-phase synchronization” is gradually enlarged as the masses of the eccentric rotors are increased and approached to equality, but in-phase synchronization is permanently maintained when the axial distance of the motor is far; in this situation, the synchronous state is hardly affected by variation of stiffness of torsion spring and masses of eccentric rotors. When the stiffness of the torsion spring is smaller, “critical distance [Formula: see text] of in-phase synchronization” is also enlarged as the masses of the eccentric rotors are increased and approached to equality; otherwise, the synchronous state is always locked in in-phase synchronization. When the stiffness of the torsion spring is smaller, “critical distance [Formula: see text] of anti-phase synchronization” is decreased as the masses of eccentric rotors are increased and approached to equality; otherwise, the synchronous state is always locked in in-phase synchronization.