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.

Aiming at the problem to diagnose soft faults in nonlinear analog circuits, a novel approach to extract fault features is proposed. The approach is based on the Wigner-Ville distribution (WVD) of the subband Volterra model. First, the subband Volterra kernels of the circuit under test are cleared. Then, the subband Volterra kernels are used to obtain the WVD functions. The fault features are extracted from the WVD functions and taken as input data into the hidden Markov model (HMM). Finally, with classification of features using HMMs, the soft fault diagnosis of the nonlinear analog circuit is achieved. The simulations and experiments show that the method proposed in this paper can extract the fault features effectively and improve the fault diagnosis.

With the rapid development of petroleum exploitation industry, vibrating screen actuated with a single frequency is unsuitable to separate cuttings from drilling fluid, since it usually results in screen blocking. Hence, for solving the above-mentioned problem, tri-motor excitation with double-frequency in far resonance system is introduced. This paper aims to explore the self-synchronization mechanism of the proposed system. First, dynamic equation is established according to physical model of the system. Then, displacement response of the system in steady state is obtained with dynamic formulas. Subsequently, synchronous condition among the three exciters is determined by small parameters method, and criterion of synchronous stability among the three exciters is derived by Poincare-Lyapunov method. Finally, in light of the differential motion equation, Runge-Kutta principle is assigned to validate the reliability of self-synchronous theory and the stability of the double-frequency system. The results indicate that electromagnetic torques of low-frequency motors are dynamically antisymmetric in synchronous operation, and synchronous ability of the system is determined by the mass ratio among the rotors. In addition, stable phase difference among the rotors is significantly influenced by the structural parameters of the system. And this study will be helpful for the improvement of separation technology.

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.

In a vibrating screen machinery, two eccentric rotors (ERs) are actuated by swung and fixed motors. When the working efficiency of vibrating screens is the highest, the motion trajectory of the vibrating body is an ellipse. However, to implement elliptical trajectory, the ideal synchronization between the two ERs must be needed. Hence, the self-synchronous theory and synchronous control method for the vibrating screen machinery are explored. First, the mathematic model of the vibration system is deduced based on Lagrange equation; then, the synchronous condition and stability criterion are inferred from averaged small parameter method. In addition, the synchronization controllers, related to speed and phase of the ERs, are designed by with sliding mode control (SMC), and the master–slave control strategy is applied to design the control structure. Meanwhile, the stability performance of the controllers is demonstrated by Lyapunov theory and Hurwitz condition. Finally, computer simulations are implemented to validate the theoretical reliability of self-synchronization and synchronous control. The simulation results show that the system can be self-synchronized, but the ideal synchronization is difficult to achieve when the two ERs are self-synchronously rotated, which leads to non-ideal dynamic characteristics; nevertheless, the ideal synchronization can be implemented by the proposed synchronous control method.