Multiple‐Frequency Controlled Synchronization of Two Homodromy Eccentric Rotors in a Vibratory System

Abstract

Multifrequency controlled synchronization of two homodromy eccentric rotors is investigated. The vibrating screen with two rotors is a typical underactuated system. So, the model of the vibrating screen is converted to a synchronization motion problem. Firstly, the mechanical-electromagnetic coupling dynamical model of the vibrating system is established. And then the fuzzy PID method is used for the two motors which are based on the master-slave control strategy. The slave motor uses the method of the phase ratio to trace the master motor and achieve the synchronous motion. Through the simulation, the two rotors cannot reach the state of multifrequency self-synchronization. And, then, it is realized by multifrequency controlled synchronization. The article presents the motion trails of the vibrating system between one and two times and realizes the zero phase difference after each period. Finally, some experiments are used to verify the accuracy and effectiveness of the conclusion in the simulation and analysis of the feature of the movement tracks.

The Phenomenon of Bistable Phase Difference Intervals in the Times-Frequency Vibration Synchronization System Driven by Two Homodromy Exciters

“…As shown in Figures 4 and 5, the different distribution intervals of phase difference are apparent, the distributions of the boxes in the same frequency and times-frequency experimental groups at l � 0.68 m and l � 1.36 m, the former groups are stable near 180 degrees, the antiphase synchronization phenomenon appears, while the latter groups are stable near 0 degrees and the in-phase synchronization phenomenon comes out. It attributes to the existence of δ in equation (22) leads to the appearance of the bistable phase difference interval. At the same time, the length of boxes denote the vibration synchronization state at n � 1, 2 which is more steady than that when n � 3. e time needed for the same frequency experimental group (n � 1) to achieve the vibration synchronization state is also shorter than other groups both at l � 0.68 m and l � 1.36 m, which can be found in Figure 6.…”

“…As mentioned above, the phenomenon of bistable phase interval in the system is caused by the angle δ when equation 21is arranged in the form of equation (22). Specifically, W sic (i � 1, 2) is greater than or equal to 0 because of β ∈ [0, π/2].…”

“…It just can explain why many vibration machines require the composite mass center of the exciters, and the mass center of the vibration system is in a line to make the steady-state phase difference of the system approach to 0 or 180, in which the synchronous state is more stable. For the experiments in the previous section, we have r l � 1.56 and β � 20.9°when l � 0.68 m and r l � 0.82 and β � 10.8°when l � 1.36 m. Substituting the value of δ and the electrical parameters of exciters into equation (22), the phase difference between the simulation values and experimental results in Figures 4 and 5 are less than ten degrees, respectively, which can also be viewed in Figure 18. Also, the corresponding synchronization performance index D calculated by equation 24is listed in Figure 19, where the vertical coordinate is logarithmic.…”

“…e difficulty in the design of the times-frequency vibration synchronization system is just as the one pointed out by Wen; it is more challenging to implement the high-order harmonics and the subharmonic times-frequency capture than the fundamental frequency capture because of the smaller frequency capture interval [19]. Recently, a timesfrequency vibration system has been investigated by Jia, who gets a stable state by way of controlled synchronization [22]. If we can control the system based on the optimal structure parameters of the mechanical model, it will raise the efficiency, enhance the stability and the robustness, and decrease the energy loss by forcing control of the system.…”

Multi-frequency Vibration Synchronization and Stability of the Nonlinear Screening System

“…It is more difficult to implement the entrainment of high order harmonic frequency and the subharmonic frequency capture than fundamental frequency capture because of the smaller frequency capture interval [13]. Therefore, Jia et al has been investigated the control synchronization of the vibrating system in the view of controlling the rotational speed and phase of the driving motor of the exciter and achieved a stable state of synchronization [21]- [23]. Compared to realizing the synchronization of the vibration system by control synchronization theory, the vibration synchronization have obvious advantages in assuring stability and reliability of the system and cost savings.…”