Double synchronization states of two exciters with horizontal asymmetric structure in a vibrating system

Li, Lingxuan; Chen, Xiaozhe

doi:10.21595/jve.2017.17868

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…where, oxy is the fixed coordinate system, m is the mass of the frame, o is the mass center of the whole vibrating Four springs with the type of ROSTA AB27, (6). Signal acquisition system, (7). Three ROLS remote optical laser sensors, (8).…”

Section: Theoretical Research a Working Principle Of Multi-frequmentioning

confidence: 99%

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

Chen

2019

IEEE Access

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For vibrating screen machinery, the granular block material can be quickly loosed and fully layered when entering the screening equipment if it is placed an exciting system with low frequency and large amplitude at the feeding end. A high frequency with small amplitude exciter is set near the discharging end. It can make the material appear high-frequency vibration and reduce the phenomenon more effectively that the granular material blocks the screen hole. Because of this, taking the elliptical vibrating screen system as our research object, the concept of compound nonlinear screening trajectories is proposed from the two times frequency vibrating synchronization system driven by three exciters. Firstly, the differential motion equation of the system is obtained by establishing the Laplace equations of the system. Then, by introducing small parameters and dimensionless time parameters, the first-order differential motion equations of the driving motor of the exciters are obtained, the second approximate motion equation of the system is obtained by applying the principle of the average method. Based on this, the criterion for the system to achieve the multi-frequency vibration synchronization state and the phase difference relations among the exciters at steady-state are drawn out by taking the two times frequency vibration synchronization as an example. Meanwhile, the stability criterion of the vibration synchronization state of the system is analyzed. Besides, the functional relation that the location and the rotational direction of the exciters influence on the phase difference of the exciters are given out. Finally, the correctness of the theoretical research is verified by experimental research; the prospect of engineering application of the system is discussed.

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Section: Theoretical Research a Working Principle Of Multi-frequmentioning

confidence: 99%

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

Chen

2019

IEEE Access

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“…Djanan et al [16] discussed the influence of the physical characteristics of the motor on the phase difference when two ERs reach the synchronous state. Introducing nonlinear springs, Li et al [17] studied synchronization theory of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Four Axisymmetrically Distributed Eccentric Rotors in a Vibration System

et al. 2022

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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.

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“…Since then, the synchronization theory in the mechanical system has been studied. Recent studies have shown that the vibration system also has double phase synchronization phenomena, which mainly exist in four forms: (1) the bistable phase synchronization phenomenon is natural to appear in some vibration systems with double vibration mass or multimass [8,9], including some rotor-pendulum systems [10,11]; (2) some vibration systems have the in-phase and antiphase synchronization phenomena when they operate in a subresonance or a superresonance state, respectively [12,13]; (3) the event of bistable phase difference intervals also exists in some near-resonance nonlinear vibration synchronous systems [8,10]; (4) it is more popularly known in the vibration synchronization system with two homodromy exciters located at a single vibration mass body [14][15][16], including rotor-pendulum systems [10] and two eccentric rotors with a common rotational axis system [17,18]. e inphase synchronization phenomenon between the two homodromy exciters appears when they are located at a relatively far distance, i.e., the stable phase difference interval is (− 90°, 90°).…”

Section: Introductionmentioning

confidence: 99%

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

Chen

2020

Mathematical Problems in Engineering

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A vibration system with two homodromy exciters operated in different rotational speed is established to investigate whether the phenomenon of bistable phase difference intervals exists in the times-frequency vibration synchronization system. Some constructive conclusions are proposed. (1) By introducing an average angular velocity perturbation parameter ε0 and two sets of phase difference perturbation parameters and ε2, the frequency capture criterion and the necessary criteria for realizing the times-frequency vibration synchronization are derived. The corresponding stability analysis is carried out. (2) By the theoretical analysis and experiments, it is verified that the times-frequency vibration synchronization system exists the phenomena of bistable phase difference interval. That is, the phase differences between the two homodromy exciters are stable around 180 degrees when they are located at a short distance; the antiphase synchronization phenomenon appears. On the contrary, they are stable around 0 degrees at the in-phase synchronization state. (3) Because of the two homodromy exciters operating in the different rotational speed, the vibration system obtains relatively complex compound motion trajectories; the corresponding application is investigated by adding a feeding material chamber. The times-frequency vibration synchronization system can be used to design the vibration mill for reducing its low-energy zone and developing chaotic mixing equipment for obtaining a better mixing effect.

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Double synchronization states of two exciters with horizontal asymmetric structure in a vibrating system

Cited by 6 publications

References 13 publications

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

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

Synchronization of Four Axisymmetrically Distributed Eccentric Rotors in a Vibration System

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

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