Stability and Sommerfeld Effect of a Vibrating System with Two Vibrators Driven Separately by Induction Motors

The idea of self-synchronization vibrating system comes from the phenomenon of synchronization. In the 1960s, Blekhman[1,2] proposed the self-synchronization theory of vibrating system driven by two induction motors. When the structure parameters of the two motors met the requirements, the system could operate synchronously. Blekhman[3] also found that even if the rotating speed and the angular phase difference of the two eccentric rotors were being disturbed or one of the motors was powered off, the system could still operate synchronously. The small parameter methods were applied to a number of problems by R.F. Nagaev[4]. It can lead to better understanding of the self-synchronization theory. Wen Bang-chun[5] applied self-synchronization theory to engineering and established a branch of the vibration utilization engineering, and numerous self-synchronous vibrating machines were invented.

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Composite synchronization of three eccentric rotors driven by induction motors in a vibrating system

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2017.09.025 ◽

2018 ◽

Vol 102 ◽

pp. 158-179 ◽

Cited By ~ 12

Author(s):

Xiangxi Kong ◽

Changzheng Chen ◽

Bangchun Wen

Keyword(s):

Induction Motors ◽

Vibrating System

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Theoretical and experimental investigation on controlled synchronization of four co-rotating coupled exciters driven by induction motors in a vibrating system

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219830437 ◽

2019 ◽

Vol 233 (13) ◽

pp. 4556-4576 ◽

Cited By ~ 2

Author(s):

Dawei Gu ◽

Juqian Zhang ◽

Bangchun Wen ◽

Xueliang Zhang ◽

Yunshan Liu

Keyword(s):

Dynamic Model ◽

Electromechanical Coupling ◽

Induction Motors ◽

Control Method ◽

Sliding Mode ◽

Coupling Model ◽

Vibrating System ◽

Synchronization Method ◽

Novel Approach ◽

The Stability

This paper aims at theoretically and experimentally investigating the controlled synchronization of four co-rotating coupled exciters in a vibrating system driven by induction motors. Using the Lagrange's equations, the motion equations of the vibrating system are derived. Combining the dynamic model of an induction motor with the dynamic model of a vibrating system, an electromechanical coupling model is developed. By virtue of the average method of modified small parameters and the Routh–Hurwitz principle, the self-synchronization criterion for four exciters and the stability criterion of synchronous states are obtained. Based on the numerical results, the stable inphase motion of four exciters fails to be implemented by means of self-synchronization, and as a result, the desired motion type of the vibrating system cannot be realized. Hence, the controlled synchronization is introduced into the vibrating system. Owing to the coupling characteristics of the vibrating system, the control challenge can be turned into a synchronization control problem between four exciters driven by induction motors. To perform the synchronized motion of zero phase differences between four exciters, sliding mode control algorithm and field-oriented control method on four induction motors are applied to develop the controlled synchronization scheme by adopting the master–slave control strategy. The stability of the closed loop system is proved by Lyapunov theorem. Experiments on a corresponding controlled synchronization bedstand are performed to examine the effectiveness of the developed controllers, including a comparison with self-synchronization method. Additionally, experimental results show the robustness of the proposed control scheme against the influence of parameter perturbations and external disturbances. The controlled synchronization method provides a novel approach to the development of vibrating machines.

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Multifrequency-controlled synchronization of three eccentric rotors driven by induction motors in the same direction

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/1461348418818734 ◽

2018 ◽

Vol 38 (2) ◽

pp. 615-632

Author(s):

Lei Jia ◽

Juqian Zhang ◽

Laihong Zhou ◽

Bangchun Wen

Keyword(s):

Numerical Simulation ◽

Dynamic Model ◽

Induction Motors ◽

Phase Ratio ◽

Fuzzy Pid ◽

Tracking Method ◽

Vibrating System ◽

Experiment Validation

This article presents the dynamic model of three eccentric rotors driven by induction motors and respectively derives the response equations of the three directions with different frequency in a vibrating system. On account of the difficulty to realize multifrequency self-synchronization, the controlling method is used to realize the synchronization of the speed and phase. In this article, the fuzzy PID method is introduced to control the vibrating system which is based on a master–slave controlling strategy. And a tracking method based on the phase ratio is proposed. The effectiveness and stability are shown in the numerical simulation and the experiment validation is given to certify the accuracy of the theory. In the meanwhile, the arbitrary of the multifrequency is also demonstrated. Finally, some conclusions are summarized to present the significant in the engineering.

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Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.3007909 ◽

2008 ◽

Vol 4 (1) ◽

Cited By ~ 3

Author(s):

J. M. Balthazar ◽

J. L. Palacios Felix ◽

R. M. L. R. F. Brasil ◽

T. S. Krasnopolskaya ◽

A. Yu. Shvets

Keyword(s):

Power Supply ◽

Degrees Of Freedom ◽

A Priori ◽

Nonlinear Interactions ◽

Sommerfeld Effect ◽

Governing Equations ◽

Vibrating System ◽

Forcing Function ◽

Limited Power ◽

Piezoceramic Transducer

Interactions between the oscillations of piezoceramic transducer and the mechanism of its excitation—the generator of the electric current of limited power-supply—are analyzed in this paper. In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a dc motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a nonideal problem. In this work, we present certain phenomena as Sommerfeld effect, jump, saturation, and stability, through the influences of the parameters of the governing equations motion.

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