Self-synchronization of unbalanced rotors and the swing equation

Smirnova, Vera B.; Proskurnikov, Anton V.

doi:10.1016/j.ifacol.2021.11.028

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…The interaction of rotating rotors at sufficiently high frequencies leads to the phenomenon of self-synchronization, which is difficult (or even impossible) to overcome by changing the electrical control signal. The rotor selfsynchronization phenomena were deeply investigated in [1,7,10,[41][42][43][44][45]. It also should be taken into account that, in the system, the industrial frequency converters (Altivar 12 Schneider Electric) are used with their own local controllers, the algorithm for which is not revealed by the manufacturer.…”

Section: Servo System Modelmentioning

confidence: 99%

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Passification-Based Robust Phase-Shift Control for Two-Rotor Vibration Machine

Andrievsky

Zaitceva

Barkana³

2023

Electronics

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In this paper, the solution to the problem of robust control of the phase shift during rotation at a given speed of the unbalanced rotors for a two-rotor vibratory machine is presented. The solution to this problem is relevant for the development of vibration technologies (for example, a vibro-transportation of bulk materials). The proposed controller includes two proportional-integral (PI) rotor speed controllers with a cross-coupling, which receive signals with opposite signs from the phase shift controller. Unlike previous works, where a PI controller for phase shift control was also taken, including the adaptive controller with an implicit reference model (IRM), in the present paper, a relay-type signal controller with an integral component without a parametric adaptation is used. This approach allows, while maintaining robustness, to increase the operation speed and accuracy of the control process, avoiding at the same time the possible divergence of the tunable parameters due to the influence of noises and disturbances caused, among other things, by vibrations of the setup’s structural elements and measurement errors. For the control law design, the speed-gradient method was employed. For various types of reference phase-shift signals (constant, harmonic, chaotic), the results of extensive experimental studies performed on the mechatronic vibration setup and the simulations accomplished based on the results of identifying the parameters of the stand drive model are presented in the paper. The obtained results confirm the efficiency and robustness of the proposed algorithm and allow one to reveal the system performance properties.

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Section: Servo System Modelmentioning

confidence: 99%

“…It was described in detail in the works by I. Blekhman and his colleagues, cf. [1,7,10,[41][42][43][44][45]. Revolving imbalanced are subject to mutual through "pushes" transmitted between the rotors by the stand structure parts.…”

Section: Limitations Of the Proposed Solutionmentioning

confidence: 99%

Passification-Based Robust Phase-Shift Control for Two-Rotor Vibration Machine

Andrievsky

Zaitceva

Barkana³

2023

Electronics

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“…7 On the ground of Sperling et al's research, Smirnova and Proskurnikov further investigated the problem of synchronization between multiple eccentric rotors (ERs) mounted on a rigid oscillating platform. 8 Besides, Paz and Cole deduced the self-synchronization conditions and stability conditions of two ERs arranged in arbitrary positions by Hamilton's principle. 9 Based on the integral average method, Wen et al discussed the synchronous characteristic between two ERs from the perspectives of torque balance in the motors, which considerably simplified the processes of the synchronization criterions and stability conditions.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and experimental study for implementation of the elliptical trajectory in dual-motor vibration system

Peng

Fang

Yang

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part K:

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In the petroleum drilling industry, the smoothly functioning vibrating screens play a critical role in control of solid–liquid and recovery of drilling fluid. Due to the mechanical coupling, the surface of the vibrating screen tends to produce unbalanced swings, which makes the motion trajectory inconsistent with the situation at the center of mass, thus affecting the screening efficiency. In order to reveal the reasons for the unbalanced swings of the vibration system and the principle of the trajectory equilibrium characteristics (TECs), the self-synchronization characteristics of two eccentric rotors (ERs) driven by elliptical trajectory dual-motor vibrating system are investigated. The kinematic differential equations of the vibration system are determined by the Lagrange method. Then, the conditions of synchronization and stability of the vibration system are determined, respectively, by the small parameter average approach and the Routh–Hurwitz criterion. Subsequently, the impact of the structural parameters about the synchronization stability is examined by numerical discussion. Furthermore, the effectiveness of the theoretical research is confirmed by comparing the results between dynamics simulation and experiment under different structural parameters. Finally, by focusing on the analysis of the trajectories of different measuring points in the experiment, the relevant conclusions on how to reduce the unbalanced swings and maintain the TECs of the vibration system are obtained. The elliptical trajectory form of the system is most affected by the motor installation angle and installation distance in vibrating body, while less affected by the installation deflection angle and installation offset distance between the motors. In addition, the elliptical trajectories of the oscillating body are in a good equilibrium when reducing the swing angle of the vibration system, in other words, increasing the installation angle and reducing the installation distance of the exciters in the stable state.

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“…Analyses concerning nonlinear systems are especially interesting. The conditions of synchronizing systems of two vibrators installed on a common platform and the criterion of global stability of the solutions obtained on the basis of analysing nonlinear equations were presented in (Smirnova and Proskurnikov, 2021). The synchronization of two exciters under the nonlinear influence of elastic elements of sectional-linear characteristics was investigated in (Zhang et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Self-synchronization of drive vibrators of an antiresonance vibratory conveyor

Cieplok

2023

Journal of Theoretical and Applied Mechanics

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A theoretical analysis of synchronization of inertial vibrators of a vibratory conveyor with a dynamic damper is presented in this paper. It is shown that for the over-resonance regime and counter-running drive vibrators, there is only one stable state of the system warranting formation of necessary sectional vibrations of the trough. The analytical form of the moment--synchronizing vibrators is also determined, and on the basis of this, the influence of angular vibrations of the body on the synchronizing process of the drive vibrators is determined. Due to the differences in the participation of angular vibrations in the self-synchronizing process in relation to classical solutions, the presented results fundamentally influence the design of long antiresonance conveyors.

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Self-synchronization of unbalanced rotors and the swing equation

Cited by 5 publications

References 20 publications

Passification-Based Robust Phase-Shift Control for Two-Rotor Vibration Machine

Passification-Based Robust Phase-Shift Control for Two-Rotor Vibration Machine

Theoretical and experimental study for implementation of the elliptical trajectory in dual-motor vibration system

Self-synchronization of drive vibrators of an antiresonance vibratory conveyor

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