Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame

This paper investigates synchronization of two self-synchronous vibrating machines on an isolation rigid frame. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. Then the stability problem of synchronization for the four unbalanced rotors is converted into the stability problems of two generalized systems. One is the generalized system of the angular velocity disturbance parameters for the four unbalanced rotors, and the other is the generalized system of three phase disturbance parameters. The condition of implementing synchronization is that the torque of frequency capture between each pair of the unbalanced rotors on a vibrating machine is greater than the absolute values of the output electromagnetic torque difference between each pair of motors, and that the torque of frequency capture between the two vibrating machines is greater than the absolute value of the output electromagnetic torque difference between the two pairs of motors on the two vibrating machines. The stability condition of synchronization of the two vibrating machines is that the inertia coupling matrix is definite positive, and that all the eigenvalues for the generalized system of three phase disturbance parameters have negative real parts. Computer simulations are carried out to verify the results of the theoretical investigation.

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Theoretical and Experimental Study on Synchronization of the Two Homodromy Exciters in a Non-Resonant Vibrating System

Shock and Vibration ◽

10.1155/2013/472407 ◽

2013 ◽

Vol 20 (2) ◽

pp. 327-340 ◽

Cited By ~ 21

Author(s):

Xue-Liang Zhang ◽

Chun-Yu Zhao ◽

Bang-Chun Wen

Keyword(s):

Phase Difference ◽

Structural Parameters ◽

Circular Motion ◽

Vibrating System ◽

Frequency Capture ◽

Rigid Frame ◽

Small Parameters ◽

Coupling Dynamic ◽

The Stability ◽

Elliptical Motion

In this paper we give some theoretical analyses and experimental results on synchronization of the two non-identical exciters. Using the average method of modified small parameters, the dimensionless coupling equation of the two exciters is deduced. The synchronization criterion for the two exciters is derived as the torque of frequency capture being equal to or greater than the absolute value of difference between the residual electromagnetic torques of the two motors. The stability criterion of synchronous state is verified to satisfy the Routh-Hurwitz criterion. The regions of implementing synchronization and that of stability of phase difference for the two exciters are manifested by numeric method. Synchronization of the two exciters stems from the coupling dynamic characteristic of the vibrating system having selecting motion, especially, under the condition that the parameters of system are complete symmetry, the torque of frequency capture stemming from the circular motion of the rigid frame drives the phase difference to approach PI and carry out the swing of the rigid frame; that from the swing of the rigid frame forces the phase difference to near zero and achieve the circular motion of the rigid frame. In the steady state, the motion of rigid frame will be one of three types: pure swing, pure circular motion, swing and circular motion coexistence. The numeric and experiment results derived thereof show that the two exciters can operate synchronously as long as the structural parameters of system satisfy the criterion of stability in the regions of frequency capture. In engineering, the distance between the centroid of the rigid frame and the rotational centre of exciter should be as far as possible. Only in this way, can the elliptical motion of system required in engineering be realized.

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Synchronization of Two Non-Identical Coupled Exciters in a Non-Resonant Vibrating System of Linear Motion. Part I: Theoretical Analysis

Shock and Vibration ◽

10.1155/2009/259149 ◽

2009 ◽

Vol 16 (5) ◽

pp. 505-515 ◽

Cited By ~ 34

Author(s):

Chunyu Zhao ◽

Hongtao Zhu ◽

Ruizi Wang ◽

Bangchun Wen

Keyword(s):

Zero Solution ◽

Moment Of Inertia ◽

Moments Of Inertia ◽

Vibrating System ◽

Frequency Capture ◽

Synchronization Problem ◽

Small Parameters ◽

Existence And Stability ◽

Synchronous Operation ◽

The Stability

In this paper an analytical approach is proposed to study the feature of frequency capture of two non-identical coupled exciters in a non-resonant vibrating system. The electromagnetic torque of an induction motor in the quasi-steady-state operation is derived. With the introduction of two perturbation small parameters to average angular velocity of two exciters and their phase difference, we deduce the Equation of Frequency Capture by averaging two motion equations of two exciters over their average period. It converts the synchronization problem of two exciters into that of existence and stability of zero solution for the Equation of Frequency Capture. The conditions of implementing frequency capture and that of stabilizing synchronous operation of two motors have been derived. The concept of torque of frequency capture is proposed to physically explain the peculiarity of self-synchronization of the two exciters. An interesting conclusion is reached that the moments of inertia of the two exciters in the Equation of Frequency Capture reduce and there is a coupling moment of inertia between the two exciters. The reduction of moments of inertia and the coupling moment of inertia have an effect on the stability of synchronous operation.

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Selected synchronous state of the vibration system driven by three homodromy eccentric rotors

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/1461348419844646 ◽

2019 ◽

Vol 39 (2) ◽

pp. 352-367

Author(s):

Xiaozhe Chen ◽

Lingxuan Li

Keyword(s):

External Disturbance ◽

Plane Motion ◽

Initial Condition ◽

Vibration System ◽

Synchronous State ◽

Frequency Capture ◽

Synchronous Motion ◽

Small Parameters ◽

Coupling Dynamic ◽

The Stability

In order to verify that the vibration system driven by multi-eccentric rotors has multiple synchronous states, a model of three eccentric rotors horizontal installation of plane motion is established to study the coupling dynamic characteristics. Based on the average method of modified small parameters, the frequency capture equation is constructed to obtain the conditions of synchronous motion and vibration synchronization transmission. According to the synchronous conditions, the stability state of achieving synchronous motion is converted into the solution of balance equation of the synchronous torque. There are multiple solutions to the torque equation because of the non-linear characteristics of the vibration system driven by multi-eccentric rotors. Then the stability condition is used to estimate which of the solutions is stable. After substituting the parameters of the experimental machine into the above method, the curves of the phase difference and its stability coefficients of three eccentric rotors system are obtained numerically. Two experiments show that the selected synchronous state depends on the initial condition and external disturbance, and if the vibration synchronization transmission conditions are satisfied, three eccentric rotors can not only achieve vibration synchronization transmission of one motor with switching off the power but also that of two motors with switching off the power.

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Synchronization of Two Asymmetric Exciters in a Vibrating System

Shock and Vibration ◽

10.1155/2011/590218 ◽

2011 ◽

Vol 18 (1-2) ◽

pp. 63-72 ◽

Cited By ~ 2

Author(s):

Zhaohui Ren ◽

Qinghua Zhao ◽

Chunyu Zhao ◽

Bangchun Wen

Keyword(s):

Average Method ◽

Structural Parameters ◽

Positive Definite ◽

Electromagnetic Torque ◽

Coupling Matrix ◽

Vibrating System ◽

Frequency Capture ◽

Small Parameters ◽

The Difference ◽

Dimensional Coupling

We investigate synchronization of two asymmetric exciters in a vibrating system. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the two exciters (NDDETE). By using the condition of existence for the zero solutions of the NDDETE, the condition of implementing synchronization is deduced: the torque of frequency capture is equal to or greater than the difference in the output electromagnetic torque between the two motors. Using the Routh-Hurwitz criterion, we deduce the condition of stability of synchronization that the inertia coupling matrix of the two exciters is positive definite. A numeric result shows that the structural parameters can meet the need of synchronization stability.

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Test of the stability of a three-phase contact line with negative line tension

Molecular Physics ◽

10.1080/002689799164568 ◽

1999 ◽

Vol 96 (9) ◽

pp. 1335-1339 ◽

Cited By ~ 1

Author(s):

ALAN E. VAN GIESSEN, DIRK JAN BUKMAN, B.

Keyword(s):

Contact Line ◽

Line Tension ◽

Phase Contact ◽

Three Phase ◽

The Stability

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A switchable bilinear discrete-time modeling for the stability analysis of the digitally controlled three-phase dual active bridge dc-dc converter

IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society ◽

10.1109/iecon43393.2020.9255075 ◽

2020 ◽

Author(s):

Mohammad Tauquir Iqbal ◽

Ali Iftekhar Maswood

Keyword(s):

Stability Analysis ◽

Discrete Time ◽

Dual Active Bridge ◽

Time Modeling ◽

Three Phase ◽

Digitally Controlled ◽

The Stability ◽

Discrete Time Modeling

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The stability of viscous flow between rotating cylinders in the presence of a magnetic field. II

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1961.0131 ◽

1961 ◽

Vol 262 (1311) ◽

pp. 443-454 ◽

Cited By ~ 3

Keyword(s):

Magnetic Field ◽

Viscous Flow ◽

Rotating Cylinders ◽

Counter Rotation ◽

Angular Velocities ◽

The Stability

The theory developed in an earlier paper (Chandrasekhar 1953) is extended to allow for counter-rotation of the two cylinders. Explicit results are given for the case when the two cylinders rotate in opposite directions with equal angular velocities.

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A new three-phase heterocrystal catalysts and their superior treatment efficiency for tetracycline

Functional Materials Letters ◽

10.1142/s1793604717500151 ◽

2016 ◽

Vol 10 (03) ◽

pp. 1750015

Author(s):

Feng-Rui Wang ◽

Hui-Ping Sun ◽

Yan Wang ◽

Jin-Ku Liu ◽

Yi Fang ◽

...

Keyword(s):

Catalytic Activity ◽

Band Structure ◽

Antibiotic Residues ◽

Treatment Efficiency ◽

Electron Hole ◽

Three Phase ◽

Catalytic Material ◽

Water Based ◽

The Stability ◽

Functional Components

An easy recyclable and interesting Ag3PO4@Pt@TiO2 (APTP) three-phase heterocrystal chains were self-assembled by the cohesive action and chemical construction of polyvinylpyrrolidone (PVP). We found that a new electron–hole transmission path has been built via the rematch of the band structure of Ag3PO4, Pt and TiO2 which extends the light absorption and promoted the electron–hole separation to treat the antibiotic residues in the water. Based on the thorough investigations, a new catalytic material was provided for antibiotics degradation. The catalytic activity of APTP toward the degradation of tetracycline solution was enhanced by 166.67% and the stability increased remarkably compared with pure Ag3PO4 through the integration of different functional components.

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