scholarly journals Synchronization of Two Asymmetric Exciters in a Vibrating System

2011 ◽  
Vol 18 (1-2) ◽  
pp. 63-72 ◽  
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.

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

2013 ◽  
Vol 20 (2) ◽  
pp. 327-340 ◽  
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.

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

2009 ◽  
Vol 16 (5) ◽  
pp. 505-515 ◽  
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.

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

2011 ◽  
Vol 18 (1-2) ◽  
pp. 73-90 ◽  
Author(s):  
Chunyu Zhao ◽  
Qinghua Zhao ◽  
Zhaomin Gong ◽  
Bangchun Wen
Keyword(s):  
Electromagnetic Torque ◽  
Frequency Capture ◽  
Generalized System ◽  
Rigid Frame ◽  
Generalized Systems ◽  
Three Phase ◽  
Small Parameters ◽  
Angular Velocities ◽  
The Absolute ◽  
The Stability

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.

scholarly journals On the Synchronization of Two Eccentric Rotors with Common Rotational Axis: Theory and Experiment

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaozhe Chen ◽  
Xiangxi Kong ◽  
Xueliang Zhang ◽  
Lingxuan Li ◽  
Bangchun Wen
Keyword(s):  
Phase Difference ◽  
Structural Parameters ◽  
Steady Motion ◽  
Rotational Axis ◽  
Vibration System ◽  
Motion Feature ◽  
Small Parameters ◽  
Dimensionless Coupling ◽  
The Difference ◽  
Approach Zero

We study synchronization of two eccentric rotors (ERs) with common rotational axis in the vibration system of the far-resonant spatial motion. We deduce the dimensionless coupling equation of two ERs with applying the average method of small parameters. We convert the synchronization problem into the existence and stability of solving the zero solutions for the dimensionless coupling equations. By introducing the synchronization torque and the difference between the residual torques of two motors, we obtain the synchronization condition that two ERs achieve the synchronized motion. We derive the stability condition of the synchronized motion, which satisfies Routh-Hurwitz criterion. We discuss numerically the choosing motion feature of the vibration system, which indicates that the vibration system has two steady motion modes. The synchronization torque forces the phase difference to approachπwhen the structural parameters of the vibration system satisfy the condition of the spatial cone motion, and the synchronization torque drives the phase difference to approach zero when those satisfy the condition of the spatial circle motion. Finally, through the comparison and analysis of experimental data, the structural parameters of the vibration system satisfying the above two conditions can guarantee the synchronization stability for two ERs.

scholarly journals Synchronization of Two Non-Identical Coupled Exciters in a Non-Resonant Vibrating System of Linear Motion. Part II: Numeric Analysis

2009 ◽  
Vol 16 (5) ◽  
pp. 517-528 ◽  
Author(s):  
Chunyu Zhao ◽  
Hongtao Zhu ◽  
Tianju Bai ◽  
Bangchun Wen
Keyword(s):  
Phase Difference ◽  
Structural Parameters ◽  
Load Torque ◽  
Equivalent Radius ◽  
Vibrating System ◽  
Frequency Capture ◽  
Coupling Dynamic ◽  
Synchronous Operation ◽  
The Stability ◽  
Phase Angles

The paper focuses on the quantitative analysis of the coupling dynamic characteristics of two non-identical exciters in a non-resonant vibrating system. The load torque of each motor consists of three items, including the torque of sine effect of phase angles, that of coupling sine effect and that of coupling cosine effect. The torque of frequency capture results from the torque of coupling cosine effect, which is equal to the product of the coupling kinetic energy, the coefficient of coupling cosine effect, and the sine of phase difference of two exciters. The motions of the system excited by two exciters in the same direction make phase difference close to π and that in opposite directions makes phase difference close to 0. Numerical results show that synchronous operation is stable when the dimensionless relative moments of inertia of two exciters are greater than zero and four times of their product is greater than the square of their coefficient of coupling cosine effect. The stability of the synchronous operation is only dependent on the structural parameters of the system, such as the mass ratios of two exciters to the vibrating system, and the ratio of the distance between an exciter and the centroid of the system to the equivalent radius of the system about its centroid.

Research on the Simulation of Self-Synchronization of Dual Mass for Vibrating System with Two-Motor Drives

2013 ◽  
Vol 300-301 ◽  
pp. 18-21 ◽  
Author(s):  
Duo Yang ◽  
Ye Li ◽  
He Li ◽  
Bang Chun Wen
Keyword(s):  
Dynamic Characteristics ◽  
Structural Parameters ◽  
System Simulation ◽  
Motor Drives ◽  
The Self ◽  
Vibrating System ◽  
Coupling Dynamic ◽  
Synchronous Operation ◽  
The Difference ◽  
The Stability

The coupling dynamic characteristics of the vibrating system with dual mass are analyzed quantitatively. Through numerical computation, the effects of translation and rotation in the system regarding self-synchronization are discussed. The phase difference of two eccentric blocks is caused by the difference of the rated revolution of two motors. The stability of the synchronous operation is dependent on the structural parameters of the system. Simulation is carried out to verify that the system can be synchronized and the model can guarantee the stability of synchronization if the parameters of the system meet the conditions of synchronous implementation and stability. Simulations are also performed for the self-synchronization of two motors with different rated revolutions.

scholarly journals Investigation for synchronization of two co-rotating rotors installed with nonlinear springs in a non-resonance system

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983411 ◽  
Author(s):  
Yongjun Hou ◽  
Mingjun Du ◽  
Luyou Wang
Keyword(s):  
Phase Difference ◽  
Phase Synchronization ◽  
Structural Parameters ◽  
Exciting Force ◽  
Resonance System ◽  
Synchronous State ◽  
Vibrating System ◽  
Nonlinear Springs ◽  
Coupling Equations ◽  
Dimensional Coupling

To avoid anti-phase synchronization for two co-rotating rotors system that occurs so that exciting force generated by the vibrating system is very small, a mechanical model of two co-rotating rotors installed with nonlinear springs is proposed to implement synchronization in a non-resonance system. The dynamic equations of the system are first built up by using Lagrange's equation. Second, an analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics of the vibrating system, the non-dimensional coupling equations of two motors are deduced, synchronization problem is converted to that of existence and stability of zero solution for the non-dimensional coupling equations of angular velocity. It is indicated that the synchronous torque of two motors coupled with nonlinear springs in synchronous state must be greater than or equal to the difference of their residual torque. Then, in light of the Routh–Hurwitz criterion, the synchronous criterion of the vibrating system is obtained. Obviously, it is demonstrated that the synchronous state and the stability criterion of the system are influenced by the structural parameters of the coupling unit, coupling coefficients and the positional parameters of two rotors, and so on. Especially, there are clearances in between two nonlinear serial springs, which result in synchronization of the vibrating system that lies in an uncertain state. At last, computer simulations in agreement with the numerical results verify the correctness of the theoretical results for solving the steady phase difference between two rotors. It is demonstrated that adjusting the value of the coupling spring stiffness can make phase difference close to zero to meet the requirements of the strongly exciting force in engineering.

scholarly journals Linear Structural Trends and Multi-Phase Intergrowths in Helvine-Group Minerals, (Zn,Fe,Mn)8[Be6Si6O24]S2

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 325
Author(s):  
Sytle Antao
Keyword(s):  
Cell Parameter ◽  
Structural Parameters ◽  
Unit Cell ◽  
Fluid Composition ◽  
Ternary Solid Solution ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Difference ◽  
Multi Phase ◽  
And Diffusion

Synchrotron high-resolution powder X-ray diffraction (HRPXRD) and Rietveld structure refinements were used to examine the crystal structure of single phases and intergrowths (either two or three phases) in 13 samples of the helvine-group minerals, (Zn,Fe,Mn)8[Be6Si6O24]S2. The helvine structure was refined in the cubic space group P4¯3n. For the intergrowths, simultaneous refinements were carried out for each phase. The structural parameters for each phase in an intergrowth are only slightly different from each other. Each phase in an intergrowth has well-defined unit-cell and structural parameters that are significantly different from the three endmembers and these do not represent exsolution or immiscibility gaps in the ternary solid-solution series. The reason for the intergrowths in the helvine-group minerals is not clear considering the similar radii, identical charge, and diffusion among the interstitial M cations (Zn2+, Fe2+, and Mn2+) that are characteristic of elongated tetrahedral coordination. The difference between the radii of Zn2+ and Mn2+ cations is 10%. Depending on the availability of the M cations, intergrowths may occur as the temperature, pressure, fugacity fS2, and fluid composition change on crystallization. The Be–Si atoms are fully ordered. The Be–O and Si–O distances are nearly constant. Several structural parameters (Be–O–Si bridging angle, M–O, M–S, average <M–O/S>[4] distances, and TO4 rotational angles) vary linearly with the a unit-cell parameter across the series because of the size of the M cation.

Sensitivity Coefficients Utilized in Nonlinear Estimation With Small Parameters in a Heat Transfer Problem

1970 ◽  
Vol 92 (2) ◽  
pp. 215-221 ◽  
Author(s):  
J. V. Beck
Keyword(s):  
Model Building ◽  
Transfer Problem ◽  
Nonlinear Estimation ◽  
Transient Heat Conduction ◽  
Computer Time ◽  
Sensitivity Coefficients ◽  
Yield Information ◽  
Small Parameters ◽  
The Difference ◽  
Building Identification

The method of nonlinear estimation for determining parameters in differential equations is extended to treat more efficiently the problem of determining dominant and small parameters. Using the sensitivity coefficients, it is shown how to determine the dominant parameters first using nonlinear estimation and then using linear least squares to find the small parameters. This procedure can save a considerable amount of computer time. Even more important is the application to model-building (identification). The residuals for the difference of the temperatures calculated, assuming the small parameters are zero, and the measured temperatures are shown to yield information for discriminating between alternate mathematical models. A transient heat-conduction example is given to illustrate some of the concepts developed.

scholarly journals DYNAMICS OF TRACTION DEVICE OF MINE SUSPENDED MONOREL ROAD

2020 ◽  
Vol 12 (3) ◽  
pp. 410-417
Author(s):  
Viktor GUTAREVICH ◽  
◽  
Marina KONDRATENKO ◽  
Keyword(s):  
Mathematical Model ◽  
Mechanical System ◽  
Structural Parameters ◽  
Low Frequency ◽  
Dynamic Loads ◽  
Pressing Force ◽  
Negative Effect ◽  
Traction Device ◽  
The Difference ◽  
Fatigue Fractures

During the operation of the mine suspension monorail track and traction device form a mechanical system experiencing high dynamic loads associated with implementation of traction and braking forces. Emerging dynamic loads lead to formation of elastic deformations and oscillations that cause vibrations, which leads to displacement of drive wheels and reduces the implementation of traction. The study of the dynamics of traction device is an important step in improving safety and reliability of monorail transport. The aim of the work is to study dynamics of a friction-type traction device moving along a suspended monorail to assess influence of parameters of the elements of device on the vibrations and nature of interaction of drive wheels with monorail. Research methods. Mathematical modeling of the oscillatory processes resulting from interaction of the running gear of the traction device with the monorail is used. Stages of research include drawing up a design diagram oscillations of drive wheels of the traction device interacting with the monorail, developing a mathematical model for the analysis of vibrations caused by moving loads, also assessing the influence of structural parameters of mechanical system under consideration on nature of oscillations. Research results. The developed mathematical model of friction-type traction device movement allows us to establish relationship between parameters of structural elements of its running gear and pressure mechanism, as well as nature of vibrations that arise. As a result, frequencies of the mechanical system under consideration and maximum deviations were found, which allows you to set optimal device parameters to increase traction and increase lifespan of monorail suspended roads. Findings. It was determined that the frequency range of vibration of drive wheels mainly corresponds to the mid-frequency local vibrations of 16–36 Hz. Increasing length of lever for fixing axles of wheels and reducing their radius leads to formation of low-frequency vibrations with a frequency of less than 15 Hz. When length of lever of drive wheels is more than 0.5 m, shoulder of the spring is more than 0.6 m and radius of drive wheels is less than 0.25 m, vibrations with frequencies below 5 Hz can occur. It was found that increasing the length of lever for securing spring increases the oscillation frequency of one drive wheel and reduces frequency of the other. The difference between these frequencies significantly affects changes in the pressure of the wheels against monorail. When difference between frequencies is more than 10–12 Hz, direction of load changes pulsed, with a maximum swing of 0.02 rad, which reduces formation of fatigue fractures of tire wheels, and moments of decrease and increase in pressing force have a negative effect on traction, leading to slippage of drive wheels. When difference between frequencies is less than 10–12 Hz, direction of the load changes sharply, with a maximum swing of 0.03 rad, which increases deformation and formation of fatigue fractures of tire wheels, and short moments of weakening and increase of pressing force, constituting 0.1–0.3 s does not have a significant negative effect on traction.

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