Vibration Synchronization Research Articles

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

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.

Self-synchronization characteristics of a class of nonlinear vibration system with asymmetrical hysteresis

The self-synchronization characteristics of the two excited motors for the nonlinear vibration system with the asymmetrical hysteresis have been proposed in the exceptional circumstances of cutting off the power supply of one of the two excited motors. From the point of view of the hysteretic characteristics with the asymmetry, a class of nonlinear dynamic model of the self-synchronous vibrating system is presented for the analysis of the hysteretic characteristics of the soil, which is induced by the relation between the stress and the strain in the soil. The periodic solutions for the self-synchronous system with the asymmetrical hysteresis are investigated using nonlinear asymptotic method. The synchronization condition for the self-synchronous vibrating pile system with the asymmetrical hysteresis is theoretical analyzed using the rotor–rotation equations of the two excited motors. The synchronization stability condition also is theoretical analyzed using Jacobi matrix of the phase difference equation of the two excited motors. Using Matlab/Simlink, the synchronous operation of the two excited motors and the synchronous stability operation of the self-synchronous system with the asymmetrical hysteresis are analyzed through the selected parameters. Various synchronous phenomena are obtained through the difference rates of the two excited motors, including the different initial phase and the different initial angular velocity, and so on. Especially, when there is a certain difference in the two excited motors, the synchronous operation of the two excited motors and the synchronous stability operation of the self-synchronous vibrating system with the asymmetrical hysteresis can still be achieved after the power supply of one of the two excited motors has been disconnected. It has been shown that the research results can provide a theoretical basis for the research of the vibration synchronization theory.

Synchronization and vibratory synchronization transmission of a weakly damped far-resonance vibrating system.

The self-synchronization of rotors mounted on different vibrating bodies can be easily controlled by adjusting the coupling parameters. To reveal the synchronization characteristics of a weakly damped system with two rotors mounted on different vibrating bodies, we propose a simplified physical model. The topics described in this paper are related to coupling dynamic problems between two vibrating systems. Both synchronization and vibratory synchronization transmission of the system are studied. The coupling mechanism between the two rotors is analyzed to derive the synchronization condition and the stability criterion of the system. The vibration of the system is described by an averaging method that can separate fast motion (high frequency) from slow motion (low frequency). Theoretical research shows that vibration torque is the key factor in balancing the energy distribution between the rotors. Taking the maximum vibration torque (MVT) as a critical parameter, we investigate the synchronization characteristics of the vibrating system in different cases. The curve of the maximum vibration torque (MVT) versus coupling frequency is divided into several parts by the coupling characteristic frequency and the input torque difference between the rotors. Simulations of the system with coupling frequencies from different parts are carried out. For the system with rotational frequencies larger than the natural frequencies, the coupling characteristic frequency or characteristic frequency curve should be considered. When the coupling frequency is close to the characteristic frequency or the vibration state is close to the characteristic frequency curve, self-synchronization of the two rotors can be obtained easily. Under certain conditions when the coupling effect between the rotors is strong enough, the rotors can maintain synchronous rotation even when one of the two motors is shut off after synchronization is achieved, which is called vibratory synchronization transmission. Vibratory synchronization transmission of the system occurs in a new synchronous condition, and the phase difference between the rotors takes on a new value, that is, the system approaches a new synchronization state.

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

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.

Phase Synchronization Control of Two Eccentric Rotors in the Vibration System with Asymmetric Structure Using Discrete‐Time Sliding Mode Control

Control synchronization of two eccentric rotors (ERs) in the vibration system with the asymmetric structure is studied to make the vibration system obtain the maximum excited resultant force and the driven power. Because this vibration system is essentially an underactuated system, a decoupling strategy for the control goal of the same phase motion between two ERs is proposed to reduce the order of state equation of the vibration system. According to the master‐slave control scheme, the complex control objects are converted into the velocity control of the master motor and the phase control of the slave motor. Considering the self‐adjusting of the vibration system as interference, controllers of the velocity and the phase difference are designed by applying the discrete‐time sliding mode control, which is proved by Lyapunov theory. A vibration machine is designed for evaluating the performance of the proposed controllers. Two control schemes are presented: controlling one motor and controlling two motors, and two group experiments are achieved to investigate the dynamic coupling characteristic of the vibration system in the state of control synchronization. The experimental results show that control synchronization is an effective and feasible technology to remove the limitation of vibration synchronization.

Vibratory synchronization transmission of two cylindrical rollers in a super-resonant vibrating system with symmetrical structure

In this paper, vibratory synchronization transmission of two cylindrical rollers (CRs) with dry friction in a vibrating system excited by two co-rotating exciters is investigated. By virtue of the averaging method of modified small parameters, the synchronization criterion for two exciters and the criterion of vibratory synchronization transmission for two cylindrical rollers are obtained. The stability criterion of synchronous state is acquired based on the Routh–Hurwitz criterion. The effects of system parameters on the ability of synchronization, vibratory synchronization transmission and stability, are quantitatively discussed, which provide a theoretical basis for the project design. Finally, an experiment on a corresponding vibratory synchronization transmission bench is performed to examine the results of the theoretical analysis and numerical discussion. Experimental results will show good agreement with the numerical results. In engineering, certain types of vibratory crusher or vibratory mill can be developed according to the vibratory synchronization transmission theory of two cylindrical rollers.

Joint excitation synchronization characteristics of fatigue test for offshore wind turbine blade

In the case of the stiffness of offshore wind turbine blade is relatively large, the joint excitation device solves the problem of low accuracy of bending moment distribution, insufficient driving ability and long fatigue test period in single-point loading. In order to study the synchronous characteristics of joint excitation system, avoid blade vibration disturbance. First, on the base of a Lagrange equation, a mathematical model of combined excitation is formulated, and a numerical analysis of vibration synchronization is performed. Then, the model is constructed via MATLAB/Simulink, and the effect of the phase difference on the vibration synchronization characteristics is obtained visually. Finally, a set of joint excitation platform for the fatigue test of offshore wind turbine blades are built. The parameter measurement scheme is given and the correctness of the joint excitation synchronization in the simulation model is verified. The results show that when the rotational speed difference is 2 r/min, 30 r/min, the phase difference is 0, π/20, π/8 and π/4, as the rotational speed difference and the phase difference increase, the time required for the blade to reach a steady state is longer. When the phase difference is too large, the electromechanical coupling can no longer make the joint excitation device appear self-synchronizing phenomenon, so that the value of the phase difference develops toward a fixed value (not equal to 0), and the blade vibration disorder is serious, at this time, the effect of electromechanical coupling must be eliminated. The research results provide theoretical basis for the subsequent decoupling control algorithm and synchronization control strategy, and have good application value.

Vibratory synchronization transmission of a cylindrical roller in a vibrating mechanical system excited by two exciters

In present work vibratory synchronization transmission (VST) of a cylindrical roller with dry friction in a vibrating mechanical system excited by two exciters, is studied. Using the average method, the criterion of implementing synchronization of two exciters and that of ensuring VST of a roller, are achieved. The criterion of stability of the synchronous states satisfies the Routh-Hurwitz principle. The influences of the structural parameters of the system to synchronization and stability, are discussed numerically, which can be served as the theoretical foundation for engineering designs. An experiment is carried out, which approximately verify the validity of the theoretical and numerical results, as well as the feasibility of the method used. Utilizing the VST theory of a roller, some types of vibrating crushing or grinding equipments, etc., can be designed.

Numerical and experimental investigation on self-synchronization of two eccentric rotors in the vibration system

In this paper, we study the coupling dynamic characteristic of a single mass vibration machine driven by two eccentric rotors rotating oppositely. According to the coordinate of rotor flux, we deduce the electromagnetic torque of an induction motor in the steady state operation. From three ways of numerical analysis, model simulation and experiment, we discuss the coupling dynamic characteristic by using the actual parameters of this vibration machine. The results show that when the synchronization condition is satisfied, not only the vibration synchronization transmission can be achieved, but also the synchronization motion of the two motors with different power supply frequencies also can be achieved. The phase of the bigger mass-radius product lags behind that of the smaller one, the phase of the bigger distance between the rotation center of eccentric rotor and the mass center of the vibration rigid body lags behind that of the smaller one, and the phase difference decreases with increasing the synchronization velocity. We present a new method that adjusting the power supply frequencies of the two motors to make the vibration system with different structure parameters carry out the 0 phase difference, and its feasibility is verified by experiment.

Investigation for Synchronization of a Rotor-Pendulum System considering the Multi-DOF Vibration

This work is a continuation for our published literature for vibration synchronization. A new mechanism, two rotors coupled with a pendulum rod in a multi-DOF vibration system, is proposed to implement coupling synchronization, and the dynamics equation of mechanism is derived by Lagrange equation. In addition, the coupling relationship between the vibrobody and the pendulum rod is ascertained with the Laplace transformation method, based on the dimensionless equation of the dynamics system. The Poincare method is employed to study the synchronization state between the two unbalanced rotors, which is converted into that of existence and the stability of solutions for synchronization-balance equations. The obtained results are supported by computer simulations. It is demonstrated that the values of the spring stiffness coefficient, the length of the pendulum, and the angular installation of the pendulum are important parameters with respect to the synchronous behavior in the rotor-pendulum system.

Wavelet-Analysis-Based Chaotic Synchronization of Vibrations of Multilayer Mechanical Structures

The chaotic synchronization of the vibrations of contacting multilayer beam–plate–shell structures under external loading is studied. There are gaps between their layers. Such systems are called structurally nonlinear. Their behavior is studied comprehensively, and the influence parameters that characterize the safe and critical modes are determined. A method to study the chaotic phase synchronization of various nature is developed. Vibration synchronization for the following systems is analyzed: (i) a stack of two-layer plates (each equation is linear; however, there is structural nonlinearity if the plates contact), (ii) a plate reinforced with a beam, (iii) a stack of two-layer beams (each component is both physically and geometrically nonlinear; their contact interaction causes structural nonlinearity), (iv) a stack of two-layer shells (each component is both physically and geometrically nonlinear; their contact interaction causes structural nonlinearity)

Vibratory synchronization transmission of two exciters in a super-resonant vibrating system

In this study, vibratory synchronization transmission (VST) of two exciters is investigated in a super-resonant vibrating system to save energy. First, the frequency capture equation of two exciters (FCETE) is deduced by the average method of small parameters. The criterion of VST being the equivalent effective residual torque of motor with power supply should be smaller or equal to the frequency capture torque of the system by setting the disturbance parameters of angular velocities in FCETE to zero. The stability criterion of synchronous states is derived by complying with the generalized Lyapunov equations. Lastly, experiment and computing simulation on VST are conducted. The VST regime of two exciters is discussed in detail from coupling characteristic, current change, visual picture, phase relation, and direct verification of parameters, respectively by comparison and analyses of corresponding data. Results indicate that the key factor in VST implementation is the torque of frequency capture, which serves as the ‘vehicle’ in transferring energy. Thus, the distance between rotational centre of each exciter and mass centre of the rigid frame should be far enough to enhance the ability of VST and ensure energy saving. The theory, experiment, and computing simulation prove that the theoretical approach used in this study is useful and feasible.

Harmonic Vibration Synchronization Analysis of Nonlinear Vibration System Based on Frequency Catching Phenomenon

Based on the electromechanical coupling dynamic model of the single-mass nonlinear vibration system, the quantitative described of the frequency catching phenomena for nonlinear vibration system are been carried out. Then considering the mutual influence between the exciting source and the nonlinear vibrating movement of non-ideal nonlinear vibration system, the frequency catching effect of nonlinear vibration system is been researched, and the theoretical conditions for double exciting motors to realize the harmonic vibration synchronization movement based on the frequency catching effect is been deduced also. Based on the coupling model between motors driving system and vibration mechanical system, and the actual measured mechanical characteristic parameters of the experiment rig, the harmonic vibration synchronization problem for double exciting motors under the frequency catching phenomenon is been verified and explained by numerical simulation and experiment. And for non-ideal and nonlinear vibration system the interrelation between the frequency catching phenomenon, the harmonic vibration synchronization conditions and the factors such as nonlinear strength, stiffness, damping and so on are been analyzed. All the research results can used to provide a certain of theoretical support and experimental basis for the frequency catching harmonic vibration synchronization problem research of the nonlinear vibration system which driven by multi-exciting motors.

Vibratory synchronization and coupling dynamic characteristics of multiple unbalanced rotors on a mass-spring rigid base

The investigation of a generalization of the model on vibratory synchronization for multiple unbalanced rotors (URs) is considered in present work. Based on the previous publications and using the average method of small parameters, the dimensionless coupling equation of multiple URs is constructed, and the criterions of synchronization and stability in the simplified form for multiple URs are given. Taking three counting-rotating URs for example, the coupling dynamic characteristics and synchronization regime of the system are discussed numerically. Then a vibrating synchronization bedstand corresponding to the dynamical model used in numerical discussion is set up, a more detailed discussion and parameter study in experiment are provided, through the analyses on experimental data such as phase differences, rotational velocities and synchronization quality, it is shown that the experimental results are in approximate or good agreement with the numerical/theoretical results, which validates the validity of the model and approach.

Harmonic Vibration Control Synchronization Simulation for Double Exciting Motors of Single-Mass Nonlinear System

For nonlinear harmonic vibration synchronization vibration machine have been widely used in metallurgy, mining, agriculture and other fields, but the harmonic vibration synchronization mechanism for the multi-excitation sources which used to driven the nonlinear vibration machine to realize the harmonic vibration synchronization movement is not clear. In order to study the problem, the nonlinear electromechanical coupling dynamic model has been established for the single-mass harmonic vibration synchronization nonlinear machine in the paper, and by analyzing the coupling dynamic characteristics of the double exciting motors, the harmonic vibration control synchronous simulation model and corresponding harmonic vibration control synchronization strategy have been established. Under the different initial conditions and different Working conditions, the harmonic vibration control synchronization process for the double exciting motors have been simulated. Based on the simulation results, the harmonic vibration control synchronization mechanism for the double exciting motors which used to drive the nonlinear vibration machine have been analyzed and discussed, and the validity of the harmonic vibration control synchronization strategy for the double exciting motors to realize the harmonic vibration synchronization movement has been verified. All these can provide the reference basis for the subsequent nonlinear vibration machine to carry out the harmonic vibration synchronization status application.Introduction

Self-Adaptive Control Synchronization Research of Double Exciting Motors

Based on the single-mass nonlinear vibration system that driven by double exciting motors, the harmonic vibration adaptive control synchronous strategy for the double exciting motors had been designed in the paper. Based on the motion feedback of the double exciting motors to adaptive modify the control parameter of the synchronization controller, make the multi-exciting motors to realize the angular speed equal and phase difference constant synchronous movement. And during the synchronous motion process, adjust the adaptive law to improve the synchronously motion stability margin. The simulation experiments had been carried out based on the simulation model that established in the paper and the experimental results showed that the harmonic vibration synchronization control strategy can achieve satisfactory control accuracy and robustness.

Harmonic Vibration Control Synchronization Analysis of Nonlinear System Based on Flux Linkage Estimate

Aimed to the nonlinear harmonic vibration synchronization system which driven by two exciting sources that, the dynamic model of the nonlinear vibration system has been established. According to the electromagnetic driving characteristics of the asynchronous motor that used to be exciting source, and based on the analysis result of the dynamic model, the two exciting sources flux linkage equations and output torque equations have been established in the paper. And the current control regulation model and flux linkage estimate model of the two exciting sources have been derived also. By numerical simulation experiment, the validity of the harmonic vibration control synchronization strategy for the two exciting sources based on the flux linkage estimation has been verified, which can used to provide the basis and protection for the application of the nonlinear harmonic vibration synchronization system that driven by two exciting sources.

Harmonic Vibration Synchronization Analysis of the Double Motors Based on Equivalent Control Synchronization Strategy

Based on the Lagrange equations, and aimed to the harmonic vibration synchronization problem of the nonlinear vibration machine that driven by double motors, the electromechanical coupling dynamic model of the nonlinear vibration system that driven by double motors had been established in the paper, and harmonic vibration response functions of the nonlinear vibration machine had been deduced also. Based on the equivalent control strategy and the state space equations of the speed difference and phase difference for the double motors that deduced in the paper, the harmonic vibration synchronization control strategy had been established. And based on the sliding surface reaching conditions, the harmonic vibration control synchronization movement law of the double motors had been discussed also. By the simulation experiment, the effectiveness and applicability of the harmonic vibration equivalent control synchronous strategy that established in the paper had been verified. All the research result in the paper can used to be one of an effective control strategy to solve the harmonic vibration synchronization movement problem of the nonlinear vibration machine that driven by dual-motor or multi-motor.

Synchronization Analysis of the Double Exciting Motors in Nonlinear Vibration System Based on Reaching Law

Based on the dynamic model of the nonlinear vibration system which driven by double exciting motors, the rotate speed difference and phase difference state space equations have been deduced. According to the design feature of the nonlinear vibration system and the vibration synchronization requirement of double exciting motors, the approach control synchronization strategy has been deduced with sliding mode reaching law. The practical examples and tests shows that the reaching law synchronization controller can effectively control the double exciting motors to realize the synchronization movement, and the synchronization controller has stronger robustness. The analysis result can provide the theoretical and test basis for the further exploitation of synchronization vibrating machine.

Analysis of Harmonic Oscillation Synchronization for the Single-mass Nonlinear System under Harmonic Wave Sharp Resonance Condition

Based on the dynamic model of single mass nonlinear system,the necessary conditions of harmonic oscillation synchronization motion are deduced,under harmonic wave sharp resonance (main resonant frequency ratio z = 0.95～1.05) condition and dual vibration exciters rotating in opposite direction are moving at the balance singular point. Using the numerical simulation,the valid of the harmonic oscillation synchronization conditions are investigated under different initial conditions. The process of theoretical derivation,consequence of simulation tests and actual tests data indicate that if the systemic characteristic parameter remain constant,the vibration synchronization phenomena of single-mass nonlinear system under harmonic wave sharp resonance condition have direct relationship with the harmonic wave sharp resonance order p/q,and harmonic oscillation synchronization order n/m. But the harmonic oscillation synchronization phenomena of the dual vibration exciters only occur at a certain radio of p/q and n/m which conform to the specific mechanical characteristic conditions of nonlinear system. And they also indicate that the realization of system main resonance synchronization is far easier than system harmonic oscillation synchronization. This research provides theoretical support and test basis for further exploitation of efficient and energy-saving nonlinear sharp resonance shaker.