Vibration Synchronization Research Articles

Synchronization phenomenon in a vibrating system driven by four eccentric rotors mounted in the orthogonal plane

The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.

Controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method.

With a requirement of miniaturization in modern vibrating screens, the vibration synchronization method can no longer meet the process demand, so the controlled synchronization method is introduced in the vibrating screen to achieve zero phase error state and realize the purpose of increasing the amplitude. In this article, the controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method is investigated. Firstly, according to the theory of mechanical dynamics, the motion state of the vibrating screen is simplified as the electromechanical coupling dynamical model of a vibrating system driven by two inductor motors. And then the synchronization conditions and stability criterion of the vibrating system are derived and numerically analyzed. Based on a master-slave controlling strategy, the controllers of two motors are respectively designed with Super-Twisting sliding mode control (ST-SMC) and backstepping second-order complementary sliding mode control (BSOCSMC), while the uncertainty is estimated by an adaptive radial basis function neural network (ARBFNN). In addition, Lyapunov stability analysis is performed on the two controllers to prove their stability theoretically. Finally, simulation analysis is conducted based on the dynamics model in this paper.

Frequency-multiplying synchronous control of the multiple counter-rotating exciters in vibration system

Frequency-multiplying synchronization vibration system is beneficial to diverse the material screening and improve the screening efficiency. In order to solve the problems of insufficient frequency-multiplying synchronous theory and low synchronization precision of the multiple exciters in vibration systems, the dynamic model of the frequency-multiplying synchronous vibration system with multi-vibration exciters is first established. A combined control strategy including the master-slave control and the adjacent cross-coupling control strategy is then proposed, together with the adaptive sliding mode algorithm to realize the frequency-multiplying synchronous control for the multiple exciters in vibration system. The stability of the proposed multiple exciters under frequency-multiplying synchronous control is proved by Lyapunov theorem and Barbalat Lemma. The performance of the proposed controller of frequency-multiplying synchronization is illustrated by comparing the simulation analysis with the vibration synchronization method at double frequency. The results show that the proposed controller of frequency-multiplying synchronization can effectively control the multiple exciters in vibration system to achieve the frequency-multiplying synchronous motion with improved control precision. The influence of different parameters on the performance of the frequency-multiplying synchronization is discussed, which shows that the controller of frequency-multiplying synchronization has good robustness against the system parameter disturbance. On this basis, the synchronization performance of the multiple exciters under different multiplied frequencies are analyzed and explained. The proposed combined control strategy can control the frequency-multiplying synchronization of the multiple exciters in the vibration system to achieve the required stable vibration trajectory.

Synchronization investigation on space vibration system driven by two vibrators with arbitrary direction axes

To reveal the more inclusive vibration synchronization mechanism, investigation is extended to space vibration system driven by two vibrators with arbitrary direction axes. Based on a reliable method for changing the relative rotation direction of vibrators, Lagrange dynamic equation is introduced to obtain vibration responses of the constructed model. Then the electromechanical coupling torque is analyzed through considering load generated by mechanical structure into two vibrators, and synchronization stability is explored by Lyapunov with Kronecker product theory. Next, some important numerical calculations are conducted to analyze synchronization characteristics further. Finally, corresponding experiments are organized to verify the reliability of theoretical and numerical analysis, and the feasibility of detection method through vibration testing displacements for phase differences (PDs) in unstable and stable states is discussed. Results indicate that in arbitrary space or plane patterns a better universality of this study is possessed whether or not identical rotation directions of two vibrators; the PDs can be accurately obtained from vibration displacements.

Dynamic characteristics analysis of a novel vibrating screen based on electromechanical coupling simulation

The vibrating screen with statically indeterminate mesh beam structure (VSSIMBS) is a novel type of large vibrating screen, which is widely used in coal preparation plants due to its high strength and processing capacity. In this study, the VSSIMBS motion differential equations were obtained via on Lagrange equation, and the dynamic vibration system model was established. The eccentric block force conditions during the operation were analyzed, and the stable vibrating screen operational conditions were obtained. The electromechanical coupling simulation model of VSSIMBS was built in Simulink, allowing frequency control and vibration synchronization experiments. Experimental frequency control results have shown that when the output characteristics of both motors are either the same or similar, synchronous movement can be achieved. Regarding vibration synchronization, experiment results have shown that when two motors are in synchronous motion, and the power supply of one motor is cut off, they still can operate synchronously. Thus, the experimental results obtained in this study provide a theoretical reference for improving the motion stability of large vibrating screens.

Моделирование движения ленточного конвейера с учетом угла наклона и натяжения канатов става

Introduction. The relevance of the work is caused by the need to eliminate the arising automatic vibration processes of the pendent roller of the conveyor linear sections relative to roller pendant and minimization of vibration synchronization processes of a significant number of pendent rollers, leading to a conveyor stop. Previous studies have established that the most effective way to transport coarse material in underground mining is a belt conveyor. These studies have identified the disadvantages of conveyor transportation.The most common ones include the auto-vibration of the pendent roller of the conveyor linear sections relative to roller pendant. The manifestation of roller automatic vibrations increases the energy intensity of the process and reduces the performance of the belt conveyor. Objective. To set the angle of the conveyor belt inclination and the tension of the ropes of the load-bearing structure with the lowest amplitude vibrations of the pendent roller in order to reduce the energy intensity of the transportation process during the deposit development and increase the operational performance of the conveyor. Task. Modeling the possibility of manifestation and causes of occurrence, as well as the circumstances of long-term preservation of roller automatic vibrationson conveyors. Materials and methods of research. The object of the study is a conveyor belt with different angles of inclination (transportation).The authors conducted analysis and summary of previously performed own research; comparison with newly obtained experimental results; as well as a generalization of theoretical and experimental studies carried out by scientists in this field; synthesizing literature and patent data. Reliabilityis confirmed with application of actual state standards and approved research methodology. Boundary conditions are accepted: conveying of ordinary medium- and small- sizedmaterials is carried out; there is a constant unit load on the belt during transportation. Two types of connection are considered: the presence of an anchoring branch of roller with the ropes; absence of an anchoring branch that is the hinged connection of roller with the ropes. Research results. It has been established that when the belt moves with a load, the pendent roller deflects along the direction of the belt movement, regardless of the type of anchoring. The angle of the side roller inclination is calculated through the sliding velocity relative to the belt. The characteristics of sliding friction or change in sliding friction coefficient are modeled. The influence of the pendent roller mass on the process of automatic vibrationsat various angles of conveyor inclination has been evaluated. The reason for the occurrence of automatic vibrationsis established. Conclusion. Design changes that prevent side roller misalignment are recommended to reduce the likelihood of automatic vibrations.The side roller misalignment angle interval, beyond which stable conveyor operation is achieved, is determined. Resume. The results of the research can be useful in designing the conveyor when transporting the extracted raw materials.

Double machine vibration synchronization system based on GA-PID

Aiming at the problem that it is difficult to realize the synchronization of motor speed under the electromechanical coupling condition of DC motor and vibrating mass in double machine drive vibration system, the PID parameters of DC motor are optimized by using master-slave control mode and genetic algorithm. Firstly, the electromechanical coupling model of the vibration system is established, and the differential equation of motion of the system is obtained by using Lagrange equation; Using master-slave control structure and genetic PID control algorithm, a controller based on master motor speed difference and slave motor phase difference is designed; The MATLAB/Simulink simulation model is established to verify the effectiveness of the control system. The experimental results show that the genetic PID algorithm based on master-slave control structure can better realize the synchronous control of dual machine driven vibration system. The research content can provide a theoretical basis for the design, control and application of this type of vibration system.

Simulation of master-slave optimal synchronous control of double motors based on Simulink

In the working process of vibration machinery, as the output device of power source, the synchronous running state of motor has a decisive influence on the working efficiency of vibration machinery. This paper mainly studies the control synchronization of the double-mass vibration system driven by two motors. Firstly, the dynamic model of the vibration system is established and the vertical displacement equation of the vibration system is derived. Secondly, using adaptive model and PD control algorithm, the controller of motor in vibration system is designed to achieve accurate control of motor and eccentric block motion. Finally, the vibration synchronization effect of the control system and the effectiveness of the control system are verified by modeling and simulation with MATLAB/Simulink software. The test results show that when the main motor is in different initial phases, the variable parameter controller can achieve the control synchronization of the main motor and the slave motor in a short time and achieve a better control synchronization effect. Relevant research results can provide theoretical basis for the design of double-motor vibration machinery.

Synchronized switch piezoelectric energy harvesting using rotating magnetic ball and reed switches

Synchronized switch harvesting on inductor (SSHI) interface circuit has been developed to boost the harvesting capability of piezoelectric energy harvesters (PEHs). Although some electronic self-powered peak-detector and switching circuits have been proposed to support the practical realization of SSHI, the energy dissipation and voltage drops in transistors and diodes of the self-powered circuits might significantly deteriorate the actual energy harvesting performance. Some mechatronic designs were proposed as well. However, most of their switches are activated by touch impacts, which might introduce undesired high-order vibrations to the main structure. In this paper, rather than using the impact-engaged strategy discussed in the literature, a new mechanism using a magnetic ball for vibration synchronization and reed switches for switching operation is proposed. A PEH shunted to an SSHI interface circuit using the proposed mechatronic approach has been prototyped. Since the peak-detection and switching operations are completed by a mechanical mechanism, less passive electrical components, which consume extra energy, are required in our proposed design. Therefore, the overall energy harvesting performance is improved. Numerical simulations and experimental tests have validated the feasibility of the proposed design. The experimental results have shown that the power output produced by the proposed mechatronic self-powered SSHI design can be increased by and , as compared with the cases using a benchmark standard energy harvesting bridge rectifier and an electronic self-powered SSHI solutions, respectively. Moreover, owing to the new mechatronic design, the auxiliary mechanical components are embedded in the tip block of the cantilevered PEH, rendering the whole system to be a compact design.

Dynamics of the Vibration System Driven by Three Homodromy Eccentric Rotors Using Control Synchronization

To solve the limitation of vibration synchronization, this paper investigates the dynamics of a vibration system driven by three homodromy eccentric rotors (ERs) using control synchronization. According to the synchronous condition and the stability condition, the changes of the phase differences of the three-ERs system and the two-third ERs system are obtained. Based on the electromechanical mathematic model of the vibration system and the master-slave control strategy, the synchronous target that three ERs achieve the same phase motion is converted into velocity and phase tracking of ERs. Considering the coupling characteristic of the self-adjusting of the system in the state of vibration synchronization, the velocity and phase controllers are designed by employing discrete-time sliding mode control. An experimental system for control synchronization is designed, including hardware composition and software programming. For the feedback signal used to match control targets, a method of calculating velocity and the phase difference is proposed from engineering. Recording the rotational velocities, phase differences, and system response, three group experiments with different control schemes are achieved. According to the experimental data, the coupling characteristic of the vibration system adopting control synchronization is analyzed, which can provide the basis for designing vibration machines using control synchronization.

Theoretical Study on Synchronization of the Counter-Rotating Exciter in the Compound Vibrating Field

Aiming at the impact of the complex vibration environment generated by the integrated vibration equipment on the vibration testing equipment, this paper proposes a new method to solve the vibratory synchronization problem in the compound vibration environment. A new concept of the compound vibrating field is proposed, and a new simple vibrating system with a single counter-rotating exciter in a compound vibrating field is established. The motion differential equation of the system is established by the integral mean method with small parameters, and then the periodic coefficient differential equation is obtained through linearization. Based on the relevant theory of the second-order differential equation with periodic coefficient, the synchronization criterion and stability criterion of the vibrating system are derived. According to the theoretical criteria, the coupling characteristics of the exciter and the vibrating field are numerically simulated and analyzed, which supports the theoretical results. The proposed compound vibrating field provides a new way for studying vibratory synchronization.

Low-loss and high-resolution mechanical mode tuning in microspheres.

Lack of tunability impedes the wide application of optomechanical systems; however, little research exists on mechanical frequency tuning. Herein, ultra-fine low-loss dynamical mechanical frequency tuning is achieved by compressing a microsphere along the axial direction. The tuning resolution reaches approximately 4% of the mechanical linewidth, and the variation range of the mechanical quality factor (Qm) is within 2.9% of the untouched Qm. The roles of geometric deformation, spring effect, and stiffness were also evaluated through simulation and experimental analysis. Furthermore, sine function modulation was displayed, with a Pearson coefficient exceeding 99.3%, to achieve arbitrary-function mechanical resonance tuning. This method paves the way for scalable optomechanical applications, such as mechanical vibration synchronization or optomechanics-based optical wavelength conversion.

Vibration synchronization intelligent control with trajectory tracking

Based on the dynamic model of the double-mass vibrating mechanical system, the adaptive control theory is introduced to study the motor control synchronization problem in the vibrating mechanical system. First, the dynamic model of the dual-mass nonlinear vibration system is studied, and the overall relationship between the motor motion and the vibration system is analyzed. Then, a dual-motor adaptive control strategy is designed, so that the parameters in the control system can be intelligently adjusted with the synchronization state of the motors, and the synchronization stability and motion trajectory between the motors are studied. Lyapunov stability criterion is used to verify the stability of the synchronous control system. Finally, MATLAB/Simulink is used to simulate the effectiveness of the dual-motor adaptive control system, which proves that the system has good robustness. Through research, it is found that the dual-motor vibration synchronization adaptive control strategy can keep the motors in the dual-mass nonlinear vibration system with good synchronization effects, and the system has good robustness. The research content can provide a certain theoretical reference for the research and design of multi-motor synchronous machinery.

Theoretical and Numerical Studies on Vibratory Synchronization Transmission of a Vibrating Mechanical System Driven by Single Motor Considering Sliding Dry Friction

As a continuous work of the previous literatures, a special dynamical model with one cylindrical roller driven by a single exciter and one outer ring, is taken for example to explore the vibratory synchronization transmission (VST) of the system considering sliding dry friction in this paper. The motion differential equations of the system, are given firstly. Using the average method, the theory condition of implementing VST is obtained. The VST characteristics are qualitatively discussed in numerical, which are further quantitatively verified by simulations. It is shown that, the vibration amplitudes of the roller in the horizontal and vertical directions are basically identical, and less affected by the friction coefficient, but the stable phase difference between the exciter and the outer ring is affected too much by it. Based on the present work, some new types of vibrating equipments, such as vibrating crushers/mills, can be designed.

Theory of Frequency Captured of Eccentric Rotor by Vibration Environment with Same Direction

Aiming at the frequency synchronization phenomena of oscillating or rotating bodies, this paper proposes a novel solution to address the self‐synchronization problem of vibration systems. An integral mean method with small parameters and periodic coefficient (IMM‐SPPC) is proposed, which converts the relative motion of the electrically driven eccentric rotor and the vibration environment into a second‐order periodic coefficient differential equation. Through the calculation of the equilibrium point of the second‐order periodic coefficient differential equation and the study of its stability, the synchronization criterion and the stability criterion of the eccentric rotor and the vibration environment are deduced. The simulation results show the validity of the deduced synchronization criterion and stability criterion. The proposed IMM‐SPPC provides a new way for studying vibration synchronization.

The Phenomenon of Bistable Phase Difference Intervals in the Times-Frequency Vibration Synchronization System Driven by Two Homodromy Exciters

A vibration system with two homodromy exciters operated in different rotational speed is established to investigate whether the phenomenon of bistable phase difference intervals exists in the times-frequency vibration synchronization system. Some constructive conclusions are proposed. (1) By introducing an average angular velocity perturbation parameter ε0 and two sets of phase difference perturbation parameters and ε2, the frequency capture criterion and the necessary criteria for realizing the times-frequency vibration synchronization are derived. The corresponding stability analysis is carried out. (2) By the theoretical analysis and experiments, it is verified that the times-frequency vibration synchronization system exists the phenomena of bistable phase difference interval. That is, the phase differences between the two homodromy exciters are stable around 180 degrees when they are located at a short distance; the antiphase synchronization phenomenon appears. On the contrary, they are stable around 0 degrees at the in-phase synchronization state. (3) Because of the two homodromy exciters operating in the different rotational speed, the vibration system obtains relatively complex compound motion trajectories; the corresponding application is investigated by adding a feeding material chamber. The times-frequency vibration synchronization system can be used to design the vibration mill for reducing its low-energy zone and developing chaotic mixing equipment for obtaining a better mixing effect.

Synchronization of a Dual-Mass Vibrating System with Two Exciters

From the perspective of theoretical derivation, numerical simulation, and engineering application, the vibratory synchronization characteristics of a dual-mass vibrating system driven by two exciters, were studied. The differential motion equations of the total system were calculated using Lagrange’s equations, and the responses of the vibrating system in the steady state were derived by Laplace transform. The synchronization criterion between two exciters was deduced by using the averaging method. Based on the Hamilton principle, the stability criterion of the vibrating system in synchronous states is given. According to the theoretical results, the coupling characteristics between two exciters such as synchronization and stability were analyzed numerically. Some analyses of the numerical simulation of the system were carried out, which fully support the theoretical results. The rotational speed of two exciters, their phase difference, responses, and difference of responses of two rigid bodies were studied quantitatively in the subresonant state and super-resonant state of the system. This paper presents a practical example of vibratory synchronization of a dual-mass system driven by two exciters in engineering.

Analysis of material motion characteristics of vertical nonlinear synchronous vibration dryer

The nonlinear characteristics of a vertical dryer prototype under the synchronous excitation of vibration motors were analyzed. The vibration synchronization conditions of the two excitation motors of the vertical dryer were pursued. The analysis of motion characteristics of the material granules on the vertical dryer was conducted. The relationship between the structure parameters of the vertical dryer powered by two excitation motors and the motion characteristics of the material granules were discussed. Experimental results and discussion were used to verify the correctness of the theoretical analysis. This research demonstrated that the displacement of the material granules in the moving direction increased as the installment angle of the two excitation motors increased. This can improve the production efficiency; however, too large an installment angle destabilized the response of the dryer, no longer satisfying the design and use requirements. The research methods and conclusions presented in this paper can provide theoretical support and experimental basis for future development of a vibration dryer powered by two excitation motors.

Synchronous Behavior Analysis of Two Rotors in Self-synchronization System

Synchronization is widespread in many engineering fields. The double eccentric rotary exciter driven synchronous vibration system can be simplified as a dual-rotor self-synchronizing system. Taking a universal synchronous test bench as the research object, the synchronization characteristics of the self-synchronization system are quantitatively studied in several cases, which fully verifies the ability of the vibration system to self-recover synchronization. Based on the parameters of the experimental platform as a reference, and compared with the measured results, the rationality of the simulation results is proved. Moreover, through experiments and simulations, it is found that when the excitation force is not equal, even if the motor power with larger excitation force is turned off, the system can resume the vibration synchronization state by itself.

Analysis of harmonic vibration synchronization for a nonlinear vibrating system with hysteresis force

Harmonic vibration synchronization of the two excited motors is an important factor affecting the performance of the nonlinear vibration system driven by the two excited motors. From the point of view of the hysteresis force, the nonlinear dynamic models of the nonlinear vibration system driven by the two excited motors are presented for the analysis of the hysteresis force with the asymmetry. An approximate periodic solution for the nonlinear vibration system with the hysteresis force is investigated using the nonlinear models. The condition of harmonic vibration synchronization is theoretically analyzed using the rotor–rotation equations of the two excited motors in the nonlinear dynamic models and the stability condition of harmonic vibration synchronization also is theoretically analyzed using Jacobi matrix of the phase difference equation of two excited motors. Using Matlab/Simlink, harmonic vibration synchronization of the two excited motors and the stability of harmonic vibration synchronization for the nonlinear vibration system with the hysteresis force are analyzed through the selected parameters. Various synchronous processes of the nonlinear vibration system with the hysteresis force are obtained through the difference rates of the two excited motors (including the initial phase difference, the initial rotational speed difference, the difference of the motors parameters). It has been shown that the research results can provide theoretical basis for the design and research of the vibration system driven by the two-excited motors.