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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...
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... Lastly, we propose a new method to adjust the phase difference. This paper is organized as follows. Section 2 gives the experimental model and theory results. Section 3 shows numerical results. Section 4 establishes simulation model. Section 5 presents the experiment results. Finally, we summarize our conclusion at the end of this paper. Fig. 1 illustrates the dynamic model of the vibration system, in which springs are connected to a rigid frame. The two vibration motors are symmetrically installed in the vibration rigid body rotating in the opposite direction to excite the vibration system. The frame is a fixed frame, and its origin is the equilibrium point of centroid of ...
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... of the vibration in -direction. From these typical cases, it is proved to be an effective method that the load torques of the two motors aren't equal because the different structure parameters, which can be balanced by the different electromagnetic torques, finally the vibration system achieve the self-synchronization with the 0 phase difference. Fig. 10(a) shows the mechanical composition of the vibration machine, which consists of the two vibration motors, the vibration rigid, the four groups of spring and the support base. Fig. 10(b) shows the data signal collecting devices, the signals of the vibrations in the horizontal, vertical and swing directions, and the rotational velocities of ...
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... which can be balanced by the different electromagnetic torques, finally the vibration system achieve the self-synchronization with the 0 phase difference. Fig. 10(a) shows the mechanical composition of the vibration machine, which consists of the two vibration motors, the vibration rigid, the four groups of spring and the support base. Fig. 10(b) shows the data signal collecting devices, the signals of the vibrations in the horizontal, vertical and swing directions, and the rotational velocities of the two motors are collected by B&K vibration testing. Meanwhile, the signal of the root mean square of motor 1 stator current is collected by HIOKI PW3335 power meter. Numbers 1-3 ...
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... vertical and swing directions, and the rotational velocities of the two motors are collected by B&K vibration testing. Meanwhile, the signal of the root mean square of motor 1 stator current is collected by HIOKI PW3335 power meter. Numbers 1-3 represent the testing positions of the acceleration sensors, and numbers 4-5 are velocity sensors in Fig. 10(a). Fig. 11 shows the experimental results with the same schemes of numerical simulations in Section 4.1. The synchronization velocities of the two motors are close to 995 r/min, 991 r/min and 984 r/min under these three typical cases, and the phase differences are about 2.9°, 20.3° and 46.5°, respectively, which are close to the ...
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... and swing directions, and the rotational velocities of the two motors are collected by B&K vibration testing. Meanwhile, the signal of the root mean square of motor 1 stator current is collected by HIOKI PW3335 power meter. Numbers 1-3 represent the testing positions of the acceleration sensors, and numbers 4-5 are velocity sensors in Fig. 10(a). Fig. 11 shows the experimental results with the same schemes of numerical simulations in Section 4.1. The synchronization velocities of the two motors are close to 995 r/min, 991 r/min and 984 r/min under these three typical cases, and the phase differences are about 2.9°, 20.3° and 46.5°, respectively, which are close to the simulation ...
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... Fig. 11(a), it is seen that the fluctuation of the velocity curves of the two motors with same power frequencies are highest, that of the two motors with different power frequencies is the second, and that of the vibration synchronization transmission is the smallest. This phenomenon also can be observed in Fig. 11(b). The reasons are that when ...
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... Fig. 11(a), it is seen that the fluctuation of the velocity curves of the two motors with same power frequencies are highest, that of the two motors with different power frequencies is the second, and that of the vibration synchronization transmission is the smallest. This phenomenon also can be observed in Fig. 11(b). The reasons are that when there is a phase difference because of the external disturbance, the synchronization torque will join in the distribution of the load torques, which acts the driving torque on the phase lagging motor to increase its velocity and acts the load torque on the phase leading motors to decrease its velocity. ...
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... steady synchronization state. After the power of motor 2 is cut off, the fluctuation of the rotational velocities is slow because only one motor to drive the vibration system. During the last case, the synchronization torque always acts the load torque on motor 1 with higher power frequency, and acts the driving torque on motor 2 with lower one. Fig. 11(c) shows the root mean square of stator current of motor 1. Due to the load torque of motor 1 is bigger at the beginning of power supply, there is a peak value on the current curve, and the current begins to decrease after motor 1 rotating. At 7 s, the current again exist a peak value because the power of motor 2 is supplied to increase ...
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... with increasing the phase difference, and current curve is smooth under the synchronization motion. According to the change of current, we can know that the change of the electromagnetic torque of the motor in vibration system. By observing the change of the current curve of the motor's stator to study the self-synchronization is a good way. Fig. 11(d)-(f) show the vibrations in the vertical, horizontal and swing directions. Due to the phase difference is not equal to 0, the vibrations in the horizontal and swing directions are existent. It is also seen that only the 0 phase difference, the machine can carry out the vibration in the vertical direction without others. It is beneficial to ...
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... we have obtained numerically the 0 phase difference by applying the coupling dynamic characteristic. Next, we will verify the correctness of the method. We adjust the exciting force of ER 1 to 40 %, and that of ER 2 to 100 %. We adjust the distance between the rotational centre of ER 1 and the mass centre of the vibration rigid body to 0.4 m. Fig. 12 shows phases recorded by high-speed camera with same power frequency 50 Hz. the phase difference in Fig. 12 is about 27°. Fig. 13 shows phases recorded by high-speed camera with different power frequency, the power frequency of motor 1 is 49.6 Hz and that of motor 2 is 50 Hz. the phase difference in Fig. 13 is about ...
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... we will verify the correctness of the method. We adjust the exciting force of ER 1 to 40 %, and that of ER 2 to 100 %. We adjust the distance between the rotational centre of ER 1 and the mass centre of the vibration rigid body to 0.4 m. Fig. 12 shows phases recorded by high-speed camera with same power frequency 50 Hz. the phase difference in Fig. 12 is about 27°. Fig. 13 shows phases recorded by high-speed camera with different power frequency, the power frequency of motor 1 is 49.6 Hz and that of motor 2 is 50 Hz. the phase difference in Fig. 13 is about ...
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... of the vibration rigid body to 0.4 m. Fig. 12 shows phases recorded by high-speed camera with same power frequency 50 Hz. the phase difference in Fig. 12 is about 27°. Fig. 13 shows phases recorded by high-speed camera with different power frequency, the power frequency of motor 1 is 49.6 Hz and that of motor 2 is 50 Hz. the phase difference in Fig. 13 is about ...
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Citations
... Compared with pendulum synchronization, ER synchronization is more useful in engineering applications to design vibration machines. To get the maximum force, Chen et al. [8] proposed a new method to achieve zero phase difference between two ERs for vibration system with different structural parameters by adjusting the power supply frequency of motors studied the synchronization problem of two co-rotating shaft ERs in the far-resonant state, which provides a guide for designing a kind of vibration grinder. In fact, not only the same frequency has the phenomenon of synchronization, but multi-frequency also has the synchronous application. ...
This paper studies synchronization of a class of even pairs and symmetrically distributed eccentric rotors in a vibration system of a single mass body. A vibration system driven by four ERs with circular distribution structure and the same rotating direction is adopted as the dynamic model. The motion differential equations of the system are established based on Lagrange equation. The angular velocity and the phase of each rotor are perturbed by the average value of the synchronous velocity. The state equation of the system is obtained by applying the averaging method. According to the necessary condition of the steady-state motion, the synchronization condition and the dimensionless coupling torques of the system are deduced. The stability condition of the synchronous motion is derived by applying Lyapunov indirect method. The distribution law of the steady-state phase difference is discussed qualitatively by the numerical analysis of the theoretical results. Then combined with the numerical results, five sets of experiments are carried out on the experimental machine, which includes the sub-resonant state and the super-resonant state. The experimental results show that this vibration system has two super-resonant motion states and one sub-resonant motion state. The experiment proves the correctness of the theory, which can provide theoretical guidance for the design of this kind of vibration machine.
... Zhang et al. studied vibratory synchronization transmission (VST) of two exciters in a super-resonant vibrating system, and find that the most important factor effecting the VST is the torque of frequency capture. 1 Chen et al. proposed a new method that making the two rotors of the vibrating system with different structural parameters realize 0 phase difference by adjusting the power supply frequencies of the two motors. 2 Further, Zhao et al. discussed the effects of the dynamic parameters on the performance of the self-synchronization vibrating conveyor with two exciters. 3 Hou et al. proposed that the distance between the mass center of the system and the rotating center of the motor is an essential role in effecting the synchronization. ...
... 9 Though some proposed a host of methods including adjusting the power supply frequencies, control synchronization, and so on to improve the synchronization characteristics. 2,8,9 However, their research did not consider material motion. Materials, as the main working object of the vibration system, have a great effect on the synchronization and stability of the system when material mass is large, and the effects cannot be ignored. ...
Nowadays, two exciters vibration system played an indispensable role in a majority of machinery and devices, such as vibratory feeder, vibrating screen, vibration conveyer, vibrating crusher, and so on. The stability of the system and the synchronous characteristics of two exciters are affected by material motion. However, those effects of material on two exciters vibration system were studied very little. Based on the special background, a mechanical model that two exciters vibration system considering material motion is proposed. Firstly, the system's dynamic equations are solved by using Lagrange principle and Newton's second law. Then, the motion stability of the system when material with different mass move on the vibrating body is analyzed by [Formula: see text] mapping and numerical simulation methods, and the motion forms of the material are also studied. Meanwhile, the frequency responses of the vibrating body are analyzed. Finally, the influence of material on the phase difference of the two exciters is revealed. It can be concluded that with the mass ratio of the material to the vibrating body increasing, the system's motion evolves from stable periodic motion to chaotic state, the synchronization ability of two exciters decline, and the unpredictability of abrupt change about the phase difference increases. Further, the uncertainties of both the abrupt change of phase difference and the collision location affect each other and eventually lead to the instability of the system.
... Although a vibration machine introduces vibration synchronization to replace the method of forced synchronization such as gears or chains, the application of vibration synchronization is still limited by its structural parameters [11,13]. When the number of ERs exceeds two, there is no the same phase (in-phase) motion between the rotors. ...
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.
... The vibrating systems driven by two eccentric rotors are widely used in the industrial field, such as: vibrating screen, vibratory feeder, shakeout machine, vibration conveyor, etc. The vital factor, affecting the stability of the vibrating system, is the synchronous characteristics of two eccentric rotors, so the researches about the synchronization of eccentric rotors became a hot topic in the scientific research field in recent years [1][2][3][4][5][6][7][8][9][10][11]. In the meanwhile, vibration synchronization is the most common synchronization method, and is favored by the majority of scholars. ...
... Zhang et al. studied the vibration synchronization transmission of a super-resonant vibrating system driven by two exciters [1]. Based on the Zhang's study, Chen et al. investigated the coupling dynamic characteristic of a vibration system of two eccentric rotors by using numerical analysis, model simulation and experiment [2]. Further, Fang et al. discussed the synchronization characteristics of two rotors vibration system, and revealed that the synchronization performance are affected by the system's parameters, coupling coefficients, and rotation direction of rotor [4,5,7]. ...
The self-synchronizing far-resonant vibrating system of two eccentric rotors is widely used in petroleum, mining and food industries, and its motion stability is affected by material impact. However, the synchronous characteristics and stability of this kind of the system are studied rarely. Based on the background, a simplified mechanical model of the self-synchronous vibrating system driven by two eccentric rotors considering material impact is proposed. Firstly, the differential equations of motion about the system in non-collision and collision phase are established by using Lagrange equation and the theorem of momentum. Then, the section of Poincare maps and linearization matrix at the fixed point are solved. Finally, the dynamic behavior of material and system is analyzed, and then the change characteristics of the phase difference of the two eccentric rotors are revealed by numerical simulation. It can be concluded that the motion forms of the system and the rules of abrupt change about the phase difference evolve from periodic variation into chaotic state with the mass ratio of material to vibrating body increasing.
... In recent years, as vibration synchronization and the controlled synchronization have been widely used in mechanical engineering, Kong et al. used the master-slave control strategy to design a speed controller and phase difference controller by the sliding mode control and proportionalintegral control methods [18][19][20][21]. Chen et al. studied the synchronization of two eccentric rotors with common rotational axis by applying the average method of small parameters, and he found that the vibration system has two steady motion modes [22][23][24]. Fang et al. proposed a Rotor-Pendulum System with the Multi-DOF Vibration, and the Poincare method was employed to study the synchronization characteristics of the system in a far-resonant vibrating system. It is indicated that the stiffness of the support spring, the stiffness of the connecting spring and the installation location of the motors affect the synchronous state of the system [25][26][27]. ...
This work is a continuation and verification of the original literature by using experimental strategy. Based on the published paper, in order to avoid anti-phase synchronization with two co-rotating rotors system, a vibrating system with two co-rotating rotors installed with nonlinear springs have been proposed, and then, the synchronous condition and the synchronous criterion of the system are theoretically derived. From the analysis mentioned, it is shown that the synchronous state is mainly determined by the structural parameters of the coupling unit, coupling coefficients and positional parameters of the two exciters, etc. The main objective of the present work is to investigate the synchronous mechanism by experiments and simulations in this paper. Some simulation computations are firstly implemented to explain the synchronous mechanism of the system. Additionally, an experimental strategy with synchronous tests and dynamic characteristic tests of the vibrating system are carried out to validate the correctness of the simulation analysis. The simulations and experiments demonstrate that the nonlinear springs can overcome the difference of residual torques of the two motors to realize the synchronization of near zero phase difference under the condition of in-phase difference between two exciters. Finally, the error analysis results among the dynamic testing, synchronous testing results and simulations are discussed. This research can provide theoretical reference for designing large-sized and heavy-duty Vibrating Screens.
... As shown in Figure 2, it explains the dynamic coupling characteristic of the vibration system, also called the self-adjusting; meanwhile, it illuminates that control of two motors in the vibration system is different from that in the general system [18,27,28]. e selfadjusting process is that the motor directly drives ER to excite the vibration system by rotational motion φ 1 and φ 2 , while the vibration system changes the load torque of motor by motion itself in x, y, and ψ [2,29]. In this way, the vibration system reaches a steady state. ...
... In this way, the vibration system reaches a steady state. However, if the vibration system is the asymmetric structural, the phases of two ERs are usually different under the function of the selfadjusting [3,4,29]. Hence, in order to design the controller of the motor, how to decouple the motion equation of the motor becomes the control key. ...
... e motor drives ER to excite the mechanical system. Meanwhile, the mechanical system exerts the load torque on the motor through the coupling motion between the vibration body and ER, which is manifested as the change of the motor velocity and the phase of ER [29]. e selfadjusting ability of the vibration system can be regarded as a closed-loop 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.
... e differences of hydraulic motor leak of each gyration system should not be ignored. Vibration power consumption, damping force, and stiffness of the object should not be ignored [15][16][17]. e precision of electrohydraulic proportional flow valve is sufficient [3]. ...
In an eccentric rotating system driven by two hydraulic motors without synchronous gears, vibration coupling may help render motion stable. In order to investigate how vibration coupling influences the motion, the coupling characteristics of the vibration system were studied regarding the differences between two motors such as leakage network, coulomb damping network, and pressure loss network, and the sensitivity of the influence factors was also studied. The influence of tiny differences between the two motors, tiny differences in the motion pair structure, in the oil temperature and in the resistance coefficient on the coupling motion were discovered, and the criterion for synchronous motion were obtained consequently. The results show that the influence of the resistance coefficient difference on system motion stability is the greatest, accounting for 46.7%, and the influence of the difference in motion pair structure (e.g. motor piston clearance) is the second, accounting for 32.8%. For motors with displacement 80 ml/r, the condition of self-synchronization is that the difference in piston clearance between the two motors is equal to or smaller than 6 μ m. Experiments have proved the correctness of the theory and showed that the synchronization can be achieved by leakage compensation, damping compensation, and back-pressure compensation of the external system by means of control when the motors rotate slowly enough for system response. The study shows that the coupling synchronous model can reduce the force of the gear for the eccentricity rotary system with synchronous gear, and that the synchronous stability can be improved for the eccentricity rotary system without synchronous gear.
This paper focus on synchronization of four eccentric rotors (ERs) with parallel and coplanar rotational axis in a single mass vibration system, distinct from planar systems. Utilizing the average method of small parameters, the coupling motion relation are established by introducing phase differences of four ERs. The synchronous condition is determined by estimating the differences in loading torque of four ERs. The coupling dynamic characteristics are discussed numerically from coupling torque and synchronous ability. Two synchronous motion states are identified theoretically and experimentally. The results indicate that four ERs approach to in-phase when the vibration system operates in the frequency region before resonance, causing the body to move in a straight line. Conversely, when four ERs approaches to anti-phase in frequency region after resonance, the mass center of the vibration system remains nearly stationary. These conclusions play a guiding role in the design of vibratory machinery.
The paper is devoted to experimental study of possibilities for consensus control of the unbalanced rotors for the machine used in the vibration technology. This problem is treated as an ensuring the prescribed phase shift between the vibrating rotor actuators and has a significant value for the various kinds of the vibration technology, such as vibrating transportation, drilling, and so on. It can not be considered without taking into account the natural tendency of in-phase or anti-phase synchronization of the mechanically coupled oscillating units (cf. Huygens clock synchronization). This phenomenon prevents the controller efforts in maintaining the desired value of the phase shift. In the paper, the control laws for frequency stabilization simultaneously with cooperative control for assuring the desired phase shift between the rotors angular positions are derived and experimentally studied by means of the mechatronic vibration testbed. It is obtained that for the low and medium frequencies the self-synchronization of unbalanced rotors does not prevent achieving the desired phase shift between the rotors. For a high frequency band, the Huygens self-synchronization of rotors manifests itself, narrowing the range of the achievable phase shift.
