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The vibration system driven by two ERs. (a) The dynamic model. (b) The vibration machine. (c) The experimental equipment. (d) The experimental flow.
Source publication
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...
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Citations
... However, automated control systems for vibration units are still rarely used due to the complexity (nonlinearity) of their dynamics and implementation Huang et al., 2019;Long and Dudarenko, 2022;Tomchina, 2018;Tomchina, 2022]. The issues of digital implementation of control systems for vibration installations are even less studied; only a few works devoted to them are available in the literature [Chen and Li, 2019;Andrievsky et al., 2022;Shagniev and Fradkov, 2023]. ...
The work is devoted to study of the effectiveness of the algorithm for controlling the synchronization of the rotors of a vibration unit (VU) with the digital implementation of the specified algorithm. A computer study of the dynamics of a two-rotor VU with a digital implementation of the control algorithm for rotor synchronization is carried out in the MATLAB environment. As a result the permissible sampling interval for calculating discrete control values using a zero-order extrapolator circuit was estimated. Also, using modeling, a comparative analysis of the efficiency of synchronization control in digital and analog implementation of the algorithm was carried out. It is shown that with an increase in the specified operating speed of the rotors, determined by the value of the energy H^∗ specified in the algorithm, the permissible value of the sampling interval decreases significantly. Comparison of the VU dynamics with the same values of the parameters of the synchronization control algorithm shows that the time of synchronization and the transient process in both cases are almost the same.
... By investigating the dynamics of three horizontally mounted ERs, Zhang et al. [18] found that replacing two ERs with three ERs could not improve the effective power of the system. In order to overcome the above shortcomings, control synchronization is an ideal way to achieve the synchronous motion of ERs with zero phase difference [19]. Chen et al. [20] established a coupled dynamic characteristic model of the horizontal installation of three ERs and verified that the vibration system has multiple synchronous states. ...
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.
... With the rapid development of science and technology, vibrations are used commonly in many fields including petroleum machinery, mining machinery, construction industry, food industry, etc. [1][2][3][4]. In the vibration utilization engineering, dual-rotors vibrating system is one of the typical equipment and is favored by many scholars [5][6][7]. In these equipment such as vibrating screen, vibrating feeder, vibrating shakeout machine, vibration rammer, vibratory crusher and others, the dual-rotors vibrating system plays an important role [8][9][10]. ...
The stability and synchronization characteristics of vibrating system cannot be ignored to get a better form of motion. In the present work the stability and synchronous characteristics of dual-rotors vibrating system considering the material effects are studied. Firstly, the equations of motion about the vibrating system are solved using Lagrange theory, Newton’s laws of motion and momentum theorem. Then the stability of the system is discussed based on the theory of nonlinear dynamics and Poincare theory using numerical simulation. Further the effect rules of material with different mass on phase difference of dual-rotors are revealed. Finally, the reliability and correctness of theoretical analysis and numerical simulation are verified approximately based on a prototype experiment in which the amplitude errors of vertical displacement about test point P1 and P2 are within the allowable limits of experimental error. It can be concluded that the stability of the system and the synchronous characteristics of dual-rotors decline with the mass ratio of material to vibrating body increasing.
... 8 Further, Chen et al. studied the control synchronization of two ERs in the vibration system with the asymmetric structure according to the master-slave control scheme. 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. ...
... 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.
... Defining the velocity of the master motor and the phase difference between motors as the state variables, Vibration motor 1 Since there is master-slave control no matter how many motors, it is a combination of two motors. Due to the length of the paper, the detailed design process of controllers can be seen in reference [34]. ...
... The velocities of three motors are shown in Figure 11a. It can be seen from velocity curves that the characteristic of the DC motor rapidly reaches the stable state value after power supply, which is different from that of the AC motor [34]. The synchronous velocity of three motors in the state of vibration synchronization is about 1538r/min. ...
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. ...
... Li et al. presented the harmonic vibration synchronization control strategy, and discussed the motion rules of the two motors [10]. Specially, Chen et al. discussed the dynamic coupling characteristic of the vibration system based on the control synchronization [11]. The above studies mainly analyzed the effects that the synchronous characteristics of the double eccentric rotors on the motion forms of the vibration system, and their works laid a foundation for further exploring the influence of materials on the stability of the vibrating system. ...
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 oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.
This brief is devoted to the experimental study of possibilities for control of the phase shift between two vibration actuators. The control laws for frequency stabilization simultaneously with the prescribed phase shift between the rotors angular positions are proposed and experimentally studied by means of the mechatronic vibration test bed. 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. The obtained experimental results are in agreement with the simulation results obtained from the 7-DOF mathematical model. Especially important is an agreement in the vibrational field observed from simulation and experiment. The qualitative coincidence of such complex motions means both the validation of the model and the verification of the measurement and experiment methodology.
