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The model of the vibrating system: (a) the dynamic model of the vibrating system with two induction motors rotating in the same direction and (b) the reference frame system.
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The key technology of vibrating screens’ design is how to ascertain the synchronous state of vibrating systems. The occurrence of synchronization of a model, two co-rotating rotors fast excited by induction motors installed in a vibrating body, is treated in this article. The synchronization condition and stability criterion of the system are first...
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Citations
... However, the dynamic characteristics of electromechanical coupling are less taken into account. Hou and Fang considered electromechanical coupling characteristics and established the mathematic model of three exciters actuated by asynchronous motors; moreover, the electromechanical coupling mechanism and the vibrating synchronization transmissions of the selfsynchronous vibration were also revealed [7][8][9]. Based on the concept of generalized synchronization, Zhao described the synchronous behavior of the vibrating system with a dual-motor system, and illustrated the relationship of stable synchronization among inertia coupling of the motors, axial stiffness of the motors and load torque coupling [10]. Zhang employed a revisional small parameter method to explain the synchronization of the three non-uniform rotors excited by three identical motors, and found the effect of synchronization considering the inequality of exciter mass and the coupling torque of motors [11][12][13]. ...
In petroleum drilling engineering, drilling shakers are critical devices for cleansing solid particles and recycling drilling fluid. For the problem that the vibration screen with a single frequency usually results in flurry overflow due to the blocking of screen mesh, a selfsynchronous vibratory system with dual-frequency and dual-motor excitation is proposed. But it is not clear about the synchronization mechanism and dynamic characteristics of the system, which causes a lack of theoretical description for the source of synchronization phenomenon. Hence, this paper explores the synchronization mechanism and dynamic characteristics around the proposed system above. First, vibration and stability theory are employed to master the dynamic characteristics of the system, and the dynamic model is established by Lagrange equation. Then, displacement responses of the system are obtained by dimensionless formulas. Synchronous condition and synchronous stability between the unbalanced rotors are derived with small parameter method and Poincare method. Finally, some computer simulations are implemented to further verify the correctness of the theoretical analysis. The research result shows that the synchronous ability between the two unbalanced rotors actuated by dual-frequency excitation is related to the distance from the rotating center of the motor to the centroid of supporting body, and the greater the distance value, the better the synchronization of the vibrating system. This study will promote the recycle technology development of drilling fluid and settlement of the common scientific issues in vibrating synchronization.
... Analysis of the recent research and publications. Start of the vibration machine with inertia drive has been investigated in several papers, e. g. [1,4,5]. Among recent works that addressed the problem of start-up of such machines articles [6,7] are to be considered. ...
... The expression (5) shows that immediately after starting the engine a distinct transition process will occur in the coupling. It is completely determined by the first term (5) and is a damped oscillation of the cover coupling with the natural frequency p c . ...
... , they quickly fade and further occur with a frequency w cur significantly smaller than j st latter is insignificant, while it does not depend on the damping capacity of the coupling, and is determined only by the duration of the start of oscillations of the electromagnetic torque.Similar conclusions can be drawn regarding the changes of moment that occurs in the coupling at startup in the case p c w cur . Taking into account(5), its magnitude at the initial and following periods of startup can be estimated by the ...
Purpose. Investigation of start dynamic of the vibration machine with inertia vibration exciters considering the elastic connection of asynchronous electric motor rotors and unbalanced vibration exciter. Methodology. Methods of applied theory of vibrations and method of direct division of motions are used for analytical research studies. The design of processes of running start of vibration machines is executed by using the numeral integration of equalizations of motions of the mechanical vibration system and equalizations of electromagnetic transients in asynchronous electric motors in the 'Maple' software environment. Findings. It is shown that availability of elastic connection brings essential features to dynamics of vibration machine drive that should be considered when designing. Formulas for assessment of the starting deformation amplitudes and moments that occur in vibration machine drive coupling are obtained in an analytical form. It is demonstrated that oscillation amplitudes of elastic coupling at the start moment mostly depend on the remoteness of its own frequency from the current frequency in motor electricity network. An equation of coupling's torsional oscillations close to stationary rotation mode of unbalanced vibration exciter is obtained. Relation between oscillation of bearing vibration system and coupling's drive elasticity is revealed. It is found that during the start of vibration machines in case of Sommerfeld effect, resonant oscillation of elastic-damping elements (that connect motor and exciter rotors, which increase dynamic loads and energy losses in the system) excites, except resonant increase in braking vibration moment and "stopping" of engine speed. Originality. Theoretical positions of dynamics of running approach of vibration machines with inertia drive considering elastic compounds of rotors of electrical motor with limited power and unbalanced vibration exciter power got their further development. It is found that if the spring element is in the drive, natural oscillation frequencies of vibration machine are added to its critical frequencies. Practical value. The results of scientific work allow choosing options of vibration machines with unbalanced drive in a more reasonable way, which will reduce the amplitude of its start vibrations, dynamic loads and energy losses. © Yaroshevich N. P., Zabrodets I. P., Dutchak B. I., Yaroshevich T . S., 2018.
... Nowadays, the synchronization study is focused on physical, mechanical systems among others. Hou et al. [17] studied two co-rotating rotors fast excited by induction motors installed in a vibrating body. The stability criterion and synchronization condition of the system were obtained using the energy balance method. ...
... VehicleSim provides the 3D nonlinear equations of motion; these equations are obtained as the result of a modelling process. Once the exchange of energy will be tested for the coupled flap/lag motions, this system should be analysed according to the studies presented in [13,[16][17][18]. Therefore, a theoretical approach of the problem is a suggested in order to obtain the Hamilton energy and the results reported by [13][14][15] should be taken into account. ...
This paper presents a study on the energy exchange taking place on articulated helicopter main rotor blades. The blades are hinged, and the flap/lag modes are highly coupled. These dynamical couplings existing between the two degrees of freedom are clearly identifiable as the nonlinear terms that appear in the equations of motion are key to understand the energy exchange process. The work here conducted is carried out using VehicleSim, a multibody software specialized in modelling mechanical systems composed by rigid bodies. A spring pendulum system is also studied in order to examine its nonlinear behaviour and to establish existing analogies with the rotor blade nonlinear dynamics. The nonlinear couplings of both systems are compared to each other, and commensurability condition is analysed by means of short-time Fourier transform methods as well as the flap and lag amplitudes spectrum. Simulations are carried out, and the obtained results show clear analogies in the energy exchange process taking place in both systems. The stability of these modes is also studied using Poincare’ map method.
... It has been shown that using the proposed control algorithms enable the system not only to achieve both simple and multiple synchroniza-tion but also provide a way to ensure synchronization of a desired multiplicity. Hou et al. (Hou et al., 2016) studied the synchronization phenomenon for two co-rotating rotors, interacting via the vibrating body in the far-resonance vibration system by means of the energy balance method. Two rotors excited by induction motors installed in a vibrating body are considered. ...
In the paper the results of experimental examination of self-synchronization and Sommerfeld effect both in the open-loop and the closed-loop control modes are presented. The experiments are fulfilled on the novel Multiresonance Mechatronic Laboratory Setup (MMLS), which includes the unbalanced vibroactuators, mounted on the spring-suspended platform, sensors, electrical motors and the computer interface facilities. It is shown that the closed-loop control makes it possible to stabilize the rotation speed more accurately, than the open-loop motors control. Some additional effects, like low-frequency self-oscillations, may arise due to the integral (I) component of the closed-loop control action. © 2016, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences. All rights reserved.
Synchronization of coupled sub-systems in both natural and engineered systems is a commonplace occurrence, but its existence and analysis in mechanical systems has received much less attention. This is a review, written for mechanical engineers, of some of the work done on complex machines that are in common use. Theoretical characteristics of the phenomena that are present are indicated by solutions to models based on self-excited oscillations. A variety of experiments on synchronization that have been carried out are reported, including work done by the authors on vibrations of rotor blades due to airflow and of automobile parts. A large number of references on the subject has been included so that a researcher who is new to synchronization in complex machinery can use this as a starting point.
For rotating machinery, during its running, direct measuring for vibration of rotating components is very difficult. To overcome this defect, we presented a scheme to obtain dynamical responses of a rotor system by synchronizing with a derived virtual system. For a rotor system, a derived system is established, of which some parts are designed to be incorporated with the measurable part of the original rotor system. Then it is proved theoretically that the two systems can reach synchronization, which implies the two systems' responses are identical. We hope that the derived virtual system can exhibit the dynamical response of the original system, especially in the case of faults occurring. Thus in simulations, first we add a base disturbance to the rotor system. The simulation results reveal that the derived system can reach synchronization with the disturbed rotor quiet well and thus show the disturbed response. Then we assume that there occurs bolt looseness in the rotor support, the simulation shows that the derived system can maintain synchronization with the fault rotor. Thus we can obtain the response of the rotor from the derived system, even the angle response difficult to measure in practice.
The problem is motivated by observations of a rotor-pendula system, which derived from a new shale shaker. To grasp the dynamic characteristics of the shale shaker, the key research is exploring the synchronous mechanism for the system, since synchronous state between rotors is closely related to the dynamic characteristics of the system. In this paper, the dynamic equation of the rotor-pendula system is firstly derived by applying Lagrange’s equations. Through Laplace’s transformation method, the approximate responses of the system in synchronous state are obtained, which is determined coupling coefficients and synchronous state of the system. Then, the synchronous balance equation and the stability criterion of the system are obtained with Poincaré method on which stable phase difference and synchronous behavior can be ascertained. To verify the correctness of the theoretical analysis, numerical simulations are implemented by Runge–Kutta method, and it is shown that the synchronous behavior is determined by the geometry parameters, coupling coefficients, and rotor rotation direction.
