Theoretical Study of Synchronous Behavior in a Dual‐Pendulum‐Rotor System

Fang, Pan; Hou, Yaxin; Dai, Liming; Du, Mingjun

doi:10.1155/2018/9824631

Cited by 8 publications

(9 citation statements)

References 24 publications

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“…Two electric motors are used as vibration exciters of targeted action, whose shafts host rigidly mounted pendulums while rotating in opposite directions. Of interest are the simplest structures whose shafts are not connected at all [14][15][16][17]. In this case, over time, the pendulums, due to the phenomenon of self-synchronization [14], begin to rotate synchronously in opposite directions.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect

Filimonikhin

Pirogov

Hodunko

et al. 2021

EEJET

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This paper reports a study into the dynamics of a vibratory machine composed of a viscoelastically-fixed platform that can move vertically and two identical inertial vibration exciters. The vibration exciters' bodies rotate at the same angular velocities in opposite directions. The bodies host a single load in the form of a ball, roller, or pendulum. The loads' centers of mass can move relative to the bodies in a circle with a center on the axis of rotation. The loads' relative movements are hindered by the forces of viscous resistance. It was established that a vibratory machine theoretically possesses the following: – one to three oscillatory modes of movement under which loads get stuck at almost constant angular velocity and generate total unbalanced mass in the vertical direction only; – a no-oscillation mode under which loads rotate synchronously with the bodies and generate total unbalanced mass in the horizontal direction only. At the same time, only one oscillatory mode is resonant and exists at the above-the-resonance speeds of body rotation, lower than some characteristic speed. At the bodies' rotation speeds: ‒ pre-resonant; there is a globally asymptotically stable (the only existing) mode of load jams; ‒ above-the-resonance, lower than the characteristic velocity; there are locally asymptotically stable regimes ‒ both the resonance mode of movement of a vibratory machine and a no-oscillations mode; ‒ exceeding the characteristic velocity: there is a globally asymptotically stable no-oscillations mode. Computational experiments have confirmed the results of theoretical research. At the same time, it was additionally established that it would suffice, to enter a resonant mode of movement, to slowly accelerate the bodies of vibration exciters to the above-the-resonance speed, less than the characteristic speed. The results reported here could be interesting both for the theory and practice of designing new vibratory machines

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect

Filimonikhin

Pirogov

Hodunko

et al. 2021

EEJET

View full text Add to dashboard Cite

show abstract

“…The generalized forces acting on the vibrating bodies are zero, and the generalized forces acting on rotors 1 and 2 are T e1– T f1 and T e2– T f2 , respectively. When the system operates stably and the speed of the rotor d φ i /d t ( i = 1,2) fluctuates near the frequency ω n , the influence of electromagnetic leakage is neglected, and the driving force of the induction motor can be linearized as [24, 25, 29] where n i , L mi , ω si , L si and R ri ( i = 1,2) correspond to the pole number, mutual inductance, synchronous speed, stator inductance and rotor resistance of the motor, respectively; U 0 is the voltage amplitude. The vibration differential equations of the system are described as follows: …”

Section: Dynamical Equations Of the Vibrating Systemmentioning

confidence: 99%

“…Zhang [25, 26] deduced the synchronization condition and the synchronization stability for the vibrating system with three rotors. Hou and Fang [27–29] investigated a vibrating screen based on the model of a rotor-pendulum system and clarified the synchronization condition and stability of the system by the Poincare method.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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“…Such as, Zhao et al [3] proposed a small parameter method, and explained the synchronization characteristics of two ERs in a non-resonant vibration system. Based on the synchronization model of Huygens clocks, Fang et al [4]- [6] proposed a rotorpendulum vibrating system to study dynamic characteristics,…”

Section: Introductionmentioning

confidence: 99%

Synchronous Control of Multi-Motor Coupled With Pendulum in a Vibration System

et al. 2020

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In this paper, the synchronous control method for multi-motor coupled with pendulum in a vibration system is introduced. The dynamic model of three eccentric rotors (ERs) driven by three motors rotating in the same direction in the system is firstly established. However, to obtain elliptical trajectory, the ideal synchronization motion (zero-phase difference) of the three ERs should be satisfied. Therefore, the synchronous control strategy for the proposed system is described. Then, the exponential reaching law sliding mode control (ERL-SMC) with adjacent cross-coupling control structure is applied to design the controllers of rotational velocity error and synchronization error. Meanwhile, the stability performance of the controllers is demonstrated by Lyapunov theory and Hurwitz condition. Furthermore, the adaptive method is applied to the ERL-SMC to improve the control accuracy of the system. Finally, computer simulation based on Matlab/Simulink is implemented to validate the effectiveness of the control system; besides, the impact of parameter perturbations in the control system are considered to verification the robustness of controllers related to the velocity and synchronization. INDEX TERMS Synchronous control, vibration system, exponential reaching law, sliding mode control adjacent cross-coupling control.

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Theoretical Study of Synchronous Behavior in a Dual‐Pendulum‐Rotor System

Cited by 8 publications

References 24 publications

The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect

The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect

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

Synchronous Control of Multi-Motor Coupled With Pendulum in a Vibration System

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