Bifurcation and chaos of electromechanical coupling main drive system with strongly nonlinear characteristic in mill

Liu, Shuang; Ai, Hongling; Sun, Baoping; Li, Shuo; Meng, Zong

doi:10.1016/j.chaos.2017.03.013

Cited by 22 publications

(11 citation statements)

References 24 publications

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“…In previous studies, although references [8], [12]- [19] have studied the dynamic behaviors of the super-high-speed motor-driven system, the research object was mainly an induction motor or electrical excitation-based hydroelectric generators. Moreover, they generally ignored the stiffness softening effect and its impact on system design and dynamic analysis.…”

Section: Discussionmentioning

confidence: 99%

“…The mechanism of vibration evolution of the drive system with changes in parameters, such as the force ratio and time-varying mesh stiffness, was revealed. Liu [13], [14] derived a mathematical model of a super-high-speed relative rotation system taking into consideration the magnetic field energy of an AC motor. The effect of the electromagnetic stiffness on the bifurcation characteristics was studied, and the corresponding conditions of Hopf bifurcation were given.…”

Section: Introductionmentioning

confidence: 99%

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Research on the Damping Effect Mechanism and Optimization of Super-High-Speed Electric Air Compressors for Fuel Cell Vehicles Under the Stiffness Softening Effect

Wang

et al. 2020

IEEE Access

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As a typical electromechanically coupled system, the super-high-speed permanent magnet synchronous motor (PMSM)-driven compressor always exhibits complex dynamic behavior, affecting the comprehensive performance of the fuel cell system. Based on this, this paper takes electromagnetic and load excitations into account and establishes a mathematical model of the super-high-speed PMSMdriven compressor. Then, the corresponding simulation is carried out, revealing that according to different causes and manifestations, the system gradually exhibits amplitude instability and frequency instability. Considering the stiffness softening effect, the effect of the torsional stiffness and damping coefficient on the dynamic characteristics under different forms of instability is obtained. Using the Routh-Hurwitz criterion and Melnikov theory, a damping optimization methodology is given. The results show that under the condition of amplitude instability, damping reduction and stiffness softening lead to a greater resonant amplitude and a wider resonance region. Under the condition of frequency instability, the system becomes chaotic via periodic-doubling bifurcation with the decrease of damping, and the decrease of torsional stiffness increases the damping required to maintain the stability. INDEX TERMS super-high-speed permanent magnet synchronous motor, fuel cell system, stiffness softening, damping optimization

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Research on the Damping Effect Mechanism and Optimization of Super-High-Speed Electric Air Compressors for Fuel Cell Vehicles Under the Stiffness Softening Effect

Wang

et al. 2020

IEEE Access

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“…The pure virtual roots equation (17) are set to AE! 0 i, the normalized left and right eigenvectors of the matrix A (x 0 , k e ) corresponding to the eigenvalue !…”

Section: The Analysis Of Hopf Bifurcationmentioning

confidence: 99%

“…Once situation is met, the system will produce Smale horseshoe chaos. According to the Ferrari method, equation (17) can be written as follows…”

Section: The Analysis Of Chaotic Motionmentioning

confidence: 99%

“…[10][11][12] The influencing factors of the electromechanical coupling mechanism and coupling dynamics are quite complex, which are involved in the mechanics, electromagnetism, and nonlinear dynamics. [13][14][15][16][17][18] With continuous in-depth study on the torsional vibration mechanism by the scholars, 19,20 it is found that the main cause of the torsional vibration is the nonlinear factors of the system, such as bifurcation and chaos, which is also the main reason for the system instability. Liu et al 21,22 analyzed the effects of subcritical bifurcation and supercritical bifurcation on the torsional vibration systems, taking nonlinear frictional damping as the research object.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamic analysis of an electromechanical coupling transmission system: A case study on shearers

Sheng

Wang

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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The operation environment of an electromechanical coupling transmission system in shearers is significantly harsher than that of electromechanical coupling transmission system for general applications. Besides, under the combined action of electrical and mechanical factors, unstable phenomenon may appear when the complicated dynamic behaviors of electromechanical coupling transmission system of a shearer occur such as bifurcation and chaos. Therefore, to solve this problem, the stability, bifurcation, and chaotic characters of electromechanical coupling transmission system with various electromagnetism stiffnesses are investigated in this paper. Then, the nonlinear dynamic equation of electromechanical coupling transmission system of a shearer is set up by taking both air-gap field energy of permanent magnet synchronous motor and coupling impact of mechanical and electrical parameters. According to the established equations, the equilibrium point and eigenvalue of the system are discussed. Meanwhile, the parameters conditions of the system Hopf bifurcation and chaotic motion are analyzed, and the homoclinic orbit of the system is determined. The results show that bifurcation and chaotic motion can be controlled effectively when reasonable parameters are concerned, which is of great practical significance to further study the vibration of the mechanical-electromagnetic coupling transmission system and the improvement of system stability.

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Modeling and vertical torsional coupling vibration control of the rolling mill with full state constraints

Qian

Chen

et al. 2022

Intl J Robust & Nonlinear

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This article establishes a mechanical-electrical-hydraulic vertical torsional coupling vibration mathematical model, and investigates its vibration suppression control strategy with time varying full state constraints for the rolling mill vertical torsional coupling vibration system. Firstly, the mechanical-electrical-hydraulic vertical torsional coupling vibration nonlinear model is developed using dynamic theory, which takes into account nonlinear damping, nonlinear rolling force and the coupling relationship between the vertical vibration system and the torsional vibration system. Then, nonlinear constraint transformation functions and coordinate transformations are implemented to remove the feasibility condition in handling the full state constraints problem, and neural networks are used to approximate unknown nonlinear functions. Furthermore, the vibration suppression control algorithm of the mechanical-electrical-hydraulic vertical torsional coupling system is designed with the specific sequence backstepping method and dynamic surface control technique, which can resolve the problem of nesting in the controller design process. Finally, the effective of the proposed method on vibration suppression is verified by the simulation.

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Bifurcation and chaos of electromechanical coupling main drive system with strongly nonlinear characteristic in mill

Cited by 22 publications

References 24 publications

Research on the Damping Effect Mechanism and Optimization of Super-High-Speed Electric Air Compressors for Fuel Cell Vehicles Under the Stiffness Softening Effect

Research on the Damping Effect Mechanism and Optimization of Super-High-Speed Electric Air Compressors for Fuel Cell Vehicles Under the Stiffness Softening Effect

Nonlinear dynamic analysis of an electromechanical coupling transmission system: A case study on shearers

Modeling and vertical torsional coupling vibration control of the rolling mill with full state constraints

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