On the nonlinear dynamics of constant stiffness coefficients 16-pole rotor active magnetic bearings system

Kandil, Ali; Sayed, M.; Saeed, Nasser A.

doi:10.1016/j.euromechsol.2020.104051

Cited by 37 publications

(20 citation statements)

References 15 publications

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“…(2), we get According to the schematic diagram of the 6-pole Rotor-AMBs given in Fig. 1a, the net electromagnetic forces in and directions after expanding denominators of Eqs (6) using Mclaurin series up to the third-order approximation, can be expressed as follows [1][2][3][4][5][6][7][8][9][10][11][12][13][14]: This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.…”

Section: A Radial Control Strategy Mathematical Modelmentioning

confidence: 99%

“…Therefore, AMBs is an inherently nonlinear system, where every design for AMBs has its own dynamical behaviors. Therefore, many research articles have been dedicated to explore the nonlinear dynamics for different configurations of Rotor-AMBs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Ji et al [1] explored the nonlinear dynamical behaviors of the four-pole Rotor-AMBs.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the obtained results, the authors concluded that the system can exhibit period-2, period-3, period-11, quasi-periodic, and chaotic motions depending on the excitation force magnitude. Recently, Saeed et al [14] introduced an analytical and numerical investigation for the nonlinear characteristics of constant stiffness coefficients 16-pole Rotor-AMBs. The author reported that the stiffness coefficients 16-pole Rotor-AMBs can exhibits one of quadri-stable motions depending on the initial conditions at the same spinning-speed.…”

Section: Introductionmentioning

confidence: 99%

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Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

et al. 2020

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Rotor active magnetic bearings system is the most efficient supporting technique of high-speed rotating machinery. This work aims to explore the dynamical behaviors of the 6-pole rotor active magnetic bearings system for the first time. Two different control strategies are introduced to mitigate the considered system lateral vibrations and the corresponding whirling motions. The first control technique (Radial control) is suggested such that the attractive magnetic force in each pole is proportional to both the radial displacement and radial velocity of the rotating disk toward that pole. The second control strategy (Cartesian control) is proposed such that the controlled magnetic force in each pole is designed to be proportional to both the cartesian displacement and cartesian velocity of the rotating disk in two perpendicular directions. Based on the proposed control strategies, two nonlinear dynamical models are derived and then analyzed by applying perturbation methods. Different response-curves and bifurcation diagrams are plotted utilizing the disk spinning-speed and the disk eccentricity as bifurcation control parameters. The main obtained analytical and numerical results illustrated that the considered system can perform a circular forward whirling motion only under the first control technique, while four whirling modes (that are forward whirling , backward whirling, both forward and backward whirling, and oscillation along a straight line) are noticed in the second control method depending on the disk spinning speed. Moreover, it is found that the radial control method is robust against the system instability than the cartesian control one, especially at large disk eccentricity. However, the cartesian control method could exhibit a vibration suppression efficiency higher than the radial control one at small disk eccentricity.

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Section: A Radial Control Strategy Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

et al. 2020

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“…The RMB is regarded as a fully uncoupled symmetric active 8-pole magnetic bearing. Despite being one of the most basic configurations, there is still recent control development [10] and it is also used as a study base for newer configurations [11].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Modeling and Parametric Analysis of the Magnetic Stiffness on a Radial Heteropolar Rotor Magnetic Bearing (RMB)

Trentini

Santos

Reichow

et al. 2021

IJECER

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This paper presents both the dynamic modelling and the study of the variation of certain physical parameters (pole area, gap and base current) that change the magnetic stiffness of a radial heteropolar Rotor Magnetic Bearing (RMB) aiming at the analysis of the magnitude of its control current for three different equilibrium points. The RMB is modelled as a fully uncoupled symmetric active 8-pole magnetic bearing. The analysis is performed using spectral cubes for a better visualisation of the posed problem. The saturation analysis of the RMB is also performed. At last, it is shown that a control current with the same magnitude as the base current is reached with minimum pole area and air gap s0 = 528 um.

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“…The natural gas venting ignition pipeline has nonlinear vibration. The current researches on nonlinear vibration include the nonlinear vibrations of a contact-mode atomic force microscopy(AFM) model subjected to multi excitations are controlled via a time-delayed positive position feedback (PPF) controller [10], M. Sayed et al applied active control to the nonlinear dynamic beam system to eliminate its vibration [11], Ali Kandil first derived a nonlinear dynamic equation for controlling the lateral vibration of a controlled system under a constant stiffness coefficient [12], the work of N. A. Saeed et al aims to study and control the nonlinear dynamic behavior of a nonlinear asymmetric shaft system [13,14], Y. S. HAMED et al studied the nonlinear dynamics control of a contact atomic force microscope system using a time-delay proportional-differential controller [15,16]. However, the above studies have rarely studied the vibration characteristics of vented horizontal pipes and risers.…”

Section: Introductionmentioning

confidence: 99%

Vibration characteristics analysis and structural improvement of natural gas venting ignition pipeline

Chen¹,

Tan²,

Tian³

2021

J., mech. eng. autom., control. syst.

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In order to study the flow-induced vibration characteristics of the natural gas vent pipeline under the internal flow field, taking the gas transmission station pipeline as an example, the ANSYS Workbench software was used to establish models under two working conditions, uncoupling and fluid-solid coupling, for modal analysis, and analyze and compare the calculation results and propose a structural improvement plan. The results show that the maximum amplitude of the first three modes under the two working conditions is concentrated on the riser mouth, and the amplitude under the fluid-solid coupling condition is slightly larger than that of no coupling; the inner diameter of the pipe elbow is large and the pressure is small, and the outside diameter is small and the pressure is small. Large, this instability will increase the air pulsation of the flow field. In the improved scheme, adding a restriction on the top to increase the rigidity of the pipeline can significantly reduce the maximum amplitude of the gas pipeline; adding an orifice to eliminate air flow pulsation has a certain effect on reducing the maximum amplitude and natural frequency, and the combination of the two can make the pipeline more stable. The research results of this paper can provide improved ideas for vibration reduction at the natural gas venting operation site.

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On the nonlinear dynamics of constant stiffness coefficients 16-pole rotor active magnetic bearings system

Cited by 37 publications

References 15 publications

Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

Dynamic Modeling and Parametric Analysis of the Magnetic Stiffness on a Radial Heteropolar Rotor Magnetic Bearing (RMB)

Vibration characteristics analysis and structural improvement of natural gas venting ignition pipeline

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