Design and Cosimulation of Twelve-Pole Heteropolar Radial Hybrid Magnetic Bearing

Zhang, Zhixian; Duan, Yijian; Cai, Zhonghou; Qi, Yanying

doi:10.1155/2021/8826780

Cited by 4 publications

(9 citation statements)

References 22 publications

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“…In addition, the solution stability of Equations ( 34)-( 37) can be checked via using the Jacobian matrix of the corresponding dynamical system given by Equations ( 28)- (31). To check the solution stability of Equations ( 34)- (37), let the solution of Equations ( 34)-( 37) is (a 0 , b 0 , ϕ 10 , ϕ 20 ) and assume (a 1 , b 1 , ϕ 11 , ϕ 21 ) is a small deviation from this solution. Accordingly, we can write and ) are a monotonic increasing function of the eccentricity.…”

Section: Analytical Investigation and Autonomous Amplitude-phase Equationsmentioning

confidence: 99%

“…Depending on the mathematical modeling and analysis given above, the bifurcation behaviors, stability conditions, and control performance of the twelve-pole rotor system are discussed in this section. The steady-state vibration amplitudes (a and b) of the twelve-pole rotor are plotted versus the different parameters by solving the derived nonlinear algebraic Equations ( 34)- (37). In addition, the stability of these amplitudes is studied via the exploration of the eigen values of Equation (40).…”

Section: Bifurcation Analysis Stability Charts and Control Performancementioning

confidence: 99%

“…The eight-pole rotor system with time varying stiffness coefficient was investigated extensively by Zhang et al [11][12][13][14][15][16], where Shilnikov multi-pulse chaotic behavior was reported. According to the above discussions, it is noticed that nonlinear dynamical behaviors of the twelve-pole rotor system have not been studied before [34][35][36][37]. However, the twelve-pole system has many advantages over the eight-pole system such as low power consumption, negligible cross-coupling, better suspension behaviors, and high dynamic stiffness [37].…”

Section: Introductionmentioning

confidence: 99%

“…According to the above discussions, it is noticed that nonlinear dynamical behaviors of the twelve-pole rotor system have not been studied before [34][35][36][37]. However, the twelve-pole system has many advantages over the eight-pole system such as low power consumption, negligible cross-coupling, better suspension behaviors, and high dynamic stiffness [37]. Therefore, this article is dedicated to exploring the dynamical characteristics of the twelve-pole system for the first time.…”

Section: Introductionmentioning

confidence: 99%

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Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

et al. 2021

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The active magnetic bearings system plays a vital role in high-speed rotors technology, where many research articles have discussed the nonlinear dynamics of different categories of this system such as the four-pole, six-pole, eight-pole, and sixteen-pole systems. Although the twelve-pole system has many advantages over the eight-pole one (such as a negligible cross-coupling effect, low power consumption, better suspension behaviors, and high dynamic stiffness), the twelve-pole system oscillatory behaviors have not been studied before. Therefore, this article is assigned to explore the effect of the magneto-electro-mechanical nonlinearities on the oscillatory motion of the twelve-pole system controlled via a proportional derivative controller for the first time. The normalized equations of motion that govern the system vibrations are established by means of classical mechanics. Then, the averaging equations are extracted utilizing the asymptotic analysis. The influence of all system parameters on the steady-state oscillation amplitudes is explored. Stability charts in a two-dimensional space are constructed. The stable margin of both the system and control parameters is determined. The obtained investigations reveal that proportional gain plays a dominant role in reshaping the dynamics and motion bifurcation of the twelve-pole systems. In addition, it is found that stability charts of the system can be controlled by simply utilizing both the proportional and derivative gains. Moreover, the numerical simulations showed that the twelve-poles system can exhibit both quasiperiodic and chaotic oscillations besides the periodic motion depending on the control parameters’ magnitude.

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Section: Analytical Investigation and Autonomous Amplitude-phase Equationsmentioning

confidence: 99%

Section: Bifurcation Analysis Stability Charts and Control Performancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

et al. 2021

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“…However, this type of magnetic bearing has several advantages over other configurations, including high dynamic stiffness, low power consumption, a negligible cross-coupling effect, and better suspension behaviors. 37 As a result, a new control algorithm consists of both the IRC and PD-controllers is proposed within this article to control the unwanted lateral oscillations of the twelve-pole system. According to the proposed controller, the system mathematical model has been established as two nonlinear second-order differential equations coupled to two linear first-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics and static bifurcations control of the 12-pole magnetic bearings system utilizing the integral resonant control strategy

Saeed

El-Shourbagy

Kamel

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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In this study, the Integral Resonant Controller (IRC) is presented along with the Proportional-Derivative (PD) controller as a novel control technique to control the dynamical behaviors of the 12-pole rotor active magnetic bearing system. According to the proposed control strategy, the system model has been derived as a two-degree-of-freedom nonlinear dynamical system coupled with two first-order filters. The obtained mathematical model has been analyzed utilizing the asymptotic analysis. The nonlinear algebraic system that governs the steady-state vibration amplitudes and corresponding phase angles of the considered system has been extracted. The influence of the IRC control parameters on the rotor dynamics has been explored by plotting the different bifurcation diagrams. The analytical investigations demonstrated that the vibration suppression efficiency of the combined controller (i.e., PD and IRC) is proportional to the product of control and feedback gains of the IRC as well as the derivative gain of the PD-controller. In addition, it is found that the controller efficiency is inversely proportional to both the square of the internal loop feedback gain of the IRC and the position gain of the PD-controller. Accordingly, an objective function has been derived to design the best control gains of the proposed controller strategy. The analytical and numerical simulations confirmed that the suggested control method can suppress the system vibration and eliminate the catastrophic bifurcation behaviors if the control gains are selected according to the proposed objective function. Finally, the effect of failing one of the coupled integral resonant controllers on the rotor dynamics has been explored as a precautionary procedure. It is found that the failure of one of the coupled integral resonant controllers may breakdown the bifurcation symmetry of the rotor system, but the system does not lose its stability.

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Structure Design and Optimization of the Radial Magnetic Bearing

2023

Actuators

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According to different working environments and functional requirements, radial magnetic bearings (RMBs) have various design methods. Some methods’ lack of effectiveness or accuracy is likely to cause significant differences in the structural performance of magnetic bearings, which will cause serious problems such as limited bearing capacity and complex control. This paper analyzes the structure topology of a magnetic bearing according to the application scenario of RMBs, then proposes a general design example of an 8-pole magnetic bearing based on magnetic circuit analysis and reveals the linearity between electromagnetic force and current as well as air gap through finite element analysis and the influence of magnetic saturation on the load capacity of the magnetic bearing structure. After completing the preliminary design, we further optimize the structure, take the genetic algorithm as an example to iterate the influence coefficient, and summarize and prospect. The design scheme and optimization method proposed in this paper only provide a valuable reference for researchers and factories when devising RMB devices.

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Design and Cosimulation of Twelve-Pole Heteropolar Radial Hybrid Magnetic Bearing

Cited by 4 publications

References 22 publications

Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

Nonlinear dynamics and static bifurcations control of the 12-pole magnetic bearings system utilizing the integral resonant control strategy

Structure Design and Optimization of the Radial Magnetic Bearing

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