Stability and bifurcation analysis in a magnetic bearing system with time delays☆

Wang, Hongbin; Liu, Jiaqi

doi:10.1016/j.chaos.2005.03.002

Cited by 29 publications

(5 citation statements)

References 21 publications

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“…The results showed that the system model has a simple analytic solution, which deepened the understanding of rubbing phenomenon of readers. Zhang et al [17] researched nonlinear dynamics of a 5-DOF active With the development of a bearing-rotor system towards being large-scale and high-power, the design gap between the rotor and stator becomes smaller and smaller, which makes the liquid film thickness of MLDSB reduce by 10 times compared with the traditional electromagnetic air gap [12]. (Air gap = Liquid film + Chromium coating, Liquid film is (30, 50) µm, Air gap is (100, 300) µm).…”

Section: Bracket Axial Bearingmentioning

confidence: 99%

Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

et al. 2020

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As a new type of suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting. Its bearing capacity and stiffness can be greatly improved. Because of the small liquid film thickness (it is smaller 10 times than air gap), the eccentricity, crack, bending of the rotor, and the assembly error, it is easy to cause a clearance-rubbing fault between the rotor and stator. The coating can be worn and peeled, the operating stability can be reduced, and then it is one of the key problems of restricting the development and application of MLDSB. Therefore, the clearance-rubbing dynamic equation of 2-DOF system of MLDSB is established and converted into Taylor Series form and the nonlinear components are retained. Dimensionless treatment is carried out by dimensional normalization method. Finally, the rotor displacement response under different rotor eccentricity ratio and rotating speeds is numerically simulated. The studies show that the trajectory of the rotor is periodic elliptic without clearance-rubbing phenomenon when the eccentricity ratio is less than 0.2, while the rotor is greatly affected by the rotation speed and a variety of motions, such as single-period, quasi-period, double-period and chaos, are presented when greater than 0.3. Within the largest range of rotating speed and eccentricity ratio, the rotor presents the single-period trajectory, and then the number of Poincare mapping point is 1, without a clearance-rubbing fault. When the rotational speed is in the scope of (9, 13) krpm and the eccentricity ratio is in the scope of (0.27, 0.4), the number of Poincare mapping point is more than one, the maximum dimensionless rubbing force is −5.7, and then clearance-rubbing fault occurs. The research can provide a theoretical basis for the safe and stable operation of MLDSB.

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Section: Bracket Axial Bearingmentioning

confidence: 99%

Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

et al. 2020

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“…It also shows the growth rate, (real part of the eigenvalue), and the frequency of oscillation, (imaginary part of the eigenvalue). The nondimensional stiffness is given by (16) and the nondimensional damping is given by (15). If the real part of the eigenvalue is defined as positive, the vibrations grow in time and the system is unstable.…”

Section: Dynamic Signal Analyzermentioning

confidence: 99%

“…Ji [13,14] analyzed the effect of time delays on the nonlinear dynamic behavior of the magnetic bearing system. Wang and Liu [15], Li et al [16], and Ji [17] studied the Hopf bifurcation and its stability in a magnetic bearing system with time delays. However, these works only considered a simple single-degree-of-freedom (DOF) magnetic bearing without gyroscopic effects.…”

Section: Introductionmentioning

confidence: 99%

Rotation Modes Stability Analysis and Phase Compensation for Magnetically Suspended Flywheel Systems with Cross Feedback Controller and Time Delay

Ren

Chen

Cai

et al. 2016

Mathematical Problems in Engineering

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This paper analyzes the effects of time delay on the stability of the rotation modes for the magnetically suspended flywheel (MSFW) with strong gyroscopic effects. A multi-input multioutput system is converted into a single-input single-output control system with complex coefficient by variable reconstruction, and the stability equivalence of the systems before and after variable reconstruction is proven. For the rotation modes, the stability limits and corresponding vibration frequencies are found as a function of nondimensional magnetic stiffness and damping and nondimensional parameters of rotor speed and time delay. Additionally, the relationship between cross feedback control system stability and time delay is investigated. And an effective phase compensation method based on cross-channel is further presented. Simulation and experimental results are presented to demonstrate the correctness of the stability analysis method and the superiority of the phase compensation strategy.

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“…Based on the model developed by Ji (2003b), Wang and Liu (2005) further investigated the stability of a magnetic bearing system with time delays by analyzing the distribution of the roots of the associated characteristic equation. It was found that Hopf bifurcation occurs when the delay passes through a sequence of critical values.…”

Section: Stability and Dynamics Associated With Time Delaysmentioning

confidence: 99%

Nonlinear Dynamics of Magnetic Bearing Systems

Hansen

Zander

2008

Journal of Intelligent Material Systems and Structures

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Magnetic bearings use magnetic forces to support various machine components. Because of the non-contact nature of this type of suspension, magnetic bearing technology offers a number of significant advantages over conventional bearings, such as rolling element and fluid film bearings. An active magnetic bearing basically consists of an electromagnetic actuator, position sensors, power amplifiers, and a feedback controller. All of these components are characterized by nonlinear behavior and therefore the entire system is inherently nonlinear. However, in simulations of the dynamic behavior of magnetic bearing systems, the nonlinearities are usually neglected to simplify the analysis and only linear models are used. Moreover, many control techniques currently used in magnetic bearing systems are generally designed by ignoring nonlinear effects. The main reason for simplification is the intractability of the complexity of the actual model. In fact, the inherent nonlinear properties of magnetic bearing systems can lead to dynamic behavior of a magnetically suspended rotor that is distinctly different from that predicted using a simple linearized model. Therefore, the nonlinearities should be taken into account. This literature review is focused on the nonlinear dynamics of magnetic bearing systems and it provides background information on analytical methods, nonlinear vibrations resulting from a rotor contacting auxiliary bearings, and other active topics of research involving the nonlinear properties of magnetic bearing systems, such as nonlinear self-sensing magnetic bearings and nonlinear control of magnetic bearings. The review concludes with a brief discussion on current and possible future directions for research on the nonlinear dynamics of magnetic bearing systems.

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Stability and bifurcation analysis in a magnetic bearing system with time delays☆

Cited by 29 publications

References 21 publications

Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

Rotation Modes Stability Analysis and Phase Compensation for Magnetically Suspended Flywheel Systems with Cross Feedback Controller and Time Delay

Nonlinear Dynamics of Magnetic Bearing Systems

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