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Bifurcation and stability analysis of a twelve-pole active electromagnetic bearing system under 1:3 ultraharmonic resonance

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  • Ma, Wensai
  • Ji, Xianglong
  • Kai, Ge
  • Zhang, Wei
  • Lu, Shufeng

Abstract

Ultraharmonic resonance can induce nonlinear bifurcations in a dynamical system, driving it from periodic to chaotic motion. In this study, a twelve-pole active electromagnetic bearing system with a twelve-electrode support structure is modeled, and its nonlinear dynamic behavior under strong excitation is systematically analyzed for the first time. Based on electromagnetic and control theories, a mechanical model under a proportional-derivative (PD) controller that accounts for rotor gravity is established and reduced to a two-degree-of-freedom nonlinear dynamical equation. The system's stability and dynamic behavior are examined by mapping its attraction basin. Averaged equations in both polar and Cartesian coordinates are then derived, and the effects of relevant parameter variations on amplitude-frequency response are investigated for three coupling states: uncoupled, weakly coupled, and strongly coupled. Finally, the theoretical predictions are validated numerically using bifurcation diagrams, phase portraits, time-history plots, and Poincaré sections. Results show that, as the excitation amplitude F increases, the first two modes exhibit distinct dynamic characteristics: the fractal features of the first-order mode are attenuated, while those of the second-order mode are enhanced.

Suggested Citation

  • Ma, Wensai & Ji, Xianglong & Kai, Ge & Zhang, Wei & Lu, Shufeng, 2025. "Bifurcation and stability analysis of a twelve-pole active electromagnetic bearing system under 1:3 ultraharmonic resonance," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012573
    DOI: 10.1016/j.chaos.2025.117244
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    References listed on IDEAS

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    1. Yigen Ren & Wensai Ma, 2024. "Dynamic Analysis and PD Control in a 12-Pole Active Magnetic Bearing System," Mathematics, MDPI, vol. 12(15), pages 1-23, July.
    2. Xie, Jiaquan & Xie, Zhikuan & Xu, Huidong & Li, Zhanlong & Shi, Wei & Ren, Jiani & Shi, Haoming, 2024. "Resonance and attraction domain analysis of asymmetric duffing systems with fractional damping in two degrees of freedom," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
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