Configuration angle effect on the control process of an oscillatory rotor in 8-pole active magnetic bearings

Ali Kandil; Lei Hou; Mohamed Sharaf; Ayman A. Arafa; Ali Kandil; Lei Hou; Mohamed Sharaf; Ayman A. Arafa

doi:10.3934/math.2024631

AIMS Mathematics

2024, Volume 9, Issue 5: 12928-12963. doi: 10.3934/math.2024631

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Research article

Configuration angle effect on the control process of an oscillatory rotor in 8-pole active magnetic bearings

1.
Department of Applied and Computational Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab City, 21934, Alexandria, Egypt
2.
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menouf, 32952, Menoufia University, Egypt
3.
School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China
4.
Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Sohag University, 82524, Sohag, Egypt

Received: 22 February 2024 Revised: 21 March 2024 Accepted: 26 March 2024 Published: 07 April 2024
MSC : 34A34, 34C15, 34C23, 34C25, 34D20, 34E13, 37N15, 70B05, 70K05, 70K40, 70K42, 70K50

In an active magnetic bearings (AMBs) model, every pair of opposite poles is aligned at an angle with the horizontal axis. In some configurations, there is a pair of poles which is in line with the horizontal axis. In other configurations, the same pair of poles might make a nonzero angle with the horizontal axis. This paper focused on the effect of changing such a configuration angle on the control process of an oscillatory rotor in an 8-pole active magnetic bearings model. Adopting the proportional-derivative (PD) control algorithm, the radial or Cartesian control techniques were applied. It was found that the rotor's oscillation amplitudes were not affected by the change in the configuration angle, even if its rotation speed and eccentricity were varied in the radial control scheme. However, the amplitudes were severely affected by the change in the configuration angle except at a specific angle in the Cartesian control scheme. The approximate modulating amplitudes and phases of the rotor's oscillations were extracted by the method of multiple-scales and a stability condition was tested based on the eigenvalues of the corresponding Jacobian matrix.
- configuration angle,
- 8-pole active magnetic bearings,
- rotor dynamics,
- quasiperiodic response,
- chaotic response,
- unbounded response
Citation: Ali Kandil, Lei Hou, Mohamed Sharaf, Ayman A. Arafa. Configuration angle effect on the control process of an oscillatory rotor in 8-pole active magnetic bearings[J]. AIMS Mathematics, 2024, 9(5): 12928-12963. doi: 10.3934/math.2024631

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Abstract

In an active magnetic bearings (AMBs) model, every pair of opposite poles is aligned at an angle with the horizontal axis. In some configurations, there is a pair of poles which is in line with the horizontal axis. In other configurations, the same pair of poles might make a nonzero angle with the horizontal axis. This paper focused on the effect of changing such a configuration angle on the control process of an oscillatory rotor in an 8-pole active magnetic bearings model. Adopting the proportional-derivative (PD) control algorithm, the radial or Cartesian control techniques were applied. It was found that the rotor's oscillation amplitudes were not affected by the change in the configuration angle, even if its rotation speed and eccentricity were varied in the radial control scheme. However, the amplitudes were severely affected by the change in the configuration angle except at a specific angle in the Cartesian control scheme. The approximate modulating amplitudes and phases of the rotor's oscillations were extracted by the method of multiple-scales and a stability condition was tested based on the eigenvalues of the corresponding Jacobian matrix.

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