Analysis of Nonlinear Characteristics and the Factors Affecting the Operation of the Active Magnetic Bearings Rotor System Considering Alford Force

Authors

  • Siyuan Zhang College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • Jin Zhou National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • Xiaoming Han College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • Yanchao Ma College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

DOI:

https://doi.org/10.13052/2022.ACES.J.370215

Keywords:

Active magnetic bearings, Alford force, Rotor dynamics, Nonlinear

Abstract

Based on a test rig supported by active magnetic bearings (AMBs), this paper focuses on the study of the nonlinear dynamic characteristics and the factors affecting the operation of a rotor system under the coupling of magnetic bearing force and Alford force. In order to solve the nonlinear dynamic response of rotor system, a dynamic equation of the rotor which introduces Alford force and the electromagnetic force of the AMBs controlled by PID is established. By changing the control parameters (kPP and kDD), operation parameters (rotational speed), and structural parameters (clearance between impeller and volute), the equation is solved by using Runge−-Kutta method. The results show that the rotor system exhibits complex nonlinear dynamic characteristics under the coupling action of Alford force and magnetic bearing force. The rotor system appears different dynamic behaviors such as single period, multi multi-period, and quasi quasi-period when changing the control parameters. Among all the control parameters, adjusting kDD is more effective to ensure system stability. The amplitude of rotor increases from 8.2 μμm to 11.9 μμm with the increase of speed from 6000 rpm to 10,000 rpm, while that decreases from 9.6 μμm to 8.2 μμm with the increase of clearance between impeller and volute from 1mm to 4 mm. Therefore, under the influence of Alford force, apart from the control parameters, the operation parameters and structural parameters of magnetic bearings also affect the operation of the rotor system supported by the AMBs.

Downloads

Download data is not yet available.

Author Biographies

Siyuan Zhang, College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Siyuan Zhang was born in Jiangsu, China, in 1992. He received the M.S. degree from Shihezi University. He is currently working toward the Ph.D. degree in Mechanical mechanical design and theory in with the Nanjing University of Aeronautics and Astronautics (NUAA).

His research interests include active magnetic bearings and vibration control.

Jin Zhou, National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Jin Zhou was born in Jiangsu, China, in 1972. She received her the Ph.D. degree in mechanical engineering from the China University of Mining and Technology (CUMT), China, in 2001.

From 2012 to 2013, she was a Visiting Scholar in with the Rotating Machinery and Control Laboratory (ROMAC) of the University of Virginia. She was the member of Program Committee of the 14th International Symposium on Magnetic Bearings (2014) and the Program Chair of the 16th International Symposium on Magnetic Bearings (2018). She was an elected member of International Advisory Committee for ISMB in 2018. Her research interests include magnetic bearings and vibrationcontrol.

Xiaoming Han, College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Xiaoming Han was born in Shandong, China, in 1997. He received histhe B.S. degree in 2019 from Qingdao University in 2019. He is currently working toward the M.S. degree in with the Nanjing University of Aeronautics and Astronautics (NUAA).

His research focuses on magnetic bearings.

Yanchao Ma, College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Yanchao Ma was born in Shandong, China, in 1996. He received his the B.S. degree in 2019 from the Civil Aviation University of China (CAUC) in 2019. He is currently working toward the M.S. degree in with the Nanjing University of Aeronautics and Astronautics (NUAA).

His research focuses on magnetic bearings.

References

H. J. Thomas, “Unstable oscillations of turbine rotors due to steam leakage in the sealing glands and the buckets,” Bullet in Scientifique A.J.M, vol. 71, pp. 223-236, 1958.

J. S. Alford, “Protecting turbomachinery from self-excited whirl,” ASME Journal of Engineering for Power, no. 05, pp. 333-344, 1965.

M. Cheng, G. Meng, and B. Y. Wu, “Effect of Alford force and ball bearing on dynamic characteristics of a rotor system,” Journal of Vibration and Shock, vol. 30, no. 12, pp. 164-168, 2011.

D. Y. Jung and H. A. DeSmidt, “Limit-Cycle analysis of planar Rotor/Autobalancer system influenced by Alford force,” Journal of Vibration & Acoustics, vol. 138, no. 2, pp. 021018.1-021018.14, 2016.

K. Yada, M. Uchiumi, and K. I. Funazaki, “Thomas/Alford force on a Partial-Admission turbine for the rocket engine turbopump,” Journal of Fluids Engineering, vol. 141, no. 01, 2018.

W. Yang, H. Yuan, L. Hui, and K. Zhang, “Dynamic analysis of flexible shaft and elastic disk rotor system based on the effect of Alford force,” Shock & Vibration, no. PT.2, pp. 3545939.1-3545939.13, 2019.

B. Li, L. Zhang, and Y. Y. Cao. “Dynamic characteristic analysis for Rotor-bearing system with Alford force considering blade vibration,” Journal of Ship Mechanics, vol. 24, no. 1, 2020.

I. Ahmad, J Ikram, M. Yousuf, R. Badar, S. S. H. Bukhari, and J.-S. Ro, “Performance improvement of Multi-rotor axial flux vernier permanent magnet machine by permanent magnet shaping,” IEEE Access, vol. 9, pp. 143188-143197, 2021.

S. Ali, J Ikram, C. P. Devereux, S. S. H. Bukhari, S. A. Khan, N. Khan, and J.-S. Ro, “Reduction of cogging torque in AFPM machine using Elliptical-Trapezoidal-Shaped permanent magnet,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 36, no. 8, pp. 1090-1098, 2021.

S. Amin, S. Madanzadeh, S. Khan, S. S. H. Bukhari, F. Akhtar, and J.-S. Ro, “Effect of the magnet shape on the performance of coreless axial flux permanent magnet synchronous generator,” Electrical Engineering, 2021.

T. S. Ou, C. X. Hu, Y. Zhu, M. Zhang, and L. Zhu, “Intelligent feedforward compensation motion control of maglev planar motor with precise reference modification prediction,” IEEE Transactions on Industrial Electronics, vol. 68, no. 9, pp. 7768-7777, 2021.

W. R. Wang, G. J. Yang, J. H. Yan, H. Ge, and P. Zhi, “Magnetic levitation planar motor and its adaptive contraction backstepping control for logistics system,” Advances In Mechanical Engineering, vol. 13, no. 3, 2021.

M. Y. Chen, C. F. Tsai, and L.C. Fu. “A novel design and control to improve positioning precision and robustness for a planar maglev system,” IEEE Transactions on Industrial Electronics, vol. 66, no. 9, pp. 4860-4869, 2019.

H. Z. Wang, K. Liu, J. B. Wei, and H. Hu, “Analytical modeling of air gap magnetic fields and bearing force of a novel hybrid magnetic thrust bearing,” IEEE Transactions on Magnetics, vol. 57, no. 10, 2021.

Q. Liu, L. Wang, and Y. Y. Li, “Single-structured hybrid gas-magnetic bearing and its rotor dynamic performance,” Nonlinear Dynamic, vol. 104, no. 1, pp. 333-348, 2021.

K. K. Nielsen, C. R. H. Bahl, N. A. Dagnaes, I. F. Santos, and R. Bjørk, “A passive permanent magnetic bearing with increased axial lift relative to radial stiffness,” IEEE Transactions on Magnetics, vol. 57, no. 3, 2021.

G. Schweitzer and E. Maslen, Magnetic Bearing: Theory, Design, and Application to Rotating Machinery. Springer, Berlin, Germany, 2012.

X. H. Wang, G. G Yan, Y. G. Hu, and R. Tang, “The influence of Alford force and active magnetic bearing on the dynamic behavior of a rotor system,” Journal of Vibration and Shock, vol. 39, no. 08, pp. 222-229, 2020.

J. Colding-Jorgensen, “Predicting of rotor dynamic destabilizing forces in axial flow compressors,” ASME Journal of Fluids Engineering, vol. 114, no. 11, pp. 621-625, 1992.

F. Erich, “Rotor whirl forces induced by the tip clearance effect in axial flow compressors,” ASME Journal of Vibration and Acoustics, vol. 115, no. 10, pp. 509-515, 1993.

S. Chai, Y. Zhang, and Q. Qu, “An analysis on the air exciting-vibration force of steam turbine,” Engineering Science, vol. 3, no. 04, pp. 68-72, 2001.

ISO, ISO14839-2 Mechanical vibration—Vibration of rotating machinery equipped with active magnetic bearings—Part 2: Evaluation of vibration, British: Subcommittee GME/21/5, 2004.

Downloads

Published

2022-07-09

How to Cite

[1]
S. . Zhang, J. . Zhou, X. . Han, and Y. . Ma, “Analysis of Nonlinear Characteristics and the Factors Affecting the Operation of the Active Magnetic Bearings Rotor System Considering Alford Force”, ACES Journal, vol. 37, no. 02, pp. 253–261, Jul. 2022.

Issue

2022: Vol 37 Iss 2

Section

Articles

Categories