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Research Papers

Multi-Objective Optimization Design of Nonlinear Magnetic Bearing Rotordynamic System

[+] Author and Article Information
Wan Zhong

Vibration Control and Electronics Lab,
Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: zhongwan0626@gmail.com

Alan Palazzolo

James J. Cain Professor
Fellow ASME
Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: a-palazzolo@tamu.edu

Xiao Kang

Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: kangxiao1990@tamu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 21, 2015; final manuscript received September 22, 2016; published online November 23, 2016. Assoc. Editor: Patrick S. Keogh.

J. Vib. Acoust 139(1), 011011 (Nov 23, 2016) (15 pages) Paper No: VIB-15-1488; doi: 10.1115/1.4034844 History: Received November 21, 2015; Revised September 22, 2016

Nonlinear vibrations and their control are critical in improving the magnetic bearings system performance and in the more widely spread use of magnetic bearings system. Multiple objective genetic algorithms (MOGAs) simultaneously optimize a vibration control law and geometrical features of a set of nonlinear magnetic bearings supporting a generic flexible, spinning shaft. The objectives include minimization of the actuator mass, minimization of the power loss, and maximization of the external static load capacity of the rotor. Levitation of the spinning rotor and the nonlinear vibration amplitude by rotor unbalance are constraint conditions according to International Organization for Standardization (ISO) specified standards for the control law search. The finite element method (FEM) was applied to determine the temperature distribution and identify the hot spot of the actuator during steady-state operation. Nonlinearities include magnetic flux saturation, and current and voltage limits of power amplifiers. Pareto frontiers were applied to identify and visualize the best-compromised solutions, which give a most compact design with minimum power loss whose vibration amplitudes satisfy ISO standards.

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References

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Figures

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Fig. 1

(a) Eight-pole magnetic bearing stator and (b) the magnified coil geometry

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Fig. 2

(a) Finite element rotor model and (b) the six degrees-of-freedom (DOF) Timoshenko beam element

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Fig. 3

Nonlinear power amplifier model with voltage and current saturation

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Fig. 4

Block diagram for the excitation and measure point for the sensitivity function

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Fig. 5

Code flowchart of the heteropolar AMB system optimization example

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Fig. 6

(a) Pareto frontier of the heteropolar AMBs optimization and (b) side view of the Pareto frontier

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Fig. 7

Levitation simulation at point A on the Pareto frontier in Fig. 6: (a) displacement, (b) flux intensity, and (c) power amplifier current

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Fig. 8

Unbalance transient analysis at point A: (a) y-direction displacements, (b) z-direction displacements, (c) flux intensity, and (d) power amplifier current

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Fig. 9

(a) Levitation, (b) flux intensity, and (c) power amplifier current in levitation at point B on the Pareto frontier in Fig. 6

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Fig. 10

Unbalance transient analysis at point B: (a) y-axis displacements, (b) z-axis displacements, (c) flux intensity, and (d) power amplifier current

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Fig. 11

Levitation simulation at point C on the Pareto frontier in Fig. 6: (a) displacement, (b) flux intensity, and (c) power amplifier current

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Fig. 12

Unbalance transient analysis at point C: (a) y-axis displacements, (b) z-axis displacements, (c) flux intensity, and (d) power amplifier current

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Fig. 13

(a) Hot spot temperature versus actuator mass, (b) hot spot temperature versus static load, and (c) hot spot temperature versus power loss

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Fig. 14

Power loss components of the designed system at point A

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Fig. 15

Two-dimensional thermal analysis of the designed AMBs supported system at point A

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Fig. 16

Solidworks thermal modeling: (a) with actual currents in the poles and (b) under symmetric actuator model

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Fig. 17

Evaluation of the stability margin of the designed system at point A

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Fig. 18

(a) Comparison of the NSGA-II with Isight NSGA-II and Isight NCGA with (b) front view

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