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Research Papers

Magnetic Bearing Rotordynamic System Optimization Using Multi-Objective Genetic Algorithms

[+] Author and Article Information
Wan Zhong

Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: nicole626@tamu.edu

Alan Palazzolo

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

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 28, 2014; final manuscript received August 13, 2014; published online September 24, 2014. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 137(2), 021012 (Sep 24, 2014) (12 pages) Paper No: DS-14-1144; doi: 10.1115/1.4028401 History: Received March 28, 2014; Revised August 13, 2014

Multiple objective genetic algorithms (MOGAs) simultaneously optimize a control law and geometrical features of a set of homopolar magnetic bearings (HOMB) supporting a generic flexible, spinning shaft. The minimization objectives include shaft dynamic response (vibration), actuator mass and total actuator power losses. Levitation of the spinning rotor and dynamic stability are constraint conditions for the control law search. Nonlinearities include magnetic flux saturation, and current and voltage limits. Pareto frontiers were applied to identify the best-compromised solution. Mass and vibration reductions improve with a two control law approach.

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Figures

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Fig. 1

Simplified control loop and main components of the HOMB supported rotor system

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Fig. 2

Homopolar radial magnetic bearing actuator (a) and the exaggerated coil geometry (b)

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Fig. 3

1D magnetic circuit of an 8-pole HOMB

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Fig. 4

FEM rotor model and sensor, magnetic bearing locations marked with circles (a) and the Timoshenko beam element of the rotor model with 6DOF at each node (b)

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Fig. 5

Flowchart of multiple objective optimization of HOMB system with NSGA-II code

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Fig. 6

Rotor unbalance diagram

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Fig. 7

Steady state vibration amplitude obtained in unbalance transient analysis

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Fig. 8

Extended core loss map from Carpenter’s catalog

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Fig. 9

Pareto frontier of the multi-objective HOMB optimization—3600 rpm: (a) Pareto frontier and (b) top view of the Pareto frontier

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Fig. 10

Pareto frontier of multi-objective HOMB optimization—7200 rpm: (a) Pareto frontier and (b) top view of Pareto frontier

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Fig. 11

Pareto frontier of the multi-objective HOMB optimization—9000 rpm: (a) Pareto frontier and (b) top view of the Pareto frontier

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Fig. 12

Levitation simulation (a) and unbalance transient (b) analysis of point A on the Pareto frontier on Fig. 9

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Fig. 13

Levitation simulation (a) and unbalance transient (b) analysis of point B on the Pareto frontier on Fig. 7.

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Fig. 14

Pareto frontier of the multi-objective HOMB optimization with two stage control—3600 rpm: (a) Pareto frontier and (b) top view of the Pareto frontier

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Fig. 15

Top views of the Pareto frontiers of the multi-objective HOMB optimization with single controller and two stage control—3600 rpm

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Fig. 16

Top views of the Pareto frontiers of the multi-objective HOMB optimization with single controller and two stage control—7200 rpm

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Fig. 17

Top views of the Pareto frontiers of the multi-objective HOMB optimization with single controller and two stage control—9000 rpm

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