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Research Papers

Identification of Speed-Dependent Active Magnetic Bearing Parameters and Rotor Balancing in High-Speed Rotor Systems

[+] Author and Article Information
Vikas Prasad

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: vikasprasad91@gmail.com

Rajiv Tiwari

Professor
Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: rtiwari@iitg.ac.in

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 21, 2017; final manuscript received November 13, 2018; published online January 7, 2019. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 141(4), 041013 (Jan 07, 2019) (10 pages) Paper No: DS-17-1315; doi: 10.1115/1.4042026 History: Received June 21, 2017; Revised November 13, 2018

Estimating residual unbalances of a flexible rotor that is fully levitated on active magnetic bearings (AMBs) are challenging tasks due to the modeling error of AMB rotordynamic parameters. In this work, an identification algorithm has been developed for the estimation of dynamic parameters of speed-dependent AMBs and residual unbalances in a high-speed flexible rotor-bearing system. Parameters are identified during an estimation process with the help of displacement and current information at AMB locations only. For reducing the finite element model to suit the measurement availability, an improved dynamic reduction scheme has been proposed, which considers the gyroscopic matrix also in the transformation matrix. For a numerical testing of the developed identification algorithm, a multidisk flexible-shaft rotor is considered, which is fully levitated on AMBs. Speed-dependent AMB parameters have been modeled by a cubic function. Proportional–integral–derivative (PID) controllers are used to control the supply current to AMBs. Displacements and currents are generated using the finite element method of the rotor-AMB numerical model. These responses have been used in the identification algorithm for the estimation of the AMB displacement and current stiffness as well as of residual unbalances, concurrently. The algorithm with the proposed reduction scheme has shown an excellent estimation agreement in the presence of noisy responses and bias errors in rotor model parameters.

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Figures

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Fig. 1

A schematic representation of flexible rotor system fully levitated on AMBs

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Fig. 2

A schematic representation of flexible rotor system fully levitated on AMBs used for numerical simulation

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Fig. 3

Bode plot of transverse translational displacement at node 1 in x-direction

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Fig. 4

First four mode shapes for free end conditions

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Fig. 5

Effect of reduction scheme on displacement stiffness in x-direction for AMB-I (left) by the dynamic reduction (right) by the GDRM

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Fig. 6

Effect of the reduction scheme on current stiffness in x-direction for AMB-I (left) by the dynamic reduction (right) by the GDRM

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Fig. 7

Effect of the reduction scheme on displacement stiffness in x-direction for AMB-II (left) by the dynamic reduction (right) by the GDRM

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Fig. 8

Effect of the reduction scheme on current stiffness in x-direction for AMB-II (left) by the dynamic reduction (right) by the GDRM

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Fig. 9

Effect of the reduction scheme on displacement stiffness in y-direction for AMB-I (left) by the dynamic reduction (right) by the GDRM

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Fig. 10

Effect of the reduction scheme on current stiffness in y-direction for AMB-I (left) by the dynamic reduction (right) by the GDRM

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Fig. 11

Effect of the reduction scheme on displacement stiffness in y-direction for AMB-II (left) by the dynamic reduction (right) by the GDRM

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Fig. 12

Effect of the reduction scheme on current stiffness in y-direction for AMB-II (left) by the dynamic reduction (right) by the GDRM

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Fig. 13

Effect on AMB-I parameters in x-direction due to addition of noise in responses (left) displacement stiffness (right) current stiffness

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Fig. 14

Effect on AMB-II parameters in x-direction due to addition of noise in responses (left) displacement stiffness (right) current stiffness

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Fig. 15

Effect on AMB-I parameters in y-direction due to addition of noise in responses (left) displacement stiffness (right) current stiffness

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Fig. 16

Effect on AMB-II parameters in y-direction due to addition of noise in responses (left) displacement stiffness (right) current stiffness

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Fig. 17

Effect of adding modeling errors on AMB-I parameters in x-direction (left) displacement stiffness (right) current stiffness

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Fig. 18

Effect of adding modeling errors on AMB-II parameter in x-direction (left) displacement stiffness (right) current stiffness

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Fig. 19

Effect of adding modeling error on AMB-I parameter in y-direction (left) displacement stiffness (right) current stiffness

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Fig. 20

Effect of adding modeling error on AMB-II parameter in y-direction (left) displacement stiffness (right) current stiffness

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