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Gas Turbines: Structures and Dynamics

Rotor Model Validation for an Active Magnetic Bearing Machining Spindle Using Mu-Synthesis Approach

[+] Author and Article Information
Ryan J. Madden

Center for Rotating Machinery Control and Dynamics (RoMaDyC),  Cleveland State University, Cleveland, OH 44115-2214

Jerzy T. Sawicki1

Center for Rotating Machinery Control and Dynamics (RoMaDyC),  Cleveland State University, Cleveland, OH 44115-2214j.sawicki@csuohio.edu

1

Corresponding author.

J. Eng. Gas Turbines Power 134(9), 092501 (Jul 18, 2012) (6 pages) doi:10.1115/1.4006988 History: Received June 17, 2012; Revised June 18, 2012; Published July 18, 2012; Online July 18, 2012

Model-based identification and μ-synthesis are employed for model updating of the rotor for a high-speed machining spindle supported on active magnetic bearings. The experimentally validated model is compared with a nominal engineering model to identify the unmodeled dynamics. The extracted missing dynamics from the nominal rotor model provides engineering insight into an effective model correction strategy. The corrected rotor model is validated by successful implementation of a number of μ-synthesized controllers, providing robust and stable levitation of the spindle over its entire operating speed range.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

μ-controlled model-based identification strategy

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Figure 2

Cross section of AMB supported machining spindle

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Figure 3

The finite element rotor model with highlighted stations indicating known modeling difficulties

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Figure 4

Nominal engineering and measured transfer functions with input and output at the front (top figure) and rear bearing and sensor

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Figure 5

Experimentally updated and measured transfer functions with input and output at the front (top figure) and rear bearing and sensor

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Figure 6

Frequency responses of the updated rotor (true system) and the nominal rotor (engineering system) due to an input at the front bearing and an output at the front sensor location

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Figure 7

Frequency responses of the updated rotor (true system) and the nominal engineering rotor (engineering system) due to an input at the rear bearing location and an output at the rear sensor location

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Figure 8

Frequency responses of the updated rotor (true system) and the nominal engineering rotor with the addition of the unmodeled dynamics (controlled engineering system) due to an input at the front bearing and an output at the front sensor location

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Figure 9

Frequency responses of the updated rotor (true system) and the nominal engineering rotor with the addition of the unmodeled dynamics (controlled engineering system) due to an input at the rear bearing location and an output at the rear sensor location

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Figure 10

Plot of the structured singular value μ for the completed μ-controlled model-based identification

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Figure 11

Plot of the controller transfer functions with the same input and output locations

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Figure 12

Plot of the controller transfer functions with all inputs to an output at the middle of the front AMB rotor

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Figure 13

Frequency responses of the updated rotor (true system) and the nominal rotor (engineering system) due to an input at the front bearing and an output at the front sensor location: material’s modulus of elasticity reduced by 50%

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Figure 14

Frequency responses of the updated rotor (true system) and the nominal engineering rotor with the addition of the unmodeled dynamics (controlled engineering system) due to an input at the front bearing and an output at the front sensor location: material’s modulus of elasticity reduced by 50%

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Figure 15

Plot of the controller transfer functions with the same input and output locations: material’s modulus of elasticity reduced by 50%

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Figure 16

Plot of the controller transfer functions with all inputs to an output at the middle of the front AMB rotor: material’s modulus of elasticity reduced by 50%

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