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TECHNICAL PAPERS

On the Spillover of Steady State Unbalance Response of a Rotating Shaft Under Velocity Feedback

[+] Author and Article Information
S. M. Yang1

Institute of Aeronautics and Astronautics, National Cheng Kung University, Taiwan, R.O.C.smyang@mail.ncku.edu.tw

G. J. Sheu

Department of Electrical Engineering,  Hsiuping Institute of Technology, Taiwan 412, R.O.C. gjsheu@mail.hit.edu.tw

1

Corresponding author.

J. Vib. Acoust 128(2), 143-147 (Jul 21, 2005) (5 pages) doi:10.1115/1.2149391 History: Received July 27, 2003; Revised July 21, 2005

It has been stated that a uniform rotating shaft in the Rayleigh beam model has only a finite number of critical speeds and precession modes. This paper presents a controller design of optimal sensor/actuator location and feedback gain for steady state unbalance response of a rotating shaft operating in a speed range. For systems under order-limit constraint such that only part of the precession modes can be included in the reduced-order controller design, the system stability can be evaluated. The example of a hinged-hinged rotating shaft is employed to illustrate the controller design of velocity feedback in collocated and noncollocated senor/actuator configuration. Analyses show that the reduced-order controller not only guarantees the closed loop system stability but also effectively suppress the unbalance response.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Whirl speed map indicating the whirl speeds ωn dependence on rotating speed; the critical speeds Ωn are marked by solid circles

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Figure 2

Amplitude of the un-damped generalized unbalance response q(τ)

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Figure 3

Optimal sensor/actuator location (ζs,ζa) and the feedback gain in collocated design when np=2

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Figure 4

Optimal sensor/actuator locations (ζs,ζa) and the feedback gain in noncollocated design when np=2

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Figure 5

Unbalance response of the optimal noncollocated design from the reduced (np=2) and full order controller (np=4)

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