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Research Papers

Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

[+] Author and Article Information
W. C. Tai

Department of Mechanical Engineering,
University of Washington,
Box 352600,
Seattle, WA 98195-2600

I. Y. Shen

Professor
Department of Mechanical Engineering,
University of Washington,
Box 352600,
Seattle, WA 98195-2600
e-mail: ishen@u.washington.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 30, 2014; final manuscript received February 14, 2015; published online April 15, 2015. Assoc. Editor: Jiong Tang.

J. Vib. Acoust 137(4), 041011 (Aug 01, 2015) (12 pages) Paper No: VIB-14-1157; doi: 10.1115/1.4029989 History: Received April 30, 2014; Revised February 14, 2015; Online April 15, 2015

This paper is to study ground-based response of a spinning, cyclic symmetric rotor assembled to a flexible housing via multiple bearings. In particular, interaction of the spinning rotor and the flexible housing is manifested theoretically, numerically, and experimentally. In the theoretical analysis, we show that the interaction primarily appears in coupled rotor–bearing–housing modes whose response is dominated by the housing. Specifically, let a housing-dominant mode have natural frequency ω(H) and the spin speed of the rotor to be ω3. In rotor-based coordinates, response of the spinning rotor for the housing-dominant mode will possess frequency splits ω(H)±ω3. In ground-based coordinates, response of the spinning rotor will possess alternative frequency splits ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3, where k is an integer determined by the cyclic symmetry of the rotor and the housing-dominant mode of interest. In the numerical analysis, we study a benchmark model consisting of a spinning slotted disk mounted on a stationary square plate via two ball bearings. The numerical model successfully confirms the frequency splits both in the rotor-based and ground-based coordinates. In the experimental analysis, we conduct vibration testing on a rotor–bearing–housing system that mimics the numerical benchmark model. Test results reveal two housing-dominant modes. As the rotor spins at various speed, measured waterfall plots confirm that the housing-dominant modes split according to ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3 as predicted.

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References

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Figures

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Fig. 1

Finite element method (FEM) model: cyclic symmetric rotor

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Fig. 2

FEM model: housing

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Fig. 3

Mode shapes of elastic modes

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Fig. 4

FFT of free responses when ω3 = 0

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Fig. 5

FFT of free responses when ω3 = 7200 rpm (120 Hz)

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Fig. 6

Waterfall plot of ground-based response of the rotor

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Fig. 7

The assembled system: the slotted disk, spindle motor, and square plate

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Fig. 8

The experiment setup. The left schematics: the first mode LDV/hammer. The right schematics: the second mode LDV/PZT actuator. The accelerometer is not drawn for simplicity.

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Fig. 9

FRFs: housing-dominant modes. The upper: FRFs with the hammer/LDV. The lower: FRFs with the PZT/LDV.

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Fig. 10

Experimental mode shapes: ΩL(H) disk and plate

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Fig. 11

Experimental mode shapes: ΩH(H) disk and plate

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Fig. 12

Waterfall with hammer/LDV

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Fig. 13

Waterfall with PZT/LDV

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