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Modeling the Effect of Imperfections in Glassblown Micro-Wineglass Fused Quartz Resonators

[+] Author and Article Information
Yusheng Wang

Department of Mechanical
and Aerospace Engineering,
University of California, Irvine,
4200 Engineering Gateway,
Irvine, CA 92697
e-mail: yushengw@uci.edu

Mohammad H. Asadian

Department of Mechanical
and Aerospace Engineering,
University of California, Irvine,
4200 Engineering Gateway,
Irvine, CA 92697
e-mail: asadianm@uci.edu

Andrei M. Shkel

Department of Mechanical
and Aerospace Engineering,
University of California, Irvine,
4200 Engineering Gateway,
Irvine, CA 92697
e-mail: andrei.shkel@uci.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 3, 2017; final manuscript received May 1, 2017; published online May 30, 2017. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 139(4), 040909 (May 30, 2017) (8 pages) Paper No: VIB-17-1005; doi: 10.1115/1.4036679 History: Received January 03, 2017; Revised May 01, 2017

In this paper, we developed an analytical model, supported by experimental results, on the effect of imperfections in glassblown micro-wineglass fused quartz resonators. The analytical model predicting the frequency mismatch due to imperfections was derived based on a combination of the Rayleigh's energy method and the generalized collocation method. The analytically predicted frequency of the n = 2 wineglass mode shape was within 10% of the finite element modeling results and within 20% of the experimental results for thin shells, showing the fidelity of the predictive model. The postprocessing methods for improvement of the resonator surface quality were also studied. We concluded that the thermal reflow of fused quartz achieves the best result, followed in effectiveness by the RCA-1 surface treatment. All the analytical models developed in this paper are to guide the manufacturing methods to reduce the frequency and damping mismatch, and to increase the mechanical quality factor of the device.

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Figures

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Fig. 1

Hemitoroidal shell fabricated using high-temperature microglassblowing process of fused quartz

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Fig. 2

Coordinate system, middle surface (dashed line), and parameters of hemitoroidal shell

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Fig. 3

Comparison of n = 2 mode shapes from analytical model and finite element model. Displacements in φ direction are normalized.

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Fig. 4

Relation between resonant frequency of n = 2 mode and the thickness of the shell

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Fig. 5

Experimental setup to measure the resonant frequency of the device

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Fig. 6

Schematic of lapping error and the analytical result

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Fig. 7

Schematic of the attachment of device to lapping fixture and a picture of a device being asymmetrically lapped is presented. Experimental result of the effects of lapping imperfections is also shown.

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Fig. 8

Surface roughness changes over reflow time

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Fig. 10

A comparison of the local surface morphology for similar surfaces with different values of roughness exponent α

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Fig. 9

Power spectral densities of the original surface and surfaces after reflowing for 1 min, 2 min, and 5 min

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Fig. 11

Histograms of the original surface and surfaces after reflowing for 5 min, 15 min, and 60 min, showing an improvement of long-term surface roughness

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Fig. 12

AFM images of the surface of 3D fused quartz structures and histograms before and after reflow

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