Electrode Analysis and Correction of Mass Imperfection of a Fused Quartz Hemispherical Resonant Shell

本研究探討半圓球薄殼振動陀螺儀的主結構，半圓球薄殼上的瑕疵對於陀螺儀的使用上造成的影響，並建立一修正方法以避免瑕疵的存在造成陀螺儀使用上的問題。 在加工製造過程中，半圓球薄殼上將會有幾何不均以及材料不均等瑕疵，而本研究所使用之球殼材料為有高品質因數的熔質石英，產生自然頻率的範圍小，瑕疵將會造成兩廣義座標的頻率分歧，對於陀螺儀的使用造成影響。 本文以Niordson線性薄殼理論為基礎，並使用雷利位移近似解代入，接著利用漢彌頓原理作動力分析，了解半圓球薄殼上的瑕疵對於半圓球薄殼振動陀螺儀運動方程式的影響，並建立一方法修正瑕疵造成的頻率分歧。 了解瑕疵對於半圓球薄殼第2模態兩廣義座標的影響後，本研究將利用Lissajous圖找出半圓球薄殼之兩特徵方向，並於低頻特徵方向上做去質量修正，以降低頻率分歧，並且探討去質量修正感測係數的位置且不影響質量係數。 當去質量修正到達其極限後，本研究建立一靜電力修正頻率分歧的方法，利用球殼上鍍電極，外圍配置驅動電極片的方式，分配電壓修正頻率分歧，並建立修正方程式。The purpose of the study is to construct a method to correct imperfections of the hemispherical shell, which is the major component of the hemispherical resonator gyroscope. Some defects will be produced during manufacturing process, such as the voids, bubbles, geometric errors and impurities. These imperfections cause the non-uniformity in material parameters and geometry. It will result in the natural frequency splits of the hemispherical shell. This thesis is based on the shell theory written by Niordson, and employ Rayleigh’s approximate solution and utilize Hamilton principle to derive the equation of motion. After the equation of motion of an imperfect hemispherical resonator gyroscope are investigated, we use Lissajous figure to find out the eigenvector which has lower frequency, then we do mass-trimming at this location to adjust frequency bifurcation. After mass-trimming, we set the electrode sheets, which can change the stiffness of the hemispherical shell by electrostatic force when supplying voltage, to adjust micro frequency bifurcation