使用有限元素法分析與修正瑕疵石英諧振半球殼

FEM Analysis and Correction of an Imperfect Fused Quartz Hemispherical Resonant Shell

曾子恒(Tzu-Heng Tseng)

指導教授 ： 張家歐

國立臺灣大學/工學院/應用力學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201602477

摘要

半圓球殼陀螺儀之作動為以特定頻率激發諧振半球殼以產生駐波，並利用駐波之進動效應測量儀器所受之轉動，然而當諧振半球殼具有瑕疵時，其自然頻率會產生分歧而使駐波難以被激發以致陀螺儀無法作用。
故本文使用商用軟體的有限元素法(FEM)對具有密度與勁度瑕疵之半圓球殼進行數值模擬，探討密度與勁度單一瑕疵位置與分布對於頻率之影響，以及兩者間之交互關係，並模擬密度與勁度多瑕疵混合之效應。藉由了解瑕疵特性對於頻率之影響，得以更有系統與方向的進行頻率修正的參數設定與分析。
為了解決頻率分歧之問題本文先以不改變半圓球殼結構而僅改變特定區域材料參數之方法進行修正，並探討分別以密度、勁度以及同時以密度與勁度修正對頻率分歧修正的效應。而實務上是以雷射束去材料之方式進行頻率修正，因此改以直接改變半圓球殼之幾何結構，去除特定區域之材料進行數值模擬以更貼近實際情況，並且探討去除區域之修正參數設定對於頻率修正之效應。

關鍵字

半圓球殼 ； 陀螺儀 ； 數值模擬 ； 瑕疵 ； 頻率修正

並列摘要

In application to the HRG shell, Coriolis forces causes a slow precession of a standing wave which rotation is proportional to the input rotation .With this angular-gain factor we can measure the rotation acting on the HRG by sensing the standing waves precession.
Hemispherical resonator is responsible for sensing angular motion, however some defects such as the voids, bubbles, geometric errors and impurities will be produced during the manufacturing process. The defect causes a frequency difference between two working modes and leads to the loss of gyroscopic effect, and thus the resonator cannot sense angular motion. Density and stiffness imperfection are considered and based on finite element analysis software COMSOL, the finite element model of the imperfect hemispherical shell resonator is established.
Firstly, by changing the imperfection parameters of density and stiffness, to study the relationship between bifurcated frequencies and imperfections.
Secondly, trim at the location of the eigenvector of the vibration mode by setting the material properties, density and stiffness, without changing the geometry to adjust frequency bifurcation.
Lastly, to simulate laser ablation tuning, trim by removing the geometry at the bottom of the hemispherical, and study how the removing geometry parameters affect the frequency bifurcation.

並列關鍵字

hemispherical shell ； HRG ； imperfection ； trim

參考文獻

[1] David M. Rozell, 2009, "The Hemispherical Resonator Gyro: From Wineglass to the Planets," Proc. 19th AAS/AIAA Space Flight Mechanics Meeting, pp.1157-1178.

[2] A.D. Meyer and D.M. Rozelle, 2012, “Milli-HRG inertial navigation system,” Position Location and Navigation Symposium (PLANS), IEEE/ION, 23-26 April 2012, pp.24-29.

[3] Rayleigh, L, 1881, “On the Infinitesimal Bending of Surfaces of Revolution,” Proc. Math. Soc., London, Vol.13, pp. 4-16.

[4] Love, A. E. H., 1888, “On th Small Free Vibrations and Deformation on Thin Elastic Shells,” Phil. Transactions Roy. Soc., A179, pp. 491-546.

[5] Washizu, K., 1980, Variational Methods in Elasticity and Plasticit, Pergamon Press Ltd., 3rd.