單端固定石英音叉的振動模態與頻率分析

Abstract

本文主要研究對象為Z-cut單端固定音叉式石英振盪器，分析石英音叉之特徵頻率，並在單端長樑末端外加線性外力，觀察其對於石英振盪器共振頻率的影響，並利用有限元素法模擬石英音叉振盪器的振盪模態。 本文針對異相振盪行為進行分析，兩音叉樑視為尤拉樑，而質量塊則依據音叉樑異相振盪對質量塊所造成的力矩來建立翹曲形變的模型；施加外力時，則另外考慮質量塊的彎曲形變。耦合部分，假設其結構為彈性體，分別討論各自結構自由振動行為，再利用漢米頓定理推導出運動統御方程式及邊界條件，用以耦合機械與電性質之連續關係。 為瞭解製程誤差對於共振頻率的影響，本文將套用不同的外在因素進行模擬，並分析在不同尺寸以及外力作用下，對共振頻率的影響，以作為製程誤差分析設計之參考，於頻率準確度與製程難度中取得平衡，以達到良率提升之目的。

The thesis mainly studied about single-ended tuning fork quartz resonator, and analyzed the natural frequency of Quartz tuning fork (QTF) resonator, and the effect of resonant frequencies of the quartz tuning fork by linear external force, and simulated the vibration mode of Quartz tuning fork by Finite Element Method. Focusing on the analysis of the anti-phase mode, the study regards a central tuning fork as the Euler beam, and two ends of the proof masses built the warping model according to the moment caused by the anti-phase mode from the tuning fork to the proof masses. Assuming the coupling structure as an elastic body, and discussing the free vibration to each structure; using the Hamilton's principle to derive the governing equation and the boundary condition for coupling the continuous mechanical relationship. For understanding the impact of the process error to the resonant frequency and the convenience for designing, the study has analyzed the impact of the dimension to the sensitivity of the resonant frequency for being the references of the process error analysis and the design of the mask; in order to improve the yield, it must get the balance between the frequency accuracy and the difficulty during the process.