單晶石英加速規自然頻率之有限元素法分析

Finite Element Method Analysis of Natural Frequency of Single-Crystal Quartz

黃柏勳(Bo-Shiun Huang)

指導教授 ： 張家歐

共同指導教授 ： 張簡文添

國立臺灣大學/工學院/應用力學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00976

摘要

本文主要以有限元素法數值模擬 (YXl)-88°單晶石英加速規的自然頻率，各別數值模擬單樑、音叉、雙音叉的共振頻率，並對中間樑長度、中間樑寬度、厚度、中間樑間隙寬度、質量塊大小、質量塊型形狀與中間樑截面形狀等參數的改變，以求對加速規自然頻率的影響，進而探討影響石英加速規自然頻率的重要參數，以求得最佳化的石英加速規尺寸設計。最後，導入電極質量及電場所造成的壓電效應來計算石英加速規的自然共振頻率。從本文研究中可以得到各項幾何參數變化量對頻率的影響大小、求得特殊頻率的尺寸規格以及當雙樑寬度不相同時，對頻率的影響程度差異。

關鍵字

數值模擬 ； 有限元素法 ； 石英加速規 ； 自然頻率 ； 壓電效應

並列摘要

This thesis mainly simulates the natural frequency of the (YXl)-88° single-crystal quartz accelerometers by Finite Element Method; by simulating the resonant frequency of the beam, tuning fork and double-ended tuning fork, along with adjustments made in parameters of the length, width and thickness of the beam, the width of the gap, and the size and shape of the proof mass. The thesis aims at understanding the influence of these adjustments on the resonant frequency of single-crystal quartz accelerometers, and further, at finding the important parameters that would affect it, so as to derive the best design of the single-crystal quartz accelerometers. And finally, the piezoelectric effect caused by the electrode and electric field is induced, in order to calculate the natural frequency of the single-crystal quartz accelerometers. From this thesis, we are able to know the changes of natural frequency in accordance with different geometric parameters, the sizes of special natural frequency, and that as the width of beams differs, the
influence of natural frequency differs as well.

並列關鍵字

simulation ； finite element method ； quartz ； accelerometer ； natural frequency ； piezoelectric effect

參考文獻

1. Sungkyu LEE, “Photolithography and selective etching of an array of quartz tuning fork resonators with improved impact resistance characteristics”, The Japan Society of Applied Physics, 40,pp.5164-5167, Pt. 1, No.8, 2001

2. Sungkyu Lee, “Photolithography and Selective Etching of an Array of Surface Mount Device 32.768 kHz Quartz Tuning Fork Resonators: Definition of Side-Wall Electrodes and Interconnections Using Stencil Mask” , The Japan Society of Applied Physics, 40, pp.5480-5484,Pt. 1, No.9A, 2001

3. Sungkyu Lee, “Fabrication of an array of surface mount device 32.768 kHz quartz tuning fork-type crystals: photolithography and selective etching of an array of quartz tuning fork resonators with subsequent photoresist spray coating”,Vacuum 65(2):pp.161-168, 2002；

4. Sungkyu Lee,”Evaluation and evaporation to exact resonance frequency (32.768KHz) of semifinished and unsealed surface mount device (SMD) quartz tuning fork resonators”,Vacuum;67;pp.267-273,2002.

5. Sungkyu Lee ,“Design optimization of surface mount device 32.768 kHz quartz tuning fork-type crystals using finite element method and statistical analysis of test samples manufactured using photolithography”,Vacuum,68, pp.139-148.2003.