在本論文中對複合型壓電換能器進行了相關的研究，壓電換能器普遍使用於超音波的應用中，如超音波馬達、超音波溶接、超音波洗淨及水下聲學等。在這些應用中，換能器主要被用來將電能轉換為機械振動或是聲波，諸如伸長型、彎曲型與扭轉型的複合型壓電轉換器都可以找到越來越多滿足於各個目的的應用。通常在設計壓電換能器時，對於換能器結構的共振頻率與振動模態的精密計算是很重要的，而壓電換能器的共振頻率由其材料參數與幾何外形尺寸決定，對於高功率超音波的應用而言，則還需要考慮到輸出功率、電聲轉換效率、工作溫度上升情形與振動位移分布等特性。
在本研究中，對於彎曲型與扭轉型壓電換能器進行了理論分析，而且為了更精準的了解這些換能器的特性，也以有限元素分析軟體ANSYS對各型壓電結構進行自然頻率、振動模態與阻抗特性的分析。最後在實驗中，製作了彎曲型壓電換能器，進行相關的振動特性與阻抗特性的量測，並以鋼球的轉動控制為例，探討驅動電壓與鋼球轉數的關係。

In this thesis, the compound piezoelectric transducers are studied. Piezoelectric transducers are widely used in ultrasonic applications such as ultrasonic motor, ultrasonic welding, ultrasonic cleaning and underwater sound. They are mainly used to convert electric signals to mechanical vibrations or acoustic wave. In these applications, compound transducers such as longitudinal, flexural and torsional transducers have found more and more applications corresponding to various purposes. Usually, the resonance frequency and vibration mode of the piezoelectric transducer are important in the design and assembly. They are determined by its material parameters and geometrical dimensions. The high power characteristics of the transducer also include the output acoustic power, the electro-acoustic efficiency, the temperature rise, the vibration displacement distribution and others.
In this study, flexural and torsional transducers are theoretically analyzed. In addition, finite element analysis method (ANSYS) is used to verify the theoretical results. The resonant frequencies, vibration modes and input impedance of the transducer are obtained and discussed in this study. Finally, a flexural piezoelectric transducer is manufactured for the experiment. The vibration characteristics of the transducers are measured and a ball rotor rotating experiment is also conducted.

中文摘要 --------------------------------------------------------------- i
英文摘要 --------------------------------------------------------------- ii
誌謝 --------------------------------------------------------------- iii
目錄 --------------------------------------------------------------- iv
表目錄 --------------------------------------------------------------- vii
圖目錄 --------------------------------------------------------------- viii
一、 緒論--------------------------------------------------------- 1
1.1 前言--------------------------------------------------------- 1
1.2 文獻回顧---------------------------------------------------- 3
1.3 研究動機與目的------------------------------------------- 12
二、 理論分析---------------------------------------------------- 14
2.1 壓電材料---------------------------------------------------- 14
2.1.1 壓電效應---------------------------------------------------- 14
2.1.2 壓電晶體的振動模式-------------------------------------- 14
2.1.3 壓電方程氏------------------------------------------------- 15
2.2 理論分析---------------------------------------------------- 17
2.2.1 彎曲型壓電換能器結構------------------------------------- 17
2.2.2 作動原理------------------------------------------------------ 18
2.2.3 彎曲型壓電換能器的運動方程式------------------------ 19
2.2.4 扭轉型壓電換能器的結構與作動原理------------------- 21
2.2.5 扭轉壓電換能器的運動方程式-------------------------- 22
2.2.5 扭轉壓電換能器的振動模態----------------------------- 24
2.2.7 扭轉型壓電換能器的共振頻率-------------------------- 26
2.3 扭轉壓電換能器的導納分析----------------------------- 29
三、 有限元素分析---------------------------------------------- 33
3.1 彎曲振動型壓電換能器的分析-------------------------- 34
3.1.1 機械端邊界條件為固定-自由時的分析結果----------- 36
3.1.2 複合型彎曲振動壓電換能器在邊界條件為固定-自由
時的分析------------------------------------------------------
38
3.2 切向極化之扭轉型壓電換能器的分析------------------ 40
3.2.1 機械端邊界條件為固定-自由時的分析結果----------- 42
3.2.2 機械端邊界條件為自由-自由時的分析結果----------- 44
3.3 軸向極化之扭轉型壓電換能器的分析------------------ 47
3.3.1 機械端邊界條件為固定-自由時的分析結果----------- 48
3.3.2 機械端邊界條件為自由-自由時的分析結果----------- 51
3.3.3 軸向極化之扭轉型壓電圓管的分析(固定-自由邊界) 54
3.3.4 軸向極化之扭轉型壓電圓管的分析(自由-自由邊界) 57
3.4 切向極化之疊層扭轉型壓電換能器的分析------------ 59
3.4.1 切向極化之疊層扭轉型壓電換能器的分析(固定-自由邊界)--------------------------------------------------------
60
3.4.2 切向極化之疊層扭轉型壓電換能器的分析(自由-自由邊界)--------------------------------------------------------
62
3.5 結語--------------------------------------------------------- 65
四、 實驗量測與結果------------------------------------------- 68
4.1 實驗量測佈置---------------------------------------------- 68
4.2 換能器阻抗曲線量測結果與討論------------------------ 70
4.3 壓電換能器位移量測結果與討論------------------------ 71
4.3.1 換能器驅動鋼球時轉速量測結果與討論---------------- 73
4.4 結語-------------------------------------------------------- 74
五、 總結-------------------------------------------------------- 75
5.1 結論-------------------------------------------------------- 75
5.2 未來展望-------------------------------------------------- 75
參考文獻 ------------------------------------------------------------- 76

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