Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1621
標題: 雙邊固定式懸臂樑壓電變壓器
Clamped-Clamped Beam Type Piezoelectric Transformer
作者: 陳奇劭
Chen, Chi-Shao
關鍵字: piezoelectric transformers;壓電變壓器;cantilever;electromechanical modeling;懸臂樑;力電耦合模型
出版社: 機械工程學系所
引用: [1]C. A. Rosen, “Ceramic transformers and Filters,” Proceeding of electronic Components Symposium, Washington, D. C., May 1-3(1956) 205-211 [2]Y.-H. Hsu, C.-K. Lee, W.-H. Hsiao, “Optimizing piezoelectric transformer for maximum power transfer,” Smart Material and Structure, 12(2003) 373-83 [3]R.-L. Lin, “Piezoelectric transformer characterization and application of electronic ballast,” PhD Dissertation, Virginia Polytechnic Institute and state University, USA, 2001 [4]E. M. Baker, W. Huang, D. Y. Chen, F. C. Lee, “Radial mode piezoelectric transformer design for fluorescent lamp ballast application,” 33rd Annual IEEE Power Electronics Specialists, Cairns, Queensland, Australia, June 23-27 (2002) 1289-94 [5]J.-M. Seo, H.-W. Joo, H.-K. Jung, “Optimal design of piezoelectric transformer for high efficiency and high power density,” Sensors and Actuators A, 121 (2005) 520-526 [6]M. C. Do, H. Guldner, “High output voltage DC/DC converter based on parallel connection of piezoelectric transformers,” International Symposium on Power electronics, Electrical Drives, Automation and Motion, Taormina, Italy, May 23-26, (2006) S18 [7]T. Inoue, S. Hamamura, M. Yamamoto, A. Ochi, Y. Sasaki, “AC-DC converter based on parallel drive of two piezoelectric transformer,” Japanese Journal of Applied Physics, 47 (2008) 4011-4014 [8]黃威旗,「圓形疊層式壓電變壓器應用於電源轉換器之研究」,碩 士論文,國立成功大學電機工程研究所,臺南,(2003)。 [9]J.H. Park, S.M. Lee, S.J. Choi, B.H. Cho, “Design consideration of parallel–parallel connected piezoelectric transformer for thermal balance” Japanese Journal of Applied Physics, 46 (2007)7067–7072 [10]S. Roundy, P. K. Wright, J. M. Rabaey, “A Study of Low Level Vibrations as a Power Source for Wireless Sensor Nodes,” Computer Communications, 26 (2003) 1131-1144 [11]N. E. duToit, B. L. Wardle, S.-G. Kim, “Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters,” Integrated Ferroelectrics, 71 (2005) 121-160 [12]S. T. Ho, “Electromechanical Model of a Longitudinal Mode piezoelectric Transformer,” The Seventh International Conference on Power Electronics and Drive Systems, Bangkok, Thailand, November 27-30, (2007) 267-272 [13] Y.H. Huang, W. Huang, “An Improved Equivalent Circuit Model of Radial Mode Piezoelectric Transformer,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 58 (2011) 1069 [14]A. Erturk, D. J. Inman, “A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters,” Journal of Vibration and Acoustics, 130 (2008) 041002 [15]張翔,「應用壓電片於有與無缺線固定樑之模態分析」,碩士論文, 國立高雄海洋科技大學輪機工程研究所,高雄,(2005) [16]F.J. Shaker, “Effect of Axial Load on Mode Shapes Frequencies of Beams,” Lewis Research Center Report NASA-TN-8109, (1975) [17]A. Erturk, and D.J. Inman, “On mechanical modeling of cantilevered piezoelectric vibration energy harvesters,” Journal of Intelligent Material Systems and Structures, 19 (2008) 1311-1325 [18] T. K. Caughey, and M. E. J. O’Kelly, “Classical normal modes in damped linear dynamic systems,” Journal of Applied Mechanics, 32(1965) 583–588. [19] Erturk, A., and Inman, D. J., “On Mechanical Modeling of Cantilevered Piezoelectric Vibration Energy Harvesters,” Journal of Intelligent Material Systems and Structures. In press, (2008)doi:10,1177/1045389X07085639. [20] IEEE Standard on Piezoelectricity, IEEE,(1987)New York [21]彭泰龍,「壓電式發電裝置研究」,碩士論文,國立中興大學機械 工程研究所,台中,(2007) [22] A. Erturk, and D.J. Inman, “Effect of Strain Nodes and Electrode Configuration on Piezoelectric Energy Harvesting From Cantilevered Beams,” Journal of Vibration and Acoustics, submitted. [23]莊峻佑,「鋯鈦酸鉛薄膜製程參數對機電性質之影響」,碩士論文, 國立中興大學機械工程研究所,台中,(2010) [24]薛竣鴻,「低溫沉積二氧化矽和鋯鈦酸鉛複合薄膜於可撓性基板之研究」,碩士論文,國立中興大學機械工程研究所,台中,(2009)
摘要: 
本論文提出並研究雙邊固定式懸臂樑型壓電變壓器,並以尤拉-白努力樑為理論基礎推導此壓電變壓器之數學模型。
數學模型由懸臂樑在暫態運動時之力保守方程式開始進行解析解之推導,當中也考慮到了機械能與電能的耦合關係,最後推導出變壓器之輸出電壓。若考慮變壓器作用在第一諧振頻率附近時之狀況,則解析解可再進一步簡化,並且得到輸出電壓、電流以及功率等結果。從數學模型的結果得知,輸出電壓與兩電極之涵蓋區域以及長度比有關,楊氏系數與樑之厚度也影響了變壓器之輸出,但懸臂樑的長度並不影響此變壓器之變壓比。在壓電變壓器致動在第一諧振頻率下,輸入電極長度為0.22倍之懸臂樑長度時可以產生最佳之致動力矩,而較短之輸入電極可以產生較高之輸出電壓。而變壓器之諧振頻率與懸臂樑之長度的平方成反比,因此,可藉由改變懸臂樑之長度控制變壓器之工作頻率。基板之楊氏系數以及基板與壓電材料層之厚度比的不同組合會改變懸臂樑之中性軸以及斷面之彎曲剛性。然而變壓器之輸出電壓不僅因中性軸之位置而影響同時也被斷面之彎曲剛性所影響。由數學模型分析出的結果顯示,當變壓器之基板擁有較高之楊氏系數時,能達到的輸出電壓也會越高。
我們也藉由有限元素法之輔助以及實驗來驗證並修正數學模型,而最後數學模型之結果與實驗值的誤差小於10%

In this paper, we study the piezoelectric transformers in a form of fixed-fixed beam. And an analytical solution of a fixed-fixed beam type piezoelectric transformer with Euler-Bernoulli beam assumption is proposed.
The electromechanical equations are first derived for transient motions, and coupled expressions for the mechanical response and voltage output are obtained. The resulting equations are further reduced for the case of excitation around the first resonance frequency. Analyical solutions of mechanical response, voltage, current, and power outputs are presented.
From our analytical model, output voltage depends on the lengths of two electrodes, the Young's modulus ratio and thickness ratio between PZT layer and substrate, but is constant with respect to the length of beam. Besides, the lengths of input electrodes should be 0.22 times the length of beam to achieve the largest output from the largest moment. Furthermore, when the transformer is excited at first resonant frequency higher output voltage can be obtained with the shorter output electrodes. The resoance frequency using to excite the transformer are inversely proportional to the square of the lengthe of beams, so we can control the working frequency by the length of beam. The combination of Young's modului and thicknesses of PZT layer and substrate change the position of netural axis and the bending stiffness of beam, concurrently. However, output voltages of transformers depend not only on the postion of neutral axes but also on bending stiffnesses. The result is the transformer can get better performance by using the substrate with higher Young's modului
We also use the finite element methods and the experiment to verify the analytical model. Finally, the error of output voltage between the analytical model and experiment is less 10%.
URI: http://hdl.handle.net/11455/1621
其他識別: U0005-2208201113180000
Appears in Collections:機械工程學系所

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