臺灣博碩士論文加值系統

本論文旨在利用小波轉換及Morlet小波，對應用於往復式壓縮機之磁浮軸承/推桿進行磁剛性與磁阻尼的鑑別。透過小波時頻分析，擷取出代表自然頻率的骨根圖，根據骨根隨自然頻率變動的樣式，以小波的線性與非線性鑑別法則，先進行數值模擬來驗證所開發電腦程式的正確性，再透過實際的磁浮軸承/推桿系統，證實與量化非線性磁阻尼、非線性磁阻尼之負阻尼及高階磁剛性，並求得系統磁阻尼與機械阻尼的比重。本文採dSPACE 1104套裝介面、四極主動式磁浮軸承、光學測距器與Matlab程式語言作為實驗工具及設備。

The purpose of this thesis is to apply the Wavelet Transform algorithm to identify magnetic damping and magnetic stiffness coefficients of the linear compressor system in which a 4-pole active magnetic bearing (AMB) is embedded. By using time-frequency analysis of wavelet, the ridge of the processed signal shown in Wavelet form can be extracted to find the natural frequency of the system. The results of experimental simulations verify that the Wavelet identification method is able to quantify the nonlinear magnetic damping coefficients, the fundamental and higher-order stiffness of the rod dynamic in the magnetic levitation system. The test rig is equipped with dSPACE 1104 interface board, a 4-pole active magnetic bearing, a laser diode sensor and the software environment by MATLAB.

中文摘要 I
英文摘要 II
致謝 III
目錄 IV
表目錄 VII
圖目錄 VIII

第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 3
1.3 論文架構 5

第二章　小波轉換與系統鑑別 6
2.1 訊號處理與小波轉換 7
2.2 小波的時頻分析 16
2.2.1 小波的時頻中心及時頻解析範圍 16
2.2.2 小波轉換時頻分析及海森堡測不準原理 22
2.3 小波轉換與系統鑑別 25
2.3.1 平面分析小波轉換 25
2.3.2 線性系統模型鑑別 27

第三章 應用於往復式壓縮機之推桿與磁浮軸承 40
3.1 利用主動式磁浮軸承之往復式壓縮機 40
3.2 磁浮軸承系統模型 47
3.3 推桿往復運動之軸向磁力模型 48
3.3.1 以模擬軟體建立磁力模型 48
3.3.2 以電磁理論建立磁力模型 63

第四章 利用小波對非線性系統鑑別 77
4.1 Hilbert轉換鑑別簡介 79
4.2 非線性阻尼模型之小波鑑別 82
4.3 數值模擬與驗證 89
4.4 非線性阻尼模型之小波鑑別 99

第五章 具磁性阻尼之線性系統鑑別與驗證 107
5.1 AMB架構與實驗配置 108
5.2 軸承系統鑑別與量測 115
5.3 磁阻尼的鑑別 118
5.4 磁剛性的鑑別 123

第六章 結論與未來展望 126
6.1 結論 126
6.2 未來發展與建議 126

參考文獻 128
自述 131

[1]C. K. Chui, “An Introduction to Wavelet,” Academic Press, 1992.
[2]P. Goupillauda, A. Grossmann, J. Morleta, “Cycle-octave and related transforms in seismic signal analysis,” Geoexploration Amsterdam, Vol. 23, n1, p 85-102, 1984.
[3]Mallat, Stephane, “Compact Multiresolution Representation: The Wavelet Model,” Proceedings of the IEEE Computer Society Workshop on Computer Vision, p 2-7, 1987.
[4]W. J. Staszewski, “Identification of Damping in MDOF Systems Using Time-scale Decomposition,” Journal of Sound and Vibration, Vol.203, p 283-305, 1997.
[5]W. J. Staszewski, “Identification of Non-Linear Systems Using Multi-scale Ridges and Skeletons of the Wavelet Transform,” Journal of Sound and Vibration, Vol.214, p 639-658, 1998.
[6]J. Lardies, S. Gouttebroze, “Identification of Modal Parameters Using the wavelet Transform,” International Journal of Mechanical Sciences, Vol.44, p 2263-2283, 2002.
[7]S. Erlicher, P. Argoul, “Modal Identification of Linear Non-proportionally Damped Systems by Wavelet Transform,” Mechanical Systems and Signal Processing, Vol.21, p 1386-1421, 2007.
[8]J. Zhang, C. Wang, S. Hu, “Identification of Nonlinear Systems Through Time-frequency Filtering Technique,” Journal of Vibration and Acoustics, Vol.125, p 199-204, 2003.
[9]Cyril M. Harris, Charles E. Crede, “Shock and Vibration Handbook,” Vol.1,McGraw-Hill, p 4-15, 1961.
[10]M.-N. Ta, J. Lardies, “Identification of Weak Nonlinearities on Damping and Stiffness by the Continuous Wavelet Transform,” Journal of Sound and Vibration, Vol.293, p 16-37, 2006.
[11]M. Misiti, Y. Misiti, G. Oppenheim, J.-M. Poggi, “Wavelet Toolbox User’s Guide,” The MathWorks, 2002.
[12]N.-C. Tsai, C.-W. Chiang, H.-Y. Li (2009), “Innovative active magnetic bearing design to reduce cost and energy consumption, " Electromagnetics, Vol. 29, No.5, p. 406-420.
[13]S. A. Billing, H. L. Wei,” The wavelet-NARMAX representation: A hybrid model structure combining polynomial models with multiresolution wavelet decompositions,” International Journal of Systems Science, Vol.36, n 3, p 137-152, 2005.
[14] A. Rahib Hidayat, K. Okyay, “Fuzzy wavelet neural networks for identification and control of dynamic plants - A novel structure and a comparative study,” IEEE Transactions on Industrial Electronics, p 3133-3140, 2008.
[15]S. Hassani, A. Alaoui Soulimani, A. Ehrlacher, ”A nonlinear viscoelastic model: the pseudo-linear model,” European Journal of Mechanics, A/Solids, Vol.17, p 567-598, 1998.
[16]Feldman M., “Non-Linear System Vibration Analysis Using Hilbert Transform,” Proceedings of SPIE - The International Society for Optical Engineering, v 1923, p 799-805, 1993.
[17]Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C. and Liu, H.H., “The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis”, Proc. R. Soc. Lond. A 454, p 903-995, 1998.
[17]Y.-M. Chen, S.-Y. Fan, W.-S. Liu, “Electromagnetic-Force Analysis of the Magnetically Levitated Motor With Two With Two Directions of Movement,” IEEE Transactions on Industry Applications, Vol.42, p 31-41, 2006.
[18]M. Lakshmanan, S. Rajasekar, “Nonlinear Dynamics,” Springer, 2002.
[19]C. K. Chui, “Wavelet: A Tutorial in Theory and Applications,” Academic Press, 1992.
[20]S. Mallat, “A Wavelet Tour of Signal Processing,” Academic Press, 1998.
[21]A. V. Oppenheim, A. S. Willsky, S. H. Nawab, “Signals & Systems 2nd Edition,” Prentice-Hall, 1996.
[22]吳劍秋，1996，”基礎電磁學”，全華圖書公司。
[23]楊國輝，2000，”應用電磁學”，五南圖書公司。
[24]單維彰，1998，”凌波初步”，全華圖書公司。
[25]張智星，2007，”Matlab 程式設計”，鈦思科技。
[26]王栢村，2007，”振動學”，全華圖書公司。