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 本文主要是針對三極永磁無軸承馬達來建立動態模型。所謂無軸承馬達系指將磁浮軸承與馬達整合為一體，馬達本身亦當作磁浮軸承，無需額外軸承。一般而言，要得到磁浮軸承的動態模型並不容易，因為磁浮力模型牽涉到偏微分方程式(馬克思威爾方程式)的求解。由於複雜的邊界條件，它常常沒有解析解。目前普遍作法是將取近似解析解以得到磁浮力數學模型，進而建立磁浮系統動態模型。對於無軸承馬達系統，情況更是複雜，因為無軸承馬達包含了磁浮軸承的動態以及馬達的動態，並且兩者之間會互相影響，是個十分複雜的系統，以近似解推導的動態模型並不是十分精確，為改善這樣的情況，我們使用有限元素法來求解磁浮力與馬達轉矩，並以此建立較精確的無軸承馬達系統動態模型。
 This thesis is to obtain a mathematical dynamic model for a 3-pole permanent magnet type bearingless motor. The so-called bearingless motor is the integration of magnetic bearing and motor. In the other words, the motor is also served as a magnetic bearing . No additional bearing is required. In general, it is difficult to obtain a dynamic model for a magnetic bearing system since the magnetic force model involves solving partial differential equations (Maxwell equation).Due to complicated boundary conditions, analytic solution usually do not exist . A common practice is to take approximate analytic magnetic force model for the mathematical model of the magnetic bearing system.It is more complicated for bearingless motor since not only magnetic force but also motor torque are involved.Approximate models of magnetic force and motor torque will result in inaccurate mathematical dynamic model. To improve the dynamic model, finite element analysis is used to solve for the magnetic force and motor torque , and then to obtain an accurate mathematical model for the bearingless motor .
 第一章 緒論 41.1 前言 41.2 研究動機 41.3 文獻回顧 5第二章 有限元素模擬分析及系統描述 72.1 有限元素模擬分析 72.2 無軸承馬達系統描述 11第三章 無軸承馬達模擬 153.1 磁浮軸承磁通量與磁浮力模擬 173.2 無軸承馬達轉矩模擬 263.3 永久磁鐵尺寸設計 313.4 無軸承馬達磁浮力模擬 35第四章 建立模型 444.1 轉矩模型 444.2 磁浮力模型 51第五章結論與未來工作 55參考文獻 56
 [1] Ooshima, M.; Chiba, A.; Fukao, T.; Rahman, M.A. ”Design and analysis of permanent magnet-type bearingless motors” Industrial Electronics, IEEE Transactions on Volume 43,Issue 2,April 1996 Page(s):292 – 299[2] Zaki, A.; Ibrahim, S., ”Modeling and analysis of PM brushed DC motor using FEM,” Power Electronics and Applications, 2005 European Conference on 11-14 Sept. 2005 Page(s):6 pp.[3] Bianchi, N.; Canova,A., ”FEM analysis and optimisation design of an IPM synchronous motor,” Power Electronics, Machines and Drives, 2002. International Conference on (Conf. Publ. No. 487) 4-7 June 2002 Page(s):49 - 54[4] Kenny, A.; Palazzolo, A.B.; Provenza, A., “An integrated magnetic circuit model and finite element model approach to magnetic bearing design,” Energy Conversion Engineering Conference, 2002. IECEC ''02. 2002 37th Intersociety 29-31 July 2004 Page(s):223 - 226[5] Chang, L.; Eastham, A.R.; Dawson, G.E., ”Permanent magnet synchronous motor: finite element torque calculations,” Industry Applications Society Annual Meeting, 1989., Conference Record of the 1989 IEEE 1-5 Oct. 1989 Page(s):69 - 73 vol.1[6] Petkovska, L.; Cvetkovski, G., “FEM Based Simulation of a Permanent Magnet Synchronous Motor Performance Characteristics,” Power Electronics and Motion Control Conference, 2006. IPEMC ''06. CES/IEEE 5th International Volume 1, Aug. 2006 Page(s):1 – 5[7] Oshima, M.; Miyazawa, S.; Deido, T.; Chiba, A.; Nakamura, F.; Fukao, T. ” Characteristics of a permanent magnet type bearingless motor” Industry Applications, IEEE Transactions on Volume 32, Issue 2, March-April 1996 Page(s):363 – 370[8] Chen, S. L. and Hsu, C. T., “Optimal Design of a Three-Pole Active Magnetic Bearing,” IEEE Transactions on Magnetics, Vol. 38, No. 5, pp. 3458-3466, 2002v[9] Schweitzer, G., Bleuler, H., and Traxler, A., Active Magnetic Bearings, Hochschulverlag AG an der ETH Zurich, 1994.[10] 徐尚榆,“三極永磁式無軸承馬達分析與控制”,國立中正大學機械工程研究所碩士論文, 民95
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 1 三極永磁式無軸承馬達分析與控制

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 1 三極無軸承馬達之設計與分析 2 光碟機主軸馬達電壓控制之三極磁浮式軸承 3 三極永磁式無軸承馬達分析與控制 4 三極磁浮式轉子軸承系統之性能評估 5 嵌入式磁浮軸承控制系統之研發 6 繞性磁浮軸承之建模與控制 7 五軸系統之ILC循跡控制 8 三極全磁浮系統之控制與實驗驗證 9 三極全磁浮軸承之建模、控制與實驗驗證 10 三極磁浮系統之無感測控制 11 拘束多軸系統循跡控制之探討暨並聯式機構循跡之應用 12 阻抗控制應用於五軸機械手臂 13 電動式磁浮軸承設計與應用 14 渦電流位置感測器探頭之靜態性能的最佳化設計 15 應用於飛輪電池之五自由度磁浮軸承系統建模與控制器設計

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