磁阻馬達經由凸極的激磁可產生一吸引力，而此吸引力可分為切線方向與徑向的力量，切線方向的力量即為轉矩，而徑向力量會因為馬達結構而互相抵銷，在這種特殊的狀態下三相12/8磁阻馬達可經由選擇不同的激磁極來同時產生徑向力與轉矩，也就是說在可以分別激磁各極電流的情形下同時控制徑向力與轉矩，使轉子在沒有軸承的情形下控制在氣隙的中央。本論文針對12/8極磁阻馬達提出一套自軸承控制系統，即轉子僅需要單邊軸承並限制軸向移動，而徑向位置則利用徑向力控制使轉子穩定於中央，本文除了分析馬達轉矩與徑向力、建立其數學模式，並提出一自軸承控制法則，最後將控制法則以DSP控制器實現並以實驗驗證之。

Switched reluctance motors develop torque through an attraction force between the stator poles and the rotor teeth. This attraction force can be divided into tangential and radial force components. The tangential force converts to the rotational torque, and the net radial force is generally zero due to the geometrically balanced motor structure. Due to its special structure, the shaft radial force and torque of a three-phase 12/8 switched reluctance motor can be separately controlled by proper selection of pole currents. Therefore, when all the pole currents can be controlled independently, it is possible to control the radial force to counterbalance the external force acting on the shaft. Consequently, the rotor can be controlled to a position near the center of the air gap when it does not have a rotational bearing. In this paper, a control scheme for self-bearing of a 12/8 pole SRM drive is proposed. The rotor needs only one bearing for rotation and to constrain the axial movement. The other end can move freely in radial direction but is balanced with the radial force produced by the motor. Motor torque and radial force characteristics is analyzed and modeled, the self-bearing control scheme is developed and presented. The proposed control scheme is also implemented with a DSP and verified experimentally.

論文目錄
中文摘要
英文摘要
論文目錄………………………………………………………..………Ⅰ
圖目錄………………………………………………………………..…Ⅲ
表目錄…………………………………………………………………..Ⅵ
符號說明………………………………………………………………..Ⅶ
第一章	緒論……………………………………………………………1
   1.1  背景與目的………………………………………………….…1
   1.2  文獻回顧…………………………………………………….…4
   1.3  論文大綱…………………………………………………….…7
第二章	開關式磁阻馬達模式…………………………………….…...8
   2.1  開關式磁阻馬達簡介………………………………………….8
   2.2  單極轉矩與徑向力分析…………………………….………..20
   2.3  單相四極轉矩與徑向力分析……………………..………….25
   2.4  整體12極之轉矩與徑向力分析……….……………………27
   2.5  模擬分析……………………...………………………………29
第三章	自軸承控制……………………………………………….….36
   3.1  自軸承系統應用………………………………………….…..36
   3.2  產生可控制之徑向力的方法……………….………………..40
3.3  自軸承控制系統…………………………….……………..…52
第四章	實驗結果……………………………………………………..54
   4.1  實驗系統…………………………………………………….. 54
   4.2  實驗結果……………………………………………………...58
第五章  結論與未來工作……………………………………………..71
附錄一  12/8開關式磁阻馬達參數…………………………………..73
附錄二  實驗系統照片………………………………………………..74
參考文獻………………………………………………………………..76

圖目錄

圖1.1  SRM極對數組合對徑向力方向之影響………….………………….3
圖2.1  典型的12/8三相SRM結構圖……………………...……………….9
圖2.2  定子、轉子角度與電感之關係圖…………….……………….……11
圖2.3  產生正轉矩之電流電感關係示意圖…………..……………………11
圖2.4  典型的12/8極SRM之電感、電流與轉矩關係圖………………..13
圖2.5  基本的三相SRM驅動電路………………...……………………….15
圖2.6  基本的SRM開關切換模式……………………………….………..15
圖2.7  SRM控制方塊圖………………………….…………………………17
圖2.8  磁滯型電流控制驅動方塊圖………………..………………………17
圖2.9  磁滯型電流控制上下限…………………..…………………………17
圖2.10  PI電流控制驅動方塊圖…………………………………………...17
圖2.11 吸引力示意圖…………………….…...…………………..…………20
圖2.12 徑向力分布………………………………………………...………...21
圖2.13  12/8極SRM結構圖……….……………………………….……...21
圖2.14  A1極磁路示意圖…………………………………….….……….…21
圖2.15 比較FEA計算結果與式(2-5)計算之吸引力……………………….24
圖2.16 比較FEA計算結果與式(2-6)計算之 ……………………………24
圖2.17 各相相對角度計算流程……………...…….………………………..28
圖2.18  A2極電流為2安培時的徑向力與轉矩…………….……………..30
圖2.19  A相四極均為2安培時的徑向力與轉矩……………………….....31
圖2.20  A相四極弦波激磁之徑向力與轉矩………………………………32
圖2.21  B1=8、A2=6、C1=5 安培時之徑向力與轉矩……….………..……33
圖2.22 馬達各極極性關係圖…………………………………………...…...35
圖3.1  被動式磁浮軸承……………………………………………………..38
圖3.2  主動式磁浮軸承……………………………………………………..38
圖3.3  混合型磁浮軸承……………………………………………………..38
圖3.4  文獻[50]之自軸承SRM設計………………………………………..39
圖3.5  電感分布…………………………….………………………….……40
圖3.6  激磁電感上升相與一電感下降相之極時的磁力線迴路分布……..42
圖3.7  徑向力命令方向區間………………………………………………..42
圖3.8   為-7.5度、徑向力命令為75度時之激磁極與磁力線圖………...44
圖3.9  激磁電流計算流程…………………………………………………..44
圖3.10 徑向力大小改變、方向不變的激磁電流計算結果………………..49
圖3.11 徑向力方向改變、大小不變的激磁電流計算結果………………..49
圖3.12 不同轉角下，產生旋轉之徑向力所需的電流……………………..50
圖3.13 利用FEA和圖3.12之電流計算所得的徑向力…………………….51
圖3.14 利用圖3.12之電流以FEA分別計算各相所產生的徑向力……….51
圖3.15 自軸承系統控制方塊圖……………………………………………..53
圖3.16 自軸承控制參數計算流程圖………………………………………..53
圖4.1  硬體系統架構圖……………..………………………………………56
圖4.2  自軸承機構圖…………………………..……………………………56
圖4.3  徑向力量測系統……………………………………..………………57
圖4.4  程式流程圖…………………………………………..………………57
圖4.5  激磁A2極， 從-15°~15°所產生的徑向力………………………58
圖4.6  不同轉速下的徑向力分布…………………………….…………….59
圖4.7  不同轉速下，轉子偏心0.1mm時的徑向力……………………….60
圖4.8   為8°時，徑向力大小固定而方向以頻率4Hz旋轉下所量測的激磁電流回授………………………………………………………....61
圖4.9  固定 = 8°，徑向力命令不同時所量測之徑向力……………….62
圖4.10 不同轉角下，徑向力命令4N所量測之徑向力……………………63
圖4.11 旋轉徑向力命令為4N時，在各相相對角度為14°時激磁所量測之徑向力……………………………………………………………….64
圖4.12 轉速為400rpm時加入4Hz徑向力命令的電流回授(僅B相)……65
圖4.13 轉速為400rpm，旋轉徑向力命令為6N、4Hz所量測之徑向力…65
圖4.14 自軸承控制，轉速為0， 為8°時的轉子位置與電流…………..66
圖4.15 不同轉角下給予0.3mm步階位置響應……..……………….……..67
圖4.16 自軸承控制中加入0.3安培的轉矩電流……………..………….....70

表目錄

表3.1  方法一激磁極判斷表……………………………………...……..….42
表3.2  方法二激磁極判斷表……………………….……………………….46

[1] T.J.E. Miller, Switched Reluctance Motors and Their Drives, Oxford, 1993.
[2] D.E. Cameron, J.H. Lang, and S.D. Umans, “The origin and reduction of acoustic noise in doubly salient variable-reluctance motors”, IEEE Trans. on Industry Applications, vol. 28, no. 6, Nov./Dec. 1992, pp. 1250-1255.
[3] N. Sadowski, Y. Lefevre, C.G.C. Neves, and R. Carlson, “ Finite elements coupled to electrical circuit equations in the simulation of switched reluctance drives: attention to mechanical behaviour”, IEEE Trans. on Magnetics, vol. 32, no. 3, May 1996, pp. 1086-1089.
[4] B. Fahimi, G. Suresh, and M. Ehsani, “Design considerations of switched reluctance motors: vibration and control issues”, Conference Record of the 1999 IEEE-IAS, vol. 4, 1999, pp. 2259-2266.
[5] B. Fahimi and M. Ehsani, “Spatial distribution of acoustic noise caused by radial vibration in switched reluctance motors”, Conference Record of the 2000 IEEE-IAS, vol. 1, 2000, pp. 114-118.
[6] M.N. Anwar and I. Husain, “Design perspectives of a low acoustic noise switched reluctance machine”, Conference Record of the 2000 IEEE-IAS, vol. 1, 2000, pp. 99-106.
[7] W. Cai, P. Pillay, and A. Onekanda, “Analytical formulae for calculating SRM modal frequencies for reduced vibration and acoustic noise design”, 2001 International Electric Machine and Drives Conference , pp. 203-207.
[8] Yifan Tang, “Characterization, numerical analysis and design of switched reluctance motor for improved material productivity and reduced noise”, Conference Record of the 1996 IEEE-IAS, vol. 2, Oct. 1996, pp. 715-722.
[9] J. Mahn, D. Williams, P. Wung, G. Horst, J. Lloyd, and S. Randall, “A systematic approach toward studying noise and vibration in switched reluctance machines: preliminary results”, Conference Record of the 1996 IEEE-IAS, vol. 2, Oct. 1996, pp. 779-785.
[10]M.N. Anwar, I. Husain, S. Mir, and T. Sebastian, “Experimental evaluation of acoustic-noise and mode frequencies with design variations of switched reluctance machines”, Conference Record of the 2001 IEEE-IAS, vol. 1, 2001, pp. 3-10.
[11]W. Cai and P. Pillay, “Resonance frequencies and mode shapes of switched reluctance motors”, 1999 International Electric Machine and Drives Conference, May 1999, pp. 44-47.
[12]P. Pillay and W. Cai, “An investigation into vibration in switched reluctance motors”, IEEE Trans. on Industry Applications, vol. 35, no. 3, May/Jun 1999, pp. 589-596.
[13]R.S. Colby, F.M. Mottier, and T.J.E. Miller, “Vibration modes and acoustic noise in a four-phase switched reluctance motor”, IEEE Trans. on Industry Applications, vol. 32, no. 6, Nov/Dec 1996, pp. 1357-1364.
[14]R.S. Colby, F.M. Mottier, and T.J.E. Miller, “Vibration modes and acoustic noise in a 4-phase switched reluctance motor”, Conference Record of the 1995 IEEE-IAS, vol. 1, Oct .1995, pp. 441-447.
[15]A. Michaelides and C. Pollock, “Reduction of noise and vibration in switched reluctance motors: new aspects”, Conference Record of the 1996 IEEE-IAS, vol. 2, Oct. 1996, pp.771-778.
[16]M. Sanada, S. Morimoto, Y. Takeda , and N. Matsui, “Novel rotor pole design of switched reluctance motors to reduce the acoustic noise”, Conference Record of the 2000 IEEE-IAS, vol. 1, 2000, pp. 107-113.
[17]M. Rodrigues, P.J. Costa Branco, and W. Suemitsu, “Fuzzy logic torque ripple reduction by turn-off angle compensation for switched reluctance motors”, IEEE Trans. on Industrial Electronics, vol. 48, issue 3, June 2001, pp.711-715.
[18]D.S. Schramm, B.W. Williams, and T.C. Green, “Torque ripple reduction of switched reluctance motors by phase current optimal profiling”, Conference Proceedings of PESC, 1992, pp. 857-860.
[19]A.M. Stankovic, G. Tadmor, Z. J. Coric, and I. Agirman, “On torque-ripple reduction of current-fed switched reluctance motors”, IEEE Trans. on Industrial Electronics, vol. 46, no. 1, Feb. 1999, pp. 177-183.
[20]I. Husain and M. Ehsani, “Torque ripple minimization in switched reluctance motor drives by PWM current control”, IEEE Trans. on Power Electronics, vol. 11, no. 1, Jan. 1996, pp. 83-88.
[21] R.C. Kavanagh, J.M.D. Murphy, and M.G. Egan, “Torque ripple minimization in switched reluctance drives using self-learning techniques”, Proceedings of IECON '91, 1991, pp. 289-294.
[22]M. Rodrigues, P.J. Costa Branco, and W. Suemitsu, “Fuzzy logic torque ripple reduction by turn-off angle compensation for switched reluctance motors”, IEEE Trans. on Industrial Electronics, June 2001, pp. 711-715.
[23]N. Abut, B. Cakir, U. Akca, and N. Erturk, “Fuzzy control application of SR motor drive for transportation systems”, IEEE Conference on Intelligent Transportation System, ITSC ’97, pp. 135-140.
[24]M.J. Kharaajoo and H. Ebrahimirad,“Fuzzy logic torque ripple minimization of switched reluctance motors”, International Symposium on Signals, Circuits and Systems, July 2003, pp.105-108.
[25]Z. Hongtao, L. Feng, L. Liangen, J. Jingping, and X. Dehong, “Torque ripple minimization in switched reluctance motors using fuzzy-neural network inverse learning control”, The Fifth International Conference on Power Electronics and Drive Systems, Nov. 2003, pp.1203-1207.
[26]S.K. Mondal, S.N. Bhadra, and S.N. Saxena, “Application of current-source converter for use of SRM drive in transportation area”, International Conference on Power Electronics and Drive Systems, 1997, pp. 708-713.
[27]A.K. Young, J.S. Kyoo, and H.R. Guen, “SRM drive system with improved power factor”, Proceedings of IECON 97, 1997, pp. 541-545.
[28]M. Barnes and C. Pollock, “Power factor correction in switched reluctance motor drives”, 7th International Conference on Power Electronics and Variable Speed Drives, 1998, pp. 17-21.
[29]H. Ishikawa, D. Wang, and H. Naitoh,“A new switched reluctance motor drive circuit for torque ripple reduction”Power Conversion Conference, 2002. PCC Osaka 2002.April 2002, pp. 683-688.
[30]T. Kosaka and N. Matsui, “Optimal combination of pole configuration and current waveform of SRM for torque maximization”, The 34th Annual Meeting of IEEE Industry Applications Society, 1998, pp. 586-592.
[31]J.W. Lee, H.S. Kim, B.I. Kwon, and B.T. Kim “New rotor shape design for minimum torque ripple of SRM using FEM”, IEEE Trans. on Magnetics, March 2004, pp. 754-757.
[32]M. Balaji, C.A. Vaithilingam, and V. Kamaraj, “Torque ripple minimization in switched reluctance motor drives”, Second International Conference on Power Electronics, Machines and Drives , vol. 1, 31 March-2 April 2004, pp. 104-107.
[33]M.R. Harris and T.J.E. Miller, “Comparison of design and performance parameters in switched reluctance and induction motors”,  1989 International Electric Machine and Drives Conference, 13-15 Sep. 1989, pp. 303-307.
[34]M.N. Anwar and I. Husain, “Radial force calculation and acoustic noise prediction in switched reluctance machines”, Conference Record of the 1999 IEEE-IAS, vol. 4, 1999, pp. 2242 -2249.
[35]M. Gabsi, F. Camus, and M. Besbes, “Computation and measurement of magnetically induced vibrations of a switched reluctance machine”, IEEE Proceedings, Electric Power Applications, vol. 146, no. 5, Sep. 1999, pp. 463-470.
[36]I. Husain, A. Radun, and J. Nairus, “Unbalanced force calculation in switched-reluctance machines”, IEEE Trans. on Magnetics, vol. 36, no. 1, Jan. 2000, pp. 330-338.
[37]S. Ayari, M. Besbes, M. Lecrivain, and M. Gabsi, “Effects of the airgap eccentricity on the SRM vibrations”, International Electric Machine and Drives Conference, May. 1999, pp. 138-140.
[38]T.J.E. Miller, “Faults and unbalance forces in the switched reluctance machine”, IEEE Trans. on Industry Applications, vol. 31, no. 2, Mar./Apr. 1995, pp. 319-328.
[39]N.R. Garrigan, W.L. Soong, C.M. Stephens, A. Storace, and T.A. Lipo, “Radial force characteristics of a switched reluctance machine”, Conference Record of the 1999 IEEE-IAS, vol. 4, pp. 2250-2258.
[40]邱建民，“12/8極開關式磁阻馬達之徑向力控制法則設計”，淡江大學機械與機電工程系碩士論文，民國92年7月.
[41]馬玉龍，“12/8極開關式磁阻馬達之徑向力分析”，淡江大學機械與機電工程系碩士論文，民國92年6月.
[42]F.C. Lin and S.M. Yang, Oct. 2004, “Instantaneous shaft radial force control with sinusoidal excitations for switched reluctance motors”, IEEE-IAS 2004 Annual Meeting, Seattle, USA, pp. 424-430.
[43]J. Zhou and K.J. Tseng, “A Disk-type Bearingless motor for use as satellite momentum-reaction wheel”, The 33rd Annual of IEEE Power Electronics Specialists Conference, vol. 4, 23-27 June 2002, pp. 1971-1975.
[44]Y. Okada, K. Shimizu, and S. Ueno, “Vibration control of flexible rotor by inclination control magnetic bearings with axial self-bearing motor”, IEEE/ASME Trans. on Mechatronics, vol. 6, Dec. 2001, pp. 521-524.
[45]F. Wang, B. Wang, and L. Xu, “A novel bearingless motor with hybrid rotor structure and levitation force control”, The 37th IAS Annual Meeting of Industry Applications Conference, vol. 1, 13-18 Oct. 2002, pp. 212-215.
[46]Y. Okada, T. Shimonishi, S.J. Kim, and H. Kanebako, “Development of hybrid type self-bearing slice motor for small and high speed rotary machines”, The 36th IAS Annual Meeting of IEEE Industry Applications Conference, vol. 3, 30 Sept.-4 Oct. 2001, pp. 2005-2012.
[47]H. Kanebako and Y. Okada, “New design of hybrid-type self-bearing motor for small, high-speed spindle”, IEEE/ASME Trans. on Mechatronics, vol. 8, March 2003, pp. 111-119.
[48]T. Fukao, “The evolution of motor drive technologies: development of bearingless motors”, The Third International Power Electronics and Motion Control Conference, vol. 1, 15-18 Aug. 2000, pp. 33-38.
[49]Y. Okada, S. Miyamoto, and T. Ohishi, “Levitation and torque control of internal permanent magnet type bearingless motor”, IEEE Trans. on Control Systems Technology, vol. 4, Sept. 1996, pp. 565-571.
[50]M. Takemoto, H. Suzuki, A. Chiba, T. Fukao, and M.A. Rahman, “Improved analysis of a bearingless switched reluctance motor”, International Conference IEMD on Electric Machines and Drives, 9-12 May 1999, pp. 773-775.
[51]M. Takemoto, A. Chiba, and T. Fukao, “A method of determining the advanced angle of square-wave currents in a bearingless switched reluctance motor”, IEEE Trans. on Industry Applications, vol. 37, Nov.-Dec. 2001, pp. 1702-1709.
[52]M.Takemoto, A. Chiba, H. Akagi, and T. Fukao, “Radial force and torque of a bearingless switched reluctance motor operating in a region of magnetic saturation”, The 37th IAS Annual Meeting of Industry Applications Conference, vol. 1, 13-18 Oct. 2002, pp. 35-42.
[53]G.R. Slemon, Electric Machines and Drives, Addison Wesley, 1992.
[54]H.K. Bae and R. Krishnan, “A study of current controllers and development of a novel current controller for high performance SRM drives”, IEEE Trans. on Industrial Electronics, vol. 37, no. 6, 1996, pp. 68-75.
[55]S.C. Mukhopadhyay, J. Donaldson, G. Sengupta, S. Yamada, C. Chakraborty, and D. Kacprzak, “Fabrication of a repulsive-type magnetic bearing using a novel arrangement of permanent magnets for vertical-rotor suspension”, IEEE Trans. on Magnetics, vol. 39, issue 5, Sept. 2003, pp. 3220-3222.
[56]陳明祥，“單軸主動式磁浮軸承在軸流式心室輔助氣之設計與控制”，淡江大學機械與機電工程系碩士論文，民國93年6月.
[57]R. Schoeb, “Gas forwarding apparatus for respiration and narcosis devices”, America Patent, No:6637433, Oct. 2003.
[58]F.C. Lin, W.T. Liu, and S.M. Yang, “An Approach to Produce Controlled Radial Force in Switched Reluctance Motor”, to appear in 2005 IECON.
[59]黃忠良，“磁懸浮與磁力軸承” ，復漢出版社，民國90年11月.