Abstract
This dissertation gives numerical analyses of magnetic field distributions(1) in air gaps with the effects of slot depth, slot width,air gapcurvature and armature reaction, and (2) in a squirrel cage inductionmotor. In the first part of this dissertation, the Carter coefficient andaverage reluctance with the effect of armature reaction are studied on asimplified model, and a dimensionless parametric approach is utilized tocover wide ranges of parameters that frequently appear in electric machinedesign. A nonlinear dimensionless Maxwell equation is solved by using afinite-difference successive relaxation technique. In the region of study,various constant fluxes and load currents are applied. The Cartercoefficient in a straight or a curved air gap and the coefficient ofaverage reluctance with the effect of armature reaction are calculated andcompared with the data in the existing literature.In the second part, the application of the finite-element method forpredicting the performance of a squirrel cage induction motor isdescribed. The field region is discretized into triangular elements andthe Galerkin approach is employed to solve a nonlinear Maxwell equation.In teh analysis, core saturation and the induced rotor bar currents areconsidered. Based on the obtained field solution, the induced back voltageand inner impedance in the equivalent circuit are obtained, the statorcurrent is then determined iterately by using a fixed phase voltage and anexternal and an inner impedances. The characteristics studied are (1) themagnetizing inductances, the slot leakage inductances, the iron corelosses and power factors in the wide ranges of magnetizing currents andthe four rotor positions (2) slip performance of stator current, sorqueand power factor with various applied voltages. Finally, a 1 hpsquirrel-cage motor is tested to verify the calculated results.本文利用數值法來分析?氣隙中具有槽深、槽寬、氣隙曲率與電樞效應的及?一鼠籠式感應馬達內的磁場分佈。在第一部份中採用無因次參數法並以涵蓋常見於電機設計之廣泛無因次之參數範圍來探討。文中以有限差分連續鬆弛法來解非線性之馬克斯威爾方程式。在研究區域中加入不同之定磁通密度、槽電流密及變化槽曲率半徑或槽數來計算氣隙之平均磁阻並與現存文獻之卡特係數相比，結果尚屬合理。第二部份中，吾人採用有限單元法（Galerkin approach） 來預測感應馬達的性能。在分析中，鐵心的飽和及轉子棒的感應電流都必須考慮，根據所得的磁場分佈，吾人可計算等效電路中的內感應電壓及內阻抗，而定子上的電流便可由固定的外加相電壓與總阻抗重複計算求得。所探討的性能有?在無轉子棒情況下，磁飽和度及不同轉子位置對磁化電感、槽漏電感、鐵損及功因的影，?不同外加電壓下，馬達的定子電流、轉矩及功因的轉差特性。最後吾人用一具20KVA 的變壓器來測試一大同的1hp 感應馬達，以證實上述??所得之計算值。