本論文針對兩相混合式步進馬達建立數學模型，提出一種新型磁飽和理論，其能夠對非線性之磁飽和現象進行建模，以應對步進馬達中難以忽略之磁飽和問題。同時，本文彙整通用氣隙磁場調制理論，一方面將眾多相關理論之文獻歸納整理得其建立流程；一方面則將該理論延伸應用至三維結構之混合式步進馬達。最終結合所提出之新型磁飽和理論，建立一種能夠代表兩相混合式步進馬達之磁場調制模型。
文中利用ANSYS模擬軟體進行有限元素分析。在混合式步進馬達之三維模擬中，為確保該模擬之有效性，需確認氣隙網格之設定足夠使結果收斂。最終，模擬得出氣隙磁通密度、磁交鏈、電動勢、電感與總轉矩；並將模擬結果與所提出之數學模型相比對，其結果顯示所提出之數學模型對於反映磁飽和影響具有相當之準確性。

This thesis establishes a mathematical model for a two-phase hybrid stepper motor and presents a novel magnetic saturation theory capable of modeling the nonlinear magnetic saturation phenomenon, which is significant in the context of stepper motors. Furthermore, this work consolidates general theories of air-gap magnetic field modulation, synthesizing existing literature to create a structured development process. Additionally, the theory is extended to apply to three-dimensional structures of hybrid stepper motors. Ultimately, by integrating the proposed novel magnetic saturation theory, a magnetic field modulation model representing the two-phase hybrid stepper motor is developed.
The thesis employs ANSYS simulation software for finite element analysis. In the three-dimensional simulation of the hybrid stepper motor, the validity of the simulation is ensured by confirming that the air-gap mesh settings are sufficiently refined to achieve convergence of results. The simulation yields data on air-gap magnetic flux density, magnetic cross-linkage, electromotive force, inductance, and total torque. A comparison of the simulation results with the proposed mathematical model demonstrates that the model accurately reflects the effects of magnetic saturation.

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