傳統馬達驅動性能驗證常使用實體電機與驅動器進行驗證，存在高成本、儀器損壞等缺點，因此藉由建置馬達數學模型進行驅動器模擬與驗證的方式較易實現高性能驅動器及減少開發時程，目前文獻上常見的數學模型以永磁同步馬達為主，特殊結構之馬達數學模型較為稀少，本文提出的馬達為一雙氣隙架構之磁性齒輪電機，發展此電機架構起因是因為永磁同步馬達需透過齒輪箱來達到變速比效果，但是機械齒輪容易造成磨損及噪音，在技術進步下，發展出同軸式磁性齒輪藉由內外層永久磁鐵改變磁場並由調磁鐵芯環作調製，以非接觸傳動方式降低機械齒輪的問題，但是同軸式磁性齒輪需依靠外部動力，故後續又提出磁性齒輪電機架構，改以線圈繞組激磁產生電磁場帶動永久磁鐵環並保留減速比特性，能由激磁方式主動傳遞動力。
本研究首先分析與建置磁性齒輪電機之方塊圖，著重說明三環轉矩關係及電樞電氣角度與轉子電氣角之間的關聯，模擬磁性齒輪電機轉速和轉矩減速比關係，此外根據步進馬達結構將磁性齒輪電機之調磁鐵芯環鎖固，以此等效至步進馬達模型，且為貼近實際馬達運作，將於步進馬達模型中加入頓轉轉矩進行模擬並驗證及繪製其轉矩特性圖。

Traditional motor drive performance verification often uses physical motors and drivers for verification, which has shortcomings such as high cost and instrument damage. Therefore, to achieve high-performance drivers and reduce development time, building mathematical model of motors for driver simulation and verification is a good choice. At present, there are relatively few mathematical models of motors with special structures in the literature. In this study, the motor proposed is a magnetic gear motor with a double air gap structure. This motor structure makes the permanent magnet synchronous motor (PMSM) to achieve the functions of variable speed ratio just like a mechanical gearbox but without the wear and noise problem associated with mechanical gearboxes.
The motor, dubbed “motoring-gear” is developed based on the structure of coaxial magnetic gear, but have two mechanical ports and one electrical port. One of the PM rotors of the coaxial magnetic gear is been replaced with a stationary three-phase wound stator to generate electromagnetic field, and retains the gear ratio characteristics, and can actively transmit power through the excitation.
This study first analyzes and constructs the block diagram of the motoring-gear, focusing on torque relationship, the armature magnetic field angle and the rotor electrical angle. Toque and rotational speed of each port were simulated. A special feature of the motoring-gear can be achieved by locking the modulator thus, making the motoring-gear equivalent to the stepper motor model. In order to make the mathematical model close to the actual operation, the detent torque is added to the stepper motor model, the torque-speed curve (TN curve) of the proposed motor is plotted using the mathematical model to provide insight into motor characteristics.

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