###### Abstract  
To improve electromagnetic performance, an axial-flux permanent magnet brushless DC motor (AFPMBLDCM) with unequal-thickness arc permanent magnets is proposed in this paper. Firstly, the structure and magnetic circuit of the AFPMBLDCM with unequal-thickness arc permanent magnets were designed. Then, the mathematical models and design method of the main parameters were derived. According to the rated power and rated speed, the main parameters were further designed, and the analytical model was established by using Maxwell 3D. The air-gap flux density, back electromotive force (EMF) and torque under no-load and load conditions were calculated and analyzed to verify the validity of the model and design. Finally, based on a parameter scanning optimization method, the effects of the permanent magnet thickness, pole arc coefficient and permanent magnet radius on cogging torque were analyzed. The optimized parameters of the AFPMBLDCM with unequal-thickness arc permanent magnets were obtained. The results show that the sinusoidal degree of the air-gap magnetic field is improved, and the maximum torque ripple of the AFPMBLDCM is reduced to 2.92%.  
AFPMBLDCM; unequal-thickness magnets; optimization; cogging torque +
Footnote †: journal: Applied  
permanent-magnet synchronous machine was proposed [26]. The magnetic circuit and air-gap flux intensity were analyzed to improve the stable operation of the motor. Based on the finite element method, the relationship between the air-gap flux density and the parameters was clarified. Furthermore, the winding structure and power driver topology with fault tolerance were presented. To improve the torque density, permanent magnets were placed between the adjacent rotor teeth with a switched-flux feature. Based on the three-dimensional finite element optimization method, the loss and efficiency were about 60.7 W and 90.8%, respectively, at the rated speed on a rated road [27]. In [28], the arc-shaped permanent magnet was proposed. It has notches so that it produces a discrete skew effect, which reduces the cogging torque and torque ripple. Compared with the radial-flux permanent magnet brushless DC motor, the AFPMBLDCM has many advantages, such as high power density, high efficiency, a high torque/current ratio and flat shape. The AFPMBLDCM can be classified according to the number and relative positions of stators and rotors. In particular, the torque quality assessment of the AFPMBLDCM is a challenging task, as torque ripple should also be considered along with torque density. Thus, torque ripple and its reduction are currently of research interest to many researchers [29]. As is well known, the main sources of torque ripple are cogging torque [30], distorted stator current [31] and counter-EMF waveforms [32]. An effective method to reduce cogging torque is the optimization design of motor parameters based on the finite element method [33; 34; 35].  
In this study, an AFPMBLDCM with arc-shaped permanent magnets was designed. It is characterized by a sinusoidal air-gap magnetic field and low cogging torque ripple. Firstly, the topology structure of the AFPMBLDCM with unequal-thickness arc permanent magnets was designed. The mathematical models and design of the main parameters were derived. According to the rated power and rated speed, the analytical model was established by using Maxwell 3D. The air-gap flux density, back electromotive force (EMF) and torque were calculated and analyzed to verify the model and design. Finally, based on the parameter scanning optimization method, the effects of the permanent magnet thickness, pole arc coefficient and permanent magnet radius on cogging torque were analyzed. The optimized parameters of the AFPMBLDCM with unequal-thickness arc permanent magnets were obtained. The results show that the sinusoidal degree of the air-gap magnetic field is improved, and the maximum torque ripple of the AFPMBLDCM is reduced to 2.92%.