Conventionally, the designers of electrical machinesElectrical machines assume the employment of regular shaped magnets such as rectangular, sector or tiled-shapes etc. The geometry of magnet poles is fixed, and the design purpose is mainly to optimize the dimensional values. However, these regular shapes employed may not be the best choice, unavoidably limiting the final design result, and compromising the output performance of the electrical machinesElectrical machines. An alternative scheme is to conduct topology optimization for rotor poles. By this method, the geometrical shape of magnets along with the iron core is no longer fixed, but automatically obtained through the optimal distribution of materials such as iron, magnet and air. It helps to achieve better optimization results with less shape constrains. Therefore, this article proposes a multi-material topology optimization method based on variable density representation for surface-mountedSurface-mounted permanent-magnet synchronousSynchronous motor (PMSM) to obtain an optimal rotor pole pattern, and thus improve the output performance of electrical machinesElectrical machines, especially the torque density which is crucial in aerospace industry. The computational speed is increased by improving the objective function and the arbitrary volume constraints become clear by combining size and topology optimization. To validate the design method, theoretical, numerical and experimental studies are conducted. First, the operating principle, design variables, constrains, optimization objective and procedure of the method are introduced in detail. Then the optimization method is implemented into the rotor design of one surface-mountedSurface-mounted electric machine, and the result is presented and discussed. Subsequently, the magnetic flux density and torque output of electric machine with the optimized rotor poles is compared with conventional design, and it shows that the former can achieve better output performance relatively. Finally, one research prototype of the electrical machineElectrical machines is developed, and experiments are carried out on torque output and back-EMF. The experimental results validate the optimization method. In the other hand, when designing a motor, the input current density is used to calculate the output torque. When studying the influence of structural parameters on motor performance, the output torque always changes, resulting in the inability to immediately obtain the optimal design at rated torque. Therefore, an optimization method for fixed output torque is proposed to address the issue of the inability to obtain the optimal solution for the stator design of a permanent magnet synchronousSynchronous motor directly under rated conditions. This method simplifies the calculation process and is proved high precision. By conducting sensitivity analysis on the stator teeth of the stator core, the impact of stator teeth width on the motor output performance is obtained, and the optimal solutions for torque and efficiency are obtained. Comparing the two optimal solutions, it is found that the performance of the efficiency optimal solution is better. Furthermore, it is found that the stator material only works below the knee point of its BH curve when the efficiency is optimal. Therefore, the optimal solution of the motor is not directly related to the knee point of the stator, and using the method described in this chapter can achieve better performance.