# Multi-Objective Optimization for Outer Rotor Low-Speed Permanent Magnet Motor
## 3 Comprehensive Sensitivity Analysis
### Response-Surface Analysis
Figures 6 and 7 show the effect of the pole arc coefficient and PM thickness on the efficiency, no-load back EMF, power factor, core loss, thermal load and copper loss. In Figure 6a, as the pole arc coefficient and PM thickness increase, the efficiency increases significantly. This is due to the fact that with the increase in the pole arc coefficient and PM thickness, the magnetic flux density increases significantly, and the efficiency also increases. In Figure 6b, the no-load back EMF increases with increasing PM thickness; in addition, the no-load back EMF also increases with the pole arc coefficient, but when the pole arc coefficient is close to 0.95, the no-load back EMF decreases slightly. Figure 6c shows the effect of the pole arc coefficient and PM thickness on the power factor. The variation law of the power factor is similar to Figure 6a, with the increase in pole arc coefficient and PM thickness, the power factor gradually increases. Unfortunately, in Figure 7a, the core loss also dramatically increases with the increasing pole arc coefficient and PM thickness; this is due to eddy current losses on the motor core due to changes in the magnetic force, thereby increasing the core temperature. In Figure 7b, the thermal load decreases with the increasing pole arc coefficient and PM thickness, and in Figure 7c, the copper loss decreases with the increasing pole arc coefficient and PM thickness, which can significantly reduce the winding temperature. The effect of the core length and stator outer diameter on the efficiency, no-load back EMF and core loss are shown in Figure 8. In Figure 8a, the efficiency increases with the increasing core length and stator outer diameter, and the stator outer diameter has a greater effect on the efficiency than the core length. In Figure 8b, the no-load back EMF is also greatly affected by the core length and the stator outer diameter. The no-load back EMF increases significantly with the increasing core length and stator outer diameter. Figure 8c shows the influence of the core length and stator outer diameter on the core loss. With the  
Figure 8: Response surface of core length and stator outer diameter to electromagnetic performance parameters. **(a)** Efficiency; **(b)** back EMF; **(c)** core loss. Figure 9: Response surface of air gap length and stator outer diameter to electromagnetic performance parameters. **(a)** Back EMF; **(b)** copper loss; **(c)** thermal load. increase in the stator outer diameter, core loss first increases and then decreases; this is because the stator outer diameter is too large or too small, which leads to the saturation of the iron core, and a larger field strength is required to generate the same amount of magnetic induction, leading to increased core loss. In addition, the core loss also increases with the increasing core length. Figure 9 shows the effect of the air gap length and stator outer diameter on the no-load back EMF, copper loss and thermal load. In Figure 9a, the air gap length has a great influence on the no-load back EMF. As the air gap length increases, the no-load back EMF decreases significantly, which causes the current to increase. In Figure 9b, with the increase in the air gap length, the copper loss increases significantly, while with the increase in the stator outer diameter, the copper loss decreases slightly. In Figure 9c, the thermal load is affected by the air gap length and stator outer diameter in almost the same manner as the copper loss. However, as the air gap length approaches 2 mm, the thermal load tends to level off and does not decrease.