# Multi-Objective Optimization for Outer Rotor Low-Speed Permanent Magnet Motor
## 3 Comprehensive Sensitivity Analysis
### Optimization Parameters  
In order to obtain a better electromagnetic performance and temperature rise, in the optimization process, six parameters are set as the optimization variables, including the pole arc coefficient, PM thickness, stator outer diameter, core length, number of conductors per slot and air gap length. The influence curves of the single factors on the efficiency and thermal load are shown in Figures 3 and 4. Figure 3: Influence curves of single factors on efficiency and thermal load. (**a**) Pole arc coefficient; (**b**) PM thickness; (**c**) stator outer diameter. Figure 2: Flowchart of the multi-objective optimization. Figure 3 shows the effect of the pole arc coefficient, PM thickness and stator outer diameter on the efficiency and thermal load. In Figure 3a, as the pole arc coefficient increases, the efficiency increases and the thermal load decreases, and when the pole arc coefficient approaches 1, the changes in efficiency and thermal load gradually become stable. Therefore, the variation range of the pole arc coefficient is limited to 0.65-0.95. In Figure 3b, the effect of the PM thickness on the efficiency and thermal load is almost the same as that of the pole arc coefficient. With the increase in PM thickness, the efficiency increases and the thermal load decreases, and both level off. Therefore, the minimum and maximum PM thicknesses are set to 10 mm and 15 mm, respectively. Figure 3c shows the effect of the stator outer diameter on the efficiency and thermal load. As the stator outer diameter increases, the efficiency increases and the thermal load decreases gradually. However, when the stator outer diameter is larger than 880 mm, the thermal load starts to increase again, which is due to the saturation of the iron core when the outer diameter of the stator is too large. Therefore, the optimized range of the stator outer diameter is limited to between 840 mm and 880 mm. The effect of the air gap length, core length and number of conductors per slot on the efficiency and thermal load are shown in Figure 4. In Figure 4a, with the gradual increase in the air gap length, the efficiency decreases and the thermal load increases, because the long air gap length reduces the air gap magnetic density and the loss increases accordingly. At the same time, considering the assembly of the stator and rotor, the variation range of air gap length is set to 2-5 mm. Figure 4b shows the effect of the core length on the efficiency and thermal load. As the core length increases, both the efficiency and the thermal load decrease. However, when the core length is less than 940 mm, the efficiency decreases slightly with the increase in the core length, and when it is greater than 940 mm, the efficiency begins to decrease greatly. Therefore, the optimized range of the core length is limited to 900-940 mm. In Figure 4c, due to the use of double-layer windings, the number of conductors per slot should only be an even number, so the number of conductors per slot is optimized among 8, 10 and 12. When N= 8, the efficiency is the lowest and the thermal load is the highest, while when N = 10, the electromagnetic performance is better, with the maximum efficiency of 93.01% and the minimum thermal load of 154.9 A\({}^{2}\)/mm\({}^{3}\). After the above analysis, the variation ranges of the six optimized design parameters are listed in Table 2. In the analysis, if the pole arc coefficient is too small, then the efficiency is low and does not meet the requirements. When the pole arc coefficient approaches 1, the efficiency gradually becomes stable and the change is not large. Considering the cost factor, the variation range of the pole arc coefficient is set as 0.65-0.95. In addition, the PM thickness has the same influence characteristics as the pole arc coefficient. If the PM thickness is too small, then it will not meet the magnetic field requirements, and if the PM thickness is too large, then the permanent magnet will be wasted. Therefore, the PM thickness variation range is limited to 10-15 mm.