## 4 Analysis and Comparison of Air-Gap Flux Density and Torque Performance  
### Distribution of Air-Gap Flux Density  
To further study the influence of cross-shaped flux-barriers on the distribution of air-gap flux density, the air-gap between stator and rotor in one-eighth motor model was divided more accurately from the original six regions to obtain 16 regions, as shown in Figure 6, which were mainly divided according to the width of the flux-barriers end. These 16 regions can be divided into three parts for research: one is the region A1-A6 corresponding to the segments, and the other is the region B1-B5 and C1-C5 corresponding to the end of the flux-barriers. The influence of the structural parameters of the cross-shaped flux-barriers on the air-gap flux density is studied by finite element analysis at rated current 21.79 A and rated speed 1500 rpm. The finite element results are shown in Figures 7-9. Among them, the flux density of each region is analyzed by taking the value at the geometric midpoint of each region. Figure 7 shows the influence of parameters of cross-shaped flux-barriers on the air-gap flux density of region A1-A6 which are mainly located in the corresponding air gap at the end of the segment of the rotor. It can be seen that when the parameter \(k_{seg}\) remains unchanged, the value of flux density of region A1, A2 and A3 all remain unchanged first and then decrease with the increase of \(k_{arc}\). When \(k_{arc}\) is constant, the value of flux density decreases with the increase of \(k_{arc}\) for regions A1 and A2, while the value of flux density increases first and then decreases with the increase of \(k_{arc}\) for region A3. Furthermore, the value of flux density decreases to the minimum when \(k_{seg}=k_{arc}=0.8\) for all three regions. The variation trend of A5 and A6 are basically the same as each other when one parameter of \(k_{seg}\) and \(k_{arc}\) remains unchanged. The value of flux density decreases first and then increases with the change of the other parameter. The change of flux density value in region A4 is different from the above regions while the cross-shaped flux-barrier parameters change, which is approximately funnel-shaped, and the value of flux density  
Figure 6: Detailed partition diagram of air-gap between stator and rotor of one-eighth motor. Figure 7: The influence of cross-shaped flux-barriers parameters on flux density in each region of air-gap: (**a**) region A1; (**b**) region A2; (**c**) region A3; (**d**) region A4; (**e**) region A5; (**f**) region A6. is the minimum when \(k_{seg}=k_{arc}=0.4\). The main reason is that the change of value \(k_{arc}\) and \(k_{seg}\) changes the equivalent reluctance of the flux-barriers in MEC, which leads to the corresponding change of the value of flux-density of the air-gap at different positions. Figure 8 shows the influence of parameters of cross-shaped flux-barriers on the air-gap flux density of region B1-B5 which are mainly located in the air gap corresponding to the upper half of the end of the flux barriers. It can be seen from Figure 8b,c that the cross-shaped flux-barrier parameters have the same influence on regions B2 and B3. That  
Figure 8: The influence of cross-shaped flux-barriers parameters on flux density in each region of air-gap: (**a**) region B1; (**b**) region B2; (**c**) region B3; (**d**) region B4; (**e**) region B5. Figure 9: The influence of cross-shaped flux-barriers on flux density in each region of air-gap: (**a**) region C1; (**b**) region C2; (**c**) region C3; (**d**) region C4; (**e**) region C5. is, when \(k_{seg}\) is fixed, the value of flux density increases with the increase of \(k_{arc}\), while the value of flux density has little change with \(k_{seg}\) when \(k_{arc}\) is fixed. When one parameter is fixed, the value of flux density increases first and then decreases with the increase of the other parameter.