## 4 Analysis and Comparison of Air-Gap Flux Density and Torque Performance
### Comparison of Air-Gap Flux Density and Torque Performance  
The 3D view of the rotor of initial motor (left) and proposed motor (right) are showed in Figure 12a. Figure 12b shows the comparison of torque waveform between the initial motor and the proposed motor with the cross-shaped flux-barriers rotor. The torque ripple decreases by 34.06%, and the average torque increases by 11.34% with the comparison of the initial motor. Figure 12c highlights that the shaped of flux-barriers affects the intent of torque harmonic the proposed rotor structure with cross-shaped flux-barriers with low torque ripple has lower torque harmonics. Figure 13 shows the contrast diagram of air-gap flux density distribution and harmonic content of no-load motor at rated current. Figure 13a reflects the existence of stator slot and rotor anisotropy, and it can be seen from Figure 13b that there are odd harmonics in addition to the fundamental components. The third and its multiple harmonics are primarily caused by magnetic saturation, and the 17 th and 19 th harmonics are primarily related to stator slotting, and the 11 th, 13 th, 23 rd, 25 th and 29 th harmonics are mainly caused by rotor structure. As for the two motors in this paper, the harmonic components vary with the shape of the flux barrier in the rotor. It can be seen from the Figure that the amplitude of the fundamental wave of the air-gap flux density of the proposed SynRM with cross-shaped flux-barriers rotor structure is higher than that of the initial SynRM, and the majority contents of harmonics are reduced, which makes the air-gap flux density distribution more sinusoidal and leads to reduced torque ripple. Figure 14 is the flux line distribution of the initial motor and the proposed motor in steady state. As can be seen that the trend of flux lines is basically the same as the shape of flux barrier, and the flux lines are symmetrically distributed. Most of the flux lines of the two motors go along the segment, and only a few of them pass through the flux barrier, that is, to ensure the inductance of \(d\)-axis is maximum and the inductance of \(q\)-axis is minimum. Table 2 show the output characteristics of initial model and proposed motor. As can be seen from the table, the performance of the proposed motor is better than that of the first motor, with lower core loss and stranded loss and higher efficiency. At the same time, the sensitivity of the proposed motor is lower than that of the initial motor, which verifies the feasibility of the proposed method. Figure 15 shows the efficiency map of initial motor and proposed motor. The rated speed is 1500 rpm. In order to ensure that the voltage is not higher than the rated voltage, it is necessary to reduce the current or change the current angle thus reducing the torque \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Contents** & **Initial Motor** & **Proposed Motor** & **Unit** \\ \hline \(d\)-axis inductance & 108.2 & 112.1 & mH \\ \(q\)-axis inductance & 19.3 & 17.8 & mH \\ Core loss & 112.05 & 90.05 & W \\ Stranded loss & 692.47 & 670.58 & W \\ Sensitivity & 0.32 & 0.12 & - \\ Efficiency & 91.15 & 92.67 & \% \\ Power factor & 0.69 & 0.72 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Output characteristics of initial motor and proposed motor. Figure 11: The effect of \(k_{eq}\) and \(k_{arc}\) on average torque and torque ripple of motor with different number of flux barrier layers (**a**) average torque of three-layer flux-barriers; (**b**) average torque of four-layer flux-barriers; (**c**) torque ripple of three-layer flux barriers; (**d**) torque ripple of four-layer flux-barriers. when the speed exceeds 1500 rpm. In the constant torque region, the efficiency of both can reach 88%, and in the constant power region can reach 94%. Figure 12: Comparison of the rotor structure and the torque waveforms: (**a**) 3D view of the rotor of initial motor (**left**) and proposed motor (**right**); (**b**) torque waveforms at rated current 21.79 A; (**c**) torque harmonic.