## 3 Characteristics of Spoke Type IPM Model and Flared Type IPM Model
### Characteristics at Load Condition  
The surfaced permanent magnet motor is a structure in which permanent magnets are attached to the surface of the rotor. This structure has a constant magnetic resistance on the magnetic circuit, so there is no difference in inductance between the d and q axes. Therefore, it is difficult to generate additional reluctance torque, so the load analysis can be carried out by zero degrees of the advance angle for the current source analysis.  
However, the IPM motor has different magnetic resistance on the d and q axes. This is because permanent magnets are inserted inside the rotor. The difference in magnetic resistance produces additional reluctance torque. Therefore, the basic model and the proposed model should set an advance angle by analyzing the changes in the torque according to the advance angle. Table 6 shows the average torque of the basic model and proposed model according to the advance angle. As a result of the torque analysis according to the advanced angle, both the basic model and the proposed model are found to have maximum torque at 5 degrees.  
Figure 13 shows the torque ripple of the proposed flared-shape IPM model compared to the basic spoke type IPM model. As shown in Figure 13, the average torque is equivalent and the torque ripple is reduced by 76.7% compared to the basic spoke type IPM model. So, the improvement of torque ripple at rated load has the advantage of reducing model noise and vibration. Therefore, the proposed flared type IPM model can be used in applications where noise and vibration improvements are required.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Item** & **Unit** & **\(-\)15** & **\(-\)10** & **\(-\)5** & **0** & **5** & **10** & **15** \\ \hline Basic model (at 6.00 Apeak) & Nm & 0.680 & 0.698 & 0.711 & 0.719 & 0.722 & 0.718 & 0.710 \\ Proposed model (at 5.47 Apeak) & Nm & 0.667 & 0.688 & 0.704 & 0.714 & 0.719 & 0.718 & 0.711 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Characteristics of torque according to the advance angle.  
Figure 13: Torque waveform at rated load (at 4020 rpm).  
Figure 14 shows the nodal force waveforms applied to stator teeth. When the nodal force by the electromagnetic force is applied to the stator teeth as an exciting force, it causes noise and vibration at operating point. In particular, the maximum change of the nodal force causes noise and vibration in the stator teeth. Therefore, the nodal force applied to stator teeth should be minimized during the initial design.  
Figure 15 shows the comparison of the nodal force of the proposed flared type IPM model compared to the basic spoke type IPM model at the operating point; as shown in Table 7, the average value of the nodal force of the proposed flared type IPM model is reduced by 3.0% compared to that of the basic spoke type IPM model.  
Table 8 shows the 2D FEM analysis results of the proposed flared type IPM model in comparison with the basic spoke type IPM model. As shown in Table 8, the proposed flared-shape ferrite IPM model decreased copper loss by 16.3% and iron loss by 15.8%. The decrease in copper loss is due to the decrease in rated current caused by the back EMF increase. Additionally, iron loss was relatively reduced because the electrical steel usage of the rotors was reduced. Therefore, the efficiency of the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Item** & & **Unit** & **Basic Model** & **Proposed Model** & **Rate** \\ \hline Nodal force & x-axis & Nm & 10.93 & 11.62 & **4**6.31\% \\ (peak to peak) & y-axis & Nm & 121.24 & 117.60 & **7**3.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of nodal force of basic and proposed model.  
Figure 14: Nodal forces applied to stator teeth at the load condition.  
Figure 15: Comparison of the nodal force at the load condition.