## 2 Structures of Basic Spoke Type IPM Model and Proposed Flared Type IPM Model
### Characteristics of the Basic Spoke Type Ferrite IPM Model  
The performance analysis of motors can be divided into two main categories. First, the no-load analysis confirms the winding specifications and the rotor geometry. Permanent magnet grade and winding specifications are checked through the magnitude of the back EMF; the shapes of the rotor and the stator are evaluated through the generated the back EMF waveform. Load analysis confirms torque magnitude and ripple at the rated speed, and efficiency at the rated load point is confirmed through copper and iron loss analysis. The noise vibration generation is compared relatively through torque ripple and nodal force analysis. The characteristics of the basic spoke type IPM model were investigated by conducting no-load and load analyses on the basic spoke type IPM model. Figures 3 and 4 show the back EMF waveform and the cogging torque waveform from the no-load analysis. The back EMF is generated by a sinusoidal waveform, generating 23.65 Vrms per phase, and the THD (total harmonic distortion) of the back EMF is 0.69%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Unit** & **Basic Model** & **Proposed Model** \\ \hline Slot/Pole & - & 12/8 & 12/8 \\ Output power & W & 300 & 300 \\ Speed & rpm & 4020 & 4020 \\ Stack length & mm & 27.5 & 27.5 \\ Stator & Outer diameter & mm & 120.0 & 120.0 \\ Material & - & 35 PN270 & 35 PN270 \\ Stack length & mm & 27.5 & 27.5 \\ Outer diameter & mm & 60 & 60 \\ Material & mm & 35 PN270 & 35 PN270 \\ Air-gap & mm & 0.75 & 0.75 \\ Shape & mm & Bar-type & C-type \\ Magnet & Dimensions & mm & \(16.5\times 7.4\)t & \(70\deg\times 3.4\)t \\ Material & - & Ferrite (9 BE) & Ferrite (9 BE) \\ Number of turns & turns & 30 & 30 \\ Winding & Diameter & mm & 0.9 & 0.9 \\ Material & - & Copper & Copper \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the basic model and proposed model. Figure 3: Back EMF of basic spoke type IPM model. Table 2 shows the results of the performance analysis of the basic spoke type model under no-load and load conditions. The torque ripple at rated load is 0.068 Nm and the ripple rate is 9.4% based on the magnitude of the average torque. The efficiency is 92.7% at rate load. In the case of a motor using a permanent magnet, the teeth of the stator are excited by the electromagnetic force of the permanent magnet inside the rotor, when the rotor rotates at a rated speed. Electromechanical force with the teeth of the stator eventually causes noise and vibration of the motor. The analysis of electromagnetic force must be performed in the load analysis, and nodal force analysis is mainly performed to calculate the electromagnetic force. Figure 5 shows the nodal forces that are applied to the stator teeth of the basic spoke type IPM motor. When the rotor is rotated, the nodal force in the teeth region has two components. As shown in Figure 5, it has the x-axis components along the direction of rotation and y-axis components perpendicular to the direction of rotation. In particular, the y-axis component is perpendicular to the electromagnetic force, which is the main cause of noise vibration [24; 25]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Item** & **Unit** & **Basic Model** \\ \hline \multirow{4}{*}{No-Load} & Back EMF & Vrms & 23.65 \\  & THD & \% & 0.69 \\  & Cogging torque ripple & Nm & 0.034 \\ \hline \multirow{4}{*}{Load} & Rated speed & rpm & 4020 \\  & Average torque & Nm & 0.72 \\  & Torque ripple (ripple rate) & Nm & 0.068 (9.4\%) \\ \cline{1-1}  & Phase current & Apeak & 6.0 \\ \cline{1-1}  & Output power & W & 303.7 \\ \cline{1-1}  & Copper loss & W & 14.4 \\ \cline{1-1}  & Iron loss & W & 9.3 \\ \cline{1-1}  & Efficiency & \% & 92.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of the basic spoke type ferrite IPM model. Figure 4: Cogging torque of basic spoke type IPM model. Figure 6 shows a nodal force waveform applied to teeth under rated load conditions, and Table 3 shows a nodal force component along the x-axis and y-axis.