# FEA-Based Design Procedure for IPMSM and IM for a Hybrid Electric Vehicle
## 4 Design of the IPMSM and IM Using the Proposed Procedure
### IM Design Example  
The geometry requirements are also applied for the design of the IM and the same number of slots and poles, and ratio of inner to outer stator diameters was chosen.  
Considering a maximum DC-link voltage of 750 V, the number of turns per slot are calculated using Equation (1) for a 0.7 T average airgap flux density and a 280 Hz operating frequency. Considering these values, the obtained number of turns per slot is 6 turns.  
To find the stator slot and yoke dimensions, the initial value of the number of rotor slots \(N_{R}\) is assumed to be equal to the stator slots (\(N_{R}=72\)). The process described in the design procedure was used to obtain the stator tooth width and back-iron thickness as 7 mm and 17 mm, respectively, and then the optimum rotor dimensions as the rotor tooth width and bar depth as 5.7 mm and 24.5 mm, respectively.  
Figure 7 shows the effect of changing the number of rotor bars on the rated performance of the IM while keeping the total rotor slot area constant. Figure 7a shows that the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Outer diameter [mm] & 370 & Inner diameter [mm] & 260 \\ \hline Slot depth [mm] & 38 & Tooth width [mm] & 7.3 \\ \hline PM thickness [mm] & 6 & PM length [mm] & 43 \\ \hline Length of air barriers [mm] & 2 & Airgap length [mm] & 1 \\ \hline Shaft diameter [mm] & 130 & Stator stack length [mm] & 65 \\ \hline Winding end-winding length [mm] & 40 & Number of poles & 12 \\ \hline Number of turns per slot & 6 & Number of slots & 72 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dimensions of the designed IPMSM.  
torque ripple becomes larger when the difference between the number of rotor and stator slots is increased. The minimum torque ripple occurs with 72 rotor bars which is similar to the conclusion of the previous work conducted by [PERSON] [30; 58]. As shown in Figure 7b the generated torque, output power, and power factor are increased by increasing the number of rotor bars because the airgap flux is found to increase. The higher airgap flux does increase the core loss and consequently the iron temperature by a small amount. Figure 7c shows that with a larger number of rotor bars (i.e., 78 to 92 bars) the rotor iron temperature is slightly (about 1 \({}^{\circ}\)C) higher. The stacked loss of the machine with different numbers of rotor bars is presented in Figure 8. As expected, the loss is increased slightly by the increase in the number of rotor bars. The 2D FEA results show that the rotor core loss increased by about 1% from 64 to 92 bars. These results show that the design with 78 bars offers an acceptable performance with small torque ripple, and it was selected. The geometry and cross-section of the proposed machine are presented in Table 4 and Figure 9, respectively.  
Figure 8: Two-dimensional FEA results of the IM loss breakdown for different numbers of rotor bars.  
Figure 7: Effect of the number of rotor bars: (a) 2D FEA results of torque ripple at rated torque, (b) 2D FEA results of performance parameters, (c) 3D FEA results of hot spot temperatures. The current, torque, and output power are per unit based on their rated values which are 120 A, 260 Nm, and 80 kW, respectively.