# FEA-Based Design Procedure for IPMSM and IM for a Hybrid Electric Vehicle
## 3 Design Procedure
### IM Design Procedure  
As shown in Figure 6, the design process for the IM starts with the determination of the number of poles and slots based on the same principles as for the IPMSM design. The number of turns is found using Equation (1) with the assumption of 0.7 T for the airgap flux density.  
Figure 5: Stacked bar graphs of the losses of the three PMSM designs obtained from 2D FEA.  
Figure 6: The proposed step-by-step design process for the induction machine design.  
According to [30], it is reasonable to select the number of rotor bars (\(N_{R}\)) in the following range:  
\[0.5N_{S}\leq N_{R}\leq 1.5N_{S}, \tag{3}\]  
where \(N_{S}\) is the number of stator slots. The results of the analysis in Ref. [58] demonstrates that the torque ripple is zero but the machine cannot be line started when \(N_{S}=N_{R}\). Because the line-start operation of the IM is not an important criterion for the considered HEV, the initial value of \(N_{R}\) is assumed to be equal to the stator slots (\(N_{R}=N_{S}\)). An arbitrary, but reasonable, value (i.e., 10-15% of the rotor radius) is assumed for the bar depth and their width is chosen to be roughly equal to the stator slot width.  
The power factor of induction machines is normally in the range of 0.7 to 0.9. Based on this it was assumed that \(\eta\cos(\varphi)=0.65\). Considering this value, a possible rated current for the IM is calculated at this stage. Normally, the no-load current in IMs is 40% to 60% of the rated current. It is assumed that the no-load current in this design is 50% of the rated current. The calculated no-load current is injected into the winding in 2D FEA when the rotor is rotated at the no-load speed. The no-load simulation is executed for different slot heights and widths to achieve the desired back-iron and tooth flux densities in both the rotor and stator. The desired values have been indicated in Figure 6 which have been selected based on the information in Refs. [55; 59]. The rotor tooth width is kept 1 mm less than the stator tooth width during the analysis, based on the e-mobility IM design described in Ref. [48]. At this stage the rotor slot height is kept constant.  
In published IM designs for EVs and HEVs, the IM typically operates at 0.1-1% slip over a wide range of torque and speed. Hence, the rotor of the machine is rotated with 0.5% slip when a current-driven IM is simulated using 2D FEA at rated frequency. The amplitude of the current is increased to reach the limits of the Class F insulation. The stator voltage is checked to ensure that the machine does not exceed the DC-link voltage limit. This current is selected as the rated current of the designed IM.  
The dimensions of the rotor bars are then optimized to improve performance. Increasing the rotor bar width and depth reduces the rotor resistance and hence losses and can also produce less torque ripple. On the other hand, the increase in the bar width reduces the rotor tooth cross-sectional area which can lead to saturation and hence torque reduction. Also, the increase in the bar depth leads to an increase in the length of the flux path and, consequently, possible additional saturation and core loss. Hence, the width and depth of the rotor bars are varied to find the optimum value through the FEA simulations.  
After the rotor bar dimensions have been optimized for a given number of rotor bars, the number of rotor bars, which gives minimum torque ripple, is optimized keeping the bar depth and total rotor bar cross-sectional area constant.