# FEA-Based Design Procedure for IPMSM and IM for a Hybrid Electric Vehicle
## 3 Design Procedure
### IPMSM Design Procedure  
Figure 3 shows the flowchart of the proposed design procedure for the IPMSM. The number of poles and stator slots are selected in the first step. For the number of poles, a higher number of poles reduces the required stator and rotor yoke thicknesses and hence achieves higher torque density. However, increasing the number of poles leads to increasing the operating frequency and hence core losses of the machine for a given operating speed. For reasonable lamination thicknesses, the operating frequency is normally selected in the range of 250 Hz to 500 Hz [47; 49; 50]. For the stator slots, it is preferable to use a larger number of narrower slots to improve the stator winding cooling. This is limited by the mechanical strength of the stator laminations and achieving reasonable winding fill factors for the narrow slots. The number of slots is selected based on observations of similar commercial designs to guarantee the feasibility of the lamination design. The literature shows that IPMSMs with a number of slots per pole per phase (SPP) of two introduces lower torque ripple and cogging torque compared to an SPP of one and fractional values [51]. This SPP value also has low total harmonic distortion of the back-emf. Thus, the numbers of poles and slots are selected to give a value of SPP of two. Figure 2: The schematic of the proposed spiral cooling system for the stators of both machines. The generated torque is proportional to the product of the airgap area, airgap diameter, magnetic loading, and electric loading. Increasing the airgap diameter also increases the airgap area but reduces the available stator slot cross-sectional area and hence the electric loading. In most IPMSMs with normal axial length to outer diameter aspect ratios, like the IPMSMs studied in Refs. [16; 52; 53], the ratio of the inner to stator outer diameter is in the range 0.6 to 0.7. When the available axial length is limited, it is reasonable to increase this ratio to 0.7 or higher [52]. After the determination of the machine geometry and number of slots/poles, the stator slot dimensions and PM volume should be found. An initial magnet design with a pole pitch of 80% and thickness of 6 mm was used. The literature shows that optimum IPMSM  
Figure 3: The design flowchart of the studied 100 kW interior permanent magnet synchronous machine. designs with the laminated steel generally have a stator back-iron flux density of 1.2-1.4 T at no load [54]. So, the average airgap flux density (\(B_{ag}\)) is checked to be in the range of 0.8 T to 0.9 T, and the PM amount is adjusted, if necessary, to achieve this. After the desired value of \(B_{ag}\) is obtained, the stator back-iron thickness is adjusted to reach a flux density of 1.2 T to 1.4 T in the back-iron. Then, the stator teeth width is adjusted to obtain a flux density of 1.5 T to 1.6 T in the teeth [55]. The stator teeth should be roughly 50% to 66% of the slot pitch at the mean stator slot diameter. The voltage equation presented in (1) is used to determine the number of turns per phase (\(N_{ph}\)). In this equation, \(A\) and \(B_{ag}\) are the airgap area of each pole and the airgap flux density. The frequency of the operation at the rated speed is shown by \(f\). \[E=4.44B_{ag}AN_{ph}f \tag{1}\]  
The stator winding copper wire diameter is chosen to be about 1 mm which is easier for winding. Assuming a copper slot fill factor of 0.45, the number of parallel branches for the obtained number of turns is then determined. High-power PMSMs normally offer a high efficiency and power factor in their constant torque region. It is assumed that the product of power factor (\(\cos\varphi\)) and efficiency (\(\eta\)) for this machine should be around 0.95 [56].