## 3 Mechanical-Electromagnetic Performance Analysis
### Electromagnetic Performance Comparison  
After design optimization, the electromagnetic performance of HSPMSMs with different rotor configurations was analyzed and investigated on no-load and rated-load states by using Ansys Maxwell. Figure 2a shows the no-load back-EMF of these machines at the rated speed. The amplitude of the back-EMF of M3 was maximal, but it also had great 3 rd and 5 th harmonics. The waveform of M1 was close to that of sinusoidal waves, and its harmonics were the least. Figure 2b shows the Fourier analysis of the back-EMF of these HSPMSMs. Higher-order harmonics result in higher loss. The total harmonic distortion of M1 was much lower than that of other HSPMSMs; thus, loss in M1 was low. In other HSPMSMs, though the 3 rd harmonics of M3 were the highest, M4 had highest total \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Rate power & \(P_{n}\) & 19 & kW \\ Rate speed & \(n_{n}\) & 160 & krpm \\ Current density & \(C_{n}\) & 10 & A/mm\({}^{2}\) \\ Rate torque & \(T_{n}\) & 1.1 & Nm \\ Efficiency & \(\eta\) & \textgreater{}95\% & - \\ Frequency & \(f_{n}\) & 2666 & Hz \\ \hline Number of poles & \(p\) & 2 & - \\ Number of slots & \(Q_{S}\) & 6 & - \\ No. of turns per coil & \(N_{s}\) & 20 & - \\ \hline Stator outer diameter & \(D_{so}\) & 80 & mm \\ Core stack length & \(L\) & 80 & mm \\ Air gap & \(\delta_{ag}\) & 2 & mm \\ \hline PM material & NdFeB (N42 SH) & - & - \\ PM remanence & \(B_{nr}\) & 1.05 & T \\ PM relative permeability & \(\mu\) & 1.05 & - \\ Bulk conductivity & \(\sigma_{PM}\) & 646,381 & S/m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: HSPMSM specifications. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **M1** & **M2** & **M3** & **M4** \\ \hline Initial outer diameter (mm) & 15–25 & 15–25 & 15–25 & 15–25 \\ Optimized outer diameter (mm) & 15.8 & 18 & 21.4 & 21.4 \\ PM thickness (mm) & 5.9 & 4.1 & 5.2 & 2.3 \\ Shaft diameter (mm) & - & 8.8 & - & 5.2 \\ PM length (mm) & - & - & 16.4 & 16.2 \\ Sleeve material & Ti-6 Al-4V & CPC & 10)NEX900 & 10)NEX900 \\ Density (kg/m\({}^{3}\)) & 4428 & 1800 & 7350 & 7350 \\ Young’s modulus (GPa) & 124.6 & 125 & 200 & 200 \\ Poisson’s ratio & 0.33 & 0.28 & 0.29 & 0.29 \\ Permitted stress (MPa) & 1000 & 1300 & \textgreater{}700 & \textgreater{}700 \\ Bulk conductivity (S/m) & 591,572 & 20,000 & 1,219,510 & 1,219,510 \\ Thermal conductivity (W/(m\text{\text{\textminus}}K)\) & 8.5 & 0.7 & 39 & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main parameters and material properties of HSPMSMs. harmonic distortion. Figure 2c shows the no-load PM flux linkage for these HSPMSMs at the rated speed. The output torque of the PMSM can be obtained by:  
\[T_{em}\ =\ \frac{P_{out}}{\omega_{r}}\ =\ \eta\frac{m}{2}\eta\varphi_{m}k_{sf} \frac{N_{s}}{m}A_{s}J_{m}\]  
where \(\eta\) is the efficiency of the machine, \(m\) is the number of phases, \(p\) is the number of rotor poles, \(\varphi_{m}\) is the flux linkage of winding per turn, \(k_{sf}\) is the slot fill factor, \(N_{s}\) is number of stator slots, \(A_{s}\) is slot area, and \(J_{m}\) is current density. On the basis of the equation above, the electromagnetic torque of the PMSMs is proportional to the product of flux linkage and winding current. Output torque is another key performance aspect for designing an HSPMSM. As these four HSPMSMs were designed with the same output power level, their torque ripple and PM usage are other key factors. Figure 3 shows the torque waveform, torque ripple, and PM usage comparison of these HSPMSMs. The torque ripple of M1 was 0.88%, which was the lowest compared with that of the other HSPMSMs, and the torque ripple of M3 was 10.01%, which was the highest. Regarding PM usage, that of M4 was 1150.1 Nm/cm\({}^{3}\), which was the highest. M2, on the other hand, had the lowest (854.2 Nm/cm\({}^{3}\)).