# Less Rare-Earth Electromagnetic Design for a High-Performance Permanent Magnet Motor
## 4 Workflow to Obtain the Motor Electromagnetic Design Candidate
The torque was chosen to be maximized (while minimizing the magnet weight) and not constrained in order to have the additional degree of freedom of  
Figure 15: (**Left**) Minimum Joule losses for each \(D_{si}\) in the stator optimization results. (**Middle**) Sketch showing the distance between magnet poles for the reference case. (**Right**) Plot of minimum Joule losses for each \(D_{si}\) and the selected candidate. stack length reduction. In addition, less magnet weight, stack length reduction provides additional material reduction, such as less copper and electric steel. The next stage of Figure 12 is to find the tilt angles. Following the same process mentioned in Section 3, the angles and the fundamental flux density values are shown in Table 7.  
Finally, using the angle values for the maximum flux density with the same tilt angles, the stack length is adjusted for the same torque and speed operating point until reaching the baseline motor's thermal performance (copper and magnet temperature). In other words, iterations for different stack lengths were executed until the temperatures were considered close enough. Figure 17 shows the 2D appearance of the optimized motor, which can be compared with the initial geometry shown in Figures 4 and 10. Table 8 shows the final performance comparison between the baseline motor with straight magnetization and the optimized one. The optimized motor has a 21.82% less magnet weight than the baseline motor. Therefore, achieving the objective of a less rare-earth electromagnetic design motor candidate that satisfies the requirements in Table 3. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Magnetization Pattern** & \(\overset{\text{\tiny{A}}}{B_{g1}}\left[\mathbf{p}\mathbf{u}\right]\) & \(\mathbf{\kappa}_{1}\left[\circ\right]\) & \(\mathbf{\kappa}_{2}\left[\circ\right]\) \\ \hline \(\hat{B}_{g1}\) maximum with a different angle & 0.99694 & 37.4 & 21.5 \\ \(\hat{B}_{g1}\) maximum with same angle & 0.98727 & 28.6 & 28.6 \\ \(\hat{B}_{g1}\) straight angle & 0.88292 & 0 & 0 \\ \(\hat{B}_{g1}\) radial & & 0.98628 [T] & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Peak fundamental flux density result and corresponding tilt angles. Figure 16: Rotor optimization process results and Pareto front. Finally, similar to Section 3, Figure 18 shows that the BH values of the magnet nodes are on or above the magnet demagnetization curve, so there is no risk of demagnetization for the working temperature. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Baseline Motor**} & \multicolumn{1}{c}{**Optimized Motor**} \\  & & **with Parallel** & **with Tilted** \\  & & **Magnetization** & **Magnetization** \\ \hline Mechanical torque & Nm & 39.34 & 39.30 \\ Speed & RPM & 2400 & 2400 \\ Efficiency & \% & 93.11 & 93.27 \\ Torque ripple & \% & 6.7 & 3.225 \\ Winding temperature & \({}^{\circ}\)C & 133 & 132.8 \\ Magnet temperature & \({}^{\circ}\)C & 100.3 & 98.4 \\ Tilt angles & \(\circ\) & 0 & 28.6 \\ Stack length & mm & 66 & 61 \\ Magnet weight & kg & 1.3098 & 1.02406 \\ Magnet weight decrease & \% & - & 21.82 \\ Electromagnetic torque & Nm & 39.40 & 39.35 \\ Current & A & 109.77 & 123.66 \\ Current angle & \(\circ\) & 29.86 & 25.05 \\ Copper losses & W & 603.46 & 583.49 \\ Iron losses & W & 114.25 & 116.00 \\ Mechanical losses & W & 14.17 & 12.88 \\ Input active power & W & 10,620.1 & 10,588.28 \\ Input reactive power & VAR & 2785.43 & 2547.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance comparison of same operating point performance between the baseline motor of Figure 1 with parallel magnetization and the selected candidate with tilted magnetization. Figure 17: Less rare-earth motor selected candidate (**a**) Motor 2D view; (**b**) No-load flux density distribution.