# Less Rare-Earth Electromagnetic Design for a High-Performance Permanent Magnet Motor
## 4 Workflow to Obtain the Motor Electromagnetic Design Candidate  
The contribution of this paper was described in Section 3, which demonstrates that tilted magnetization for the same motor structure (same magnet weight) provides better performance than the conventional application of parallel magnetization (straight) but with the advantage of still using parallel magnetization. Accordingly, this makes possible a reduction of magnet weight in a motor for the same motor performance. Therefore, this section aims to obtain a motor candidate with less rare-earth with tilted magnetization. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Unit** & **Straight Magnetization** & **Tilted Magnetization** \\ \hline Mechanical torque & Nm & 39.34 & 42.15 \\ Speed & RPM & 2400 & 2400 \\ Efficiency & \% & 93.11 & 93.4 \\ Torque ripple & \% & 6.7 & 10.0 \\ Winding temperature & \({}^{\circ}\)C & 133 & 134.6 \\ Magnet temperature & \({}^{\circ}\)C & 100.3 & 101.2 \\ Tilt angles & \({}^{\circ}\) & 0 & 29.4 \\ Magnet weight & kg & 1.3098 & 1.3098 \\ Electromagnetic & Nm & 39.40 & 42.21 \\ torque & A & 109.77 & 109.86 \\ Current angle & \({}^{\circ}\) & 29.86 & 24.82 \\ Copper losses & W & 603.46 & 607.09 \\ Iron losses & W & 114.25 & 127.34 \\ Mechanical losses & W & 14.17 & 14.17 \\ Input active power & W & 10,620.1 & 11,343.3 \\ Input reactive power & VAR & 2785.43 & 2098.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison between straight and tilted magnetization for the baseline motor model of Figures 1 and 4. Figure 11: Magnet nodes BH values for each position in one electrical period and magnet demagnetization curve at 100 \({}^{\circ}\)C. (**a**) Baseline motor BH values for straight magnetization; (**b**) Baseline motor BH values for tilted magnetization. The finding in Section 3 that tilted magnetization increased the baseline motor performance would allow the optimization of the magnet geometry in the rotor for the same stator. Nevertheless, in this use case study, the objective is to obtain a new design candidate that could significantly reduce the magnet weight using tilted magnetization for the same performance. Therefore, it is opted to optimize both stator and rotor. This section reports the implemented route in a systematic approach. From Section 3, parallel magnetization could be used better than its conventional application in two ways. One way is by using an optimum angle for each magnet and the other way is choosing the maximum that uses the same tilt angle. In any case, the computational time spent on finding the tilt angle is high, specific for this case study in FEM took around four hours, which is too high for an optimization iteration process within an acceptable time. However, based on the previous results (in Table 5), it is noticed that the difference between radial and the \(\hat{B}_{g1}\) maximum point is 0.709%. The difference between the radial and the second option using the same angle is 1.933%. Therefore, radial magnetization is used in the optimization process to facilitate and reduce computational time in iterations. Afterward, the tilt angles can be searched to obtain the final electromagnetic design with less rare-earth for the same baseline motor performance. A predetermined MOGA algorithm is used for the rotor optimization from the commercial software Altair HyperStudy 2020. Although different solution routes could have been taken, the workflow followed is devised to accomplish the objective of a less-rare earth electromagnetic design candidate satisfying the requirements of Table 3 and at the same time, intending it could serve as a guideline to the reader. The main processes carried out to obtain the less rare-earth motor candidate can be seen in Figure 12 and more details about the first two actions are given in the activity diagrams in Figures 13 and 14. Figure 12: Optimization workflow. In the first stage, a parametrized stator optimization takes place, keeping the same magnet shape and weight.