# Less Rare-Earth Electromagnetic Design for a High-Performance Permanent Magnet Motor
## 3 Proposed Magnetization Pattern for Banana-Shaped Magnets with Parallel Magnetization  
Section 1 reviewed the banana-shaped magnets in motor design in terms of other shapes comparisons and magnetization. [PERSON] et al. [4], [PERSON] et al. [3] and [PERSON] et al. [5] compared this arced topology with block-type magnets. From their work, aside from the spoke topology, it can be concluded that this kind of topology allows more magnet material to be inserted than the block type. Usually, the insertion of more magnet material results in higher air gap magnetic flux density (\(\hat{B}_{g}\)) values, therefore increasing the PM torque component. Moreover, even if the same magnet weight is used, their work demonstrates that the arced topology increases the reluctance torque component. Nonetheless, regardless of the motor's magnet topology, the air gap flux density decreases once it passes the maximum magnet length point for a fixed rotor structure. Figure 6 illustrates this behavior for a radial magnetized single-layer banana-shaped magnet at no-load operation. The curve in the figure shows the results obtained directly from FEM. The magnet length (\(l_{m}\)) is varied from one millimeter to sixteen millimeters and the peak flux density fundamental harmonic (\(\hat{B}_{g1}\)) value is extracted for each simulation. It can be noticed that once \(\hat{B}_{g1}\) reaches its maximum limit, increasing \(l_{m}\) does not increase \(\hat{B}_{g1}\). However, it increases the magnet reluctance, which has more influence on the magnetic circuit. So, an effective tradeoff between \(l_{m}\) and \(\hat{B}_{g1}\) should be considered. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Coolant & - & Water \\ Number of channels & - & 1 \\ Flow rate & L/min & 6 \\ Inlet temperature & \({}^{\circ}\)C & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Baseline motor thermal model parameters. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Unit** & \begin{tabular}{c} **Baseline Motor** \\ **Performance** \\ \end{tabular}  & **Requirement** \\ \hline Mechanical Torque & Nm & 39.34 & \textasci{}=\)9.34 \\ Speed & RPM & 2400 & \textasci{}=\)2400 \\ Torque ripple & \% & 6.7 & \textasci{}\leq\)6.7 \\ Efficiency & \% & 93.11 & \textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasci{}\textasciasci{}\textasci{}\textasciasci{}\textasci{}\textasciasci{}\textasciasci{}\textasciasci{}\textasciasci{}\textasciasci{}\textasciasciasci{}\textasciasciasci{}\textasciasciasci{}\textasciasciasciasci{}\textasciasciasciasciasci{}\textMoreover, this topology offers flux concentration capability that depends on the implemented magnetization. Equation (1) shows the well-known analytical relation to computing \(\hat{B}_{g}\) without accounting for leakage [25]. Equation (1) is shown only to highlight that the \(\hat{B}_{g}\) is affected by the magnet and air gap surface ratio (i.e., Equation (1) is not used to compute any result, all results are obtained directly from FEM). This ratio is the flux concentration factor (\(C_{\varphi_{S}}\)), separated in Equation (2). The origin of this ratio is no other than saying that the flux leaving the magnet is equal to the flux crossing the air gap [25]. Therefore, one of the advantages of IPM machines with flux concentration techniques is the possibility of having a \(C_{\varphi_{S}}\) greater than 1.