## 3 Design of a CMG for SWT
### Model Validation by FEA
\begin{tabular}{c} \hline \hline
**Parameter** & **Symbol** & **Case 1** & **Case 2** & **Case 3** \\ \hline Outer rotor magnet axial length (mm) & \(l_{m1}\) & 4 & 7 & 4 \\ Pole-piece axial length (mm) & \(l_{p}\) & 7 & 5 & 4 \\ Inner rotor magnet axial length (mm) & \(l_{m2}\) & 5 & 4 & 7 \\ Axial magnet area of outer permanent & \(A_{m1}\) & 261.2 & 248.3 & 239.8 \\ Axial magnet area of inner permanent & \(A_{m2}\) & 222.6 & 218.4 & 214.1 \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \end{tabular} \begin{tabular}{c} \hline \hline
**Parameter** & **Symbol** & **Case 1** & **Case 2** & **Case 3** \\ \hline Outer rotor magnet axial length (mm) & \(l_{m1}\) & 4 & 7 & 4 \\ Pole-piece axial length (mm) & \(l_{p}\) & 7 & 5 & 4 \\ Inner rotor magnet axial length (mm) & \(l_{m2}\) & 5 & 4 & 7 \\ Axial magnet area of outer permanent & \(A_{m1}\) & 261.2 & 248.3 & 239.8 \\ Axial magnet area of inner permanent & \(A_{m2}\) & 222.6 & 218.4 & 214.1 \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{c}{} \\ \end{tabular} 
\begin{tabular}{c} \hline \hline
**Parameter** & **Symbol** & **Case 1** & **Case 2** & **Case 3** \\ \hline Outer rotor magnet axial length (mm) & \(l_{m1}\) & 4 & 7 & 4 \\ Pole-piece axial length (mm) & \(l_{p}\) & 7 & 5 & 4 \\ Inner rotor magnet axial length (mm) & \(l_{m2}\) & 5 & 4 & 7 \\ Axial magnet area of outer permanent & \(A_{m1}\) & 261.2 & 248.3 & 239.8 \\ Magnet rate of inner permanent & \(A_{m2}\) & 222.6 & 218.4 & 214.1 \\ Magnet rate of inner permanent & \(A_{m2}\) & 222.6 & 218.4 & 214.1 \\ Magnet rate of inner permanent & \(A_{g1}\) & 241.9 & 233.3 & 226.9 \\ Outer air-gap axial area (mm) & \(A_{g2}\) & 224.8 & 220.5 & 216.2 \\ \multicolumn{4}{c}{} \\ \multicolumn{4}{cFigure 6: Magnetostatic field analysis of case 1 of the CMGT by FEA: (**a**) flux density distribution, (**b**) outer air-gap waveform, (**c**) inner air-gap waveform. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Flux Density** & **EMC Results (T)** & **FEA Results (T)** & **Error (\%)** \\ \hline \multirow{2}{*}{\(1\)} & Outer air-gap & 0.7925 & 0.8157 & 2.8\% \\  & Inner air-gap & 0.7306 & 0.8156 & 10.4\% \\ \hline \multirow{2}{*}{\(2\)} & Outer air-gap & 0.8621 & 0.8155 & \(-\)5.7\% \\  & Inner air-gap & 0.7700 & 0.7687 & \(-\)0.2\% \\ \hline \multirow{2}{*}{\(3\)} & Outer air-gap & 0.8567 & 0.9031 & \(-\)5.1\% \\  & Inner air-gap & 0.7532 & 0.6847 & \(-\)10.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the air-gap flux density for EMC and FEA results. Finally, the analytical equations are confirmed with the finite-element analysis simulation method. The mathematical modeling is valid, so the equations can then be used to determine the magnetic gear parameter of a magnet and pole-piece length.