# Simplified Design of Magnetic Gear by Considering the Maximum Transmission Torque Line
## 4 Validation of Simplified Design of Magnetic Gear
### Validation of Design Analysis  
The performance of an MG depends on the total volume of PMs used and the magnetic flux flowing through the structure of the MG. If the total volume of PMs is high but the magnetic flux densities are saturated inside the MG, the performance is lower than the MG that has a smaller total volume of PMs but a better magnetic flux density. Thus, the MTTL represents the highest performance of MG achieved at every total volume of PMs used in the MGs. As shown in Figure 6, the simulated data of the tested models are plotted on the MTTL, to observe the errors. It is observed that the simulated transmission torque of the models is very close to the targeted value that can be seen from the plotted data of the models which are closed to the MTTL. The percentages of errors are calculated to represent the inaccuracy of the proposed reference which is the MTTL. The lowest percentage of error is achieved by Model 2 and Model 4, which is only 0.6%. Model 2 targeted 140 Nm of transmission torque and achieved 140.8 Nm for a magnetic gear with 120 mm required radius, while Model 4 targeted 85 Nm of torque and achieved 84.5 Nm with the same required radius. The MG with the highest percentage of error is Model 5, which has 8.5% from 95.9 Nm of simulated transmission torque instead of 100 Nm of targeted transmission torque. This shows that the percentage of error of the simulated transmission torque of the MG design which referred from the MTTL can reach up to 8.5%, which is considered to be a small error. Table 3 shows the structure of tested models with the simulated result based on the conditions created from Table 2 for the design verification. As shown in Table 3, the magnetic flux flow of all models has the same pattern since the configuration and gear ratios of the MGs are fixed. From the magnetic flux densities, it is observed whether the models have saturated magnetic flux or not. Based on the observation, the highest flux densities can be seen at Model 3, where the flux density on the iron parts reached 1.8 Tesla. Since the transmission torque of the model is high, it is assumed that the magnetic flux density has not over-passed the 1.8 Tesla, which is considered the maximum flux density. Model 2 and Model 4 show almost the same maximum flux density, which is around 1.6 Tesla, while Model 1  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Design Requirement**} & \multicolumn{3}{c}{**Estimated Parameter**} \\ \cline{2-10}
**Model** & \begin{tabular}{c} **Transmission** \\ **Torque**, **\(\boldsymbol{T_{18}}\) (Nm)** \\ \end{tabular}  & \begin{tabular}{c} **Outer Radius**, \\ **\(\boldsymbol{R_{0}}\) (mm)** \\ \end{tabular}  & \begin{tabular}{c} \(\boldsymbol{V_{\mathrm{pm}}}\) \\ **(\(\boldsymbol{cm^{3}}\))** \\ \end{tabular}  & \begin{tabular}{c} \(\boldsymbol{t_{\mathrm{pm}}}\) \\ **(mm)** \\ \end{tabular}  & \ \begin{tabular}{c} \(\boldsymbol{t_{\mathrm{o}}}\) \\ **(mm)** \\ \end{tabular}  & \begin{tabular}{c} \(\boldsymbol{t_{\mathrm{i}}}\) \\ **(mm)** \\ \end{tabular}  \\ \hline
1 & 100 & 80 & 179 & 70 & 3.3 & 8.3 & 13.2 & 16.5 \\
2 & 140 & 120 & 250 & 50 & 4.5 & 11.3 & 18.0 & 22.5 \\
3 & 200 & 195 & 357 & 30 & 6.0 & 15.0 & 24.0 & 30.0 \\
4 & 85 & 120 & 152 & 30 & 4.5 & 11.3 & 18.0 & 22 shows a lower maximum flux density, which is around 1.4 Tesla, and the lowest flux density is achieved by Model 5, at around 1.35 Tesla. In a paper that studied a novel magnetic geared generator, the flux density also shows around 1.8 Tesla maximum density is achieved [13]. Thus, it is considered that all the models have a good magnetic flux distribution, since the appearance of the red region on the flux densities are not significant. This is due to the proposed ratio of thickness of the PMs and the iron parts of MG, which as expressed in Section 3.2, have considered the saturation of magnetic flux.