## 3 Results and Discussions
### Optimization Analysis of Cooling Channel Dimension
Second, the cooling channel height P2 and front bearing temperature P4 present positive sensitivity levels, which means that the front bearing temperature can be reduced by reducing the channel height and the heat transfer efficiency will improve. Last, in terms of the cooling channel width P1, an increase or decrease in the cooling channel width has a slight effect on the front bearing temperature P4. \begin{table}
\begin{tabular}{c c c c} \hline  & **Cooling Channel Dimensions** & **Coolant Condition** \\ \hline Key Parameter & Width (P1) & Height (P2) & Oil Flow Rate (P3) \\ Setting Range & 6.0\(\sim\)9.0 mm & 3.5\(\sim\)5.0 mm & 0.1\(\sim\)0.2 Kg/sec \\ \hline \end{tabular}
\end{table} 
Table 4: Cooling channel dimension and relevant parameter setting ranges. Figure 9: Schematic of critical dimensions of front bearing channel. (**a**) Critical dimension of front bearing cooling channel; (**b**) optimization variable settings. According to the correlation matrix in Figure 11 and the response surface diagram in Figure 12, the front bearing temperature P4 is highly correlated with the cooling oil flow rate P3, and the cooling channel width P1 and channel height P2 are correlated with the front bearing temperature P4. As shown in Figure 11, a slight interaction between the cooling channel width P1 and the cooling oil flow rate P3 was observed. Generally, the cooling oil flow rate P3 is inversely proportional to the front bearing temperature P4, and the cooling channel height P2 is proportional to the front bearing temperature. The response surface in Figure 12a indicates the effect of the cooling channel width P1 and cooling oil flow rate P3 on the front bearing temperature P4. When the cooling channel width P1 is 7.5 mm, the optimal front bearing temperature is 308 K. When the cooling oil flow rate P3 is 0.2 kg/s, the most significant effect on the front bearing cooling is observed. However, when the cooling channel width P1 is 6.0 mm and 9.0 mm, the front bearing temperature is 309 K and the cooling oil flow rate P3 of 0.1 kg/s has the worst cooling effect on the front bearing. Figure 11: Correlation matrix diagram. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Width (P1) (mm)** & **Height (P2) (mm)** & **Cooling Oil Flow (P3) (kg/s)** & **Temperature (P4) (K)** \\ \hline
1 & 7.5 & 4.25 & 0.15 & 308.37 \\
2 & 6 & 4.25 & 0.15 & 308.38 \\
3 & 9 & 4.25 & 0.15 & 308.38 \\
4 & 7.5 & 3.5 & 0.15 & 308.31 \\
5 & 7.5 & 5 & 0.15 & 308.4 \\
6 & 7.5 & 4.25 & 0.1 & 308.97 \\
7 & 7.5 & 4.25 & 0.2 & 308.04 \\
8 & 6.2804 & 3.6402 & 0.10935 & 308.75 \\
9 & 8.7196 & 3.6402 & 0.10935 & 308.75 \\
10 & 6.2807 & 4.8598 & 0.10935 & 308.88 \\
11 & 8.7196 & 4.8598 & 0.10935 & 308.88 \\
12 & 6.2804 & 3.6402 & 0.19065 & 308.07 \\
13 & 8.7196 & 3.6402 & 0.19065 & 308.07 \\
14 & 6.2804 & 4.8598 & 0.19065 & 308.1 \\
15 & 8.7196 & 4.8598 & 0.19065 & 308.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Channel dimension optimization parameter list and results. Figure 10: Sensitivity analysis. The response surface in Figure 12b shows the effect of the channel height P2 and cooling oil flow rate P3 on front bearing temperature P4. According to the analysis results, when the channel height P2 is approximately 4.0 mm, the optimal front bearing temperature is approximately 308 K. When the cooling oil flow rate P3 is 0.2 kg/s, the most significant effect on the front bearing cooling is observed. However, when the channel height P2 is 5.0 mm, the front bearing temperature is approximately 309 K and the cooling oil flow rate P3 of 0.1 kg/s has the worst cooling effect on the front bearing. The response surface in Figure 12c shows the effect of the relation between channel width P1 and the channel height P2 on the front bearing temperature P4. The match dimension between the channel width P1 and the channel height P2 can be evaluated by the analysis results of the response surface diagram.