## 2 Transmission Mode Analysis and System Modeling
### Analysis of Simulation Results Obtained Using the Range Method
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**(a) A \(\times\) D Tie-in Effect**} & \multicolumn{2}{c}{**(b) C \(\times\) D Tie-in Effect**} & \multicolumn{2}{c}{**(c) B \(\times\) C Tie-in Effect**} \\ \hline A \(\times\) D & A\({}_{1}\) & A\({}_{2}\) & C \(\times\) D & C\({}_{1}\) & C\({}_{2}\) & B \(\times\) C & B\({}_{1}\) & B\({}_{2}\) \\ D\({}_{1}\) & 1.801 & 2.218 & D\({}_{1}\) & 2.042 & 1.976 & C\({}_{1}\) & 1.943 & 1.849 \\ D\({}_{2}\) & 2.198 & 1.798 & D\({}_{2}\) & 1.749 & 2.246 & C\({}_{2}\) & 1.928 & 2.295 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The collocation effect of dynamic load coefficient. Figure 17: Analysis result of impact strength of output shaft. Figure 18: Analysis result of switching time. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**(a) C \(\times\) D Tie-in Effect**} & \multicolumn{2}{c}{**(b) A \(\times\) D Tie-in Effect**} & \multicolumn{2}{c}{**(c) B \(\times\) C Tie-in Effect**} \\ \hline C \(\times\) D & C\({}_{1}\) & C\({}_{2}\) & A \(\times\) D & C\({}_{1}\) & C\({}_{2}\) & B \(\times\) C & B\({}_{1}\) & B\({}_{2}\) \\ D\({}_{1}\) & 8.289 & 8.171 & D\({}_{1}\) & 6.176 & 10.286 & C\({}_{1}\) & 7.329 & 5.925 \\ D\({}_{2}\) & 4.965 & 10.946 & D\({}_{2}\) & 8.498 & 7.413 & C\({}_{2}\) & 8.198 & 10.919 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The collocation effect of impact strength. Based on the collocation effects in Table 6(a-c), the optimal scheme to optimize the switching time is A\({}_{1}\)D\({}_{1}\)C\({}_{1}\)B\({}_{1}\), which can reduce the switching time from 2.13 to 1.01 s.  
According to the above evaluation indexes, A\({}_{1}\)D\({}_{1}\)C\({}_{1}\)B\({}_{2}\) is the overall optimal scheme. The simulation results of the overall optimal scheme and the non-optimized scheme are compared. Figure 19a shows the velocity of the output shaft. Using Equation (10), the reduction in the output shaft speed was found to decrease from 17.647% to 6.591%. Figure 19b illustrates the output shaft torque. Applying Equation (11), the output shaft dynamic load coefficient was found to decrease from 2.743 to 1.857. Figure 19c demonstrates a reduction in the output shaft impact strength from 14.125 to 5.67 m/s\({}^{3}\), accompanied by a decrease in switching time from 2.13 to 1.71 s.  
A comparison of the results before and after optimization, as well as the degree of optimization of each evaluation indicator, is shown in Table 7.  
The indicators of velocity drop amplitude, dynamic load coefficient, and impact degree have been significantly reduced, effectively improving the smoothness and operational comfort of the entire vehicle. The reduction in the switching time effectively improves the transmission efficiency of the entire vehicle. These results demonstrate that the optimal scheme's simulation results exhibit improved mode switching quality compared to simultaneous clutch engagement, thus verifying the correctness of the optimal scheme for predicting clutch switching timing. The above results show that, before optimization, the impact strength caused by vehicle mode switching already meets the Chinese impact strength standard \(\mid\mid\mid\)\(\leq\) 17.64 m/s\({}^{3}\). This is because the hydraulic system transfers energy by transferring liquid through pressure. Liquid has a certain elasticity and compressibility in the process of energy transfer. This \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**(a) A \(\times\) D Tie-in Effect**} & \multicolumn{2}{c}{**(b) A \(\times\) C Tie-in Effect**} & \multicolumn{2}{c}{**(c) B \(\times\) D Tie-in Effect**} \\ \hline A \(\times\) D & A\({}_{1}\) & A\({}_{2}\) & A \(\times\) C & A\({}_{1}\) & A\({}_{2}\) & B \(\times\) D & B\({}_{1}\) & B\({}_{2}\) \\ D\({}_{1}\) & 1.435 & 1.901 & C\({}_{1}\) & 1.585 & 1.826 & D\({}_{1}\) & 1.618 & 1.718 \\ D\({}_{2}\) & 1.865 & 1.643 & C\({}_{2}\) & 1.715 & 1.718 & D\({}_{2}\) & 1.789 & 1.719 \\ \hline \hline \end{tabular}
\end{table}