## 2 Transmission Mode Analysis and System Modeling
### Analysis of Simulation Results Obtained Using the Range Method  
An analysis of the results for the velocity drop amplitude obtained using the range analysis method can be seen in Figure 15, which presents the range analysis results for the output shaft, with R representing the range value. According to the range value R, from large to small, the primary and secondary order of each factor and interaction is A \(\times\) D, C \(\times\) D, B \(\times\) C, C, A \(\times\) C, A, B \(\times\) D, B, A \(\times\) B, D.  
First, the collocation effect of A \(\times\) D, C \(\times\) D and B \(\times\) C was considered to determine the optimal treatment combination. The collocation effect of A \(\times\) D is calculated as shown in Table 3(a), and it was concluded that A\({}_{1}\)D\({}_{1}\) is the optimal horizontal combination of A and D.  
The collocation effect of C \(\times\) D is calculated as shown in Table 3(b). It was concluded that D\({}_{2}\)C\({}_{1}\) is the optimal level combination of C and D, but to maintain consistency with the optimal level D\({}_{1}\) determined by the former equation, D\({}_{1}\)C\({}_{2}\) is finally determined as the optimal level combination of C and D.  
Similarly, by calculating the collocation effect of B \(\times\) C, as shown in Table 3(c), C\({}_{2}\)B\({}_{1}\) was found to be the optimal horizontal combination of B and C.  
In summary, the optimal scheme to optimize the output shaft velocity drop is A\({}_{1}\)D\({}_{1}\)C\({}_{2}\)B\({}_{1}\), which can reduce the output shaft speed drop from 17.647% to 6.233%. Figure 16 presents the range analysis results for the output shaft's dynamic load coefficient. According to the range value R, from large to small, the primary and secondary order of each factor and interaction is A \(\times\) D, C \(\times\) D, B \(\times\) C, C, A \(\times\) C, B, B \(\times\) D, A \(\times\) B, D, A.  
Figure 16: Analysis result of dynamic load coefficient of output shaft. Figure 15: Analysis results of velocity drop amplitude. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{3}{c}{**(a) A \(\times\) D Tie-in Effect**} & \multicolumn{3}{c}{**(b) C \(\times\) D Tie-in Effect**} & \multicolumn{3}{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\({}_{1}\) & 6.589 & 11.829 & D\({}_{1}\) & 9.665 & 8.752 & C\({}_{1}\) & 9.412 & 7.066 \\ D\({}_{2}\) & 11.391 & 8.397 & D\({}_{2}\) & 6.813 & 12.975 & C\({}_{2}\) & 8.677 & 13.051 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The collocation effect of velocity drop amplitude. Similarly, based on the collocation effects shown in Table 4(a-c), the optimal scheme for minimizing the output shaft's dynamic load coefficient is A\({}_{2}\)D\({}_{2}\)C\({}_{1}\)B\({}_{2}\), reducing it from 2.743 to 1.544. Figure 17 displays the range analysis results for the output shaft's impact strength. According to the range value R, the major to minor order of each factor and interaction is C \(\times\) D, C, A \(\times\) D, B \(\times\) C, A \(\times\) C, A, B \(\times\) D, B, A \(\times\) B. Based on the collocation effects in Table 5(a-c), the optimal scheme to optimize the impact strength of the output shaft is C\({}_{1}\)D\({}_{2}\)A\({}_{2}\)B\({}_{2}\), which can reduce the impact of the output shaft from 14.125 to 2.23 m/s\({}^{3}\). Figure 18 displays the range analysis results for switching time. According to the range value R, from large to small, the primary and secondary order of each factor and interaction is A \(\times\) D, A, A \(\times\) C, B \(\times\) D, D, A \(\times\) B, B \(\times\) C, C \(\times\) D.