## 2 Transmission Mode Analysis and System Modeling
### Transmission Mode Analysis
The vehicle enters hydraulic mode after engaging the clutches C0, C1, C3, and C5. The engagement of clutch C1 immobilizes the front planetary gear mechanism, creating a unified structure. The power provided by the engine passes through the front planetary gear mechanism and enters the hydraulic system. After the power flows out of the hydraulic system, it is finally output from the output shaft. The transmission route of the hydraulic mode is shown in Figure 4. The speed relationship between its input and output is shown in Equation (4)  
\[n_{o}=\frac{e}{is_{i}t_{i}}n_{e} \tag{4}\]  
where \(n_{o}\) represents output shaft speed; \(e\) represents the pump-motor displacement ratio; \(n_{e}\) represents engine output speed; \(i\) represents the gear pair ratio. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Project** & \(\mathbf{i_{1}i_{2}}\) & \(\mathbf{i_{3}i_{4}}\) & \(\mathbf{i_{5}}\) & \(\mathbf{i_{6}}\) & \(\mathbf{i_{7}}\) & \(\mathbf{k_{1}}\) & \(\mathbf{k_{2}}\) \\ \hline Value & 1 & 1 & 1 & 1 & 5/14 & 2.5 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: HMCVT transmission parameter assignment. Figure 3: Pump-motor drive system. The mechanical hydraulic compound transmission mode is driven by the engine. The shunt mechanism can expand the speed regulation range of the hydraulic mechanism. And it can realize the linear stepless speed regulation of the vehicle, which can reduce the operating difficulty of the driver and improve the working quality. Moreover, it can meet the higher power requirements of tractors, and further improve the power performance and fuel efficiency of the whole vehicle [13]. After engaging the clutches C0, C2, C3, and C4, the tractor enters the mechanical hydraulic compound transmission mode. The transmission route of the mechanical hydraulic compound transmission mode is shown in Figure 5. The power provided by the engine is divided between two paths after entering the front planetary array. One path goes into the front planetary sun wheel and flows into the hydraulic system. The other path goes into the front planetary gear ring and flows to the sun wheel of the back planetary row. The two power flows eventually converge and are output from the rear planetary row. The speed relationship between the input and the output is shown in Equation (5):  
\[n_{o}=\frac{(1+k_{1})e}{(is_{6}+k_{1}e)}n_{e} \tag{5}\]  
where \(k_{1}\) represents the characteristic parameter of the front planetary row. The speed regulation characteristic curve of the transmission process from hydraulic mode to A mode is shown in Figure 6. In the figure, no represents the output shaft speed, H represents the hydraulic mode speed regulation characteristic curve, HM\({}_{1}\) represents the mechanical hydraulic composite transmission mode speed regulation characteristic curve, and (0.1, 0.28) represents the hydraulic system displacement ratio and output input  
Figure 4: Hydraulic mode transmission route. Figure 5: The mechanical hydraulic compound transmission mode. speed ratio corresponding to the switching from hydraulic mode to mechanical hydraulic composite transmission mode.