## 2 Transmission Mode Analysis and System Modeling  
### Transmission Mode Analysis  
Figure 1 shows the basic transmission principle of mechanical hydraulic composite transmission [10]. The power input to the shunt mechanism divides the total power flow into two parts: one part flows through the hydraulic system, and the other flows through the mechanical variable speed mechanism, and the two power flows are coupled into the total power flow output in the confluence mechanism. A mechanical hydraulic composite transmission device not only has the advantage of stepless speed regulation of the hydraulic transmission, but also has the high efficiency and stability of mechanical transmission [11]. The directions of the speed and torque in the shunting mechanism and the confluence mechanism are shown in Figure 2. The shunting mechanism (a) and the confluence mechanism (b) adopt a planetary gear mechanism, which includes the sun wheel, gear ring, and planetary frame. The speed relationship between the three is constrained by the characteristic formula shown in Equation (1), and the torque relationship between the three has a fixed proportion, while the speed relationship among the three does not have a fixed proportion. As shown in Equation (2):  
\[n_{S}+kn_{R}=(1+k)n_{C} \tag{1}\]  
\[T_{S}:T_{R}:T_{C}=1:k:-(1+k) \tag{2}\]  
where \(n_{S}\), \(n_{R}\), and \(n_{C}\), respectively, represent the rotational speeds of the sun gear, ring gear, and planetary carrier in the planetary gear; \(T_{S}\), \(T_{R}\), and \(T_{C}\), respectively, represent the torque of the sun gear, ring gear, and planetary carrier; \(k\) is the characteristic parameter of the planetary arrangement. The core of implementing a continuously variable speed in HMCVT lies in the hydraulic system. Hydraulic systems typically use a volumetric speed control circuit composed of variable displacement pumps and quantitative motors to achieve high-power  
Figure 1: The principle of mechanical hydraulic composite transmission. Figure 2: Transmission principle of shunt mechanism and confluence mechanism. transmission. By changing the working volume of the pump, the displacement of the hydraulic pump can be adjusted to achieve stepless speed regulation. As shown in Figure 3, the prime mover serves as the power source to drive the hydraulic pump, converting mechanical energy into pressure energy in the oil. The hydraulic system circuit transfers pressure energy to the motor in the form of flow and pressure. The motor converts the pressure energy from the oil into mechanical outputs in the form of torque and speed, driving the actuator to complete its work. In the actual operation of hydraulic systems, power loss is inevitable, mainly including volume loss caused by oil leakage and mechanical losses caused by friction during the operation of mechanical components. In an ideal scenario, without considering volumetric and mechanical losses, according to the law of conservation of energy, the input-output relationship between the pump and motor can be expressed as:  
\[T_{P}\times\omega_{P}=\Delta P_{p}\times Q_{p}=\Delta P_{M}\times Q_{M}=T_{M} \times\omega_{M} \tag{3}\]  
where \(T_{P}\) and \(T_{M}\) represent the input torque of the pump and the output torque of the motor, respectively; \(\omega_{P}\) and \(\omega_{M}\) represent the input shaft angular velocity of the pump and the output shaft angular velocity of the motor, respectively; \(\Delta P_{P}\) and \(\Delta P_{M}\) represent the pressure difference between the inlet and outlet ports of the pump and motor, respectively; \(Q_{P}\) and \(Q_{M}\), respectively, represent the output flow rate of the pump and the input flow rate of the motor. The values of the transmission system characteristic parameters of HMCVT are shown in Table 1.  
The hydraulic mode is driven by the engine, which is suitable for the starting condition of the tractor at a low speed and a large torque, and the hydraulic system can carry out efficient stepless speed regulation when the tractor is working [12].