## 3 Construction of the Shifting Dynamics Model
### Test Verification  
As shown in Figure 9, the test bench comprised a diesel engine (132.5 kW, 2200 r/min), two speed and torque sensors, a hydrostatic power split CVT, a magnetic powder brake, a clutch hydraulic control system, a TCU (transmission control unit), and a remote PC. The information of test equipment used in the test bench is shown in Table 1. Considering the following reasons, the test was only conducted between the range R1 and the range R2: the magnetic powder brake could only be used at low speed; the tractor worked in ranges R1 and R2 most of the time (the speed range of 4-12 km/h accounted for 68% of the total working time of the tractor [29]); the shifting process between ranges R1 and R2, R2 and R3, and R3 and R4 was the same.  
After starting the engine, the speed regulation instruction was sent to TCU through the industrial computer. TCU energized the solenoid valve to engage the clutch C1 and adjusted the displacement ratio of the variable displacement pump to \"-1\". Then, the loading instruction was sent to the magnetic powder brake through the industrial computer and the special control circuit. When the load was stable, the engine speed was adjusted to the specified value through the electronic throttle. Finally, the shift instruction was sent to TCU through the industrial computer. TCU separated the clutch C1 and engaged the clutch C2. During the test, the computer read the sensor data of speed, torque, pressure, flow, and so on, in real time through the data acquisition card and recorded them in the disk file by software developed under LabVIEW at a frequency of 60 Hz. In order to ensure the reliability and repeatability of the test results, the engine needed to be preheated for more than 30 min before the start  
\begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Name** & **Model** & **Parameter** & **Manufacturer** \\ \hline
1 & Diesel engine & WP6T180E21 &
\begin{tabular}{c} Rated power: 132.5 kW \\ Rated speed: 2200 r/min \\ \end{tabular} & Weichai Power \\ \hline
2 & \
\begin{tabular}{c} Hydrostatic power \\ split CVT \\ \end{tabular} & - &
\begin{tabular}{c} Rated power: 132.5 kW \\ Transmission ratio: \\ 0.687–8.585 \\ \end{tabular} & Self-development \\ \hline
3 &
\begin{tabular}{c} Magnetic powder \\ brake \\ \end{tabular} & CZ50 & Braking torque: 500 N-m & Hangyu \\ \hline
4 & Speed sensor & JC3A & Speed range: 0–3000 r/min & Xiangyi \\ \hline
5 & Oil pressure sensor & NS-F & Pressure range: 0–100 bar & Tianmu \\ \hline \end{tabular}
\end{table}
Table 1: Test equipment.  
Figure 9: Test bench of the power shift for the hydrostatic power split CVT.  
of the test, and each group of tests needed to be repeated many times until the three consecutive test results were basically the same.  
The purpose of this study was not to predict the absolute true values of the shifting quality, but to reveal the influence law of hydraulic system failure on the shifting quality of the CVT tractor. Therefore, only the transmission model needed to be tested and verified. It was the core component of the CVT tractor. Four groups of shifting experiments were carried out under different limited flow, pump displacement, shift timing sequence, engine speed, and load, as shown in Table 2. The measured and simulated results are shown in Figure 10a-d. According to the figure, the output shaft speed response of the simulation model to the same pressure input was consistent with the test results.