# Development of a Simulation Model for HMT of a 50 kW Class Agricultural Tractor
## 3 Results
### Power Transmission Efficiency  
Figure 9 provides the power transmission efficiency for the prototype of the HMT based on the gear stage. In the bench test, the ranges of the power transmission efficiency for each of the gear stages were 0-80.26, 76.00-83.13, and 64.50-78.28%, respectively. As a result of the simulation, the ranges of power transmission efficiency for each of the gear stages were 0-77.64, 73.78-81.93, and 63.02-77.99%, respectively. The power transmission efficiency of the first gear stage appeared to increase, and the power transmission efficiency of the second and third gear stages appeared to decrease after increasing to the maximum point. The result is because the HMT had the highest power transmission efficiency when the swash plate angle of the hydraulic pump was 0\({}^{\circ}\)[15]. The overall power transmission efficiency of HMT showed the same trend with the proposed results in previous research [25]. The simulation results showed similar trends in all gear stages. Table 5 lists the comparison of power transmission efficiency between the measured and simulated results based on gear stages. The averages of the measured power transmission efficiency for each gear stages were 66.76, 79.96, and 78.56% respectively, and the averages of simulated power transmission efficiency were 62.14, 78.56, and 72.44%, respectively. In general, an HMT has low power transmission efficiency at the low gear stage because it mainly uses HSU power to generate high torque [43]. In this study, the average power transmission efficiency was the lowest in the 1 st gear stage, and the highest in the 2 nd gear stage. The maximum differences of power transmission efficiency between the measured and simulated results for each of the gear stages were 13.24, 2.29, and 2.45%, respectively. The simulation results were similar to the bench test results. As a result of the t-test, the \(p\)-values for each of the gear stages were more than 0.05 under all gear stages, and there was no significant difference for the power transmission efficiency between the measured values and simulation results. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Gear Stage**} & \multicolumn{2}{c}{**Axle Rotational Speed (rpm)**} & \multirow{2}{*}{_p-Value_} \\ \cline{2-2} \cline{4-4}  & **Measured** & & **Simulated** \\ \hline
1 st & 18.13\(\pm\)12.41 * & 16.33\(\pm\)12.64 & 0.728 \\
2 nd & 53.97\(\pm\)13.01 & 53.67\(\pm\)10.53 & 0.951 \\
3 rd & 107.95\(\pm\)19.66 & 107.95\(\pm\)20.45 & 0.818 \\ \hline \hline \end{tabular} Note. * Average \(\pm\) standard deviation.  
\end{table} 
Table 4: Comparison of the axle rotational speed between the measured and simulation results based on the gear stages. Figure 8: Comparison of axle rotational speed of the HMT for the measured and simulated results according to the gear stages. Therefore, the simulation model was available to evaluate the power transmission efficiency of the HMT tractor during operation. Figure 9: Comparison of the power transmission efficiency of the HMT for the measured and simulated results according to the gear stages: (**a**) first gear stage; (**b**) second gear stage; (**c**) third gear stage. Figure 10 provides the results of a linear regression analysis for the power transmission efficiency between the measured and simulated values according to gear stages. In the first gear stage, the results of linear regression showed an R-squared value of 0.988, an RMSE of 5.461, and an RD of 8.18, as shown in Figure 10a. The results of linear regression at the second gear stage showed an R-squared of 0.971, an RMSE of 1.473, and an RD of 1.84, as shown in Figure 10b. On the other hand, the results of linear regression at the third gear stage showed an R-squared of 0.980, an RMSE of 1.345, and an RD of 1.84, as shown in Figure 10c. The RMSE and RD of the first gear stage were the highest. The most engine power was generally transmitted through the HSU in the first gear stage, which required more torque [16].