## 4 Conclusions  
To establish an accurate test method for deriving the spring constant and damping coefficient of a suspension, this study performed a characteristic test on a semi-active hydro-pneumatic suspension under changing velocity and current conditions, and generated force-displacement and force-velocity curves representing suspension characteristics for input into a simulation model for control logic development. A semi-active hydro-pneumatic suspension combines a hydraulic spring whose performance is determined by the characteristics of the accumulator (nitrogen pressure, capacity) and a semi-active damper technology controlled by the flow rate inside the suspension. The test utilized an exciter capable of controlling the displacement and velocity of a hydraulic cylinder, and a method of fixing one side of the suspension and reciprocating the other side. The test was performed under six velocity conditions and eight current conditions. In order to obtain the spring constant of the hydro-pneumatic suspension, the test configured the piston to move at a low speed to prevent the damping force from occurring and to ensure an accurate \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Velocity**} & \multirow{2}{*}{**Value**} & \multicolumn{8}{c}{**Current (mA)**} \\ \cline{3-10}  & & **1580** & **1350** & **1080** & **900** & **720** & **540** & **360** & **280** \\ \hline \(-\)0.200 & & 3130 & 4010 & 7315 & 13,200 & 25,915 & 50,050 & - & - \\ \(-\)0.150 & & 3260 & 3707 & 6240 & 10,680 & 19,233 & 37,153 & - & - \\ \(-\)0.100 & & 3630 & 4090 & 5810 & 8580 & 13,550 & 25,800 & 77,100 & 93,570 \\ \(-\)0.075 & & 3973 & 4587 & 5827 & 7880 & 11,173 & 19,200 & 60,680 & 78,467 \\ \(-\)0.050 & & 5700 & 5760 & 6440 & 7440 & 10,380 & 13,840 & 46,120 & 58,520 \\ \(-\)0.025 & Damping & 9600 & 9680 & 11,880 & 11,040 & 12,160 & 9960 & 27,400 & 33,880 \\
0 & Coefficient & - & - & - & - & - & - & - & - \\
0.025 & (Ns/m) & 6720 & 7080 & 5880 & 7400 & 9080 & 11,960 & 22,640 & 24,520 \\
0.050 & & 3980 & 3940 & 3860 & 5080 & 7900 & 12,400 & 33,140 & 37,080 \\
0.075 & & 2813 & 3293 & 3920 & 5560 & 8480 & 15,067 & 43,000 & 48,973 \\
0.100 & & 2520 & 2920 & 3660 & 5960 & 9670 & 18,220 & 53,590 & 60,070 \\
0.150 & & 2240 & 2593 & 4087 & 7340 & 12,807 & 24,887 & - & - \\
0.200 & & 2215 & 2700 & 4720 & 9085 & 16,905 & 32,980 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of damping coefficient for current-velocity. Figure 17: Force-velocity curve according to applied valve current change. spring constant measurement. The reaction force according to the displacement was measured, and the spring constant was obtained. In order to obtain the damping coefficient of the hydro-pneumatic suspension, it had to be moved at a high speed to generate a large reaction force. The reaction force was measured at the point where the displacement was zero, and the damping coefficient was obtained using the force-velocity diagram. The test method used in this study could not fully implement the nonlinear characteristics with hysteresis of the hydro-pneumatic semi-active suspension. However, it was considered to be sufficient for the purpose of creating a simulation model for control logic development. This study presented a method for accurately testing the dynamic characteristics of a semi-active hydro-pneumatic suspension that could change its performance according to the terrain or the needs of the operator. In future research, if the dynamic suspension characteristics obtained in this study can be applied to a tractor simulation model, the characteristics of tractor ride vibration could be more accurately predicted. Further, by employing the tractor ride vibration model, the findings of this study could be used in the development of control logic to minimize ride vibration. Conceptualization, G.-H.L. and Y.-J.P.; methodology, K.C. ; validation, K.C. and J.O. ; formal analysis, J.O. and [PERSON]-[PERSON]; investigation, H.-[PERSON], [PERSON]-W.H., and [PERSON]-H.P. ; data curation, J.S.