# Research on the Use of Hydro-Pneumatic Shock Absorbers for the Rear Suspension of a Vehicle Cabin
## 4 Results and Discussion
### Experimental Analysis Results on the Proposed Materials of the Air Socket  
This section presents the experimental analysis results obtained from the tensile testing of four types of samples of reinforced rubber material designed for shock absorber air sockets. The mechanical properties that were analyzed include tensile strength, stress and strain at break, stiffness, and Young's modulus, providing crucial insights into the materials' performance under uniaxial tension (Table 8). The samples cut at 45\({}^{\circ}\) (D_45) and 60\({}^{\circ}\) (D_60) exhibit a significantly higher stress at break and tensile strength compared with samples cut on the longitudinal (L) and transversal (T) direction. Notably, the ones cut at 60\({}^{\circ}\) show the highest values in these categories, indicating that it has the strongest direction of the cut material among the tested sample directions. The low Young's Modulus for the longitudinal cut and the transversal cut samples means that the material will deform more under a given stress in these directions. This might be desirable for applications requiring flexibility or shock absorption. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Value** \\ \hline Outer diameter [mm] & 80 \\ Thickness [mm] & 11.5 \\ Length [mm] & 270 \\ Coil number & 10 \\ Active coils & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Helical spring parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Empty Cabin** & **Loaded Cabin** \\  & **Maximum Mass** & **Minimum Mass** \\ \hline Pressure on the elastic element p [N/m\({}^{2}\)] & 3.5 \(\times\) 10\({}^{5}\) & 4.62 \(\times\) 10\({}^{5}\) \\ Stiffness of the helical spring c [N/m] & 270 \\  & 10 \\  & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Compared values for empty and loaded cabin for the helical spring. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sample L** & **Sample T** & **Sample D\_45** & **Sample D\_60** \\ \hline Stress at Break [MPa] & 9.821 & 9.453 & 19.054 & 30.483 \\ Strain at Break [-] & 2.508 & 0.613 & 0.764 & 0.375 \\ Stiffness [N/m] & 2489.9 & 2456.1 & 8800.4 & 4402.3 \\ Young’s Modulus [kN] & 4.192 & 4.266 & 14.818 & 7.192 \\ Load at Maximum Load [MPa] & 0.441 & 0.610 & 0.959 & 1.542 \\ Stress at Maximum Load [MPa] & 9.915 & 14.131 & 21.547 & 33.589 \\ Machine Extension at Maximum Load [mm] & 186.9 & 44.567 & 56.990 & 28.108 \\ Strain at Maximum Load [-] & 2.491 & 0.593 & 0.759 & 0.374 \\ Tensile Strength [MPa] & 9.915 & 14.131 & 21.547 & 33.589 \\ Elongation at Fracture [mm] & 188.17 & 45.994 & 57.307 & 28.140 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Mean values for the 4 samples. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Empty Cabin** & **Loaded Cabin** \\  & **Maximum Mass** & **Minimum Mass** \\ \hline Pressure on the elastic element p [N/m\({}^{2}\)] & 3.5 \(\times\) 10\({}^{5}\) & 4.62 \(\times\) 10\({}^{5}\) \\ Stiffness of the elastic element c [N/m] & 15,550 & 20,530 \\ Natural oscillations n [min\({}^{-1}\)] & 84.67 & 84.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Compared values for empty and loaded cabin for the pneumatic element. During the analysis we considered two distinct thermodynamic conditions represented by varying polytropic indices: an isothermal process (\(n=1\)) and a more general case (\(n=1.3\)). This dual approach allows for a comprehensive understanding of how air properties within the shock absorber influence its characteristics under different operational scenarios. The deformation of the elastic element is constrained within a practical range, specifically from \(-0.03\) to \(0.035\) m, simulating realistic compression and extension. Furthermore, this study investigates the impact of variable air volumes, ranging from 0 to 300 cubic centimeters, and initial pressures spanning 1 to 6 bar. These ranges are essential for mapping the stiffness and load capacity across diverse operating conditions.