# Evaluation of Mechanical Performance of a New Disc Spring-Cable Counter Pressure Shock Absorber
## 4 Mechanical Property Test
### Dynamic Test Results
#### 4.4.2 Result Discussion  
The influence of loading frequency on the equivalent stiffness and damping ratio of the DSCCP shock absorber is shown in Figure 14. It can be seen that the loading frequency has a certain degree of influence on the equivalent stiffness and damping ratio for the shock absorber under different pre-compression deformations. As the loading frequency increases, the equivalent stiffness and equivalent damping ratio show a gradually decreasing trend, but the degree of reduction is not significant. For example, when the loading frequency increases from 0.5 Hz to 2 Hz, reductions of equivalent stiffness are 2.59%, 1.98%, and 1.97% under pre-compression deformation of 6 mm, 8 mm, and 10 mm, respectively. Correspondingly, reductions of equivalent damping ratio are 7.89%, 3.37%, and 5.31%, respectively. Figure 15 shows the curves of the equivalent stiffness and additional damping ratio of the DSCCP shock absorber with changing of the pre-compression deformation in different \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{\begin{tabular}{c} **Frequency** \\ **(Hz)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Equivalent Stiffness** \\ **(kN/mm)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Error** \\ **(I - ID)/I \(\times\) 100\%** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Equivalent Damping Ratio** \\ **(I - ID)/I \(\times\) 100\%** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Error** \\ **(III - IV)/III \(\times\) 100\%** \\ \end{tabular} } \\ \cline{1-1} \cline{2-7}
1 & 0.5 & 5.41 & 5.11 & 5.55\% & 0.076 & 0.075 & 1.32\% \\ \hline
2 & 1 & 5.4 & 5.36 & 0.74\% & 0.075 & 0.077 & \(-2.67\%\) \\ \hline
3 & 1.5 & 5.29 & 5.29 & 0.00\% & 0.07 & 0.075 & \(-7.14\%\) \\ \hline
4 & 2 & 5.27 & 5.27 & 0.00\% & 0.071 & 0.078 & \(-9.86\%\) \\ \hline
5 & 0.5 & 6.58 & 6.55 & 0.46\% & 0.089 & 0.086 & 3.37\% \\ \hline
6 & 1 & 6.49 & 6.28 & 3.24\% & 0.086 & 0.091 & \(-5.81\%\) \\ \hline
7 & 1.5 & 6.49 & 6.11 & 5.86\% & 0.087 & 0.09 & \(-3.45\%\) \\ \hline
8 & 2 & 6.45 & 6.01 & 6.82\% & 0.087 & 0.091 & \(-4.60\%\) \\ \hline
9 & 0.5 & 7.6 & 7.63 & \(-0.39\%\) & 0.153 & 0.158 & \(-3.27\%\) \\ \hline
10 & 1 & 7.56 & 7.39 & 2.25\% & 0.107 & 0.1 & 6.54\% \\ \hline
11 & 1.5 & 7.48 & 7.21 & 3.61\% & 0.107 & 0.101 & 5.61\% \\ \hline
12 & 2 & 7.45 & 7.19 & 3.49\% & 0.109 & 0.108 & 0.92\% \\ \hline
13 & 1 & 8.21 & 8.07 & 1.71\% & 0.086 & 0.078 & 9.30\% \\ \hline
14 & 1 & 6.76 & 6.75 & 0.15\% & 0.107 & 0.112 & \(-4.67\%\) \\ \hline
15 & 1 & 6.14 & 6.12 & 0.33\% & 0.143 & 0.134 & 6.29\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison results of equivalent stiffness and equivalent damping ratio. Figure 14: Influence of loading frequency on equivalent stiffness and damping ratio. loading frequencies. Figure 16 shows the force-deformation relationship curves in different pre-compression deformations. It can be observed that as the pre-compression deformation increases, the equivalent stiffness and equivalent damping ratio of the DSCCP shock absorber show a linear increasing trend. For example, under the condition of the loading frequency of 1.0 Hz, the equivalent stiffness of the shock absorber at pre-compression deformations of 6 mm, 8 mm, and 10 mm are 5.4 kN/mm, 6.5 kN/mm, and 7.6 kN/mm, respectively. Correspondingly, the equivalent damping ratios are 7.5%, 8.6%, and 10.7%, respectively. Under the conditions of the other loading frequencies, the relationships between equivalent stiffness and pre-compression deformation, equivalent damping ratio and pre-compression deformation are also similar. The reason is that the pressure between the disc springs will be increasing with the increase of pre-compression deformation, leading to an increase in Coulomb friction. Therefore, the equivalent damping ratio of the DSCCP shock absorber increases gradually.