# Evaluation of Mechanical Performance of a New Disc Spring-Cable Counter Pressure Shock Absorber
## 2 Design of the DSCCP Shock Absorber
### Key Parameter Calculation and Design Process  
#### 2.2.1 Axial Bearing Capacity  
When using a combination of disc springs, the influence of the frictional force between the disc springs must be considered. The magnitude of the frictional force depends on the method of combining the disc springs, the number of discs in each group, and the lubrication of the disc surfaces. Due to the damping effect caused by the frictional force, the use of multiple-disc spring combinations increases the number of discs compared to the theoretical calculation of a single-disc spring. As the number of disc springs in the combined group increases, the deformation of each disc in the group gradually decreases, so the number of discs in a composite disc spring group should not be too high. Frictional force mainly exists between the contact surfaces of the disc springs and between the contact surfaces of the external world. When an axial load is applied to the disc spring, the load increases. When considering the friction force, the vertical bearing capacity \(P_{\text{R}}\) of shock absorber can be calculated according to the following equation [22]:  
\[P_{R}=P\cdot\frac{n}{1+f_{M}(n-1)\pm f_{\text{R}}}=P_{c}\times\frac{f}{h_{0} }[(\frac{h_{0}}{t}-\frac{f}{t})(\frac{h_{0}}{t}-\frac{f}{2t})+1]\cdot\frac{n} {1\pm f_{M}(n-1)\pm f_{\text{R}}} \tag{1}\]  
Figure 1: Construction of the DSCCP vertical shock absorber.  
in which, the negative sign is taken when applying the load, otherwise, the positive sign is taken. \(f_{\text{M}}\) is the friction coefficient between the contact surfaces of the disc spring pieces; \(f_{\text{R}}\) is the friction coefficient at the edge of the disc spring carrying the load, \(h_{0}\), \(t\) are the free height and thickness of disc spring; \(n\) is the number of disc spring; \(f\) is the deformation of the disc spring. In this study, the vertical bearing capacity of the DSCCP shock absorber is designed to be 498 kN and allows a maximum deformation of 33 mm. Under this condition, the special design parameters of the disc spring are as follows: \(D\) = 250 mm, \(d\) = 127 mm, \(t\) = 14 mm, \(h_{0}\) = 5.6 mm, \(H_{0}\) = 19.6 mm. Based on the GB1972-2005, when \(f\) = 0.75\(h_{0}\), \(P\) = 249 kN, \(\sigma_{\text{OM}}\)b = -1200 N/mm\({}^{2}\), \(\sigma_{\text{R}}\)c = 1220 N/mm\({}^{2}\), the friction coefficients between the discs are \(f_{\text{M}}\) = 0.02, \(f_{\text{R}}\) = 0.03 [36]. Using 2 stacked and 8 paired disc spring sets, the relationship between the vertical bearing capacity \(P_{\text{R}}\) and the deformation\(f\) (\(0\leq f\leq 0.75h_{0}\)) of the DSCCP shock absorber can be expressed as:  
\[P_{\text{R}}=P_{\text{c}}\times\frac{f}{h_{0}}[(\frac{h_{0}}{t}-\frac{f}{t})( \frac{h_{0}}{t}-\frac{f}{2t})+1]\times\frac{n}{1\pm f_{M}(n-1)\pm f_{R}}=5777 0\times f[(\frac{2}{5}-\frac{f}{14})(\frac{2}{5}-\frac{f}{28})+1]\times\frac{ 2}{1\pm 0.02\pm 0.03} \tag{2}\]  
When loading:  
\[{P_{\text{R}}}^{+}=121621\times f[(\frac{2}{5}-\frac{f}{14})(\frac{2}{5}-\frac {f}{28})+1] \tag{3}\]  
When unloading:  
\[P_{\text{R}}^{-}=110038\times f[(\frac{2}{5}-\frac{f}{14})(\frac{2}{5}-\frac {f}{28})+1] \tag{4}\]  
Figure 2 shows the load-deformation relationship curve during loading and unloading.