# Evaluation of Mechanical Performance of a New Disc Spring-Cable Counter Pressure Shock Absorber
## 3 Numerical Simulation and Modal Validation  
### Model Establishment  
The DSCCP shock absorber consists of a group of 16 disc springs, which are stacked in pairs of two and coupled in eight sets, as shown in Figure 4. A disc spring is mainly made of spring steel materials such as 60 Si\({}_{2}\)MnA or 50 CrVA, with an elastic modulus of 206,000 N/mm\({}^{2}\), a yield strength of 1375 MPa, an ultimate tensile strength of 1570 MPa, and a Poisson's ratio of 0.3. The ideal elastic-plastic model is adopted for a disc spring.  
The contact surface between discs is thought to be a free contact surface, which includes two parts: the normal force and the tangential force. The normal force on the contact surface works once the contact pressure is greater than 0. At the same time, the tangential force on the contact surface also begins to work, which is defined as the product of the friction coefficient and normal stress. The contact surfaces are initially maintained in a static friction equilibrium state. The tangential force increases linearly with the increase  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(D\) (mm) & \(d\) (mm) & \(t\) (mm) & \(h_{0}\) (mm) & \(H_{0}\) (mm) & \(f\) (mm) & \(F\) (kN) & \(\sigma_{\text{II}}/\sigma_{\text{III}}\) (N/mm\({}^{2}\)) \\ \hline
250 & 127 & 14 & 5.6 & 19.6 & 4.2 & 249 & 1220 \\ \hline \hline \end{tabular}
\end{table}
Table 1: General parameters of the DSCCP shock absorber.  
Figure 4: Finite element model.  
Figure 3: Sketch of disc spring.  
of normal pressure. After that, once the tangential force reaches the critical shear stress \(\tau_{\text{bond}}\), the contact surface begins to slide. The friction coefficient between disc springs is taken as \(\mu_{1}=0.005\) based on the study of [PERSON] [37]. The disc spring model established using the ABAQUS platform is shown in Figure 4. The C\({}_{3}\)D\({}_{8}\)R element is used, which is a three-dimensional solid reduced integration element with only one integration point at the center of the element. This element has eight nodes, with each node having translational degrees of freedom along the X/Y/Z directions and rotational degrees of freedom around the X/Y/Z axes. The element has the ability to handle hyper elasticity, stress stiffening, creep, swelling, large deformation, and large strain, which can effectively simulate the deformation characteristics of disc springs and the stress characteristics of the upper and lower floating pressure plates.  
To ensure that the disc spring group does not experience lateral displacement during loading, horizontal constraints are applied at the bottom of the disc spring set, i.e., U1 = U3 = 0. The upper floating pressure plate is located inside the sleeve, and its horizontal displacement is also restricted to ensure the horizontal constraint of the disc spring set. The load is applied on the upper surface, which is coupled at a point. The grid division of the disc spring is: 50 grids for the inner ring, 100 grids for the outer ring, 16 grids for the radial direction, and three grids for the thickness direction. Two types of static loadings are adopted, namely linear static loading and semi-periodic sin-function loading, as shown in Figure 5. During static loading, the loading velocity is very slow to eliminate the dynamic effect of the DSCCP shock absorber.