## 4 Simulation Analysis of Mechanical Properties of Composite Rubber Elements
### Stress and Displacement Analysis of the Rubber Element  
Firstly, the stress and strain analysis of the single rubber element was performed, and the single rubber element was divided into the same element type and number of grids as in the figure on the right in Figure 11. All degrees of freedom were restricted for the cylindrical hole of the rubber element connected to the middle rib plate. Two planes of the rubber element were constrained by displacement in U3 direction only. The degrees of freedom except in U1 direction were restricted at the cylindrical hole of the rubber element connected to the fixed circular plate. The compression displacement in the direction of U1 of the cylindrical hole of the rubber element connected to the fixed round plate was 3 mm. The analysis step type was static general, and the analysis step duration was set to 1 s. The stress and the displacement distribution of a single rubber element at 3 mm were obtained. Figure 12a shows the stress nephogram of the rubber element at a compression displacement of 3 mm. It can be seen from Figure 12a that the stress of the rubber element was mainly distributed around the cylindrical hole connected with the fixed circular plate, and the stress gradually decreased from the right half of the inner part of the cylindrical hole to the right end. The reason for this result is that the stiffness of the bolt is greater than the stiffness of the rubber element, and when the bolt squeezes the rubber element, the top of the bolt compresses the cylindrical hole surface at the bottom of the rubber element as the bolt moves. With the increase in bolt pressure, the relative dislocation of the cylindrical holes at both ends of the rubber element becomes more significant, and the support reaction also increases. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Modulus of Elasticity (MPa)** & **Poisson’s Ratio** & **Density (kg/mm\({}^{3}\))** \\ \hline cam plate & \(2.03\times 10^{5}\) & 0.3 & \(7.85\times 10^{-6}\) \\ \hline fixed circular plate & \(2.03\times 10^{5}\) & 0.3 & \(7.85\times 10^{-6}\) \\ \hline cam internal rib plate & \(2.03\times 10^{5}\) & 0.3 & \(7.85\times 10^{-6}\) \\ \hline press plate & \(0.5\times 10^{5}\) & 0.35 & \(1.44\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties of each part of elastic cam. Figure 12b shows the stress nephogram of the rubber element in section view when the compression displacement of the rubber element was 3 mm. According to Figure 12b, the maximum stress of the rubber element was 1.717 MPa, the maximum stress position was on the dividing line of the upper and lower semicircle of the cylindrical hole of the bolt, and the main bearing area was within about 160\({}^{\circ}\) of the radiation area of the lower half surface of the cylindrical hole. The reason is that when the elastic cam is rotating the extrusion tamping hammer, with the change in the actual contact radius, the bolt on the cam fixed round plate will transfer the force to the elastic element inner hole, and in the extrusion transition area of the rubber element cylindrical hole there will appear stress concentration. In actual working conditions, each time the cam rotates, its rubber elements will undergo a process of extrusion and deformation recovery; therefore, the rubber elements are subjected to alternating stress in duty-cycle operation, and these rubber elements are prone to fatigue failure. The location of fatigue failure in the rubber element is mainly in the contact range of 160\({}^{\circ}\) between the cylindrical hole of the rubber element and the bolt of the fixed circular plate, and at the two stress concentration positions of the bolt hole it is the most significant. Figure 13 shows the stress nephograms of the rubber elements at different times. With the increase in time, the stress also increased continuously.