## 4 Analysis of the Three-Dimensional Micro-Contact Model  
Using a non-contact 3D surface analysis system to scan the surface of the contact group, morphological images and point cloud height data are obtained. Extracting the surface micro-morphological characteristics of the contact group at various test stages, a contact model of the contact group is then established. The impact of morphological characteristics on the arc erosion and ablation of the contact group is analyzed, exploring the mechanism of electrical contact failure, providing a theoretical basis for future research on the reliability of switching electrical appliances. The values for the contact model are shown in Table 3.  
As shown in Figures 14 and 15, during the contact process of the interface with asperity levels ranging from 10 to 34, the relationship between the normal contact area and the normal load increases in proportion to the deformation as a percentage of the maximum height of the asperities. The dimensionless real contact area is approximately proportional to the 3/2 power of the contact load when the contact load is small, and during a complete contact process, the rough surface is approximately an elastic deformation. The difference in the base radius also affects the size of the contact area. When the base radius increases, the contact area will decrease for the same downward contact pressure relative to the whole, but the normal load in the contact area will increase, making the contact state more stable and improving the reliability of electrical contact. In Figure 16, at the initial contact of the joint surface, the normal stiffness of the elastic deformation part accounts for 90% of the total normal stiffness, as the contact load increases, the proportion of normal stiffness due to elastic deformation to the total normal stiffness gradually decreases, and when the maximum deformation is reached, this proportion is 65%. Since asperities with a level of 14 to 7 only undergo elastic deformation, the normal contact stiffness of this interface is non-linearly related to the normal load. This theory explains why, under conditions of low contact pressure, most deformations are elastic, and there may even be gaps, which makes it easier for arc breakdown and erosion to occur; accordingly, appropriately increasing the contact pressure can enhance contact stability. At the same time, permanent deformation may occur in areas with a smaller contact surface, leading to easier erosion when environmental temperatures rise. Therefore, the contact surface should be processed to remove any small particles adhering to it as much as possible, to prevent them from becoming areas where ablation growth may occur. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Micro-asperity level & \(10-34\) \\ Fractal dimension \(D\) & \(2.1-2.9\) \\ Characteristic scale parameter \(G\) & \(10^{-6}\sim 10^{-9}\) m \\ Elastic modulus \(E\) & \(6.32\times 10^{10}\) Pa \\ Hardness \(H\) & \(2.5\times 10^{9}\) \\ Poisson’s ratio \(\
u\) & \(0.38\) \\ Resistivity of Ag & \(1.65\times 10^{-8}\) m\(\Omega\) \\ Resistivity of AgCdO & \(2.8\times 10^{-8}\) m\(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model parameter values. Through the analysis and comparison of the model [28], as the fractal dimension D increases, the surface becomes smoother, and the real contact area of the rough surface is larger under the same contact pressure. When the degree of surface refinement is high or the surface is relatively smooth, as the fractal dimension increases, the critical level also gradually rises, leading to an increase in the number of elastic contact points, which causes the overall normal contact stiffness of the interface to increase, thereby reducing the contact area; to improve contact stability, it is generally necessary to increase the contact area to reduce the contact resistance [29].