# Quasi-Static Sliding Wear Analysis of 3D Rough Surface Considering Changes in the Point of Contact
## 3 Result and Discussion
### Wear Simulation by Deterministic Quasi-Static Model
#### 3.2.1 Surface Topography Evolution  
Figure 8g-i show the lower stationary surface after 250 cycles, and Figure 8j-l show the upper moving surface after 250 cycles. After 250 cycles, the peaks were removed and both surfaces became flat, showing a difference in the number and depth of the valleys. The upper moving surface is always in contact, and the sliding distance is \(S\). In the case of the lower stationary surface, the sliding distance is \(L_{M}\), as discussed in Section 2.3, because wear occurs only when the upper moving surface passes the lower stationary surface. Thus, the wear depth of the lower stationary surface is smaller, which is the cause of the difference in shape between the upper and lower surfaces. In Figure 8j-l, a wear scar is formed on the upper moving surface in the sliding direction, which is a trace left on the upper moving  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Value**} \\ \cline{2-4}  & \multicolumn{1}{c}{**Surface 1**} & \multicolumn{1}{c}{**Surface 2**} & \multicolumn{1}{c}{**Surface 3**} \\ \hline \(\sigma\) & 0.67 \(\mu\)m & 0.67 \(\mu\)m & 0.67 \(\mu\)m \\ \(Sk\) & 0 & 0.5 & \(-\)0.5 \\ \(Ku\) & 3 & 4 & 3.3 \\ \(L\) & 0.889 mm & 0.889 mm & 0.889 mm \\ \(n_{x}=n_{y}\) & 257 & 257 & 257 \\ \(\beta\) & 0.04 mm & 0.04 mm & 0.04 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Rough surface generation parameters.  
\begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline \(E_{1}=E_{2}\) & 200 GPa \\ \(v_{1}=v_{2}\) & 0.3 \\ \(H_{1}=H_{2}\) & 3 GPa \\ \(F_{2}\) & 3.9516 N \\ \(k_{\text{near},1}=k_{\text{near},2}\) & \(5\times 10^{-5}\) \\ \(S\) & 12.78 mm \\ \(L_{S}\) & 12.78 mm \\ \(L_{M}\) & 3.6 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Contact and wear analysis parameters.  
surface by the asperities of the lower stationary surface. The wear scars created on surfaces 1 to 3 have different shapes depending on the characteristics of the two surfaces in contact. Since the lower stationary surface wears relatively slowly, the characteristics of the lower stationary surface affect the wear scar of the opposite surface. The wear scar is formed deepest on the upper moving surface of surface 2 because the roughness of the contact surface is the most severe due to high kurtosis and positive skewness. On the other hand, on surface 3, which has fewer asperities and is gentle, the contact area is wide and the wear depth is shallow, so the wear scar is relatively light.  
Figure 8: Gaussian and non-Gaussian surfaces for wear analysis: (**a–c**) Probability density functions of generated surfaces; (**d–f**) generated rough surfaces; (**g-i**) worn lower stationary surface; (**j–l**) worn upper moving surface.  
Figure 9a shows the PDF change of the Gaussian surface. As the peaks wear out at the beginning of the cycle, the values located at the right tail of the PDF create small peaks on the PDF. As the wear progresses, the existing peak and the newly created peak are combined to become higher, and the position gradually shifts to the left. From the PDF at 20 cycles, it can be predicted that kurtosis will tend to decrease at the beginning of wear. Figure 9b shows the ACF change of the Gaussian distribution surface at 40-cycle intervals, which verifies that the rough surface is properly generated by the surface generation algorithm when compared with the theoretical ACF. The autocorrelation length \(\beta\), which is the distance to the point where the ACF value becomes 0.1, is also equal to 0.04 mm. As the surface becomes flat as the wear progresses, the height values gather in a relatively similar range, and thus the ACF value indicating the degree of similarity gradually increases overall. Above 90 cycles, \(\beta\) is no longer definable because the ACF value does not have a value below 0.1.