# Contact Analysis and Friction Prediction of Non-Gaussian Random Surfaces
## 4 Results and Discussion
### Effect of Roughness Amplitude and Skewness  
As indicated in Figure 7a,b, the rough surface with negative skewness presents blunt peaks and more sharp valleys, as opposed to a surface with a positive skewness. Those result in different contact performances and friction behavior. As demonstrated in Figure 8, it is evident that, when the surface with positive skewness comes into contact, larger contact pressures are observed at most contact points compared to the negatively skewed surface. The reason for this is that the surface with the positive skewness has less summits to sustain the applied load, leading to higher local pressure. In turn, the negatively skewed surface with more flat protrusions results in a larger contact area, leading to lower contact pressure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Surfaces** & \(R_{q}(\upmu\upmu)\) & _Load_ (\(\times 10^{5}\) N/m) & \(S_{k}\) & \(K_{u}\) \\ \hline
1–5 & 0.1–0.5 & 2 & \(-1\) & 3 \\
6–10 & 0.1–0.5 & 2 & \(1\) & 3 \\
11–15 & 0.3 & 2 & \(-1\) & 3–7 \\
12 & 0.3 & 0.5–8 & \(1\) & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rough surfaces generated by the current method for investigating a friction coefficient.  
Figure 7: Rough surface with different skewness.  
Based on the friction theory introduced in Section 2.2, a friction coefficient is influenced by contact pressure, contact deformation, and contact area. Under elastic contact, the interfacial adhesion dominates the overall friction. When the contact pressure exceeds the material yield, the plowing effect of asperity combined with interfacial adhesion collectively contribute to the friction during sliding. In this paper, the average contact pressure, plastic ratio, and contact area ratio are used as the indications to represent the trend of contact pressure, contact deformation, and contact area. The average contact pressure represents the average of the pressures of all contact points. The contact area ratio is evaluated as the real contact area divided by the Hertzian contact area. Similarly, the plastic ratio is determined as the ratio of the number of contact points where contact pressure exceeds the material yield to the number of contact points. To account for the effect of the amplitude parameter, contact analyses were performed on a series of rough surfaces with identical skewness and different amplitudes. The numerical calculations are displayed in Figures 9 and 10. Figure 9 shows that the trend of friction coefficient is similar for negatively skewed surfaces and positively skewed surfaces. Initially, a friction coefficient has a slightly decreasing trend. This is because the friction coefficient is dominated by interfacial adhesion for relatively smooth surfaces. As the roughness amplitude increases, the actual contact area presents a significant reduction. A further increase in surface roughness amplitude leads to an increase in local contact pressure. As depicted in Figure 10, the average contact pressure increases with increasing roughness amplitude. Consequently, the increase in local pressure causes an increase in the plastic ratio, resulting in a significant increase in the plowing effect. Finally, the plowing mechanism becomes important role in determining friction of the rough surface. The distinction between negatively skewed surfaces and positively skewed surfaces is that the changes of average contact pressure, contact area ratio, and the plastic ratio of surfaces with positive skewness are more dramatic.  
Figure 8: The distribution of contact pressure and gap under different skewness.  
Figure 9: The effect of roughness amplitude on the friction coefficient.