# Simplified Calculation Model for Contact Resistance Based on Fractal Rough Surfaces Method
## 3 Results and Analysis  
### Surface Morphological Analysis  
The method for simulating surface morphology proposed in Section 2.1 is analyzed. The morphological features of the asperity set are determined by the two-dimensional W-M function. Subsequently, the Monte Carlo method is used to construct the rough surface and simulate the three-dimensional rough surface morphology under different fractal parameters, as shown in Figure 7. Both parameters, \(D\) and \(G\), are found to be negatively correlated with the height of the rough surface profile. The range of values of \(G\) under different surfaces is much larger than that of \(D\) (\(1<D<2\)), which has a greater effect on the height of the asperity than that of \(D\) as a power. According to \(N=[(l_{max}/l_{min})^{D}]\), the fractal dimension \(D\) is positively correlated with the number of asperity sets. The increase in \(D\) leads to a decrease in the distance between the asperities and the rough surface becomes more complex. Furthermore, a decrease in \(G\) causes a significant reduction in the surface profile height. However, the effect of parameter  
Figure 8a shows that at the fractal dimension \(D\) less than 1.5, the increase in \(D\) leads to increase the contact rate and improves the contact properties of the material surface. When \(D\) is greater than 1.5, the size of larger contacts decreases, while the increase in the number of small asperities on the rough surface is much faster than the decrease in the size of large asperities, and the proportion of large asperities contacts increases rather than decreases. Small-size asperities cannot contact the rigid plane and the actual contact area gradually decreases. Figure 8b shows that \(A_{r}*\) increases linearly with the increase in \(F*\) when the fractal dimension \(D\) is a constant value. With constant \(F*\), the actual contact area decreases as the characteristic scale \(G\) increases. The reason for this phenomenon is that the size of \(G\) determines the flatness and roughness of the overall surface, and the larger the \(G\), the greater the difference in asperity amplitude. Under the same contact load, the presence of higher asperities causes a large number of low asperities to fail to make contact, which, in turn, reduces the overall contact area. Therefore, improving the machining accuracy and reducing the roughness of the contact part surface is beneficial to enhancing the contact performance. Figure 9 shows the variation in the average contact separation with contact pressure for different fractal parameters. As shown in Figure 9a, there exists an optimal value of the fractal dimension (\(D=1.5\)), corresponding to the maximum mean separation. At high loads, the results corresponding to different fractal dimensions tend to be consistent. However, the effect of the characteristic scale parameter \(G\) on the average contact separation is rather different, as shown in Figure 9b. The contact pressure at lower d can vary by several orders of magnitude at most. This result becomes more significant as \(G\) decreases. Figure 8: Variation relationship between \(A_{r}*\) and \(F*\) for different fractal parameters: (**a**) \(G=10^{-11}\) m, \(D=1.3\)–\(1.7\); (**b**) \(D=1.53\), \(G=10^{-11}\)–\(10^{-15}\) m.  
The asperity base diameters will significantly affect the contact mechanical properties of the rough surface. As shown in Figure 10, the increase in \(l_{max}\) expands the scale of all the asperity sets in the plane, leading to an increase in the average contact separation. According to Equations (9) and (10), the asperity set scale leads to an increase in the proportion of elastic deformation, and the surface is more likely to be contact deformed.