# 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
#### 3.2.2 Roughness Parameters, Contact and Wear Properties vs. Wear Cycle  
We investigated the main statistical parameters of the surface and changes in contact and wear properties during 250 cycles. Figure 10a shows the change in RMS roughness of the upper and lower surfaces for three cases. As the surface wears, the RMS roughness decreases, and the wear depth of the lower stationary surface is less than that of the upper moving surface. Surface 3 has a relatively high contact area because the contact surface is blunt. Therefore, since the pressure acting on the asperities is small, the wear depth is also proportionally small according to the wear equation, and as a result, the change in RMS roughness is the smallest. Surface 2 has sharp asperities due to high kurtosis and a contact surface with few peaks because the skewness is positive. Therefore, the pressure is concentrated on the peaks of asperities, and the wear depth is deeper than that of surfaces 1 and 3, and consequently, the change in RMS roughness is the largest. Figure 10b shows the change in skewness. Since a surface with more peaks than valleys has a positive skewness, and a surface with the opposite characteristic has a negative skewness, as the peaks are removed by wear, the skewness increases in the negative direction. Surface 2 has a sharp decrease in skewness compared to other surfaces in the initial cycle because peaks are rapidly removed by high pressure due to the asperity shape. Figure 10c shows the change in kurtosis. As mentioned in Section 3.2.1, kurtosis decreases and then increases on surfaces 1 and 2 because the high asperities disappear at the initial wear cycle. After all the peaks are removed, kurtosis increases as the flat area expands. Figure 10d shows the wear depth defined as the distance between the maximum value of the unworn profile and the maximum value of the worn profile in each cycle. Severe wear and steady wear were well observed based on the point where the slope of the graph changed.  
Figure 9: Evolution of functions representing rough surface properties: (**a**) Probability density function; (**b**) autocorrelation function.  
Figure 10: Parameters vs. wear cycle: (**a**) RMS roughness; (**b**) skewness; (**c**) kurtosis; (**d**) wear depth; (**e**) mean contact pressure and plastic contact area ratio.  
Figure 10e shows the average contact pressure and plastic contact area ratio in three cases. As wear progresses, the number of contact asperities increases, so the real contact area continues to increase. Thus, the contact pressure at the contact node continues to decrease. The rapid decrease in pressure is because the peaks are concentrated under the pressure and rapidly worn. The average contact pressure is greatest on surface 2 because of the small number of peaks and the small contact area of the asperities. Since plastic contact exists only at the beginning of the cycle, where the plastic contact area to the total contact area at the beginning is 43% and plasticity occurs in most of the contact nodes, it is essential to consider plasticity in the contact analysis of rough surfaces. However, since there is no node where plasticity occurs after 40 cycles at surface 1, 70 cycles at surface 2, and 20 cycles at surface 3, there is no need to perform plastic contact analysis after a certain cycle. Although the EPP model, which is the simplest model of plasticity, is used, the efficiency will be significantly different depending on the presence or absence of plasticity analysis when a more sophisticated model is selected.