# Quasi-Static Sliding Wear Analysis of 3D Rough Surface Considering Changes in the Point of Contact
## 1 Introduction
This model determines the contact node by setting the rigid body displacement, and then calculates the average wear depth with the Archard wear model based on the contact pressure. Since the contact pressure is obtained using the Hertzian contact solution, the asperity radius must be approximated for each contact asperity. [PERSON] and [PERSON], who proposed a stochastic rough surface contact model, determined the radius using the '3-point peak' method of fitting the peak and adjacent points with a parabola [27], and [PERSON] and [PERSON] simplified the calculation by assuming that the asperities shape is a sphere [28]. [PERSON] used the intersections of the rigid plane-surface profile detected by the algorithm for the radius assumption, and when multiple asperities were in contact, the peak height distribution was reflected in the approximated asperity radius [23]. They analyzed wear on rough surfaces with a wide range of RMS roughness, skewness, and kurtosis. As a result, high wear rates were observed on positively skewed, high-kurtosis surfaces, and wear regimes of severe and mild wear were observed. [PERSON] developed a numerical 3D wear model by extending [PERSON]'s model to elastic-plastic contact and observed changes in parameters that occur during the wear process. The results of the wear analysis of the surface with the same characteristics as the specimen were in good agreement with the experimental results [22]. If the deterministic method is used, more precise wear analysis is possible compared to the statistical method. The main reason is that since deterministic wear analysis deals with the actual rough surface itself, the assumptions used in statistical methods such as fitting asperities into a spherical shape in the process of contact pressure calculation or calculating the average wear depth are no longer necessary. Since the contact pressure only varies greatly depending on the surface shape but is also the main factor that governs the wear depth, the surface shape must be reflected as it is in the process of contact pressure calculation. In that way, the change in the contact area, the shape of the worn asperities, and the surface parameters of the worn surface can be obtained in detail. [PERSON] analyzed wear under elastohydrodynamic lubrication (EHL) through a deterministic method and suggested a method of calibrating the wear coefficient by comparing it with the experiment, and also found that the surface change and wear scar shown in the analysis results were in good agreement with the experiment [29]. [PERSON] predicted the surface topography and friction coefficient in rolling-sliding contact under mixed lubrication conditions using [PERSON]'s model and showed that the slide-to-roll ratio had a great influence on the wear rate [21]. [PERSON] analyzed torsional refitting wear using SAM [20]. In a real phenomenon, the asperity passes over the asperity on the opposite surface and the point of contact changes with time. In most of the existing studies on rough surface wear, the relative point of contact of the asperities does not change, so the wear depth at some locations may be overestimated. Therefore, it is necessary to consider the movement of asperities so as to obtain a result more similar to reality. [PERSON] analyzed the sliding wear by moving the disk a small distance at each time step to analyze the wear of the ball-on-disk in rolling-sliding contact under mixed lubrication and intensively analyzed the surface topography evolution and friction coefficient [21]. [PERSON] also considered the motion of asperities in the same way [30], and they used the wear mechanism proposed by [PERSON], which states that wear particles are generated when the energy between sliding surfaces is sufficient to overcome the kinetic barriers [31]. [PERSON]'s model is also consistent with [PERSON]'s hypothesis that wear particles are generated in the asperities where a strong junction occurs when two surfaces slide against each other [32].