# Quasi-Static Sliding Wear Analysis of 3D Rough Surface Considering Changes in the Point of Contact
## 1 Introduction  
Sliding wear is a major problem commonly encountered in a variety of engineering problems. Over the past few decades, the most difficulty in mechanical design has been encountered in achieving the required performance that corresponds to the beginning of the Bathtub curve of the product. However, with rapid advances in science, technology, and computing power, the cost of solving these initial deficiencies has significantly decreased. On the other hand, as the recognition of the importance of product reliability is increasing gradually, failure due to repeated use of mechanical components is one of the research topics that is currently receiving the most attention. Typical examples of failure caused by repeated use are wear and fatigue failure, and fatigue failure is also greatly affected by wear [1]. [PERSON] closely analyzed the economic losses from wear, and the amount was found to be enormous [2]. Not only from an economic point of view but also from a biomedical engineering and environmental point of view, wear is a factor that must be reduced. For example, it is recognized that the biggest problem with joint replacement surgery is wear. If wear debris enters a sliding surface, the lifespan of the artificial joint is greatly shortened, and in severe cases, failure may occur [3]. In terms of environmental pollution, approximately 35% of wear particles generated from brake pads are emitted asfine dust PM10 in the air [4] and cause environmental pollution along with the fine dust generated by tire and road wear [5; 6; 7]. As the problems caused by wear become more important, related studies are being actively conducted. To reduce wear, efforts are being made to experimentally verify the effect of wear reduction through the application of new materials [8; 9; 10], coating [11; 12; 13; 14; 15], heat treatment [16; 17], and texturing [18; 19] in a wide variety of environments. Nevertheless, it is very difficult to obtain accurate data from the wear test for the following reasons: (1) It takes a great deal of time and (2) the result has a large dispersion. In addition to the difficulty of data acquisition itself, there is also a problem in identifying the main parameters that cause wear because changes in the surface and interaction at the interface during the process are unknown. On the other hand, numerical analysis of wear based on the generated surface is economical because it takes less time and does not require additional processing such as noise removal or equipment required for the experiment. It also has the advantage of being able to observe changes in the surface as wear progresses. Numerical wear analysis consists of procedures for calculating the contact pressure and then calculating the wear depth. The method of calculating the contact pressure is divided into a deterministic method and a probabilistic method. The former method calculates the wear depth at each node after calculating the pressure using the semi-analytical method (SAM) [20; 21], and the latter method statistically calculates the average contact pressure based on the Greenwood-Williomson (GW) model and then analyzes the wear depth using the truncation model [22; 23]. The concept of the truncation model is to obtain the average wear depth over the entire surface and cut the surface profile into a rigid plane. [PERSON], who first proposed the truncation model, analyzed the wear of a Gaussian surface by setting 10% of the height difference between the highest and the lowest points of the surface profile as the wear depth [24]. [PERSON] applied the Pearson system to analyze wear on a non-Gaussian surface [25], and [PERSON] used [PERSON]'s model to observe the change in the root mean square (RMS) roughness of the engine bore [26]. Considering the extreme skewness and kurtosis values of numerous worn surfaces, they showed that the wear of cylinder liners and bores can be predicted through the truncation model. [PERSON] used an average wear model similar to the truncation model for wear analysis of 2D surface profiles [23].