## 2 Wear Prediction Procedures  
The wear prediction procedures employed in this work are similar to those found in the works of [PERSON] [21], [PERSON] [22], and [PERSON] [23, 24]. These procedures utilize an iterative wear prediction approach based on the linear [PERSON] wear model [25]. In this model, originally published in [PERSON] work [26], the worn volume is proportional to the normal load. In differential form, the wear model is expressed as follows [27]:  
\[\frac{dh}{ds}=kp(s) \tag{1}\]  
where \(s\) is the relative sliding distance, \(h\) is the wear depth, and \(p\) is the contact pressure between two surfaces in contact. The term \(k\), in Equation (1), is a wear coefficient that characterizes the tribological behavior of the two materials in relative sliding. The wear coefficient quantifies the rate of material loss (wear) from a surface when two surfaces are in contact and move relative to each other. Its unit is expressed as volume per unit force per unit sliding distance (mm\({}^{3}\)/Nm). In contrast, the friction coefficient is a unitless ratio of the frictional force to the normal force acting between two contacting surfaces. Itrepresents the degree of resistance to motion between the surfaces. The wear coefficient in Equation (1) is determined experimentally for a specific pair of materials and test conditions. While various test methods exist, the experiments commonly utilize a pin-on-disk setup conducted on tribometers. During a typical test, a known load is applied to a pin in contact with the disk (the counter surface). Relative sliding motion is introduced between the pin and disk through either reciprocating or rotary movement of the disk, while the pin remains stationary. This can be achieved using a reciprocating Pin-on-Disk Tribometer (see [28]) or a rotary Pin-on-Disk Tribometer (see [29]). The sliding distance is calculated by tracking the reciprocation cycles or disk rotations. After measuring the mass loss from the test, the wear coefficient is calculated using the following formula [28]:  
\[k=\frac{(\Delta m/\rho)}{d_{s}F_{N}} \tag{2}\]  
where \(F_{N}\) is the normal force between the pin and disk pair, \(d_{s}\) is the cumulative relative sliding distance, \(\Delta m\) is the overall worn mass, and \(\rho\) is the sample density. A more detailed discussion on wear coefficient determination measurements can be found in [28; 30; 31]. In Equation (1), the wear depth \(h\) can be estimated using a numerical solution (e.g., a finite difference approach). A temporal discretization of the relative motion produces the following result for the wear depth [30]:  
\[h_{i}=h_{i-1}+kp_{i}\Delta s_{i}. \tag{3}\]  
In Equation (3), \(\Delta s_{i}\), \(h_{i}\), and \(p_{i}\), respectively, are the incremental sliding distance, the wear depth, and the contact pressure for the current iteration (iteration \(i\)), whereas \(h_{i-1}\) is the wear depth of the previous iteration. The wear depth can be estimated from Equation (3), once the incremental sliding distance, the contact pressure, and the wear coefficient are known. The incremental sliding distance is usually specified (or determined in the contact analysis), whereas the wear coefficient may be determined through experiments [28; 30]. In previous wear prediction procedures, the contact pressure has been determined via a variety of techniques including the finite element method (FEM) [24; 27; 30], the elastic foundation method (EFM) [21; 23; 32; 33], and the boundary element method (BEM) [34; 35; 36]. In this study, the EFM and FEM were utilized and wear results compared. The EFM is a simple procedure to estimate contact pressure between two surfaces in contact. The procedure assumes that the contact surface is composed of a set of elastic springs (forming an elastic layer) that act independently of each other. The independence of the springs is indeed a violation of how contact occurs, as it neglects how the pressure in one location affects the deformation in neighboring regions.