## 5 Methodology Used in This Study
dimensions are described in Figure 4. The joint forces obtained from the dynamic analysis are used to perform wear analysis on the bushing at the joint of interest, as shown in Figure 2. Four categories of numerical tests with varying bushing geometry dimensions were conducted. These categories are as follows: (1) fixed bushing depth and fixed outer diameter with varying inner diameters, (2) fixed bushing depth and fixed inner diameter with varying outer diameters, (3) fixed rim thickness and fixed depth with varying outer and inner diameters (both adjusted to maintain the rim thickness), and (4) fixed inner and outer diameters with varying bushing depth. The four categories, along with the corresponding dimensions and geometric depictions, are presented in Table 3.  
The FEM-based model utilizes the finite element representation shown in Figure 5, where a rigid element represents the journal. This assumption is based on the journal being much harder than the bushing, meaning its deformation is negligible compared to that of the bushing. It is also assumed that the journal experiences minimal wear and retains its original shape. The bushing's geometry is represented by an eight-node quadrilateral element, while the contact surface on the inner bushing is modeled using three-node contact elements. The nodes on the outer surface of the bushing are constrained in translation and contact between the two components is established by applying the joint reaction force to the pilot node, which is connected to the rigid journal element. Figure 4: Description of the bushing geometry terminology. Figure 5: Finite element model of the journal bearing pair used in this study. The wear simulation process is carried out in three main steps (outlined in Figure 2): (1) calculating the contact pressure resulting from the interaction between the journal and bushing, (2) determining the incremental wear amount, and (3) updating the geometry to account for wear in the next iteration. In the EFM approach, the entire analysis was conducted using MATLAB (Version R2018b) with in-house software, whereas for the FEM-based analysis, ANSYS (Version 14.5) was used for contact analysis in conjunction with MATLAB to automate and manage the study. As previously mentioned, the finite element model (Figure 5) comprises eight-node quadrilateral elements, while three-node contact elements represent the contact surfaces (i.e., the inner surface of the bushing). The Newton-Raphson iterative method was employed in ANSYS to solve the nonlinear contact problem, with contact pressure obtained at the Gauss integration points. A sensitivity study was conducted to determine the optimal step size, ensuring numerical stability and independence from discretization. Further \begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **(1) Fixed Outer Diameter** \\ **with Varying Inner** \\ **Diameter (Fixed Depth)** \\ \end{tabular} & \begin{tabular}{c} **(2) Fixed Inner Diameter** \\ **with Varying Outer** \\ **Diameter (Fixed Depth)** \\ \end{tabular} & \begin{tabular}{c} **(3) Fixed Rim Thickness (Varying Outer and** \\ **Inner Diameters but Fixed Depth)** \\ \end{tabular} & \
\begin{tabular}{c} **(4) Varying Depth with Fixed** \\ **Inner and Outher Diameters** \\ \end{tabular} \\ \hline \hline
\begin{tabular}{c} \(t=25.4\), \(D=50\) mm \\ \end{tabular} & \(t=25.4\), \(d=20\) & \(t=25.4\) & \(D=31.75\), \(d=19.07\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Four categories of numerical tests with the corresponding bushing dimensions (all dimensions are in mm). reduction beyond the selected step size did not affect solution accuracy. Additionally, a mesh refinement study was performed to confirm that the results were not influenced by mesh discretization. Several mesh densities were tested, with contact pressure as the key output parameter, and the results indicated that beyond the chosen refinement level, variations in pressure distribution were negligible.