## 1 Introduction  
Friction and wear represent critical factors in assessing mechanical systems' tribological behavior, with surface characteristics serving as a key determinant of these properties. Recent research has increasingly focused on surface engineering techniques, particularly texturing approaches, as a promising strategy for enhancing lubrication performance and wear resistance. Surface texturing offers significant tribological benefits across various mechanical components, including bearings, liners, piston assemblies, seals, and drilling tools, by optimizing friction characteristics, reducing wear rates, and improving lubrication efficiency. The pioneering work of [PERSON] and [PERSON] [1] on hemispherical surface texturing demonstrated its potential to significantly enhance mechanical seal performance through improved lubrication and reduced friction. This breakthrough spurred global research efforts, leading to extensive theoretical and experimental investigations into surface texturing techniques and their tribological benefits. An investigation by [PERSON] et al. [2] examined how cavitation modeling influences the lubrication analysis of micro-textured journal bearings. The study compared two approaches--the conventional Reynolds model and the Elrod-Adams P-\(\theta\) model--in evaluating bearing performance under uncertain operating conditions. While both models yielded nearly identical predictions for load capacity and frictional torque, the Reynolds formulation demonstrated superior numerical stability, making it the preferred choice for such analyses. Furthermore, it was indicated that when journal bearings with a micro-textured inner surface are considered, the Reynolds model significantly leads to errors in estimating several variables, such as frictional torque. Therefore, when analyzing this type of micro-textured bearing, only the mass-conserving model developed by [PERSON] and [PERSON] provides accurate results. Building upon previous research, [PERSON] [3] systematically investigated how groove-like surface textures affect journal bearing performance, examining critical parameters including pattern geometry, size, and orientation. The study combined neural network modeling with experimental validation, demonstrating that textured surfaces significantly enhance load carrying capacity compared to smooth surfaces, with important implications for various tribological applications. Subsequently, [PERSON] and [PERSON] [4] expanded this research by analyzing textured journal bearings with non-Newtonian lubricants using a power-law model. Their numerical simulations revealed that while shear-thickening fluids generally increase both load capacity and friction, specific texture patterns--particularly fully positive wave textures--optimize performance characteristics. Further advancing this field, [PERSON] et al. [5] conducted comprehensive analyses of partially textured surfaces in both journal and thrust bearing configurations. The findings demonstrate that parallel groove textures on bearing surfaces can simultaneously enhance load carrying capacity while reducing friction in the lubricating film for both bearing types examined. [PERSON] et al. [6] performed an elastohydrodynamic analysis of textured journal bearings, evaluating how different groove designs affect load capacity. By solving the Reynolds equation with a parallel iterative RB-SOR method while accounting for bearing deformations, they demonstrated that flash-like grooves enhance load capacity more effectively than rectangular grooves, particularly at higher eccentricity ratios. Building on this work, [PERSON] et al. [7] examined how large-scale texturing influences bearing performance, with particular attention to cavitation effects.