## 1 Introduction
Their findings demonstrated that the effectiveness of surface texturing is highly dependent on its spatial distribution, with textures positioned in pressure-enhancing regions significantly boosting load capacity, while those in cavitation-prone or pressure-reducing areas yield either minimal improvement or potentially adverse effects. Together, these studies highlight the importance of both texture geometry and strategic placement for optimizing bearing performance. [PERSON] et al. [8] examined the performance of partially textured journal bearings with grease lubrication using CFD analysis. Their investigation revealed that strategically positioned surface textures enhance load capacity while influencing friction characteristics, with texture geometry playing a critical role in determining these effects. Subsequently, [PERSON] et al. [9] investigated textured bearing stability with complex lubricants, developing a comprehensive lubrication model incorporating piezo-viscous and shear-thinning effects. Their findings highlighted that partial grooving in specific bearing regions effectively reduces friction, particularly at lower eccentricity ratios, while emphasizing the significant impact of shear-thinning behavior on system stability. [PERSON] and [PERSON] [10] comprehensively reviewed the effects of partial surface texturing on journal bearings lubricated with Newtonian fluids. Their analysis confirmed that controlled surface texturing can simultaneously reduce friction coefficients and enhance load carrying capacity, though these benefits diminish at higher eccentricity ratios. Building on these findings, [PERSON] et al. [11] conducted numerical optimization of partially textured journal bearings using finite element analysis. Their work specifically investigated triangular textures in pressure-enhancement regions, systematically evaluating the influence of texture density and depth on bearing performance under iso-viscous, Newtonian lubrication conditions. The simulation results demonstrate that strategically positioned textures in the pressure-enhancing region of the bearing surface significantly improve steady-state performance. Optimal performance is achieved with shallow textures and low eccentricity ratios, yielding a maximum performance improvement factor of 2.198--quantified as the ratio of enhanced load capacity to reduced friction coefficient. Recent studies have increasingly focused on dimensional uncertainty effects in surface textures for mechanical systems, particularly journal bearings. Research demonstrates that manufacturing variations in texture patterns significantly influence tribological performance, necessitating meticulous analysis of their effects. Dimensional uncertainties in surface texture design and production can lead to substantial deviations from optimal system performance parameters [12; 13]. The dynamic stability analysis of mechanical systems, particularly journal bearing supports under critical operating conditions (e.g., heavy, oscillatory, or impact loads, and high-speed operations that induce motion instabilities), has long been a focal point in mechanical system condition monitoring research [14; 15]. Investigators have employed various analytical models to examine perturbed motions of system components, such as rotors in journal bearings under critical operational states [16; 17; 18]. Both linear and nonlinear approximation models have been historically significant in tribological research for analyzing bearing system performance. In linear dynamic stability analysis of journal bearing systems, the rotor center's perturbed motion within the bearing clearance space is typically constrained to limit-cycle perturbations around the static equilibrium point. This assumption facilitates the development of an equivalent vibrational model for a rotor supported by a lubricant film, characterized through equivalent stiffness and damping coefficients.