## 1 Introduction
Studies utilizing 3D topography analysis have shown that burnishing pressure between 15 and 20 MPa typically yields optimal surface quality improvements, with surface roughness reductions of up to 90% compared to conventionally machined surfaces [15]. Furthermore, the process induces a beneficial grain refinement in the surface layer, contributing to enhanced mechanical properties and wear resistance [16]. In particular, 3D topographic analyses have shown that burnishing under 20 MPa pressure results in a significant grain refinement on the surface, which improves wear resistance. Despite extensive investigations into ball burnishing, a comprehensive understanding of how the process parameters affect Ti grade 2, particularly under different lubrication conditions, is still needed [17]. This study aims to bridge that gap by thoroughly examining these effects. Optimizing these parameters is essential for achieving the desired surface quality characteristics. The Taguchi method, combined with ANOVA, provides a robust approach for assessing the significance of various parameters and their interactions while minimizing the number of experimental trials [18]. In this study, the effects of LPB on Ti-6 Al-4V were investigated by both experimental and numerical methods, and it was confirmed that the optimum parameters increase the fatigue life. Such optimization enhances product quality and reduces production costs and time. The relationship between burnishing parameters and surface integrity characteristics has been extensively studied through both experimental and numerical approaches. Recent finite element analyses have demonstrated that the distribution of residual stresses is more significantly influenced by burnishing pressure than by the number of passes [19]. Additionally, research has shown that the combination of appropriate burnishing pressure and optimal number of passes can result in significant improvements in surface hardness and the formation of a stable compressive residual stress layer [20]. Several studies have explored the optimization of ball burnishing parameters for titanium alloys. For instance, [PERSON] et al. focused on optimizing parameters for Ti-6 Al-4V to enhance surface roughness and hardness, employing the Taguchi method to systematically explore the effects of burnishing speed, feed, force, and the number of passes [21]. Similarly, [PERSON] investigated the influence of ball burnishing on the lubricated fretting behavior of Ti-6 Al-4V, highlighting its potential to improve friction and wear resistance [22]. In machining, [PERSON] et al. utilized a hybrid Fuzzy-MOORA optimization approach to optimize machining parameters for commercially pure Ti grade 2, addressing challenges such as excessive tool wear and poor surface quality [23]. [PERSON] and colleagues introduced a novel ball burnishing-assisted electrical discharge cladding process, demonstrating significant improvements in surface roughness and microhardness for biomedical applications [24]. Further, [PERSON] et al. analyzed roller burnishing parameters for Ti-6 Al-4V, developing predictive models for surface quality under various cooling conditions [25]. [PERSON] et al. explored diamond burnishing for additively manufactured Ti-6 Al-4V parts, providing empirical formulas for optimizing surface quality [26]. Lastly, [PERSON] et al. examined vibration-assisted ball burnishing on AISI 316L, showing enhancements in surface integrity and tribological performance [27]. These studies have demonstrated the potential of ball burnishing to improve surface quality, but there is a lack of comprehensive investigations on commercially pure titanium materials such as Ti grade 2 under different environmental conditions (dry and MQL). In this context, this study aims to fill this important gap in the literature and contribute to sustainable production processes by systematically evaluating the effects of ball burnishing under dry and MQL conditions.