## 2 Materials and Methods
### Process Parameters and Design of Experiments  
The experimental investigation was structured to evaluate the influence of multiple process parameters on the surface quality enhancement of Ti grade 2 specimens. Three fundamental process parameters were identified as critical control factors: burnishing force (F), feed rate (f), and number of passes (n). The workpiece rotating speed was held constant throughout each experiment to isolate the impacts of the key process parameters (burnishing force, feed rate, and number of passes) on surface quality. The feed rate in this study refers to the linear movement speed of the burnishing tool per unit time (mm/min), which was regulated independently of the workpiece's rotation speed. This ensures that the deformational speed on the surface remains consistent for each experimental condition. The burnishing force levels of 50 N, 100 N, and 200 N were selected to achieve effective plastic deformation while avoiding material degradation. Feed rate values of 0.5 mm/min, 1 mm/min, and 2 mm/min were used to study the effects of different burnishing speeds, and the number of passes was set to one, two, and four to evaluate the cumulative impact of repeated burnishing. Furthermore, two distinct processing environments (dry and MQL) were incorporated to assess the role of lubrication conditions in surface quality optimization. The specific levels for each process parameter are presented in Table 1, which served as the foundation for the experimental design matrix.  
Figure 2: A visual depiction of the experimental setup (**a**) and the burnishing tool (**b**).  
The experimental design methodology employed a systematic approach to parameter optimization by implementing the Taguchi technique. This statistical method has emerged as a powerful tool in manufacturing process optimization, offering significant advantages in experimental efficiency and resource utilization [29; 30]. As shown in Table 1, the process parameters were arranged at different levels, and a mixed-level L18 orthogonal array was selected as the experimental framework. This provided a balanced investigation of parameter effects while minimizing the required experimental trials [31].  
In the context of surface quality optimization, the Taguchi method facilitates three distinct analytical approaches: maximization (\"Larger is better\"), minimization (\"Smaller is better\"), and target value optimization (\"Nominal is best\") [32; 33]. The \"Smaller is better\" characteristic was adopted for this investigation, aligning to minimize surface roughness values. The quantitative evaluation of parameter effects was conducted using signal-to-noise (\(S/N\)) ratio analysis, expressed mathematically as follows:  
\[s/N=-10\log\left(\frac{1}{N}\left(\sum_{i=1}^{n}Y_{i}^{2}\right)\right)\, \tag{1}\]  
\(Y_{i}\) represents individual surface roughness measurements from each experimental trial, and n denotes the number of observations per trial. This analytical framework enables a comprehensive evaluation of parameter effects while accounting for process variability and experimental uncertainty. Implementing this methodology ensures robust optimization of the ball burnishing process parameters, enhancing surface quality outcomes while maintaining experimental efficiency.