## 4 Experimental Validation of Predicted Feed Rate  
To verify the effectiveness of the proposed machine learning-based feed rate prediction model in practical robotic machining applications, validation experiments were conducted using a UR10e robotic arm equipped with a voice-coil-motor-driven active end-effector  
Figure 10: Residual analysis of the XGBoost model predictions: (**a**) Residuals versus predicted values and (**b**) Histogram of residuals. and an ATI-9105 force/torque sensor. Surface roughness parameters were measured using a SURFCOM TOUCH 35 contact-type profilometer, with the evaluation conducted in accordance with the ISO 21920:2021 standard [18]. The purpose of the experiment was to determine whether the feed rates predicted by the model could effectively reduce chatter-induced surface irregularities in a real-world setup. The workpiece used in this experiment was a rectangular block of S45C carbon steel with dimensions of 50 mm \(\times\) 20 mm \(\times\) 13.5 mm. The machining tests were carried out using a fixed axial depth of cut of 1.8 mm and a radial depth of cut of 0.9 mm. Figure 11 illustrates the machining setup, highlighting the relative orientations of the axial, radial, and feed directions on the surface of the workpiece during the cutting process. Under these controlled conditions, four feed rates were evaluated:  
* 120.0 mm/min (baseline low feed)
* 156 mm/min (moderate empirical setting)
* 162 mm/min (predicted optimal by XGBost model)
* 180 mm/min (higher conventional setting)  
Surface integrity was evaluated using two standard metrics:  
* Pt (maximum peak-to-valley height), which is sensitive to sudden tool deflections and chatter marks. * Ra (arithmetic average roughness), commonly used to characterize surface finish. Figure 12 presents the surface profiles measured using a contact-type surface profilometer for each tested feed rate. These profiles reveal topographical variations across a 4 mm span of the machined surface. Notably, the profile corresponding to the predicted optimal feed rate of 162 mm/min exhibits the most consistent trajectory, with relatively gentle peak-to-valley transitions and minimal chatter-induced irregularities. In contrast, the 120 mm/min condition shows pronounced undulations, while the 180 mm/min condition exhibits sharper peaks, indicating increased dynamic instability. The numerical results are summarized in Table 3, which compares the Pt and Ra values obtained at each feed rate. The 162 mm/min feed rate yielded the lowest Pt value of 19.493 \(\upmu\)m, indicating superior dynamic stability. In comparison, feed rates of 120 mm/min, 156 mm/min, and 180 mm/min produced Pt values of 24.858 \(\upmu\)m, 22.723 \(\upmu\)m, and 21.649 \(\upmu\)m, respectively, corresponding to reductions of:  
* \(\downarrow\) 21.6% compared to 120 mm/min
* \(\downarrow\) 19.9% compared to 156 mm/min
* \(\downarrow\) 9.9% compared to 180 mm/min  
Figure 11: Orientation of feed, radial, and axial directions on the workpiece surface. While the Ra value corresponding to the predicted feed rate of 162 mm/min (0.94 \(\upmu\)m) was slightly higher than that of 180 mm/min, both values remained well below the 1 \(\upmu\)m threshold, which is commonly considered acceptable for high-quality surface finishes. As such, the small difference in Ra is not deemed critical in assessing machining performance. In contrast, Pt, which captures peak-to-valley deviations and is more sensitive to chatter-induced defects, was significantly lower at 162 mm/min. Therefore, Pt is adopted as the primary indicator of surface quality in this study, and the 162 mm/min feed rate is validated as achieving an optimal balance between surface consistency and dynamic stability. To further validate the robustness of the observed surface improvements, each feed rate condition was repeated four times, and the resulting surface roughness metrics were statistically analyzed. As illustrated in Figure 13, the boxplots capture the distribution and variability of Pt and Ra values across these repeated trials.