## 3 Results and Discussion
### Modeling Surface Roughness Based on Cutting Force Components  
In machining operations, surface roughness is one of the most critical quality attributes, directly influenced by cutting forces. Variations in cutting forces during the process reflect the complex interaction between the cutting tool and the workpiece, encompassing factors such as tool vibration, material deformation, and process dynamics. Recent advancements in sensor technologies and machine learning algorithms have significantly enhanced the capacity to model these intricate interactions with high precision.  
The existing literature has consistently demonstrated that cutting force signals, particularly when treated as time-series data, serve as powerful predictors of surface roughness. For instance, convolutional neural networks (CNNs) applied to frequency-transformed force data have achieved prediction errors below 10%, indicating strong predictive capabilities [54]. Furthermore, interpretable machine learning models such as random forests have achieved high levels of accuracy even when fewer sensors are used, thereby contributing to cost-effective smart manufacturing systems [55]. In grinding operations, LightGBM has been identified as the most effective model for predicting surface roughness from force-derived features, outperforming other algorithms in terms of error rates [56].  
The experimental findings of the present study are in strong alignment with the prevailing literature. Multiple regression models--namely, random forest, gradient boosting, CatBoost, LightGBM, and k-nearest neighbors--were developed based on the primary cutting force components Fx, Fy, and Fz to estimate the arithmetic average surface roughness (Ra). Among these, the Fx and Fy components were found to have a direct correlation with tool deflection patterns and surface vibration effects, while Fz was associated with the depth of penetration and subsurface plastic deformation during cutting.  
Figure 18 presents a comparative visualization of the predicted and actual Ra values for all regression models considered. The results show exceptionally high predictive accuracy, with R\({}^{2}\) values exceeding 0.95 across all models on the test dataset. Notably, both RFR and CatBoost exhibited a nearly perfect prediction performance (R\({}^{2}\approx\) 1.000), underscoring their robust generalization capabilities.  
Figure 18: Comparison of actual and predicted surface roughness (Ra) values using Fx, Fy, and Fz cutting force components across various regression models. The figure has been refined to emphasize deviations and model performance clarity through enhanced color coding and error range bands.  
These findings indicate that cutting force-based models are not only highly accurate but also practical for real-time implementation through sensor-integrated CNC systems. This makes them particularly suitable for industrial applications requiring adaptive control of surface finish. Furthermore, the ease of integrating force sensors into existing machining setups enhances the scalability of these models for smart factory environments.  
In conclusion, the use of cutting force signals as input features provides a highly reliable alternative to conventional surface roughness prediction methods that rely solely on process parameters. The results underscore the potential of force-based models in the development of intelligent, predictive quality control systems for digital manufacturing environments. Future research could focus on fusing real-time sensor data with adaptive ML models to enable closed-loop surface quality regulation, which is critical for achieving high consistency in high-precision machining operations.