Mathematical Modeling and Multi-Criteria Optimization in Dry Turning for Enhanced Functional Surface Using Bearing Area Curve

This research examines the parameters of the bearing area curve (BAC) as delineated by ISO 21920-2:2021 (Rpk, Rk, Rvk, Mr1, and Mr2), within the framework of dry turning of AISI 1045 steel (C45), to assess the impact of machining conditions on surface integrity. A combination of methodological tools is applied. Pareto analysis highlights the most significant machining factors: cutting speed (Vc), feed (f), depth of cut (ap), nose radius (rε), and principal cutting angle (Xr). Linear regression models are used to quantify the relationship between these variables and the BAC parameters. For multi-response optimization, both grey relational analysis (GRA) and the desirability function (DF) method from response surface methodology (RSM) are employed. The findings offer practical insights for improving surface finish by determining optimal cutting conditions. Specifically, the optimal setup includes a high cutting speed (420 m/min), low feed (0.031 mm/rev), maximum depth of cut (0.4 mm), large tool nose radius (0.8 mm), and low principal cutting angle (45°). The optimization yields a GRG of 0.773 and a stable DF value around 0.638, confirming the robustness and coherence of the proposed approach.