Prediction Modeling and Parameter Optimization for Robotic Belt Grinding 42CrMo Steel Using Response Surface Methodology and Grey Relational Analysis

To address high-precision robotic abrasive belt grinding of 42CrMo steel, this study adopted the orthogonal central composite design with grinding force, feed rate, and rotational speed as key parameters, establishing and verifying regression models for material removal depth (MRD) and surface roughness (Ra). Results showed that the models’ relative errors are within 6% (MRD) and 10% (Ra). Grinding force and feed rate exert a strong coupling effect on MRD, while feed rate–rotational speed and grinding force–feed rate interactions significantly influence Ra, with “saddle-shaped” response surfaces. Grey relational analysis determined the optimal parameters: 75 N grinding force, 22.4 mm·s−1 feed rate, and 3261 rpm rotational speed, achieving a maximum MRD of 1.975 mm and a minimum Ra of 3.506 μm. The tolerance range of the optimal parameters is F = 70–80 N, vf = 20–24 mm·s−1, and ω = 3000–3500 rpm. This research provides robust support for process parameter prediction and optimization in high-precision robotic abrasive belt grinding of 42CrMo steel.