Mechanism of surface roughness formation in robot-assisted polishing using flexible ball-end tool

This study establishes a theoretical model of microscale surface roughness for an industrial-robot-based flexible ball-end tool (FBET) under vibration conditions, revealing the quantitative relationship between pressure fluctuations and surface microstructures. Based on Hertz contact theory, the dynamic pressure distribution at the tool-workpiece interface in a vibrating environment is derived, and a complete material-removal-rate model is constructed in combination with the Preston equation. This research study finds that vibration frequency is inversely proportional to surface-waviness wavelength and that vibration amplitude exhibits an approximately linear positive correlation with surface roughness. Through numerical simulation and experimental verification, the effectiveness of active-force-control systems at vibration suppression is quantified. Experimental results show that after active force control was applied, the energy peak of the dominant vibration frequency component decreased by 80%, whereas the surface roughness Ra under linear-trajectory polishing was reduced from 1.670 to 0.760 nm, reducing surface roughness from 1.670 to 0.760 nm (54.5% convergence); by comparison, surface roughness under grating-trajectory polishing exhibited more complex interference structural characteristics. This study provides a theoretical basis for optimizing polishing process parameters and controlling surface quality under vibration conditions, offering scientific evidence for high-efficiency, high-precision manufacturing in the field of ultraprecision optical processing.