Effects of the V-groove property for machining miniature balls using a plate with discontinuous sectors of fixed abrasives

To achieve efficient, high-accuracy machining of miniature balls, this study proposes a novel lapping method using a plate with discontinuous sectors of fixed abrasives (PDSFA). By varying friction coefficients across different plate sectors, the method promotes the formation of uniform, full-coverage lapping trajectories on the ball surface, enhancing machining accuracy and efficiency. A kinematic model is developed to analyze the properties of the eccentric V-groove and its effect on the distribution of the machining trajectory. Simulation and experimental results confirm that optimizing groove eccentricity significantly improves trajectory uniformity and coverage. An experimental platform was constructed to evaluate the performance of the PDSFA approach using GGr15 bearing steel miniature balls. At an optimal groove eccentricity degree of 0.3, after 6 h of lapping, the balls achieved an average roundness (RON_t) of 0.118 μm and surface roughness (R_a) of 17.5 nm. A subsequent 3-h polishing process further reduced RON_t to 0.082 μm (±0.02 μm) and R_a to 9 nm (±0.8 nm), demonstrating the method's effectiveness and precision.