Analytical model of dynamic and overlapped footprints in abrasive air jet polishing of optical glass

Thanks to the superior machined surface integrity, high machining feasibility, and limited tool wear, the Abrasive Air Jet Polishing (AAJP) has been considered as a widely used finishing process, especially for high-valued small and complex optics products. Therefore, many experimental, theoretical and processing technology studies have focused on this topic. However, experimental studies cannot provide an in-depth understanding of the process principle while most of the theoretical models/methods have been established based on many unrealistic assumptions. To fill this gap, this paper suggests an analytical model of the polished surface topography (or footprint) considering (i) the horizontally asymmetric cross-section profiles of a single-abrasive impact footprint, (ii) the abrasive-workpiece elastic deformation and further springback when the abrasive bounces back, and (iii) the overlapping footprints generated by multiple abrasives having a normal-distributed size. The systematic validation trials proved the model accuracy and feasibility. Based on the validated model, the effects of the polishing parameters including the jet pressure, jet angle, and abrasive size on both machined surface roughness and removed material volume are studied. The proposed model is anticipated for not only exploring and laying the theoretical foundation of the AAJP process in more depth, but also to provide guidance for industrial manufacturing in terms of polishing parameter optimization and polished surface prediction.