Micro-scale modeling and analysis on material removal mechanisms for flexible ball-end tool polishing incorporating the curvature effect

Abstract

Optical freeform surfaces (OFS) have been extensively employed as core components in advanced optical systems for their excellent performances. However, the surface complexity and the high surface accuracy do impose challenges to the processing of OFS, especially the surface form maintaining or control during polishing. As one of the promising ultra-precision machining technologies to fabricate OFS, the flexible ball-end tool (FBET) polishing becomes available due to its attractive technical advantages. Nevertheless, there are still lack of more comprehensive insights on material removal mechanisms for FBET polishing incorporating the curvature effect, particularly from a microscopic scale, which is of great significance to determine the surface quality and form control in ultra-precision polishing process. In this paper, different from those published macro-scale Preston law-based models, a micro-scale material removal model is developed based on the mutual interaction of the slurry, polishing pad and curved workpiece among the FBET polishing interfaces with micro-contact theory and tribology theory, wherein various parameters embodied in FBET polishing are formulated quantitatively, such as slurry characteristics, pad properties, tool features, processing conditions, as well as workpiece curvature effect. The FBET is designed and adopted to conduct the spot polishing experiments within the concave curvature radius range from 75 mm to 225 mm, wherein the curvature radius range from 225 mm to 800 mm is theoretically chosen as an extension of this research. The predicted results agree well with the experimentally measured section profiles of polishing spots, thereby demonstrating the correctness and effectiveness of the proposed model. Furthermore, the effective relative velocity U together with the separation gap d between reference plane and workpiece surface are known as the two key parameters to account for the material removal mechanisms, and the latter is figured out to be the sensitive one to the curvature effect rather than the former. Through the analysis of key parameters, the established model is capable of helping to strengthen the understanding of material removal mechanisms for FBET polishing with the consideration of curvature effect, addressing those cannot be interpreted by the classical Preston equation previously, which is meaningful for precision control of material removal during polishing of OFS.