Modeling and prediction of generated local surface profile for ultrasonic vibration-assisted polishing of optical glass BK7

Abstract

• Preston coefficient is affected by ultrasonic amplitude. • Contact pressure is affected by ultrasonic amplitude. • Large ultrasonic amplitude helps to improve the polishing ability. • Local surface profile can be well predicted by the proposed calculation model. • Prediction of surface profile is a basis for free-form surface polishing of UVAP. With the rapid progress of science and technology, many applications of hard and brittle materials require advanced and suitable machining-techniques. One technique in particular, ultrasonic vibration-assisted polishing (UVAP), has been studied intensively by researchers worldwide. These studies indicate that UVAP has the capability to improve the surface quality as well as the machining efficiency. However, few studies focus on the deterministic material-removal of UVAP. The difference between generated and theoretical surface profiles determines the surface accuracy. Therefore, this paper focuses on predicting the generated local surface profile and providing a theoretical basis to reduce this error by controlling the polishing parameters. In addition to the axial ultrasonic vibration of polishing tool, ultrasonic atomization was adopted to provide uniformly distributed polishing slurry. To ensure sufficient surface-accuracy, it is necessary to predict the generated surface profile for a fixed spot as a basis research. This means, to enable accurate predictions the following improvements are realized: (i) A novel model for the elastic spherical contact-deformation of the polishing tool is used to calculate both the polishing force and contact radius. It takes into account the nonlinear elasticity of the polishing tool and the lateral extension of the contact area, which makes it more consistent with the actual deformation. (ii) A novel model for the material-removal distribution function for UVAP is proposed, based on the Preston equation. It considers the periodic changes of polishing force and contact radius caused by ultrasonic vibration. (iii) A series of fixed-spot polishing experiments on BK7 glass are carried out to verify the proposed models. The results show that the Preston coefficient is affected by axial ultrasonic amplitude, and large ultrasonic amplitude improves the polishing ability. In addition, the generated local surface profile, the maximum contact radius, as well as the material-removal depth and material-removal rate (MRR) can be predicted well. The new models not only provide a possibility to realize deterministic material removal but also enables in-depth-understanding of UVAP. It also represents a basic theoretical foundation for future, flat or free-form surface-polishing.