Model of Surface Topography in Ultrasonic-Assisted Rotary Vertical Grinding of BK7 Optical Glass Using a Spherical Grinding Head

The surface roughness generated during BK7 glass grinding critically influences subsequent polishing efficiency. While conventional rotary grinding employs constant process parameters, this approach fails to produce uniform surface quality. To address this limitation and further enhance surface characteristics, this study proposes ultrasonic-assisted rotary grinding (UARG) for BK7 processing and establishes a comprehensive model of the grinding process. It investigates surface topography by integrating the influences of ultrasonic vibration, grinding head topography, and brittle–ductile transition behavior. A new computational model for grinding head surface topography is established, with regard to the stochastic arrangement of the abrasives, size, and shape. The proposed model can predict the surface topography properly, which is subsequently validated through experiments conducted with varying grinding parameters. Furthermore, a control strategy aimed at achieving uniform surface roughness is presented, based on the validated model. The proposed theory provides an in-depth understanding of the rotary ultrasonic grinding mechanism and serves as a foundation for surface quality prediction.