Optical freeform surfaces on difficult-to-machine materials are used widely in a range of areas such as optical engineering, semiconductor and biomedical products. However, it is a challenge to achieve both a high surface quality and complex surface shape because of their tendency of being damaged in brittle fracture in the machining process. In this article, non-resonant three-dimensional elliptical vibration cutting method is proposed to obtain optical freeform surfaces of some difficult-to-machine materials, which is realised by making the diamond tool vibrate at a three-dimensional ellipse in the non-resonant manner. The elliptical motion parameters of this method can be taken active control under different machining conditions, which can make us get optimal cutting performance. Based on this new elliptical vibration cutting method, the algorithm of the tool path generation considering the tool arc radius compensation is proposed, which can avoid excess turning. The three-dimensional surface topography prediction model is established to verify the tool path. Simulation analysis on a typical optical freeform surface, toric surface, has shown that the tool path generation algorithm with the proposed elliptical vibration cutting method can envelope the toric surface, which has illustrated the validity of the proposed algorithm and technique. The tool path generation algorithm can be used to direct one to machine the optical freeform surface in the cutting experiments.
