An Investigation on the Effect of Curvatures and Corners along Path

The unit removal function (URF) of special tools and tool paths are required for the modern sub-aperture deterministic polishing technologies. Paths may affect the amount of removed material because of the curvatures and corners existing on them. This study proposes a mathematic model along path for analyzing the effects of curvatures and corners on material removal during polishing. A numerical method was used to calculate the integration of segments covered by the URF. The length covered by the URF was also determined to predict the amount of material removed from a given location of a path. For the effects of curvatures, the maximum material removed is a distance of about 0.5 to the normalized radius of the URF. For the effects of corners, the peak removal is a distance between 0.5 and 1 to a corner. The Harris corner detection algorithm was used to estimate corner distribution. Aside from curvatures and corners, the space between adjacent paths is another key parameter that affects the amount of removed material. The combined effect of curvatures, corners, and spaces was comprehensively analyzed, and two typical paths -- spiral and raster paths -- were introduced in polishing experiments. The experimental results are consistent with the numerical prediction.