An investigation of the effects of the tool path on the removal of material in polishing

Uniformity of removal affects the finishing, and in some cases, the form accuracy of the polished surface. Tool paths are required for the automation of surface polishing. How the tool path may affect the removal of material in polishing is investigated in this paper. An analysis of how removal at a location due to polishing along adjacent path lines is presented. Four tool paths reportedly used in polishing are covered: scanning, bi-scanning, Hilbert and Peano paths. Removal in the inner surface as well as near the edges of surfaces is examined through simulations and analysis. The results show that, for the same path pitch, the peak-to-valley height (hpv) in the inner part of the removal map is the same for scanning, bi-scanning and Peano, while the texture of the removal maps can be quite different. The hpv values of Hilbert are more than double those of Peano, although both are fractal paths. Removal near the edges is particularly severe for scanning-type tool paths. The ratio of the edge peak height to the inner peak height is about 1.6 on average for scanning. The uniformity of removal further deteriorates as the ellipticity of the tool contact increases. When the contact direction is closely aligned with the path line direction, that ratio goes up to about 2.9 for contact ellipticity of 2. Polishing experiments have also been conducted. Both experiments and simulations point to the presence of edge effects in scanning paths and its absence in Peano paths. It is further proposed that, for more uniform removal of material: (1) changes in the tool path direction should be well distributed and (2) the direction of the path lines should be well balanced over the entire surface.