Tam Hon-Yuen, Cheng Haobo, Dong Zhichao
Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong, China.
Appl Opt. 2013 May 20;52(15):3624-36. doi: 10.1364/AO.52.003624.
Polishing can be more uniform if the polishing path provides uniform coverage of the surface. It is known that Peano paths can provide uniform coverage of planar surfaces. Peano paths also contain short path segments and turns: (1) all path segments have the same length, (2) path segments are mutually orthogonal at the turns, and (3) path segments and turns are uniformity distributed over the domain surface. These make Peano paths an attractive candidate among polishing tool paths because they enhance multidirectional approaches of the tool to each surface location. A method for constructing Peano paths for uniform coverage of aspherical surfaces is proposed in this paper. When mapped to the aspherical surface, the path also contains short path segments and turns, and the above attributes are approximately preserved. Attention is paid so that the path segments are still well distributed near the vertex of the surface. The proposed tool path was used in the polishing of a number of parabolic BK7 specimens using magnetorheological finishing (MRF) and pitch with cerium oxide. The results were rather good for optical lenses and confirm that a Peano-like path was useful for polishing, for MRF, and for pitch polishing. In the latter case, the surface roughness achieved was 0.91 nm according to WYKO measurement.
如果抛光路径能均匀覆盖表面，那么抛光就能更均匀。众所周知，皮亚诺路径可以均匀覆盖平面。皮亚诺路径还包含短路径段和转弯：（1）所有路径段长度相同；（2）路径段在转弯处相互正交；（3）路径段和转弯在整个区域表面均匀分布。这些使得皮亚诺路径成为抛光刀具路径中一个有吸引力的选择，因为它们增强了刀具对每个表面位置的多方向加工。本文提出了一种构建用于均匀覆盖非球面的皮亚诺路径的方法。当映射到非球面上时，该路径同样包含短路径段和转弯，并且上述特性大致得以保留。需要注意的是，路径段在表面顶点附近仍能良好分布。所提出的刀具路径被用于使用磁流变抛光（MRF）和氧化铈抛光沥青对多个抛物面BK7试样进行抛光。对于光学镜片，结果相当不错，这证实了类似皮亚诺的路径对于抛光、MRF和沥青抛光是有用的。在后一种情况下，根据WYKO测量，所达到的表面粗糙度为0.91纳米。
