A spiral path generation method for achieving uniform material removal depth in aspheric surface polishing

The uniformity of material removal can affect the profile accuracy and surface quality of the polished curved surface. In the aspheric surface polishing, the Archimedes spiral path may result in poor consistency of material removal due to the changes of the surface curvature and the projection path interval. Firstly, under the constant process parameters, the material removal characteristic is inconsistent throughout the aspheric surface due to the curvature change characteristics of the surface. Secondly, the projection path interval variations on the surface may lead to the inconsistency of the adjacent paths overlapping. In this study, a new path called optimized Archimedes spiral path is proposed to ensure the uniform material removal depth in aspheric surface polishing. The path generation method takes into account the effect of the surface curvature variations on material removal and the effect of the path interval on the adjacent paths overlapping. First, the model of material removal profile is proposed based on the Preston equation. Subsequently, a path interval search algorithm based on material removal profile is developed to generate the optimized Archimedes spiral path. Lastly, a group of comparative experiments between the traditional path and the optimized path was conducted to verify the effectiveness of the proposed path generation method. Compared with the traditional path, the fluctuation of the material removal depth attributed to the optimized path is reduced by 49.7%. It indicates that the proposed path generation method is effective for improving the uniformity and consistency of material removal depth in aspheric surface polishing. Furthermore, the surface roughnesses of the two workpieces polished by the traditional path and optimized path are 0.9493 μm and 0.8893 μm, respectively. The reduction in surface roughness indicates that the uniform material removal depth can improve surface quality.