Tool Path Planning Based On Conformal Parameterization For Free From Surface Polishing

Due to the complexity of polishing material removal mechanism, material removal depth and the polishing bandwidth changes with the principal curvature of work piece, the polishing feed rate, the polishing stress and so on. The changes results in uneven polishing material removal depth and low polishing efficiency. Conventional tool path planning methods are designed for curved surface milling, the processing parameters usually can’t adjust with polishing condition. The conventional tool path planning methods of free from surface polishing shows the limitations and shortcomings.According to the characteristics of free-form surface polishing process, a new polishing tool path planning method is proposed, based on conformal parameterization. The basic idea of the method is to map a complex triangle meshes to planar domain, tool path is generated on planar domain and reflected onto triangle meshes. In the process of tool path planning, the geometry information of triangle mesh surface is used to optimizing tool path parameters. Tool path suitable for freeform surface polishing is generated at last. The content of this paper includes :(1) Implemented angle based flattening(ABF) algorithms for triangular mesh surface parameterization. Based on the original algorithm, we introduces a topology data analysis stage to speed up the processing of triangular mesh surfaces. In addition, parameterize from boundary, which is adopted by this paper, may help reducing accumulation error.(2) Iso-parametric path and circular path was generated on triangular mesh surface. The practice of tool path planning on triangular mesh surfaces is roughly divided into stages as: the tool path planning on parametric plane, the inverse mapping of parametric path, the parameters optimization of tool path, cutter location generating and NC files output. During the inverse mapping, quick positioning of triangle chip is achieved by using neighbor point’s location.(3) Feed rate adaptive model and contact area superposition model was derived from material removal depth model, both of them are mathematic model. The former one is aiming at uniform material remove depth along a single path, while the later one turn to the uniformity of the whole surface.(4) Simulations and polishing experiments was conducted. The results indicate that both optimizing methods can improve surface quality of work piece, and keep material removal depth more uniform.