多重連結自由曲面における境界適合スパイラル工具経路のための位相保存スカラー場最適化

原文アブストラクト

Multiply connected freeform surface features are widely encountered in industrial components, where toolpath generation often suffers from discontinuities, sharp turns, non-uniform scallop heights, and incomplete boundary coverage. This paper proposes a scalar-field variational optimization method for milling that produces continuous, boundary-conforming, and non-self-intersecting toolpaths with smoother transitions, more uniform spacing, and reduced redundant path length. A feasible singularity-free initial scalar field with boundary-conforming iso-level sets is first constructed via conformal slit mapping. The optimization is then reformulated as a topology-preserving mesh deformation process governed by boundary-synchronous updates, whereby the continuity, boundary-conformity, and non-self-intersection requirements of the toolpath are converted into mesh-shape constraints maintained throughout the iterative optimization. As a result, the proposed method achieves globally optimized path spacing and improved scallop-height uniformity while preserving trajectory smoothness. Milling experiments show that, compared with a state-of-the-art conformal slit mapping-based method, the proposed approach improves machining efficiency by 14.24%, enhances scallop-height uniformity by 5.70%, and reduces milling impact-induced vibrations by over 10%. The proposed strategy provides an effective solution for high-performance machining of complex multiply connected freeform components.