Ball-end milling path planning on multiply connected freeform surfaces is pivotal for high-quality and efficient machining of components in automotive and aerospace manufacturing. Although scalar-field-based optimization provides a unified framework for multi-objective toolpath generation, maintaining boundary conformity while eliminating zero-gradient singularities that cause iso-curve branching or termination and disrupt toolpath continuity remains challenging on multiply connected surfaces. We propose an efficient strategy to robustly enforce these constraints throughout optimization. Conformal slit mapping is employed to construct a feasible, singularity-free initial scalar field. The optimization is reformulated as a topology-preserving mesh deformation governed by boundary-synchronous updates, enabling globally optimized spacing, scallop-height uniformity, and smooth trajectory transitions. Consequently, the toolpaths are continuous, boundary-conforming, and free of self-intersections. Milling experiments demonstrate that, compared with a state-of-the-art conformal slit mapping-based method, the proposed approach increases machining efficiency by 14.24%, improves scallop-height uniformity by 5.70%, and reduces milling impact-induced vibrations by over 10%. The strategy offers broad applicability in high-performance machining scenarios.

翻译：多连通自由曲面上的球头铣刀路径规划对汽车与航空航天零部件的高质量高效加工至关重要。尽管基于标量场的优化为多目标刀具路径生成提供了统一框架，但在多连通曲面上，如何在消除导致等值线分叉、终止及路径不连续的零梯度奇异点的同时保持边界适配性仍具挑战。本文提出一种高效策略，可在优化过程中稳健地强制执行这些约束。通过共形狭缝映射构建可行且无奇异的初始标量场，将优化问题重构为受边界同步更新控制的拓扑保持网格变形，从而实现全局优化的刀轨间距、残余高度均匀性及平滑轨迹过渡。由此生成的刀具路径具有连续性、边界适配性且无自交。铣削实验表明，与基于共形狭缝映射的最新方法相比，所提方法加工效率提升14.24%，残余高度均匀性改善5.70%，铣削冲击振动降低逾10%。该策略在高性能加工场景中具有广泛适用性。