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：在多连通自由曲面上进行球头铣削路径规划，对于汽车和航空航天制造中零部件的高质量、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一个统一框架，但在多连通曲面上，如何在消除导致等值线分支或终止、破坏刀具路径连续性的零梯度奇异点的同时，保持边界贴合性，仍然具有挑战性。我们提出了一种高效策略，可在整个优化过程中稳健地强制执行这些约束。采用共形缝隙映射来构造一个可行的、无奇异性的初始标量场。该优化被重新表述为由边界同步更新控制的保拓扑网格变形，从而实现了全局优化的间距、残留高度均匀性以及平滑的轨迹过渡。因此，所生成的刀具路径是连续的、边界贴合的且无自相交。铣削实验表明，与最先进的基于共形缝隙映射的方法相比，所提方法将加工效率提高了14.24%，将残留高度均匀性改善了5.70%，并将铣削冲击引起的振动降低了10%以上。该策略在高性能加工场景中具有广泛的适用性。