Title: Conformal Slit Mapping Based Spiral Tool Trajectory Planning for Ball-end Milling on Complex Freeform Surfaces Show Chinese title

Title: 基于共形裂纹映射的螺旋刀具轨迹规划用于复杂自由曲面的球头铣削

Abstract: This study presents a spiral-based complete coverage strategy for ball-end milling on freeform surfaces, utilizing conformal slit mapping to generate milling trajectories that are more compact, smoother, and evenly distributed when machining 2D cavities with islands. This approach, an upgrade from traditional methods, extends the original algorithm to effectively address 3D perforated surface milling. Unlike conventional algorithms, the method embeds a continuous spiral trajectory within perforated surfaces without requiring cellular decomposition or additional boundaries. The proposed method addresses three primary challenges, including modifying conformal slit mapping for mesh surfaces, maintaining uniform scallop height between adjacent spiral trajectories, and optimizing the mapped origin point to ensure uniform scallop height distribution. To overcome these challenges, surface flattening techniques are incorporated into the original approach to accommodate mesh surfaces effectively. Tool path spacing is then optimized using a binary search strategy to regulate scallop height. A functional energy metric associated with scallop height uniformity is introduced for rapid evaluation of points mapped to the origin, with the minimum functional energy determined through perturbation techniques. The optimal placement of this point is identified using a modified gradient descent approach applied to the energy function. Validation on intricate surfaces, including low-quality and high-genus meshes, verifies the robustness of the algorithm. Surface milling experiments comparing this method with conventional techniques indicate a 15.63% improvement in scallop height uniformity while reducing machining time, average spindle impact, and spindle impact variance by up to 7.36%, 27.79%, and 55.98%, respectively. Show Chinese abstract

Abstract: 本文提出了一种基于螺旋的完整覆盖策略，用于自由曲面上的球头铣削，利用保形裂纹映射生成更紧凑、更平滑且分布均匀的铣削轨迹，以加工带有岛屿的二维腔体。 该方法是对传统方法的升级，将原始算法扩展以有效解决三维穿孔表面的铣削问题。 与传统算法不同，该方法在穿孔表面上嵌入连续的螺旋轨迹，而无需进行单元分解或额外的边界。 所提出的方案解决了三个主要挑战，包括修改适用于网格表面的保形裂纹映射、保持相邻螺旋轨迹之间的均匀波峰高度，以及优化映射的起始点以确保波峰高度分布的均匀性。 为克服这些挑战，将表面展平技术引入原始方法中，以有效地适应网格表面。 然后使用二分搜索策略优化刀具路径间距以调节波峰高度。 引入了一个与波峰高度均匀性相关的功能性能量度量，用于快速评估映射到起始点的点，通过扰动技术确定最小功能能量。 使用修改后的梯度下降法应用于能量函数来识别该点的最佳放置位置。 在复杂表面（包括低质量和高亏格的网格）上的验证测试验证了算法的鲁棒性。 与传统技术相比的表面铣削实验表明，波峰高度均匀性提高了15.63%，同时减少了高达7.36%的加工时间、27.79%的主轴冲击和55.98%的主轴冲击方差。