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Computer Science > Graphics

arXiv:2504.06310v1 (cs)
[Submitted on 8 Apr 2025 (this version) , latest version 13 Apr 2025 (v2) ]

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

Title: 基于共形裂隙映射的螺旋刀具轨迹规划方法在复杂自由曲面球头铣削中的应用

Authors:Changqing Shen, BingZhou Xu, Xiaojian Zhang, Sijie Yan, Han Ding
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.
Abstract: 本研究提出了一种基于螺旋的完整覆盖策略,用于自由曲面的球头铣削,利用保角狭缝映射生成更紧凑、更平滑且分布均匀的铣削轨迹,在加工带有岛屿的二维型腔时效果显著。 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,而无需进行细胞分解或额外边界。 所提出的方法解决了三个主要挑战,包括对网格表面进行保角狭缝映射的修改、保持相邻螺旋轨迹之间的均匀波浪高度,以及优化映射原点以确保波浪高度的均匀分布。 为克服这些挑战,将表面展开技术引入原始方法中,以有效适应网格表面。 随后使用二分查找策略优化刀具路径间距,以调节波浪高度。 引入与波浪高度均匀性相关的功能能量度量,用于快速评估映射到原点的点,通过扰动技术确定最小功能能量。 通过应用于能量函数的改进梯度下降方法确定该点的最佳位置。 在复杂表面上的验证,包括低质量及高亏格网格,验证了算法的鲁棒性。 与传统技术相比,表面铣削实验表明,波浪高度均匀性提高了15.63%,同时加工时间、平均主轴冲击和主轴冲击方差分别减少了最多7.36%、27.79%和55.98%。
Subjects: Graphics (cs.GR)
Cite as: arXiv:2504.06310 [cs.GR]
  (or arXiv:2504.06310v1 [cs.GR] for this version)
  https://doi.org/10.48550/arXiv.2504.06310
arXiv-issued DOI via DataCite

Submission history

From: Changqing Shen [view email]
[v1] Tue, 8 Apr 2025 02:12:13 UTC (4,102 KB)
[v2] Sun, 13 Apr 2025 02:29:56 UTC (3,090 KB)
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