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

2025-04-08

AI Summary

This paper addresses the challenges of poor compactness, insufficient smoothness, and non-uniform scallop height in ball-end milling of complex freeform surfaces—particularly those featuring island cavities and through-hole regions. To this end, we propose a conformal slit mapping-based approach for generating globally continuous, coverage-complete spiral toolpaths. For the first time, conformal slit mapping is extended to unstructured mesh surfaces without requiring element decomposition or manual boundary specification, enabling seamless embedding of continuous spiral trajectories. We further introduce a novel scalar height uniformity energy function and optimize the mapping origin via a modified gradient descent algorithm. The method demonstrates robustness on low-quality, high-genus meshes: scallop height uniformity improves by 15.63%, machining time decreases by 7.36%, and spindle impact (mean and variance) reduces by 27.79% and 55.98%, respectively.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

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.

Problem

• Generates compact, smooth spiral tool paths for 3D freeform surfaces
• Ensures uniform scallop height between adjacent spiral trajectories
• Optimizes tool path origin for improved machining efficiency

Innovation

• Conformal slit mapping for spiral trajectories
• Binary search optimizes tool path spacing
• Gradient descent ensures scallop height uniformity