Topology-Preserving Scalar Field Optimization for Boundary-Conforming Spiral Toolpaths on Multiply Connected Freeform Surfaces

2025-12-27

AI Summary

To address contour discontinuities and toolpath non-continuity arising from boundary misalignment and zero-gradient singularities in multi-connected freeform surface ball-end milling, this paper proposes a topology-preserving mesh deformation optimization framework. The method initializes a scalar field via conformal slit mapping and integrates boundary-synchronized updating with topology-constrained scalar field optimization to globally eliminate singularities while strictly enforcing boundary consistency. Subsequently, it generates self-intersection-free, continuous, and equidistant spiral toolpaths. Compared with state-of-the-art approaches, the proposed method improves machining efficiency by 14.24%, enhances scallop height uniformity by 5.70%, and reduces milling vibration by over 10%. It is the first method to simultaneously guarantee singularity elimination, precise boundary alignment, and toolpath continuity.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Learning with Manifolds

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
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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.

Problem

• Optimizes scalar fields for spiral toolpaths on complex surfaces
• Ensures boundary conformity and eliminates gradient singularities
• Improves machining efficiency and reduces vibrations in milling

Innovation

• Conformal slit mapping for singularity-free initial scalar field
• Topology-preserving mesh deformation with boundary-synchronous updates
• Optimized toolpaths for continuous, boundary-conforming, self-intersection-free milling