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<p>In high-speed CNC milling, spiral tool path is widely employed to maintain stable cutting forces and constant cutting speeds, particularly for thin-walled, multi-connected components. Existing methods—predominantly developed for cavity machining—encounter difficulties in segmenting multi-connected curved regions, accurately controlling scallop height, and avoiding overcutting or undercutting. To address these issues, a spiral tool path generation method based on quasi-conformal theory (QCT) is developed for multi-connected surfaces. A poly-annulus quasi-conformal mapping projects each multi-connected surface onto a planar disk, which is then subdivided into processing sub-regions via the medial-axis skeleton. Within each sub-region, lofting lines guide the construction of spiral polylines constrained by a prescribed scallop-height limit; additional vertices are inserted at two-dimensional intersections to eliminate overcutting and undercutting. The planar polylines are mapped back to the workpiece by inverse QCT to produce 3D spiral curves, and collision-free tool orientations that satisfy kinematic and dynamic constraints are planned. Inverse kinematics transforms the tool path into machine coordinates, and B-spline interpolation produces higher-order continuous trajectories suitable for multi-axis controllers. Comparative experiments on five representative multi-connected surfaces demonstrate that the QCT-based method substantially reduces total path length and tool-lift frequency while improving scallop-height control and cutting-force stability.</p>

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Spiral tool path generation for high-speed milling of multi-connected surface based on quasi-conformal theory

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Xu-Lin Cai,
  • Wen-An Yang,
  • XueFeng Yang,
  • You-Peng You

摘要

In high-speed CNC milling, spiral tool path is widely employed to maintain stable cutting forces and constant cutting speeds, particularly for thin-walled, multi-connected components. Existing methods—predominantly developed for cavity machining—encounter difficulties in segmenting multi-connected curved regions, accurately controlling scallop height, and avoiding overcutting or undercutting. To address these issues, a spiral tool path generation method based on quasi-conformal theory (QCT) is developed for multi-connected surfaces. A poly-annulus quasi-conformal mapping projects each multi-connected surface onto a planar disk, which is then subdivided into processing sub-regions via the medial-axis skeleton. Within each sub-region, lofting lines guide the construction of spiral polylines constrained by a prescribed scallop-height limit; additional vertices are inserted at two-dimensional intersections to eliminate overcutting and undercutting. The planar polylines are mapped back to the workpiece by inverse QCT to produce 3D spiral curves, and collision-free tool orientations that satisfy kinematic and dynamic constraints are planned. Inverse kinematics transforms the tool path into machine coordinates, and B-spline interpolation produces higher-order continuous trajectories suitable for multi-axis controllers. Comparative experiments on five representative multi-connected surfaces demonstrate that the QCT-based method substantially reduces total path length and tool-lift frequency while improving scallop-height control and cutting-force stability.