Lamé Curve-based Spiral Tool Path Generation for Rough Milling

Abstract

Automatic tool path generation for milling has been a subject of research for decades. The primary challenge in this area lies in simultaneously satisfying both geometric and technological constraints. Although various methods have been developed for spiral trajectory generation to meet these strict criteria, the potential of Lamé curves (also known as superellipses) has remained unexplored. This paper aims to address this gap by introducing a new algorithm that parametrises Lamé curves and transforms them into spirals using polar coordinate functions. The novel method generates a continuous tool path that smoothly fills the region between two closed boundaries without interrupting the cutting process. The algorithm was validated through case studies involving various pocket-like and island-like geometries. For the comparative analysis, two widely used strategies were selected as benchmarks: the traditional contour-parallel strategy and the advanced adaptive milling strategy. The simulation and cutting experiments conducted to analyse cutter engagement, tool load, and machining time demonstrated that the Lamé-based spiral paths achieved 1–44% improvements in machining time and 3–17% reductions in peak cutting force. These improvements are attributed to the smooth path curvature and the stable cutter engagement along the path, which enables effective tool load control. Although the strategy has certain geometric limitations, the results indicate that Lamé-based spirals offer a promising alternative for improving productivity and tool life in rough milling.