Arc length–angle space-based overlap-free asymmetric corner smoothing method for five-axis toolpaths

Abstract

Smoothing of linear toolpaths is critical to ensure quality and efficiency in computer numerical control (CNC) machining, particularly in 5-axis machining. However, existing corner smoothing methods often impose overly restrictive constraints on the transition lengths at corners, increasing curvature extremes and reducing the feedrate. To address this issue, this paper presents a five-axis toolpath asymmetric corner smoothing method based on the arc length–angle space. First, an arc length–angle space analysis method is introduced that can synchronize the tool tip position and tool orientation, decoupling the tool tip position and tool orientation smoothing processes. The tool tip position is smoothed with an asymmetric Pythagorean-hodograph (PH) curve in the workpiece coordinate system, whereas the tool orientation is smoothed with an asymmetric B-spline curve in the arc length–angle space. Then, to prevent overlap of adjacent transition curves, transition length adjustment strategies in the workpiece coordinate system and arc length–angle space are proposed to improve the corner feedrate within the set approximate error range. The simulation and machining experiment results show that, compared with existing asymmetric smoothing methods, the proposed method generates smoother toolpaths and achieves higher machining efficiency.