Lexicographic optimization for real-time CNC feedrate planning with coupled orientation handling

Abstract

Optimization-based feedrate planning offers the potential to significantly increase machining productivity, but its industrial adoption has been limited by high computational cost and extensive tuning effort. This paper proposes a lexicographic feedrate optimization principle that adaptively balances finishing time and motion smoothness in a tuning-free manner. To further improve computational efficiency, the optimization scheme is extended by a sparsity-exploiting formulation combined with a sequential windowing strategy, enabling real-time capable execution. In addition, a unified toolpath parameterization scheme is incorporated to synchronously handle tool position and orientation within the optimization framework. For a five-axis freeform test contour, the proposed method takes 14 s on an Intel i5-3470 CPU to optimize feedrate profiles for long toolpaths with 100,000 constraint checkpoints, and 52 s on a high-performance AMD 9950X CPU to handle one million checkpoints. Compared to an industrial CNC kernel, the resulting finishing time is reduced by more than 15 %.