Feed Rate-Adaptive Predictive PH Interpolation for Real-Time NURBS Toolpath Execution in High-Speed CNC Machining

Abstract

This study presents a novel feed rate-adaptive predictive interpolation algorithm that combines Pythagorean-hodograph (PH) curves with non-uniform rational b-splines (NURBS) to improve real-time toolpath generation in high-speed CNC machining. Unlike traditional NURBS interpolators, which are prone to feed rate fluctuations and poor curvature handling, the proposed method incorporates a curvature-aware predictive module that dynamically adjusts the feed rate based on local geometry and system dynamics. Key innovations include sharp corner detection, PH-based smoothing, and jerk-limited feed rate profiling. Simulation and experimental results show that the proposed algorithm significantly reduces path-following errors (on average by more than 60 % RMS error reduction) while ensuring smoother, bounded-acceleration trajectories. The algorithm consistently maintains geometric accuracy across different toolpath orientations, making it a robust solution for precision manufacturing tasks that require both real-time responsiveness and high accuracy.