Improving surface quality and profile accuracy of five-axis machining via vector error coupling modeling and compensation

In five-axis machining, ensuring geometric accuracy while maximizing efficiency is a critical challenge. Conventional adaptive interpolation strategies often rely on a single local curvature threshold, which overlooks the complex interaction between Tool Center Point (TCP) path errors and Tool Axis Vector (TAV) orientation errors, leading to inefficient use of computationally expensive interpolation modes. To address this, this paper proposes a novel adaptive hybrid interpolation strategy based on a vector error coupling model. The strategy uses a "dual-check" decision logic: first, local curvature is measured to identify low-risk regions, where efficient linear interpolation (LERP) is applied. In high-curvature regions, a subsequent check predicts the total geometric error by summing the chord height and swing errors, capturing the additive or subtractive coupling effects linked to surface concavity or convexity. The system switches to high-precision Non-Uniform Rational B-Splines (NURBS) and spherical linear interpolation (SLERP) only if the coupling is additive, or if the predicted error in a subtractive mode exceeds the tolerance. This logic enables efficient LERP even in high-curvature regions as long as the total error remains within limits. Physical machining experiments on 6061 aluminum alloy validate the strategy, demonstrating a 91.7% reduction in maximum measured profile error (from 42.31 µm to 3.52 µm) and a 54% improvement in surface roughness. Concurrently, this strategy reduces computation time by nearly 40% compared to a full NURBS and SLERP approach, enhancing efficiency without compromising precision. This research offers a practical solution that significantly improves both surface integrity and processing efficiency in high-performance machining.