An error-controlled G3-continuous oriented toolpath optimization algorithm and modified speed planning for five-axis machining

Abstract

Converting micro-segment toolpaths into high-order curves can significantly enhance the stability of five-axis CNC machining processes. However, conventional toolpath optimization approaches tend to simultaneously cause both undercutting and overcutting on the workpiece surfaces. Overcutting leads to irreversible morphological damage to the workpiece, thereby resulting in scrapped parts. Furthermore, the asynchronous variation between speed limit trends and speed planning curves undermines the effectiveness of conventional speed planning strategies in the machining of complex structural workpieces. To achieve effective control over machining stability and accuracy in five-axis CNC machining of complex workpieces, this work proposed an error-controllable G3-continuous oriented toolpath optimization algorithm. Based on the G3-continuous quartic symmetric Bezier curve, the toolpath was directionally offset according to the viewing-angle theorem. To ensure toolpath reachability, the Sobolev seminorm method and CVE method were subsequently employed to further optimize toolpath stability. Additionally, an enhanced speed planning strategy with an extra verification mechanism was designed. By incorporating adaptive quintic Gauss-Legendre quadrature and S-shaped speed model, a numerical model was established to characterize the relationships among curvature radius, arc length, and motion time. The activation conditions for the verification mechanism were derived using quartic non-uniform difference formulas. The secant method was applied to dynamically adjust local snap parameters of current toolpath segments for speed profile modulation. Five-axis machining experiments on dentures were conducted to validate the effectiveness of optimization algorithms. Experimental results demonstrated that, compared with traditional strategies, the modified toolpath optimization and speed look-ahead algorithms reduced machine tool vibration by 6.62% and 19.46%, respectively, while increasing dimensional compliance rates by 283.79% and 439.774%, respectively. This work successfully mitigates the challenges of overcutting, machine chatter, and accuracy drift in the five-axis CNC machining of complex structural components, thereby offering theoretical support for the development of high-precision and stable machining technologies for such components.