Optimized dual NURBS curve interpolation for high-accuracy five-axis CNC path planning

As the demand for high-precision and high-efficiency machining increases in modern industrial manufacturing, five-axis CNC systems have become the primary solution for complex surface processing. This study presents a dual NURBS curve interpolation algorithm specifically designed for five-axis synchronized motion. Unlike traditional linear and circular interpolation methods, the dual NURBS interpolation utilizes a master-slave curve strategy to achieve synchronous control of tool position and orientation. In the proposed method, the master curve determines the tool path, while the slave curve adjusts the tool's posture in real-time. Simulation experiments were performed on three representative surface models: Spiral Surface, Blade Surface, and Freeform Surface. The results indicate that the maximum chord error of the dual NURBS method on the Spiral Surface is only 0.0006 mm, with an average error of 0.0004 mm, significantly lower than traditional OC methods (0.01876 mm) and equal chord length interpolation (0.01532 mm). Furthermore, error analysis demonstrated that the dual NURBS method reduced the chord error over 68.6% compared to conventional methods and achieved more than a 16% improvement in processing efficiency. In addition, the dual NURBS algorithm showed smooth velocity planning, with speed fluctuation controlled within 10 mm/s, significantly better than traditional OC and equal chord length methods. These improvements not only enhance path smoothness but also significantly reduce tool vibration and surface defects during machining. The findings verify the effectiveness of the dual NURBS interpolation algorithm in improving machining accuracy and efficiency for complex five-axis CNC operations, offering a robust solution for high-precision surface processing.