Jerk-Continuous Feedrate Optimization Method for NURBS Interpolation

Abstract

Feedrate scheduling is one of the most critical technologies in CNC machining, requiring a reasonable balance between efficiency and quality. This paper proposes a jerk-continuous feedrate smoothing (JCFS) method to generate a low-vibration and smooth feedrate profile for non-uniform rational B-spline (NURBS) interpolation. Firstly, the segmentation concept is introduced to subdivide the entire trajectory into segments to accommodate curvature changes of the NURBS curve, accelerating the acceleration/deceleration process. Secondly, a length threshold-based curve segment classification method is proposed to overcome the complexity of the traditional acceleration and deceleration algorithms. The curve segments are divided into long, medium, and short types, and the length threshold calculation model is derived. Next, to avoid computational complexity for engineering applications, a model is established for the first time to calculate the actual maximum feedrate for different types of segments. Finally, the horizontal-8-shaped and butterfly-shaped NURBS curves are simulated and analyzed. The simulation results indicate that the machining quality is steadily improved while several key indicators remain within the given tolerances. Compared with the traditional method, the proposed method reduces the computational and interpolation time by 17.2% and 22.8%, respectively, demonstrating the feasibility and effectiveness of the method.