High-cutting-accuracy NURBS curve interpolation with suppressing its feed acceleration fluctuation

Abstract

For the conventional NURBS curve interpolation, such as the one based on Taylor series expansion, it is difficult to synchronize the feed travel with the arc length for scheduled feedrate, resulting in serious acceleration fluctuation. Aiming at this issue, a high precision interpolation is proposed in this paper based on the preceding work. The curvature monotonicity of the NURBS curve was analyzed, and it was segmented according to its critical curvature point, the critical curvature value point and knots; meanwhile, the arc length of each subsegment was calculated under the predefined accuracy index. Then, the feedrate of each subsegment was scheduled with S-shape acceleration and deceleration profile, respectively. Afterward, on the basis of the scheduled feedrate datum, two cubic splines relating to arc length relative to time and parameter relative to arc length were constructed, respectively. In the real-time interpolation, the arc length corresponding to the actual feed step was calculated using the arc length relative to time splines, and then, the parameters corresponding to the arc length were obtained with parameter relative to arc length splines. Compared with Taylor series expansion interpolation, the results show that the proposed one significantly suppresses the acceleration fluctuation and improves the interpolation accuracy.