B-Spline-Based Corner Smoothing Method to Decrease the Maximum Curvature of the Transition Curve

Abstract

Toolpath represented by linear segments leads to tangency discontinuity between blocks, which results in fluctuation of feedrate and reduction of machining efficiency and quality. To eliminate these unwanted external factors, optimal corner smoothing operation is essential for computerized numerical control systems to achieve a smooth toolpath. This work proposes a corner smoothing approach by generating a B-spline transition curve with seven control points. By adjusting the position of the control points, the resulting transition curve is not limited to smooth the corner in the convex side of the corner, but shuttles back and forth between the convex and concave sides to decrease the maximum curvature, while respecting the given error tolerance. The approximation errors in convex and concave sides can be analytically calculated. Experimental results demonstrate the effectiveness of the proposed method on machining efficiency improvement.