CNC tool path in terms of B-spline curves

Abstract

We present an accurate and efficient method to generate a CNC tool path for a smooth free-form surface in terms of planar cubic B-spline curves which will be fed into a free-form curve interpolator. We assume the use of a three-axis CNC machine tool with a ball end-mill cutter. We first interpolate break points, which are generated by computing the offset surface– driving plane intersection curve reflecting the curvature, by a planar cubic B-spline curve. We then evaluate the maximum scallop height along a scallop curve by computing the stationary points of the distance function between the scallop curve and the design surface. Furthermore, we compute the maximum pick feed such that the maximum scallop height along a scallop curve coincides with the prescribed tolerance. Illustrative examples show the substantial improvements this method achieves over conventional methods where the tool path consists of linear or circular paths.