A composite B-spline method for cutter path generation on free-form surfaces

Abstract

This paper presents a composite B-spline method for cutter path generation on free-form surfaces on a point-by-point basis, with appropriate radial offset and interference checking along the cutter path. It is aimed at developing a more efficient and accurate free-form surface machining method for an open-architecture CNC system with B-spline interpolation capability. In this method, the cutter paths over the free-form surface are composed of a sequence of B-spline segments. The length of each spline segment is determined by the desired deviation, within some given tolerance, from the curve of the surface over which the cutter path is to be generated. If the spline segment does not satisfy the specified dimensional tolerance, control points of the spline segment are adjusted to modify the curve shape according to the required accuracy. As a result, the deviation between the actual cutter paths and the desired surface curves will always fall within the allowable tolerance. In addition, by adjusting the position of the control points, the adjacent spline segments are made at least C1 geometrically continuous. The distance between adjacent cutter paths in the side step direction is determined by checking the scallop height between them. To make the cutting process more efficient, a modified adaptive iso-parametric curve generation approach is employed. The resulting cutter paths are more compact and accurate compared with those from commonly used cutter path generation techniques.