CNC tool path in terms of B-spline curves

• Published in: Computer aided design Vol. 33; no. 4; pp. 307 - 319
• Main Authors: Lartigue, C., Thiebaut, F., Maekawa, T.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 02.04.2001; Elsevier Science
• Subjects: Applied sciences; CNC machine tool; Computer aided design; Computer science; control theory; systems; Exact sciences and technology; Free-form curve interpolator; Offset surface; Pick feed; Scallop height; Software; Tool path; Tool path; Offset surface; Pick feed; CNC machine tool; Free-form curve interpolator; Scallop height; B spline; Ball; Plane surface; Computer digital control; Ball mill; Free form; Milling cutter; Grinding(comminution); Free surface; Geometrical model; Spline approximation; Stationary condition; Cubic spline; Field emitter; Machine tool; Interpolator; Cutting tool; Curvature; Smooth surface; Computer aided design
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/S0010-4485(00)00090-7

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.