Contour machining of free-form surfaces with real-time PH curve CNC interpolators

Abstract

Two strategies for contour milling of free-form surfaces, using real-time CNC interpolators for Pythagorean-hodograph (PH) curves, are described. The first method, applicable to convex surfaces, employs a flat-end mill and approximates the surface section curves by planar PH quintics. The second approach, which employs a ball-end mill, approximates the tool-center trajectory by quintic PH space curves, and can accommodate nonconvex surfaces by choosing a sufficiently small tool radius. Both schemes generate compact part programs, in which numerous short linear/circular G code motions are replaced by fewer analytic path segments, and eliminate the need for explicit offset curve or surface representations to compensate for the tool radius. The surface sectioning and PH curve approximation algorithms required by these methods are presented, with appropriate tolerance analyses, and preliminary results from machining experiments performed on an open-architecture 3-axis CNC mill are described.