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Optimal Contour Orientations for Machining of Free-Form Surfaces (2001)
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BibTeX
@TECHREPORT{Smith01optimalcontour,
author = {Tait S. Smith and Rida T. Farouki and Mohammad al-Kandari},
title = {Optimal Contour Orientations for Machining of Free-Form Surfaces},
institution = {},
year = {2001}
}
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Abstract
In contour machining of free--form surfaces with a ball-end cutter, the tool contacts the surface along loci that correspond to sections by a set of parallel planes, with equidistant spacing \Delta and common normal N. For a given tool radius, the greatest scallop height between successive tool paths is suppressed by choosing an orientation for the contouring planes that will maximize, over the entire surface, the minimum angle between N and the local surface normal n. This optimization problem is solved by computing the (symmetrized) Gauss map for the surface, projecting it stereographically onto a plane, and using the medial axis transform for the complement of its image to identify the contouring orientation N that is "most distant" from the symmetrized Gauss map boundary. Invoking a Gauss map algorithm described elsewhere, the method is implemented in the context of bicubic B'ezier surfaces, with tool paths on the offset surface approximated by PH space curves that can be directly passed to real-time CNC interpolators. Empirical tests show significant improvements in the quality of machined surfaces over cases where the contouring orientation is chosen in an ad hoc manner.
Keyphrases
optimal contour orientation free-form surface contouring orientation machined surface parallel plane gauss map boundary ad hoc manner ezier surface gauss map algorithm significant improvement common normal real-time cnc interpolators entire surface successive tool path minimum angle local surface offset surface optimization problem contouring plane empirical test contour machining scallop height ph space curve free form surface ball-end cutter gauss map medial axis transform tool path tool radius
