Geometric Modeling of Cutter/Workpiece Engagements for Helical Milling With Flat End Mills

Helical milling is a 3-axis machining operation where a cutting tool is feed along a helix. This operation is used in ramp-in and ramp-out moves when the cutting tool first engages the workpiece, for contouring and for hole machining. It is increasingly finding application as a means for roughing large amounts of material during high speed machining. Modeling the helical milling process requires cutter/workpiece engagements (CWEs) geometry in order to predict cutting forces. The calculation of these engagements is challenging due to the complicated and changing intersection geometry that occurs between the cutter and the in-process workpiece. In this paper we present a geometric modeling methodology for finding engagements during helical milling with flat end mills. A mapping technique has been developed that transforms a polyhedral model of the removal volume from Euclidean space to a parametric space defined by location along the tool path, engagement angle and the depth-of-cut. As a result, intersection operations are reduced to first order plane-plane intersections. This approach reduces the complexity of the cutter/workpiece intersections and also eliminates robustness problems found in standard polyhedral modeling and improves accuracy over the Z-buffer technique. The reported method has been implemented and tested using a combination of commercial applications. This paper highlights ongoing collaborative research into developing a Virtual Machining System.