Analytical Calculation of Cutter/Workpiece Engagements for Helical Hole Milling

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. Simulating the helical milling process requires Cutter/Workpiece Engagement (CWE) 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. For hole milling an additional complication comes from self-intersections that occur with the tool swept volume. This makes the generation of the instantaneous in-process workpiece needed for finding the CWE difficult. In this paper we present an analytical approach for finding the engagement geometry that utilizes the intersection curves between a cylinder representing a flat end mill and the helicoidal surface generated by the bottom of the tool as it feeds downwards along the helix. This technique can be integrated into a solid modeler based approach for machining simulation. It has the advantage of not require instantaneous updates of the workpiece as is typically the case in finding CWEs.