Tool Contact Maps by Rectangular Grid Decomposition

Abstract

This paper is intended to contribute to ongoing research [1–3] in geometric modeling of the virtual machining. In geometric modeling the tool paths are verified by performing the machining simulations and also the cutter workpiece engagements (CWEs) are extracted. CWE geometry is a key input to force calculations and feed rate scheduling in milling operations. Finding these engagements is challenging due to the complicated and changing intersection geometry between the cutter and the in-process workpiece. This paper presents a discrete model based methodology for extracting CWEs generated during a multi axis machining of free form surfaces using a range of different types of milling tools. In this method the in-process workpiece is represented by a set of z-axis aligned rectangular grids. Each grid is made up of four planes, with their normals aligned with respect to the x and y-axis of the Cartesian coordinate system. In developing the methodology the parametric representations of the automatically programmed tool (APT)-type milling cutters are used. The milling tool surfaces are decomposed into circles. During the material removal process only some portions of those circles which are called the engagement arcs may contact the in-process workpiece. To find the geometric limits of those arcs the concept of the feasible contact surface is utilized. The CWE extraction simulation is performed through intersecting those arcs with the planes of each rectangular grid. Thus the intersection calculations reduce to circle/plane intersections which can be performed analytically for the geometry found on milling cutters. To be used in the force model, the CWE boundaries are mapped from Euclidean 3D space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. Then using a sort algorithm the neighboring engagements in the same arc level are combined.