On initialization of milling paths for 5-axis flank CNC machining of free-form surfaces with general milling tools

We propose a path-planning algorithm for 5-axis flank CNC machining with general tools of varying curvature. Our approach generalizes the initialization strategy introduced for conical tools Bo et al. (2017) to arbitrary milling tools. Given a free-form (NURBS) surface and a rotational milling tool, we look for its motion in 3D to approximate the input reference surface within a given tolerance. We show that for a general shape of the milling tool, there exist locally and generically four 3D directions in which the point-surface distance follows the shape of the tool up to second order. These directions form a 3D multi-valued vector field and its integration gives rise to a set of integral curves. Among these integral curves, we seek straight line segments that correspond to good initial positions of the axes of the milling tool. We validate our method against synthetic examples with known exact solutions and, on industrial datasets, we detect approximate solutions that meet fine machining tolerances. We also demonstrate applicability of our method for efficient flank milling of convex regions that is not possible using traditional conical tools.