A multipoint tool positioning method for five-axis machining in the region of two intersecting tensor product Bézier surfaces

Abstract

The Drop and Spin Method (DSM), a multipoint tool positioning technique for five-axis machining of corners formed by the intersection of two bi-quadratic Bézier surfaces with a toroidal end mill is presented in this paper. In the DSM the tool is dropped onto one of the surfaces to identify the first point of contact. The second point of contact is determined on the second surface. These two points of contact ensure that the toroidal tool can be positioned in the closest possible proximity to the two surfaces along the common edge. The method results in a multitude of solutions; our algorithm chooses the solution that fits the tool snug to the edge, resulting in a radiused corner with a radius matching the tool insert radius. A classification method is used to identify the region of the radiused corner and an algorithm is presented to generate tool path for machining it. The DSM was tested and verified by graphical simulations in a custom OpenGL based graphical CNC simulator, a custom simulator developed in Maple graphics™, and test pieces machined using five-axis DSM toolpaths are presented.