Determining gouge-free ball-end mills for 3D surface machining from point cloud data

This paper presents an algorithm to automatically determine the optimal size of the ball-end milling tool used for the three-axis finish machining of free-form surfaces directly from discrete coordinate data points. The tool is considered optimal if it is of the largest possible diameter that can access every data point without causing an overcut situation or gouging the other data points. Two well-developed techniques in computational geometry, Voronoi diagram and Delaunay triangulation, are used to establish the geometric relationship among data points from which the information required to determine the optimal tool size is extracted. The result of Delaunay triangulation is a set of tetrahedrons, with the data points as vertices, which define a corresponding set of empty circum-spheres. Each data point is a vertex of several tetrahedrons and the largest of the corresponding circum-spheres represents a valid estimation of the optimal tool size at the point. Since the data points are only a sample of the original 3D surface, accuracy of the estimated tool size can be improved by using the approximated normal vector at the data point. The estimated tool size is evaluated by comparing it to its theoretical value. Extensive simulation tests show that a robust and accurate method of determining the optimal ball-end mill size has been developed.