A geometric approach of working tool diameter in 3-axis ball-end milling

When machining free-form surfaces with a ball-end milling tool, the working tool diameter is constantly changing even if the tool path is constant. The reason is that the surface normal of the milled surface is continuously changing along the milling path. When the working diameter is changing, the cutting parameters also change. This variation effects the roughness homogeneity of the smoothed surface. Simultaneous five-axis milling solves this problem; however, the price and complexity of this technology can be a problem for some industrial sectors. In the paper, the geometrical background of a solution to this problem is presented for a 3-axis ball-end milling process for machining a free form surface. The paper provides the deduction of the theory by the use of homogeneous transformations. The geometrical problem of the cutting process is treated locally where the general machined surface is substituted at every point by its tangent plane. From the result of the presented method, a milling strategy can be formulated for ball-end milling that minimises the change in the momentary working diameter thus providing a more constant cutting parameter.