Improved positioning of cylindrical cutter for flank milling ruled surfaces

An optimized positioning procedure for flank milling ruled surfaces with cylindrical cutter is described in the paper. The tool axis trajectory surface is a ruled surface, which is generated by moving the tool axis. The proposition that the envelope surface of cylindrical cutter is the offset surface of tool axis trajectory surface is proved using kinematics approach. It is a complement of Bedi's [Bedi S, Mann S, Menzel C. Flank milling with flat end cutter. Comput Aided Des 2003; 35:293-300] analysis about the envelope surface of cylindrical cutter. Subsequently, we get another proposition that the deviation at extremum point between the designed surface and the envelope surface of cylindrical cutter is equal to that between the offset surface of designed surface and the tool axis trajectory surface. Based on this proposition, we propose three points offset (TPO) strategy to approximate the offset surface. In order to reduce errors further, a simple least square approximation scheme is established to make the tool axis trajectory surface fit the offset surface of designed surface as much as possible. By solving the linear system of equations, the tool axis trajectory surface is deformed. Simultaneously, the corresponding envelope surface is deformed to approximate the designed surface better. Two examples are given to verify the effectiveness of the developed 5-axis flank milling technique.