Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

This article presents an approach to generate optimal couples of tool size and tool path for flank milling ruled surface with a conical cutter based on normal mapping, while at the same time keeping this couples within the given bounded constraints. For given initial pairs of taper tool and tool path, tool envelope surface is calculated. Then, the tool axis trajectory surface is related to envelope surface through the normal mapping. On this basis, the correspondence between the surface pair “design ruled surface–envelope surface–tool axis trajectory surface” is established, and it is used to obtain the signed flank milling error. By using this signed error, tool size and tool path optimization for flank milling is formulated as an optimization model subjected to bounds, and the trust-region-reflective least-squares method is used to solve this problem. Numerical example is given to confirm the validity of the proposed method.