Abstract: Optimum positioning of the conical tool for five-axis flank milling of non-developable ruled surface is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. Based on the observation that conical surface can be treated as a canal surface, i.e. the envelope surface of a one-parameter family of spheres, the swept envelope of a conical tool is represented as a sphere-swept surface. Then, an approach is presented to efficiently compute the signed distance between the swept surface and a point in space without constructing the swept surface itself, and the first order differential increment of the signed point-to-surface distance with respect to the differential deformation of the tool axis trajectory surface is also derived. By using the distance function, tool path optimizations for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework, and a sequential approximation algorithm along with a hierarchical algorithmic structure is developed to solve them. Numerical example is given to confirm the validity of the proposed approach.

Key words: Conical tool, Distance function, Flank milling, Surface approximation, Tool path optimization