Complete swept volume generation, Part I: Swept volume of a piecewise C1-continuous cutter at five-axis milling via Gauss map

In this paper, we present a methodology to generate swept volume of prevailing cutting tools undergoing multi-axis motion and it is proved to be robust and amenable for practical purposes with the help of a series of tests. The exact and complete SV, which is closed from the tool bottom to the top of the shaft, is generated by stitching up envelope profiles calculated by Gauss map.The novel approach finds the swept volume boundary for five-axis milling by extending the basic idea behind Gauss map. It takes piecewise C1-continuous tool shape into account. At first, the tool shape is transformed from Euclidean space into Tool map (T-Map) on the unit sphere and the velocity vector of a cutter is transformed into Contact map (C-Map) using Gauss map. Then, closed intersection curve is found between T-Map and C-Map on the Gaussian sphere. At last, the inverse Gauss map is exploited to get envelope profile in Euclidean space from the closed curve in the range. To demonstrate its validity, a cutting simulation kernel for five-axis machining has been implemented and applied to mold and die machining.

Research highlights► Complete and exact swept volume of a milling tool is generated in geometrically efficient manner. ► The envelope profile portions of the sharp edges of the milling tool is well identified. ► An intuitive and comprehensive cutting behavior is described by C-Map and T-Map. ► The proposed method is proved to be robust and amenable for the practical purpose of NC verification.