Abstract: Aiming to the problem of complex tool axis trajectory planning for flank milling non-developable ruled surface with conical milling tools, an intuitive and simple tool axis trajectory generation method is presented. According to the properties of conical surface, the normal mapping curve is defined, i.e. the set of points which are the normal projection of all points of tool axis on the design curved surface, so that the problem of tool envelope surface approximating to design surface, is convert into the least squares approximation problem of normal mapping curve to characteristic curve for every tool position, and the generation method of ideal feature line of single tool position before the formation of tool envelope surface is given. Using the two-offsetting method the initial tool position is generated. Then based on this, the tool axis pose can be described by a function of three rotational and three translational motion parameters, consequently, a non-dominant function between single tool position optimization condition and six motion parameters is built. In the solving process, the experimental design method of Latin hypercube is used, and through analyzing and optimizing the influence factors of calculation, the optimal tool position is obtained, and then the optimized tool axis trajectory surface is obtained. The actual example calculation showed that the envelope error of optimized tool axis is reduced significantly, and the calculation results are stable. This method provides the theoretical basis for flank milling non-developable ruled surface with conical tools.

Key words: conical tools, feature line, flank milling, non-developable ruled surface, tool axis trajectory planning