Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank Milling Considering Cutter Runout

Abstract

Cutter runout is a common and inevitable phenomenon impacting the geometry accuracy in the milling process. However, most of the works on tool path planning neglect the cutter runout effect. In this paper, a new approach is presented to integrate the cutter runout effect into envelope surface modeling and tool path optimization for five-axis flank milling with a conical cutter. Based on the geometry model of cutter runout which consists of cutter axis and cutter tilt, an analytic expression of cutter edge combined with four runout parameters is derived. Then the envelope surface formed by each cutter edge is constructed using the envelope theory of sphere congruence. Due to the cutter runout effect, the envelope surfaces formed by the cutter edges are different from each other, and the valid envelope surface is the combination of these envelope surfaces which contribute to the final machined surface. To measure the machining errors, the geometry deviations between the valid envelope surface and the design surface are calculated with the distance function. On the basis of the differential property of the distance function, tool path optimization considering cutter runout is modeled as a mixed-integer linear programming (MILP) problem, which can be solved by the branch-and-bound method. Finally, numerical examples are given to confirm the validity and efficiency of the proposed approach. The results show that the geometry errors induced by runout can be reduced significantly using the proposed method.