State Key L a b o ra to ry o t M e cha n ical System and V ib ra tio n , S c h o o l o f M e cha n ical E n g in e erin g, S h a ng h ai Jia o T o n g U nive rsity, S h a ng h ai 2 0 0 2 4 0 , C hin a e -m a il: lzl@ s jtu .e d u .c n L i-M in Z h u 1 State Key L a b o ra to ry o f M e cha n ical System and V ib ra tio n , S c h o o l o f M e cha n ical E n g in e erin g, S h a ng h ai Jia o T o n g U nive rsity, S h a ng h ai 2 0 0 2 4 0 , C hin a e -m a il: z h u lm @ s jtu .e d u .c n Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank M illing Considering Cutter Runout Cutter runout is a common and inevitable phenomenon impacting the geometry accuracy in the milling process. However, most o f the works on tool path planning neglect the cut ter runout effect. In this paper, a new approach is presented to integrate the cutter runout effect into envelope surface modeling and tool path optimization fo r five-axis flank mill ing with a conical cutter. Based on the geometry model o f cutter runout which consists o f cutter axis and cutter tilt, an analytic expression o f cutter edge combined with four run out parameters is derived. Then the envelope surface formed by each cutter edge is con structed using the envelope theory o f 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 o f 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 dis tance function. On the basis o f the differential property o f the distance function, tool path optimization considering cutter runout is modeled as a mixed-integer linear program ming (MILP) problem, which can be solved by the branch-and-bound method. Finally, numerical examples are given to confirm the validity and efficiency o f the proposed approach. The results show that the geometry errors induced by runout can be reduced significantly using the proposed method.
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