Smooth tool path generation for five-axis flank milling using multi-objective programming

Flank milling provides an efficient way to machine turbo-machinery components. However, the trajectory smoothness is seldom considered in the existing tool positioning strategies. In this paper, the tool trajectory is smoothed with a constraint on the resulting geometric error for five-axis flank milling. Unlike existing methods, this new method simultaneously considers the geometric smoothness and geometric deviation. The geometric smoothness is characterized by the strain energy of the cutter axis trajectory surface (S-A). The geometric deviation is measured by the signed maximal orthogonal distance between the design surface (S-D) and the tool envelope surface (S-E). For finish and semi-finish flank millings, smooth tool path optimizations are then modelled as multi-objective programming (MOP) problems. Given a prescribed geometric tolerance, the MOP problems are reformulated as constrained nonlinear programming (NLP) problems. Based on the Taylor expansions of the strain energy and the signed distance on the differential deformation of S-A, the constrained NLP problems are solved efficiently by the sequential quadratic programming (SQP) method. The existence of the optimal solutions is also discussed. The validity of the approach is confirmed by two numerical examples that generate five-axis flank milling tool paths with cylindrical and conical cutters, respectively.