Shape optimization of generic rotary tool for five-axis flank milling

This paper presents an approach to optimize the shape of a general rotary cutter for five-axis flank milling of ruled and non-ruled surfaces. Based on the observation that tool shape optimization is equivalent to repositioning the control points of its B-spline meridian, the optimization of tool surface is reduced to that of a B-spline curve. Then, the meridian of rotary tool surface is represented by cubic B-spline curve, and it is used to obtain the analytic tool envelope surface. Subsequently, the flank milling error is measured by the distance between a point sampled from envelope surface and the design surface. On this basis, shape optimization of a general rotary cutter is formulated as an optimization problem from the perspective of approximating the tool envelope surface to the designed surface. Two examples are given to confirm the validity of the proposed method. The approach also applied to multi-pass five-axis flank milling.