Five-axis flank machining of ruled surfaces with developable surface approximation

This paper presents a novel approach that generates tool path for five-axis flank milling. Two geometric algorithms are proposed for approximating a ruled surface with a series of developable patches. First, develop ability is obtained in certain regions through re-parameterization of the directrices of the ruled surface. The second algorithm places the control points of a Bezier developable patch using the five DOF´s for the patch design. Consecutive patches with geometric continuity are thus generated for the regions not covered in the first approximation. Due to the develop ability property, a tapered tool can move along the rulings of those patches without local tool interference. The machining deviation is determined by the surface approximation error. Thus this work transforms tool path planning in five-axis flank milling into a geometric modeling problem. It also demonstrates an effective application of developable surfaces in machining.