Optimal Archimedes' spiral interpolation for cutter path generation in NC machining of noncircular contours

In NC machining of noncircular contours with a rotation table, the cutter is fed along a straight line intersecting perpendicularly the rotation axis of the work piece. In this situation, the cutter path usually consists of a series of Archimedes' spiral segments. This paper proposes an optimal interpolation approach of Archimedes' spiral segments to generate the cutter path for machining noncircular contours. The number of segments for the cutter path resulted from the approach is the fewest under the condition that the interpolation accuracy completely satisfies the specified limit value. It has been also evidenced that the profile error of the machined contours corresponding to the cutter path is perfectly controlled within the specified interpolation accuracy limit. The effectiveness of the proposed approach has been sufficiently confirmed by applying it to machining a disc cam and an algebraic spiral type of scroll wrap.