Optimal Interpolation of Archimedes's Spiral for NC Machining of Noncircular Contours

Abstract

In NC machining of noncircular contours, where cutter is fed along a straight line intersecting perpendicularly the roration axis of work piece, the cutter path usually consists of Archimedes's spiral segments. From machining precision and efficiency point of view, a desired cutter path should be composed of the fewer segments as possible under the condition of satisfying the specified interpolation error limitation. In this paper, an optimal interpolation principle of Archimedes's spiral for planar curves is presented and then a practical algorithm is constructed. The segment number of the cutter path resulted from the algorithm not only is the fewest but also the interpolation accuracy agrees with the specified value. It is also evidenced that the profile error of machined contour corresponding to the cutter path is perfectly controlled within the desired value, i. e. the specified interpolation error value, through detailed analyses. The interpolation results of using the presented algorithm for machining disc cam profile are compared with those obtained by Nishioka's methods (3) . The comparison results sufficiently confirm the validity of the algorithm developed by the authors.