A CNC interpolation algorithm for boundary machining

This paper presents an efficient and accurate algorithm for machining boundaries formed at the intersection of two surfaces, an important manufacturing problem in CNC machining. The algorithm is developed using a locus tracing technique implemented on the basis of Danielson's step selection rules. A vertical ball-end milling cutter moves along the considered boundary, in contact with the two surfaces. The algorithm guides the center of the spherical end of the cutter, to maintain exact contact (within 1 step) along the entire path. A seamless formulation is used, allowing the contact points to move freely from the ball-end to the cutter periphery and vice-versa. The surfaces forming the boundary may be implicitly or parametrically defined. The reliability of the algorithm is demonstrated for both cases, by treating a complex boundary machining example. The boundary considered is formed by the intersecting quadratic surfaces of a sphere and an elliptic hyperboloid.