A moving knot sequence-based feedrate scheduling method of parametric interpolator for CNC machining with contour error and drive constraints

Abstract

The feedrate scheduling of parametric interpolator is one of the most important factors for a high-performance CNC machining, since it directly concerns the machining efficiency, machining accuracy, and cutting stability. In this paper, an adaptive feedrate scheduling method with limited contour error and axis jerks is proposed for free-form contour machining based on a strategy of moving knot sequence. The analytical relations between dynamic contour error and feedrate are first derived explicitly, and then the formula of maximum feedrate limit under confined contour error and axis jerks is yielded using a numerical decoupling scheme. Consequently, the maximum feedrate limit satisfying the above constraints is obtained for each predefined parametric segment of the tool path. Further, a bidirectional scanning algorithm is employed to globally adjust the local minimum feedrate values of all feedrate segments. On the basis of feedrate segments with local minimum value and maximum recommendation value, an exact knot sequence configuration method for the B-spline curve, which is used to express the initial feedrate profile, is proposed. Finally, a simple feedrate relaxation algorithm is performed to generate the final feedrate profile with entirely limited contour and axis jerks by utilizing a strategy of moving knot sequence. The proposed feedrate scheduling method is validated by several typical experimental tests, and the results demonstrate the effectiveness and reliability of the proposed method.