An NC system that machines a curved shape at fixed depth of cut experiences time-varying cutting forces due to the 'curvature effect' - the material removal rate is higher than nominal in concave regions, and lower in convex regions. A curvature-dependent feedrate function that automatically compensates for this effect is formulated, and it is shown that, for Pythagorean-hodograph (PH) curves, the periodic real time computation of reference points in accordance with this function can be analytically reduced to a sequence of root-finding problems for simple monotone functions. Empirical results from an implementation of this variable-feedrate interpolators on an open-architecture CNC milling machine are presented and compared with results from fixed-feedrate interpolators. The curvature-compensated feedrate scheme has important potential applications in ensuring part accuracy and in optimizing part programs consistent with a prescribed accuracy. © 1998 Elsevier Science Ltd. All rights reserved.

Farouki, R.T.Manjunathaiah, J.Nicholas, D.Yuan, G.-F.Jee, S.2026-02-05Variable-fCAD Computer Aided Design, 1998, 30, 8, pp. 631-640104485https://doi.org/10.1016/S0010-4485(98)00020-7https://idr.nitk.ac.in/handle/123456789/280471998CNC interpolatorsCurvaturesCutting forceFeedrateMachining accuracyOffset curvesOsculating circlePythagorean hodographsAn NC system that machines a curved shape at fixed depth of cut experiences time-varying cutting forces due to the 'curvature effect' - the material removal rate is higher than nominal in concave regions, and lower in convex regions. A curvature-dependent feedrate function that automatically compensates for this effect is formulated, and it is shown that, for Pythagorean-hodograph (PH) curves, the periodic real time computation of reference points in accordance with this function can be analytically reduced to a sequence of root-finding problems for simple monotone functions. Empirical results from an implementation of this variable-feedrate interpolators on an open-architecture CNC milling machine are presented and compared with results from fixed-feedrate interpolators. The curvature-compensated feedrate scheme has important potential applications in ensuring part accuracy and in optimizing part programs consistent with a prescribed accuracy. © 1998 Elsevier Science Ltd. All rights reserved.