1998/07/01 by RidaT. Farouki, Jairam Manjunathaiah, David Nicholas +2 · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #Algorithm #Computation #Computer science #Constant (computer programming) #Constant curvature #Control theory (sociology) #Curvature #Function (biology) #Geometry #Hodograph #Manufacturing Process and Optimization #Mathematical analysis #Mathematics #Regular polygon
paper · pdf · doi:10.1016/s0010-4485(98)00020-7
openalex publication_date 1998/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.