The feedrate scheduling of NURBS interpolator for CNC machine tools

This paper proposes an off-line feedrate scheduling method of CNC machines constrained by chord tolerance, acceleration and jerk limitations. The off-line process for curve scanning and feedrate scheduling is realized as a pre-processor, which releases the computational burden in real-time task. The proposed method first scans a non-uniform rational B-spline (NURBS) curve and finds out the crucial points with large curvature (named as critical point) or G⁰ continuity (named as breakpoint). Then, the NURBS curve is divided into several NURBS sub-curves using curve splitting method which guarantees the convergence of predictor–corrector interpolation (PCI) algorithm. The suitable feedrate at critical point is adjusted according to the limits of chord error, centripetal acceleration and jerk, and at breakpoint is adjusted based on the formulation of velocity variation. The feedrate profile corresponding to each NURBS block is constructed according to the block length and the given limits of acceleration and jerk. In addition, feedrate compensation method for short NURBS blocks is performed to make the jerk-limited feedrate profile more continuous and precise. Because the feedrate profile is established in off-line, the calculation of NURBS interpolation is extremely efficient for CNC high-speed machining. Finally, simulations and experiments with two free-form NURBS curves are conducted to verify the feasibility and applicability of the proposed method.