Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Abstract

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.