A Real-Time Feedrate Planning Method and Efficient Interpolator with Minimal Feedrate Fluctuation for Parametric Toolpath

Abstract

Different from linear and circular interpolation, feedrate fluctuation is inevitable for parametric toolpath, which is caused by the nonlinear relation between spline parameters and arc-length. In order to improve the accuracy and efficiency of real-time interpolation algorithm with minimal feedrate fluctuation, this thesis presents an iterative feedback interpolator to restrain the feedrate fluctuation. Estimator and corrector stage are two essential steps of our proposed method. The result of the first-order Taylor expansion is used for the iterative initial value in the estimator stage. Thereafter, based on Steffensen iterative accelerator method, the feedback of current feedrate and command feedrate will control to update parameters value repeatedly until feedrate fluctuation rate reaches the allowable value in the corrector stage. By means of the numerical method, it is proved that this iteration method can satisfy the high-order convergence and fast convergence theoretically. In the simulation, the third-degree B-spline curve is utilized to test the proposed method which is equipped with obvious effects on restraining the feedrate fluctuation and improving computation efficiency compared with four existing methods.