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.
Highlights
With the development of CAD/CAM technology, traditional linear and circular interpolation cannot meet the requirements of modern CNC machining in grinding apparatus, aviation and other fields [1]–[4]
The spline curve is a presentation of the parametric toolpath, which is usually determined by a group of control points
A feedrate feedback interpolation algorithm based on Steffensen iterative acceleration is presented
Summary
With the development of CAD/CAM technology, traditional linear and circular interpolation cannot meet the requirements of modern CNC machining in grinding apparatus, aviation and other fields [1]–[4]. Huang [9] and Koren [10] made use of the first and second order time-based Taylor expansion (TTE) to confirm the parametric value of the approximate curve under constant feedrate, but the truncation error still exists It is the simple form of this method that satisfies normal requirements, so TTE method could be frequently chosen. An iterative feedback interpolation algorithm was proposed to eliminate the feedrate fluctuation caused by the nonlinear relationship between curve parameters and arc length in the interpolation process.
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