Development of an improved CNC interpolator and performance evaluation in terms of chordal error and feedrate deviation

Abstract

The parametric interpolators of modern CNC machines use Taylor's series approximation to generate successive parameter values which, after substituting into the curve equation, gives the x, y, z coordinates of the tool positions. In order to achieve greater accuracy, higher order derivatives are required which complicates the calculation when the curve is represented by NURBS curve. This method calculates the chordal error on a given segment by estimating the curvature which neglects a fraction of the error. In order to avoid calculating higher derivatives and make the calculations easier the classical fourth-order Runge-Kutta (RK) method is proposed in this research, which only requires the first derivative to be calculated, but achieves the accuracy of Taylor's approximation with higher order terms. This paper also proposes the estimation of chordal error on the average value of the parameters at the end points of a given curve segment, which does not require calculation of curvature at every segment. Finally computer simulation is performed on different types of spline curves to show that the proposed method results in reduced chordal error and less fluctuation in feedrate.