A parametric interpolator with minimal feed fluctuation for CNC machine tools using arc-length compensation and feedback correction

• The trajectory deviation is found as another primary source of feedrate fluctuations.
• An arc-length compensation scheme is presented to eliminate the trajectory deviation.
• A feedback correction method is proposed to further overcome the approximation error.
• An interpolator with arc-length compensation and feedback correction is proposed.

Traditionally, approximation methods are utilized in the parametric interpolation because of the nonanalytic relationship between the spline parameter and the arc length. The approximation error has been considered as the source of the feedrate fluctuation. This paper shows that the discrepancy between the desired tool path and the target trajectory of the motion system is another primary source, and presents a feedback interpolator to eliminate the feedrate fluctuation. To evaluate the initial parameter value for the interpolator, an arc-length based Taylor's expansion with arc-length compensation is proposed, which alleviates greatly the feedrate command error caused by the trajectory deviation. Then, a feedback correction scheme is developed to further reduce the feedrate command error that results from the approximation error. Both computational load analysis and numerical simulations are conducted, and the results show that the present interpolator has very good performance in both efficiency and accuracy, thus is a good choice for high speed and high precision CNC machines.