NURBS interpolator with pre-compensation based on discrete inverse transfer function for CNC high-precision machining

Abstract

In the field of computerized numerical control (CNC) machining, high-speed and high-precision machining has been regarded as the key research by many scholars. In conventional methods, high-speed machining and high-precision machining are contradictory. It is inevitable to reduce the feedrate to improve the processing accuracy. In the paper, a pre-compensation based on discrete inverse transfer function (PDIT) theory is proposed. PDIT is able to improve machining contour accuracy without decreasing feedrate. The proposed PDIT theory is divided into three parts: NURBS interpolator, feedrate scheduling, and interpolator with pre-compensation. The NURBS interpolator has great advantage of directly interpolating the parametric curve. Therefore, the paper adopts the NURBS interpolator to accomplish interpolation. In the feedrate scheduling, S-type flexible acceleration and deceleration are used for path planning, and the maximum starting feedrate is obtained under the feedrate constraint. In the interpolator with pre-compensation, the NURBS interpolator is pre-compensated by PDIT. For the input, the response of the transfer function reaches a steady-state response within periods of time. Before steady-state response, the unsteady-state response exists in the transfer function. The unsteady-state response usually sustains dozens of interpolation periods, which inevitably lead to contour error in machining. Hence, the PDIT theory is employed to compensate the contour error caused by the unsteady-state response of transfer function to NURBS interpolator. The drive system is a transfer function, so the unsteady-state response of drive system can also cause machining errors before the steady-state response. In the paper, the NURBS interpolator is pre-compensated by PDIT theory before drive system to reduce contour errors and improve machining accuracy. Finally, the performance of the proposed PDIT is evaluated by simulations and experiments. The experimental results illustrate that PDIT theory obviously improve the machining accuracy.