Generalized Taylor series expansion for free-form two-dimensional contour error compensation

Abstract

The model-based Taylor series expansion error compensation (TSEEC) method has been shown to be capable of eliminating contour errors in biaxial CNC machines. However, it has been developed for only linear and circular contours. In this paper, an extension of TSEEC, a generalized TSEEC or GTSEEC, is proposed which is capable of compensating for the contour errors of arbitrary two-dimensional contours. A new real-time algorithm is used to estimate the contour error so that GTSEEC can be applied even in cases where the function of the contour is unknown. Simulation results using linear, circular and parabolic contours are presented which show that, with perfect knowledge of the axial dynamics, GTSEEC can perfectly eliminate the contour errors for any contour, even when there is significant mismatch in the axes dynamics. Experiments on a small two-axis computer-controlled machine indicate the effectiveness and better performance of GTSEEC in reducing contour errors for free-form contour following tasks when compared with two other leading approaches, the zero phase error tracking control (ZPETC) and cross-coupled control (CCC). © 2011 Elsevier Ltd All rights reserved.