Approximating circular arcs by Bézier curves and its application to modelling tooling for FE forming simulations

When constructing a rigid tool surface with fillets using triangular Bezier surface patches for an FE forming simulation, it is difficult to determine the number of segments required to accurately model a blend are. This paper presents a combined numerical and analytical method to investigate the error of approximating circular arcs using cubic Bezier curve segments. It is established that there is a linear variation of the error with respect to the Tangent Magnitude Parameter (TMP) in certain regions, and an approximate linear variation of the error against the number of curve segments in log-log scales. In addition, the location of the maximum error and its variation with respect to the TMP are illustrated and analysed. The results obtained are applied to the creation of rigid tool surfaces for FE forming simulations. Two FE analyses are carried out: one to simulate the process of superplastically forming a 3D rectangular box with fillet surfaces, and the other to wrap a decorative pattern onto an axisymmetric ceramic pot. (C) 2001 Elsevier Science Ltd. All rights reserved.