A locally optimal transition method with analytical calculation of transition length for computer numerical control machining of short line segments

Abstract

Line segments, or G01 codes, generated by computer-aided manufacturing softwares are the most widely used toolpath format for computer numerical control systems. The linear toolpath normally consists of thousands of short line segments due to the high-accuracy requirement of the machined parts. Due to the tangential and the curvature discontinuities at the junction of two segments, the feedrates at the start and the end points of line segment have to be slowed down. In order to increase the feedrates along short line segments, a locally optimal transition method is proposed, which uses a two-step strategy to generate a blended toolpath composed of cubic Bezier curves and line segments. In the first step, the optimal proportional coefficient is represented as the function of the angle between two adjacent line segments, which can be employed to minimize the curvature variation energy of the cubic Bezier curve. In the second step, the local optimization model with the aim to minimize the sum of two curvature extrema is established to determine the optimal transition length. The transition length can be analytically obtained under the constraint of the approximation error and the constraints of the line segment lengths. The simulation and experiment results demonstrate that, by comparison with the conventional transition methods, the proposed method can significantly decrease the machining time but does not increase the contouring error.