An improved positioning method for flank milling of S-shaped test piece

Accuracy detection for five-axis numerical control (NC) machine tools that can truly reflect their practical machining precision is of crucial importance. Standard test pieces are commonly employed for this purpose. However, poor accuracy detection performance is obtained when the test pieces used here are applied to five-axis NC machine tools. This paper introduces a new S-shaped test piece that is exclusively designed for the precision detection of five-axis NC machine tools. The S-shaped test piece integrates numerous characteristics associated with aviation parts and has been widely adopted by machine tool makers. This article presents a numerical model of the latest S-shaped test piece and shows that its side surfaces represent typical undevelopable ruled surfaces. The curvature changes along the ruled lines inevitably produce a theoretical error. Thus, machining methods seek to reduce the theoretical error as much as possible. Based on basic summaries of five existing positioning algorithms, a novel algorithm is proposed to position the tool head using three points, wherein two are tangential to the top and bottom boundary curves, respectively, and the third is tangential to the midpoint of the ruled line. The proposed positioning algorithm together with five existing positioning algorithms is applied to the S-shaped test piece, and a numerical error performance analysis is conducted. The results indicate that the machined surface reduces the theoretical error by at least 96% compared to all the existing numerical positioning algorithms except for Redonnet's algorithm. Compared with Redonnet's algorithm, the accuracy of the proposed algorithm is equivalent, although the proposed algorithm reduces the calculation time by 62.7%, and is not sensitive to the initial values. Hence, the computational process demonstrates that the proposed method is efficient, robust, and universal. Finally, simulation results were confirmed through an actual machining experiment.