关键词: 数控加工, 刀具轨迹优化, Frenet坐标系, Taylor展开

Abstract: To make the CNC trajectory smoother and further improve the machining efficiency,a bidirectional fourth-order Taylor fitting method for smooth curves based on spatial axis was proposed.Through optimization,the curvature was gentler and the contour error of fitted curves was further reduced.The finite uniform data points were selected on the parametric curve to calculate the derivatives of parameters and the differential geometric quantities such as curvature and torsion to establish the Frenet coordinate system.Then,the forward and backward fourth-order Taylor expansion was performed on the first and last data points of the i interval respectively,and the fitting curve of coupling weight was determined according to the relative distance of the parameter space formed by the Cutter Location (CL) points at the first and last data points.Finally,the optimum trajectory in machine tool coordinate system XYZ was obtained by inverse coordinate transformation.The comparison between the original trajectory and the bidirectional fourth-order Taylor fitting showed that the contour error had decreased gradually with the increasing of the order,and the mean value of curvature,the range of curvature and the range of curvature derivatived all approach the original curve.A fitting test was carried out with a standard circle and a high-speed train wheel tread LM-32,which found that the optimized curve obtained by the proposed method was 4μm ~5um less than the contour error of the curve.

Key words: CNC machining, tool path optimization, Frenet coordinate system, Taylor expansion