Study On Five-axis Dual NURBS Tool Path Fitting And Its Interpolation Algorithm

With the continuous improvement of numerical control technology,five-axis CNC machine tools have made a qualitative leap both in the processing efficiency or processing accuracy.The five-axis machining tool path fitting and interpolation technique is the key technology that affects the performance of five-axis CNC machine tools.Therefore,the research of this technology will be of unprecedented significance for the development of five-axis CNC machine tools.In this paper,starting with five-axis tool path fitting method and NURBS curve interpolation algorithm,a five-axis dual NURBS tool path fitting method and its interpolation algorithm are proposed.After studying the existing five-axis machining tool path fitting methods,the idea of rational motion method is applied to the dual B-spline curve fitting method by using the properties of NURBS curve.By describing the space motion of the rigid body by dual quaternions,The rational B-spline motion is described by the B-spline dual quaternions curve which is obtained by interpolating the dual quaternions points in the dual quaternion space and finally mapped into the 3D space to obtain the dual NURBS tool path with equal distance.The points on B-spline curves and NURBS curves and their vectors are calculated quickly by using De-Boor algorithm.The method of the second-order Taylor's expansion approximation is used to calculating the curve parameters of the interpolation points.And the adaptive feedrate with limited chord error is deduced.In the look-ahead module,the classification and the searching method of feedrate sensitive points of NURBS curve are given.And the seven-segment feedrate scheduling method is applied for the feedrate scheduling of the curve segments.Aiming at the intersection of feedrate scheduling that may occur due to the short curve segments,the all intersection situations and the corresponding feedrate scheduling are given.Finally,the feedrate scheduling of the whole NURBS curve is analyzed.After analyzing the inverse kinematics of five-axis CNC machine tools,all kinds of five-axis CNC machine tools are given.The five-axis CNC machine tool which has the a table that has two roatation axies is taken as an example to analyze the inverse solution.Finally,the NURBS curve interpolation algorithm is applied to the generated the dual NURBS tool path with equal distance.Then the interpolation algorithm of five-axis dual NURBS tool path is obtained.Finally,it can be seen that the smooth tool path,the smooth interpolation feedrate and acceleration through the simulation of the algorithm in this paper.And the kinematic and dynamic requirements of the machine tools are met.