Research On NURBS Curve Approximation And Interpolation Algorithm For Complex Surface Machining

Complex surface parts are usually composed of free curves and surfaces,and the approximation and interpolation algorithms of NURBS curve are the key technology of complex surface digital manufacturing.In this paper,the NURBS interpolation and approximation theory involved in complex surface machining were studied.To reduce the control points of NURBS curve used in contour reconstruction of section of complex curved surface,a NURBS curve approximation algorithm based on feature point extraction and Particle Swann Optimization(PSO)was proposed.In order to improve the approximation precision of dual-NURBS tool path using the same node vector in sculptured surface machining,an optimization model of cutter points curve approximation with variable weight was constructed.An improved cooperative co-evolutionary genetic algorithm(CCGA)was used to solve the model,and the optimal weight values of the curve were obtained.Considering the defects of the traditional NURBS interpolation algorithm in the interpolation accuracy and the feedrate fluctuation,an interpolation algorithm based on improved S-type velocity planning and Steffensen-like parameter calculating was proposed.Taking impeller blades as an example,the effectiveness of the proposed algorithms were verified by comparative experiments.The main contents of this paper are as follows:In the first chapter,the research status of free curve approximation and interpolation algorithms in complex surface machining were reviewed.The defects and solutions in the present methods were introduced.Expounded the significance of this study,and introduced the organizational structure of this paper.In the second chapter,a NURBS curve approximation algorithm of compression control vertexs was proposed.Equal chord length method was used to calculate the curvature of the discrete points,and an initial curve was constructed with the use of feature points extracted by curvature analysis,and then partial interpolation points were added and approximation curve can be updated based on error control.An improved PSO algorithm was applied to optimize the position of the control points to get the final NURBS curve.In the third chapter,a dual-NURBS tool path generation algorithm with variable weight was proposed.Based on the error control,some of the cutter tip points and cutter points were selected to construct dual-NURBS curves with same node vector.An optimization model of cutter points curve approximation with variable weight was constructed.The improved CCGA was used to adjust the weight values of the cutter points curve,and the approximation error of the curve was reduced.In the fourth chapter,an interpolation algorithm based on improved S-type velocity planning and Steffensen-like parameter calculating was proposed.Adaptive interpolation method was used to obtain information of each curve segment,and S-type velocity planning method was improved by adaptively adjusting jerk and accurately controlling feedrate based on the information of curvature of these segments.The proposed algorithm determined the starting point of deceleration area precisely by the way of positive and reverse interpolation.To improve real time performance and to control feedrate fluctuation availably,Steffensen-like method with parameters was used to calculate the interpolation parameters without derivative calculation.In the fifth chapter,an impeller blade was taken as an example to verify the theory and algorithm presented in this paper.Experimental results showed that compared with traditional methods,the NURBS approximation curve generated by this algorithm had fewer control vertex points and higher approximation accuracy,and the improved NURBS interpolation algorithm can effectively reduce the chord error and control the feedrate fluctuation.In the sixth chapter,the main research contents of this paper are summarized,and the next research work is prospected.