Study On Interpolation Algorithm And Contour Error Control Based On NURBS Curve

Modern numerical control technology is the foundation of a country’s manufacturing industry modernization.The heigth of its technical level has a vital impact on the country’s industrial development ability and economic development.Compared with the linear and circular interpolation of traditional CNC system,NURBS interpolation technology greatly improves the efficiency and quality of parts processing in the field of modern manufacturing.However,due to the factors such as response delay,dynamic parameter mismatch and nonlinear interference of each feed axis in the servo control system,the contour error will inevitably be produced when machining the part profile.In order to improve the accuracy of contour tracking,this paper takes the NURBS track as the research object and the research is carried out from the aspects of feedrate scheduling,interpolation parameter calculation and contour error control.The main research contents are as follows.(1)The mathematical definition of NURBS curve and the calculation of evaluation and derivation.In this paper,the definition and related mathematical properties of NURBS curve are given.The calculation formulas of direct method,de Boor algorithm and matrix preprocessing algorithm in the evaluation and derivation are mainly derived.The calculation amount and applicability of the three algorithms are compared,so as to lay a mathematical foundation for the follow-up research of interpolation methods.(2)In order to obtain high efficiency and stable interpolation feed motion,a NURBS interpolation algorithm with adaptive smoothing feedrate and parameter increment compensation is studied.Firstly,according to the curvature constraint,the adaptive feedrate is obtained and the segmentation of the curve is completed.Secondly,in order to avoid the problem of feeding speed overrun,the improved S-shape acceleration and deceleration control is adopted to adjust the jerk.The adjacent segments meeting the combined planning conditions are treated comprehensively.Lastly,aiming at the problem of velocity error in interpolation point parameter calculation,an interpolation parameter calculation method based on parameter increment compensation is proposed to reduce the velocity fluctuation and improve the interpolation point parameter calculation accuracy.(3)Aiming at the problem of contour error in contour tracking task,the improved PSO algorithm optimizes the contour error control method of fuzzy PID in plane trajectory is studied.Based on the principle of optimal point approximate circle approximation,the algorithm of contour error estimation of free curve in plane trajectory is studied to improve the estimation accuracy of contour error.In the aspect of contour control,the fuzzy PID control is used to improve the traditional cross coupling control method for contour error suppression.Aiming at the optimization of control parameters,the PSO algorithm is improved and the control parameters of fuzzy PID are self optimized,so as to carry out the fuzzy self-tuning cross coupling control of contour error and realize the contour tracking in two dimensions.(4)Based on the two-dimensional x-y axis experimental platform,the comprehensive test is carried out for the methods proposed in this paper.The experimental results show that the proposed contour error control method has better effect.In the typical NURBS trajectory test,the efficiency and smoothness of trajectory interpolation are guaranteed.The maximum contour error of the proposed method is 0.00583 mm,which is 67.7% lower than that before improvement.This meets the requirements of the control accuracy,so as to verify the effectiveness of the proposed method.