Research On Velocity Planning And Contour Control Of NURBS Curve

Computer numerical control(CNC)machining technology is a key technology reflecting the advance of modern equipment manufacturing industry in China,and plays a decisive role in the development of Chinese manufacturing industries.With the CNC machining progressing towards high-speed and high-precision,NURBS curve interpolation came into being.Supported by the National Natural Science Foundation project,the thesis has studied the velocity planning and contour control in details of NURBS curve which are necessitated for the further development of high-performance CNC machining.The main contents of the research are as follows:(1)The jerk of existing acceleration/deceleration control method is realized by the step change,which causes the machine vibration.Thus,a polynomial acceleration and deceleration method is introduced in the thesis in order to meet the requirements of flexible machining,focusing on establishing the mathematical model based on a polynomial five-stage acceleration and deceleration method.This builds the theoretical basis for the later study of velocity interpolation algorithm.(2)With the characteristics of NURBS curve,a NURBS interpolation control method based on the polynomial five-stage acceleration and deceleration model is proposed for CNC machining.Firstly,the velocity is adjusted according to the adaptive control,and then the velocity sensitive points are determined by the minimum velocity,thereby the curve is segmented by the velocity sensitive points.Secondly,the new method precisely determining the starting point of deceleration area is produced,and the acceleration and deceleration planning can be performed on the segmentation curve.In the simulation of the NURBS curve velocity planning,the algorithm can not only achieve a smooth velocity,meanwhile the acceleration curve and the jerk curve are guaranteed to be continuous.(3)Aiming at improving the precision of multi-axis contour control in CNC machining,a high-precision contour control method based on NURBS interpolation is proposed.In this paper,the linear motor is firstly analyzed in the frequency domain and its dynamic equation is determined.Then according to the task coordinate frame theory,we establish the contour error estimation model of arbitrary curve,which can track and control the desired trajectory designed by NURBS interpolation.Finally,the simulation results show that the proposed method produces better contour control performance over traditional approaches.(4)Lastly,the velocity smoothing experiment and contour control experiment are carried out on linear motor multi-axis motion platform.The results show that the proposed velocity planning algorithm ensures steady velocity and makes the motor platform run more smoothly.At the same time,the proposed contour control method reduces the contour error and still guarantees better contour performance when the curvature changes.