Study On Interpolation Algorithm For Free-Form Curve And Surface In CNC System

The curve interpolation module is the core of the whole computer numerical control(CNC)system software. The interpolation algorithm directly affects the machining speed and the accuracy of the CNC system. In order to endow CNC machine tools with the function be able to machine free-form curves and surfaces directly, relevant theoretical researches and practical experiments about interpolation algorithm were made in this paper.At present, free-form curves and surfaces represented by parametric forms have become one of the most popular mathematic methods to describe the shape of machine components in CAD/CAM system. Accordingly, the technology of parametric curve real-time interpolation gradually turned into the attractive field of numerical control researches. This paper proposes two different interpolation algorithms for parametric curve. These algorithms are of great value to improve the accuracy and machining speed of numerical control system.Non-Uniform Rational B-Spline (NURBS) is the most popular parametric curve in practical industry design. The possession of NURBS curve interpolation function is the symbol of advanced performance of CNC system. The mathematic representation of NURBS curve was explained in detail in this paper. Besides this, the symmetry of NURBS curve was attested minutely. On the base of these, the method of NURBS curve real-time interpolation was presented concretely. During the time of interpolating a NURBS curve, machining speed can adapt to the curve`s curvature to limit the contour error and feed-rate within the allowable ranges. This method satisfies not only the feed-rate control requirement, but also the requirement of real-time process. In order to analyse the performance of the presented interpolation module, theoretical analyses about key factors, such as machining accuracy and feed-rate fluctuation, are implemented. Furthermore, by means of the interpolation of a given NURBS curve, the practical tests of the presented interpolation algorithm were made. Experimental results indicate that the proposed real-time NURBS interpolation algorithm can provide a satisfactory performance. In contrast to the existing linear and circular interpolation, the proposed interpolation method can maintain small contour errors and feed-rate fluctuations.In this paper, the preliminary researches about surface direct interpolation was made. The elementary structure of surface interpolation program was given too. In addition, this paper provided two realizations for NURBS surface direct interpolation, and pointed out their respective advantages and setbacks. Because the interpolation of surface involves too many factors, the real-time generation of tool trajectories is the only question studied in this paper. The NURBS surface interpolation program given in this paper, in which the tool trajectories is parametric curve, is relatively simple.Different methods discussed in this paper were realized by using the C++ programming language, and were used into the practical CNC system exploitation. Experiments showed that these methods and algorithms were of highly applied value. In a word, the study of this topic has not only important academic value but also high engineering value.