【作者】 边玉超；

【导师】 戴莺莺； 张莉彦；

【作者基本信息】 北京化工大学 ， 机械设计及理论， 2004， 硕士

【摘要】 曲线的插补模块是整个数控系统控制软件的核心，插补算法的选择直接影响到数控系统的加工精度和速度。为了使数控机床具备对自由曲线曲面直接进行加工的功能，本课题对自由曲线曲面的插补算法进行了相应的理论研究和实际验证。目前，在CAD/CAM系统中，参数形式的自由曲线曲面已经成为描述零件外形轮廓的最常用的数学方法之一。与之相适应，参数曲线实时插补技术也逐渐成为近年来数控插补技术研究的一个热点。本文介绍了参数曲线的两种不同的实时插补算法，它们在提高数控系统的速度和精度方面具有很好的效果。NURBS曲线是在实际中得到广泛应用的一种参数曲线，NURBS曲线插补功能已经成为当代高性能CNC系统的标志性功能之一。本文详细地介绍了NURBS曲线的数学模型，并给出了其对称性的证明。在此基础之上，具体地给出了实现NURBS曲线实时插补的方法。在插补过程中，通过对插补误差和实际进给速度的实时监控，使刀具沿曲线的进给速度能随着曲线曲率的变化而自动地进行调整。这种方法不仅很好地解决了NURBS曲线实时插补中的速度控制问题，而且能够满足实际插补中的实时性要求。在本文中，对所提出的插补算法中存在的精度、速度波动等问题进行了理论分析，并且通过对给定曲线的插补，对编程实现的插补模块进行了实际的检验。经过分析和检验可知，所给出的插补算法简化了自由曲线数控加工中的程序编制，能够很好地满足自由曲线高速、高精度加工对插补算法的要求。与现有的直线和圆弧插补相比较，给出的NURBS曲线实时插补方法能够实现较小的轮廓误差和进给速度波动。本文对复杂曲面的直接插补技术也进行了初步的研究，阐述了复杂曲面直接插补技术的基本思路和模块结构。对于NURBS曲面的直接插补，给出了两种不同的实现方法，比较了两者的优缺点。由于曲面直接插补涉及的问题非常多，到目前为止，其插补结构模型还没有定<WP=4>型，所以本文中只对刀具轨迹的实时产生进行了初步的研究。给出了刀具沿参数线方向进给的NURBS曲面实时插补程序的框架和简单实现。本文中所讨论的各种算法都采用C＋＋语言实现，具体应用于数控系统的开发实践中，通过具体系统集成证明具有很高的应用价值。因此开展对本课题的研究不仅具有理论价值而且具有很高的实用价值。更多还原

【Abstract】 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 <WP=6>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.更多还原