面向复杂曲面加工的NURBS曲线逼近及插补算法研究

发布时间：2019-04-02 06:37

【摘要】：复杂曲面类零件通常由自由曲线曲面构成,其中NURBS曲线的逼近和插补算法是复杂曲面数字化制造中的关键技术,本文对复杂曲面加工中涉及到的NURBS插补和逼近理论进行了深入研究。提出了基于特征点提取及改进粒子群算法的NURBS曲线逼近算法,压缩了复杂曲面断面轮廓重建中NURBS逼近曲线的控制顶点数量;为提升复杂曲面加工中采用相同节点向量生成双NURBS刀具路径的逼近精度,构建了变权重的刀轴点曲线逼近优化模型,利用改进协同进化遗传算法求解该模型,得到曲线的最优权重值;考虑传统NURIBS插补算法在插补精度与插补速度波动率方面的缺陷,提出了基于改进S型速度规划及Steffensen型参数计算的插补算法。以叶轮叶片为例进行算法对比试验,验证了本文算法的有效性。本文研究的主要内容如下:第一章综述了复杂曲面加工中自由曲线逼近和插补算法的国内外研究现状,介绍了目前方法中存在的缺陷和解决思路。阐述了本文的研究意义,介绍了本文的组织结构。第二章提出了压缩控制顶点的NURBS曲线逼近算法。利用等弦长法计算离散点的曲率,基于曲率分析提取离散点列的特征点并构造初始逼近曲线。基于误差控制增加插值点并更新逼近曲线,利用改进的粒子群算法优化控制顶点的位置,得到最终逼近曲线。第三章提出了变权重的双NURBS刀具路径生成算法。基于误差控制选取部分刀具中心点和刀轴点离散数据并采用同一节点向量构造初始双NURBS曲线,构建变权重的刀轴点曲线逼近优化模型,利用改进协同进化遗传算法调整刀轴点曲线的权重值,降低了曲线的逼近误差。第四章提出了改进S型速度规划方法和带参数的Steffensen型插补参数计算方法。通过自适应插补得到曲线分段信息,根据曲率信息自适应调整最大加加速度并进行速度精确控制,改进了传统S型速度规划算法。采用正反向插补精确确定减速点,并利用带参数Steffensen型方法计算曲线插补参数,避免了求导运算,增强了插补实时性,有效控制了速度波动率。第五章以叶轮叶片为例验证了本文所提的理论和算法。实验结果表明,与传统方法相比本文算法生成的NURBS逼近曲线具有更少的控制顶点数,更高的逼近精度。改进后的NURBS插补算法有效降低了弦高误差,控制了速度波动率。第六章对论文的主要研究内容进行了总结,并对下一步的研究工作进行了展望。
[Abstract]:Complex surface parts are usually composed of free-form curves and surfaces, in which the approximation and interpolation algorithm of NURBS curves is the key technology in digital manufacturing of complex surfaces. In this paper, the NURBS interpolation and approximation theory involved in the machining of complex surfaces are deeply studied. A NURBS curve approximation algorithm based on feature point extraction and improved particle swarm optimization (PSO) is proposed, which compresses the number of control vertices of NURBS approximation curve in profile reconstruction of complex surfaces. In order to improve the approximation accuracy of double NURBS tool path generated by the same node vector in the machining of complex surface, an optimization model of tool pivot point curve approximation with variable weight is constructed, and the improved coevolutionary genetic algorithm is used to solve the model. The optimal weight value of the curve is obtained. Considering the shortcomings of traditional NURIBS interpolation algorithm in interpolation precision and interpolation velocity volatility, an interpolation algorithm based on improved S-type velocity programming and Steffens type parameter calculation is proposed. Taking the impeller blade as an example, the validity of the algorithm is verified by comparing the algorithm. The main contents of this paper are as follows: in the first chapter, the research status of free curve approximation and interpolation algorithm in complex surface machining is summarized, and the defects and solutions of the present methods are introduced. This paper expounds the research significance of this paper, and introduces the organization structure of this paper. In chapter 2, a NURBS curve approximation algorithm for compressed control vertices is proposed. The curvature of discrete points is calculated by means of equal chord length method. The characteristic points of discrete point sequence are extracted based on curvature analysis and the initial approximation curve is constructed. Based on the error control, the interpolation point is added and the approximation curve is updated. The improved particle swarm optimization algorithm is used to optimize the position of the control vertex, and the final approximation curve is obtained. In chapter 3, a double NURBS tool path generation algorithm with variable weights is proposed. Based on the error control, some discrete data of tool center point and tool pivot point are selected, and the initial double NURBS curve is constructed by using the same node vector, and the tool pivot point curve approximation optimization model with variable weight is constructed. The improved coevolutionary genetic algorithm is used to adjust the weight value of the tool pivot point curve, and the approximation error of the curve is reduced. In chapter 4, an improved S-type velocity programming method and a Steffens-type interpolation parameter calculation method with parameters are presented. The curve segment information is obtained by adaptive interpolation, and the maximum acceleration is adjusted adaptively according to the curvature information and the speed is precisely controlled. The traditional S-type speed planning algorithm is improved. The forward and inverse interpolation is used to accurately determine the deceleration point, and the Steffensen method with parameters is used to calculate the curve interpolation parameters. The derivation operation is avoided, the real-time performance of the interpolation is enhanced, and the velocity fluctuation is effectively controlled. The fifth chapter takes the impeller blade as an example to verify the theory and algorithm proposed in this paper. The experimental results show that the NURBS approximation curve generated by this algorithm has fewer control vertices and higher approximation accuracy than the traditional method. The improved NURBS interpolation algorithm can effectively reduce the chord height error and control the velocity volatility. In the sixth chapter, the main research contents are summarized, and the future research work is prospected.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TG659

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