不同参数化法对三次NURBS曲线拟合误差的影响

根据三次NURBS曲线上的一组已知型值点,采用均匀参数化法、积累弦长参数化法以及向心参数化法等不同的参数化法构造节点矢量,以首末端点切矢条件为边界条件构造附加方程,反算三次NURBS曲线的控制顶点。通过MATLAB拟合出所求三次NURBS曲线,对该曲线的拟合误差进行计算,得到拟合误差分析图。分析结果表明,采用积累弦长参数化法构造的三次NURBS曲线具有最小的拟合误差,能够更好地适用于工程实践。     

NURBS曲线数控插补方法及误差控制

本文针对数控加工系统对空间自由曲线高速高精度加工的需求,讨论了已知型值点的三次NURBS曲线反算法,给出了求解齐次曲线的带权控制顶点的矩阵形式线性方程组,并提出相应的NURBS曲线插补算法。同时为了保证自由曲线插补精度要求,提出了进给速度能随曲线曲率自适应调整,实现高速高精度插补误差控制的方法。     

基于NURBS的弧面凸轮运动特征曲线的修正计算

利用非均匀有理B样条(NURBS),对弧面凸轮的运动特征曲线进行了修正计算.就型值点与节点矢量的确定方法、权因子的选取与优化、控制顶点的反算等修正中的关键问题,进行了较为详细地分析.通过比较B样条和NURBS修正曲线的位移误差,表明用NURBS修正后的误差明显小于用B样条修正后的误差.     

不同参数化法对多项式NURBS插值曲线的影响

给出了一种NURBS插值曲线的计算方法——取二次到五次多项式曲线上的11个点作为型值点,分别采用均匀、弦长、向心与修正弦长参数化法求得节点矢量,反算控制顶点,编写Matlab程序重新计算NURBS插值曲线,并经过光顺性分析和逼近误差分析,探究了不同参数化法对生成NURBS插值曲线的影响.结果表明,各参数化法对低次曲线的NURBS插值表现出良好的光顺性和逼近精度;对于高次曲线,在满足逼近精度的条件下,修正弦长法表现出最好的光顺性.     

基于三次NURBS曲线的凸轮轮廓插值方法

本文提出了一个用三次NURBS曲线插值凸轮轮廓的新方法,该方法首先推导出三次NURBS曲线的矩阵形式,然后根据积累弦长参数法确定节点矢量,最后运用MATLAB软件算出凸轮轮廓的控制点及其权因子.     

基于遗传算法优化权因子的NURBS曲面形状微调

文章对非均匀有理B样条(NURBS)及其权因子作了分析研究.阐述了采用遗传算法求解NURBS曲面权因子的最优解来微调NURBS曲面以达到所要求的形状的方法.最后,给出了曲面权因子调整的应用算例.     

基于MATLAB的叶片四次NURBS曲面反求重构及分析

为了提高涡轮增压器叶片曲面反求设计的精度和光顺性,在MATLAB环境下,基于曲面型值数据,利用双四次NURBS理论与方法,通过编程和大量计算等,重构了叶片曲面模型。经过与双三次NURBS叶片曲面模型误差的数据分析和图形对比,结果表明:四次NURBS曲线的误差和波动要小于三次的误差和波动;升高一次的四次NURBS曲线曲面反求设计具有更高的造型精度和光滑度。研究结论有助于在工程实践中,对复杂的自由型曲线曲面逆向工程的高效数据计算,为更精准、更光滑造型等提供支持和借鉴。     

三次NURBS曲线的插值与应用

N URBS方法已经被广泛地使用在 CA D中。本文将通过三次 NU RBS曲线的矩阵表示给出三次NU RBS曲线插值方法 ,即反求三次 N URBS曲线控制顶点的算法 ,并给出数字算例和三次 NURBS曲线插值方法在船舶型线设计中的一个应用     

自适应约束条件下过型值点的连续Bezier曲线设计方法

已知Bezier曲线型值点,利用三点圆弧近似方法获得曲线端点的自适应约束条件,根据Bezier曲线端点性质和C2连续条件建立曲线型值点与其控制点之间的关系,采用高斯顺序消去法反算出曲线控制点,从而获得过型值点的连续Bezier曲线。基于该设计方法进行了实例研究,其结果与专业三维CAD软件在同样条件下的设计结果具有较好的一致性。     

采用NURBS曲线的钢球减速器的型线设计研究

摆线钢球减速器在摆线盘型线设计与优化过程中对型线的自由度与可控性要求越来越高,由此本文提出了将NURBS曲线应用到减速器摆线盘的型线设计过程中,深入研究基于NURBS的摆线型线,通过对已知摆线型线进行采样,获取样本点,反求控制点、权因子、节点矢量,得到符合精度要求的拟合型线,并以此型线完成虚拟样机与试验样机的设计,仿真与实验结果显示NURBS曲线表示方法可以保证摆线钢球减速器的传动精度,为进一步提高摆线盘型线设计的灵活性与局部可调整性奠定了基础,并验证了减速器样机的传动误差和噪音等性能明显优于传统的行星减速器.     

NURBS curve and surface fitting for reverse engineering

Reverse engineering is an approach for constructing a computer-aided design (CAD) model from a physical part through dimensional measurement and surface modelling. This paper presents alternatives for reverse engineering of free-form parts using Non-Uniform Rational B-Spline (NURBS) surfaces. A two-step linear approach is employed for fitting NURBS curves and surfaces using the measured points. During the first step, the weights of the control points are identified from a homogeneous system using symmetric eigenvalue decomposition. The control points are further processed in a way similar to B-spline curve and surface fitting. Some examples are presented to illustrate both the steps of reverse engineering and the process of NURBS curve and surface fitting.     

High-speed contouring control with NURBS-based C2 PH spline curves

This paper presents a C² Pythagorean hodograph (PH) spline curve constructed by the non-uniform rational B-spline (NURBS) curve for high-speed contouring control. With the knot vector, weights, and control points given, the C² PH spline curve is defined to be a “good” interpolant for Hermit data obtained from a NURBS curve of degree 3 specified by the same control polygon, weights, and the knot vector. To this end, the first- and second-order derivatives are evaluated at the nodal points on the NURBS curve. These boundary conditions are imposed on the PH segments of degree 9 to preserve continuity between the connecting segments. The S-curve motion planning architecture with variable feed rate for a planar NURBS-based C² PH spline curve is also developed in this paper. In particular, C¹ cubic feed acceleration/deceleration is imposed on the first and last PH segments. Several NURBS-based C² PH spline curve-following tasks were conducted to verify the effectiveness of the proposed interpolation algorithm. Experimental results show that the proposed interpolator is not only feasible for machining the complicated parametric curves represented in the NURBS-based C² PH spline form but also yields satisfactory contouring performance under variable feed rate control.     

Implementation of online NURBS curve fitting process on CNC machines

The study aims to develop a method for implementing an online non-uniform rational B-spline (NURBS) curve fitting process on CNC machines for improving the quality and efficiency of machining. Conventional CAD/CAM/CNC systems usually induce some machining difficulties and limit the machining results in real applications. Therefore, some researchers have proposed various methods for improving the machining results. An online NURBS curve fitting process consists of the fetching and fitting stages for CNC machines is developed in this paper. The fetching stage fetches a block of NC code and generates motion commands for obtaining data points. The fitting stage executes the NURBS curve fitting method along with a given set of data points. Moreover, the optimal search method is designed for obtaining good results in the NURBS curve fitting process. Simulations and machining tests carried out on a vertical machining center show that the proposed approach reduces the machining time to about 23% while maintaining the machining quality for the sample test.     

Accuracy improvement method for flank milling surface design

In this paper, a variation of the method of designing surfaces for flank milling proposed by Li et al. 2006 (Surface design for flank milling. Submitted to CAD, July) is presented. Li’s method is based on the premise that the surface flank milled by a cylindrical tool can be represented by a NURBS surface and can be used by designers to build efficient impellers, blades and other engineering parts. In the proposed method, a four control point curve is used to approximate the grazing curves and for subsequent generation of a polynomial surface. This eliminates the need of weights for the interior control points and still results in a good surface. The accuracy of the surface can be controlled by adding control points. Examples are given to demonstrate the proposed surface design method.     

三次NURBS样条曲线插补加工螺旋转子建模与加工研究

提出在螺旋转子加工制造过程中,采用三次NURBS样条曲线插补替代通常的微直线段插补;建立了螺旋转子端面摆线段三次NURBS样条曲线方程.在Pro/E软件上比较了三次样条插补曲线和理论摆线之间的精度误差.最后通过在立式加工中心上比较了采用三次NURBS样条插补和采用微直线段插补的加工精度和加工效率,采用三次NURBS样条插补加工取得了理想的效果.     

基于NURBS的齿轮盘铣刀后刀面插补点计算

将NURBS曲线方法应用于盘铣刀后刀面插补中,通过盘铣刀后刀面上给出的一些数据点,首先反算出盘铣刀后刀面的数据点曲线的控制顶点,再根据德布尔算法求得该曲线上的点,进而找到所要求的插补点,并拟合出了插补曲线;最后给出了该算法的应用实例。     

利用ARX构造反求近似曲面

面对反求工程中仅仅具有少量测量点构造近似曲面的要求,通过利用Ob ject ARX的内置类库,提出了采用NURBS曲线构造近似曲面的方法。该方法简单有效,可以满足一般少量测量点近似曲面构造的要求。     

平行分度凸轮轮廓曲线的三次NURBS表示

为了获得供具有非均匀有理B样条(Non-Uniform Rational B-Sphne,NURBS)插值功能的CAD/CAM绘图和数控机床加工使用的设计数据,文中讨论了NURBS技术和平行分度凸轮轮廓曲线的三次NURBS表示方法,提出了用三次NURBS表示平行分度凸轮轮廓曲线后产生的设计误差的估计方法.     

燃气轮机透平叶片截面形状重构技术研究

基于逆向工程,采用NURBS(非均匀有理B样条)理论对透平叶片截面数据点阵进行整体插值,实现对透平叶片截面形状的重构;然后采用NURBS小波分解的光顺算法,对重构的自由曲线进行整体光顺。实践表明,经过重构和小波光顺后,有效地构造出透平叶片截面线,并去除了曲线上的坏点,改善了截面线的品质,达到了预定目的。     

基于NURBS曲线的凸轮廓线表达方法的研究及应用

为了使不同的凸轮廓线具有统一的表达形式,并保证凸轮廓线的光顺性,采用NURBS曲线来逼近凸轮廓线,并结合最小二乘法构建了NURBS曲线的目标函数,建立了基于NURBS曲线的凸轮廓线表达模型。将该模型用于步行式插秧机共轭凸轮推秧装置中共轭凸轮廓线的表达,拟合得到的凸轮廓线曲率变化均匀。与传统的拟合方法对比发现,用NURBS曲线拟合后得到的凸轮廓线曲率变化均匀、 误差小,需要的型值点少,从而表明采用NURBS曲线表达凸轮廓线具有明显的优势。