自由曲面模型全局美化技术

利用可微流形的无穷小变形技术,实现紧公差约束下对点云逼近的多张B-样条曲面的全局美化.根据微分流形上的Beltrami-Laplace算子,定义反映曲面整体形状变化的变形能量泛函,并得到泛函的唯一极小解.给出两张单节点B-样条曲面间G1连续的充要条件以及公共边界曲线控制顶点的本征方程,并利用局部格式构造整体收敛的G1光滑拼接的边界表示模型获得变形映射族的特解.特解的构造不可避免地导致模型在缝合区域的形状产生局部瑕疵,影响反求模型的保形性.通过特解来构造能量泛函的极小解,使得这类似应力集中的效应被逐步松弛到曲面的内部,从而改善模型的整体形状.应用实例揭示自由曲面的全局美化技术在反求工程中的意义.     

基于B样条曲面裁剪计算的局部协调设计

在反求工程曲面重构中,为了对跨多张曲面的局部矩形拓扑裁剪区域进行重新设计,提出了两种基于矩形拓扑区域的曲面局部协调设计方法:自动截面线蒙皮和最小二乘逼近。两种方法均插值于边界曲线和跨界切矢,保证了模型的整体G1连续性,并逼近或插值裁剪区域数据,具有较好的保形性,实际应用效果良好。     

基于递归分割理论的自由曲面建模技术

为应用递归分割理论增强复杂自由曲面建模能力，通过在递归分割Loop方法中引入节点加权因子，实现了对递归逼近分割曲面形状的有效控制，并可以生成不同的尖锐特征。根据曲面模型各点处的平均曲率，对节点位置进行逐步调整，实现了递归分割曲面模型的光顺处理。论述了通过计算递归分割曲面模型的法向偏置面生成薄壁件表面模型的方法，并给出了所建立的自由曲面模型直接应用于快速原型制造的实例，说明应用该项新技术可以直接建立任意拓扑结构复杂自由曲面模型，为复杂自由曲面的建模提供了新的有效途经。     

自由曲面的局部美化技术

针对反求工程中由多张B-样条曲面构成的边界表示模型在局部区域会出现的形状不规则性的问题,提出利用局部美化技术来消除这种外形的不规则性的方法.首先根据边界表示模型的拓扑给出局部美化的模式,并阐述曲面光顺与模型局部美化之间的区别和联系.然后,通过分析可接受的形状优化准则及其局部微分几何特性,给出局部美化的数学模型.最后,在利用形状分析方法构造局部形状不规则性区域的方法后,借鉴离散的非线性优化方法来保证形状修改的局部性和保持模型的拓扑.给出应用实例揭示了局部美化技术在反求工程中的意义.     

点云特征型面的边界曲线拟合及曲面裁剪算法

点云特征型面边界曲线的拟合质量直接决定了对应曲面裁剪的质量。以机械零件点云模型为研究对象,针对点云分割型面的边界点识别、排序、拟合和曲面裁剪问题展开研究。基于场力法提取的边界点集,提出了基于最短距离法的边界点集排序和方向夹角阈值限定的边界点集去噪等预处理算法;采用局部二次多项式函数拟合估算边界点集曲率,提出了基于曲率突变点归属性判断的边界点集分段和拟合算法;通过控制点投影变换求取二维裁剪边界,提出了基于特征点集多边形凹凸性的二维边界曲线方向判断法。使用机械零件模型典型型面进行实验,验证了各阶段算法。该算法具有很好的适用性,可进一步扩展应用至复杂曲面边界裁剪。     

任意拓扑结构复杂曲面模型重构新方法

分析了采用参数化方法进行复杂曲面模型重构时存在的缺点,给出了应用递归插值分割理论从离散测量点构成的初始控制网格直接构造任意拓扑结构复杂自由曲面模型时计算插值点的统一算法,设计了一种能充分体现这种曲面模型重构方法优点的四叉树型数据结构存储必要的信息,最后给出了复杂自由曲面模型重构的几个实例。从实例可以看出该方法能够避免参数化方法在复杂曲面模型重构时所必须的参数曲面片之间的拼接和裁剪等问题,为复杂自由曲面模型重构提供了有效的新方法。     

在逆向工程中用神经网络技术实现自由曲面的重建

现有自由曲面的重建和还原制造是整个逆向工程中最关键的技术。当某些表面被部分损坏或者曲面模型不甚完整时,这些技术就显得非常有用。为了能在现有自由曲面基础上建立模型,首先用坐标测量机或激光扫描仪获取数字值,随后,将这些数据用于转换成模型。本文叙述以神经网络逼近方法用计算机重建模型再现已有自由曲面及制造加工这些曲面。在这里,我们设计了三个四层神经网络并使用误差反向传播法（ＢＰ）来训练网络。     

离散点的隐式曲面重建算法研究

针对复杂自由曲面三维扫描数据多为离散点的特点,提出了一种隐式曲面重建算法,它能满足从大量离散点云数据中快速准确地建立曲面的需求。通过选择合适的形状函数,该算法可以准确描述尖锐特征比如边和角。方法是首先用八叉树细分方法来进行离散点云数据分组,然后用分段的二次函数来捕捉每组数据的局部形状,用单位分割法来组合局部的形状函数。应用实例表明,该算法可以对离散点云数据进行快速、准确、自适应的曲面重建。如果离散点云模型有指定的精度,那么隐式曲面重建算法的处理时间取决于该模型的几何复杂性和细分程度。     

微型复杂曲面零件散乱点云特征点提取

基于特征线约束的曲面不仅比自由曲面表达的模型有更高的精度,而且能够捕捉到模型其他的几何关系。微型复杂曲面零件多由曲面构成,曲面曲率变化大,曲率估算难度大,是逆向工程的难点。以皮带头复杂曲面为例,对微型复杂曲面微分几何量的估算,特征点的提取进行了研究。通过改进的空间分块策略建立散乱点云的拓扑关系,采用多种曲面模型分别拟合采样点邻域的方法估算曲率,构造协方差矩阵计算特征值和点云法矢,对曲率和协方差矩阵的特征值设置交叉阈值提取特征点。将利用交叉阈值提取到的特征点与利用单一阈值提取的特征点进行对比,结果显示:交叉阈值提取特征点的方法能够较为准确、完整的提取特征点。     

网格曲面数控加工编程分型线提取算法

针对复杂网格曲面分型线提取精度和效率不高的问题,根据非封闭自由曲面和封闭自由曲面的拓扑信息和几何特点,提出了2种基于投影方法的分型线提取算法. 对非封闭模型,首先将模型投影到平面并重新三角网格化,然后提取投影三角网格的边界,最后以平面三角网格的边界为检索信息在原始网格中检索得到自由曲面的分型线. 对封闭模型,根据模具分模的几何原理,提出通过建立封闭自由曲面凹模和凸模离散几何模型的方法提取封闭自由曲面的分型点,然后通过一环邻域点搜索法对分型点排序,得到分型线. 实验结果和数据分析表明,两种方法可以精确、高效地提取非封闭和封闭自由曲面的分型线,并可以确保分型点都是三角网格曲面的顶点.     

Topology recovery technique for complex freeform surface model after local geometry repair

Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations.Local geometry repair,such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region,where multiple surfaces meet,is a common technique used in CAD model repair and reverse engineering.However,local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling.Consequently,a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed.Firstly,construct the curve network which determine the geometry and topology properties of recovery freeform surface model;secondly,apply freeform surface fitting method to create B-spline surface patches to recover the topology of trimmed ones.Corresponding to the two levels of enforcing boundary conditions on a B-spline surface,two solution schemes are presented respectively.In the first solution scheme,non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches.In the other solution scheme,constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G 1 continuity simultaneously.The presented two different schemes are applied to the consistent surface model,which consists of five trimmed confluent surface patches and a local consistent surface patch,and a machine cover model,respectively.The application results show that our topology recovery technique meets shape-preserving and G 1 continuity requirements in reverse engineering.This research converts the problem of topology recovery for consistent surface model to the problem of constructing G 1 patches from a given curve network,and provides a new idea to model repairing study.     

Global Continuity Adjustment and Local Shape Optimization Technique for Complex Trimmed Surface Model

Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering.In recent years,a lot of progress has been made in smooth join of non-trimmed surface patches,while there has been seldom research on smoothly stitching trimmed surface patches together.This paper studies the problem of global continuity adjustment,damaged hole repair and local shape optimization for complex trimmed surface model,and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region.Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G1 continuity,and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch.The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole,and the result demonstrates the validation of our method.Furthermore,on the premise of global continuity,the proposed locally repairing damaged surface model provides a better foundation for following research work,such as topology recovery technique for complex surface model after geometric repair.     

一种基于RBF隐式曲面的离散数据快速重建方法

本文针对空间散乱数据, 提出一种基于RBF（Radial Basis Function）隐式模型的快速曲面重建方法,并实现了隐式曲面的可视化。三维离散数据由于分布稠密、不均匀,空间拓扑结构未知的特点,本文首先强调大规模散乱数据预处理的重要性。通过基于空间法向量约束和主元分析两种方法进行数据简化和特征提取。其次采用K-d tree数据结构进行空间数据分割,将全局模型转化为局部的RBF模型,从而通过求解线性方程组得到模型的权值系数。最后在局部交叠空间光滑拼接,得到一个代数表达形式的光滑曲面。实验结果表明,该方法适用于任意复杂物体的三维曲面重建,而且具有较高的重建精度。     

任意拓扑三角网格模型的Loop细分曲面重建系统

提出一种从任意拓扑密集的三角网格模型拟合Loop细分曲面系统，包含对原网格模型进行特征识别，把保持了原有特征的简化网格和拓扑优化所获得的网格作为拟合初始控制网格。系统通过对控制网格顶点的循环修正和局部自适应细分来求解最终拟合细分曲面控制网格，避免了求解线性方程组，提高了拟合曲面的质量，实现了在给定精度下用较少的控制网格反映物体细节特征的分片光滑（片内除奇异点C^1外其余C^2连续）的Loop细分曲面重建。实例表明，Loop细分曲面重建系统对于任意拓扑海量三角网格测量数据的细分曲面重建是高效可行的。     

An adaptive mesh model for 3D reconstruction from unorganized data points

Reconstructing exact topology mesh from data points is one of the most important tasks in the fields of industrial CAD/CAE/CAM, computational vision and reverse engineering. In this paper, a deflation algorithm that integrates an adaptive mesh and physical constraint model is presented for the 3D reconstruction of geometric-closed shape (genus 0) from unorganized data points. First, an initial mesh is formed using the Delaunay algorithm. Second, an asymptotic deforming performance is accomplished to deflate initial mesh towards the local concave boundary step-by-step. In this phase, a physical constraint model of coupled particle systems based on particle dynamics and Newtonian law of motion is constructed, and the model dynamically controls mesh deformation as a behavior constraint. To guarantee that the resultant mesh is homeomorphous to the original surface of data points, a continuously deforming mechanism, visibility cone and collision-detecting criterions are designed. At last, experimental results in reverse engineering which supports the usefulness of this method for reconstruction .     

On the correlation between crystallographic grain size and surface evolution in metal forming processes

Today, there is an obvious trend for implementation of net shape or near net shape forming technology products in nearly all branches of industry. Often, these components underlie specifications in terms of surface quality. However, the surface topology will change during forming operations, and cause an effect called “surface evolution”. Especially in sheet metal forming processes increase in surface roughness, caused by the in plane plastic straining, is frequently observed. Contact loading is capable to decrease surface roughness. In sophisticated forming applications, like deep drawing and ironing of small tubular-like cups the surface evolution is quite dependent on the crystallographic grain size of the workpiece. With respect to this phenomenon, often the question arises whether there is a ratio of surface topology characteristics to grain size constituting the limit of a single grain's influence on roughness evolution. Therefore, in the present work fundamental analyses on the mechanisms governing surface evolution are conducted. The influence of crystallographic grain size and grain orientation on roughening as well as on roughness reduction is shown. Moreover, a correlation between surface topology, grain size and surface evolution is derived.     

拓扑优化技术在机翼前缘设计中的应用

针对柔性机构实现机翼前缘变形问题,应用连续体拓扑优化技术,以实际位移与目标位移之间的偏差为目标函数,材料用量和屈服应力为约束,并考虑到机翼表面受载荷约束等实际情况,建立SIMP(solid isotropic material with penalization)密度刚度插值的拓扑优化模型。分别采用Mat-lab及Ansys软件对柔性机构优化设计和仿真分析,并最终进行了铝合金实物模型形变实验。研究结果显示:机翼前缘断面模型在0~1 N/mm均布外载约束下,可实现0~6.7°理想的机翼前缘变形。     

Fiber orientation in melt confluent process for reinforced injection molded part

Fiber orientation in reinforced polymer parts can greatly affect the appearance and mechanical properties. The fiber orientation process during a confluent process of two or more strands of melt in a mold cavity is discussed. Different from common polymer melts with no reinforced material, a novel model describing the confluent process for fiber-reinforced melt is established. Through finite element simulation, fiber orientation and its accumulation state in different layers of plastic parts are obtained. 3D surface morphologies of the confluent region caused by fiber orientation and distribution are tested in the laboratory, and the relationships between the mold temperature and the appearance of the confluent region are presented as well. By using SEM to observe the fiber orientation induced in different mold temperatures, the effect of the fiber orientation in confluent region process on the impact strength of the resultant parts is discussed. Testing results prove that the established model is effective in explaining the outcome of the confluent process for fiber-reinforced materials.     

基于RBF神经网络的三维网格实体模型重构的研究

提出了一种新的基于RBF神经网络的重构三维网格实体模型的算法 ,输入是未知表面的采样点坐标集 ,输出是该未知表面的三维网格近似。同时提出了一个简便而有效的在三维域上三角形网格的Laplacian光顺造型方案 ,网格光顺的结果能保证重建的结果比较光滑。算法较传统的算法更精确和更可靠。     

三维线弹性连续体的结构拓扑优化设计

研究了基于水平集模型和SIMP方法的三维线弹性结构的拓扑优化方法，优化模型的目标是结构的柔度最小。引入水平集模型隐含描述具有复杂拓扑关系的三维线弹性结构的几何边界，以材料域的形状为变量进行灵敏度分析，构造水平集方程的速度函数，通过几何边界的演化获得结构的最优形状和拓扑。同时研究了基于SIMP方法的三维连续体结构的拓扑优化设计。对基于水平集模型和SIMP的拓扑优化方法的数值算例进行比较，结果表明，基于水平集的三维结构拓扑优化具有光滑的几何边界，数值算法稳定。