一种基于能量法的自由曲面展开算法

提出了一种基于能量法的自由曲面展开算法,适用于任意复杂自由曲面的展开.根据建立的曲面能量模型,采用映射法进行曲面的Delaunay三角网格划分,并计算空间网格三角形点的变形能,然后进行变形能的释放,得到自由曲面展开后的二维平面.能量法不拘于问题的形式,可以用来求解一般的问题,该算法具有一定的通用性,适用于CAD/CAM中的曲面展开问题.     

冲压成形件毛坯设计的曲面展平截面剖分算法

分析了复杂参数曲面的展开原理，采用了截面剖分算法实现自由曲面的近似展平，推导了曲面和截面线的展开算法，开发了C＋＋语言应用程序，给出了应用实例。该方法对中等复杂曲面零件展开毛坯有良好的适应性。     

板材多步逆成形中的滑移约束曲面优化构造方法

针对板材成形多步逆成形法中,滑移约束曲面构造的方法不能处理复杂形状零件的问题,提出一种基于优化的伪最小面积算法。该算法从优化的角度以滑移约束曲面的面积属性为研究对象,从而降低对零件形状的依赖度。该算法假定冲压时刻板材上的各物质点不发生流动,以冲压某一时刻凸、凹模的离散网格信息为已知量,此时刻凸、凹模各网格节点的z向坐标为约束,以所求滑移约束曲面的面积平方最小为目标函数,计算各三角形网格单元的面积,按与力学有限元中整体刚度矩阵相同的组装方式形成曲面的整体面积方矩阵,将空间曲面构造问题转化为一个标准二次规划问题,采用基于信赖域的方法求解该二次规划问题。弹簧支座和中柱算例的迭代次数和中间滑移约束曲面形状表明,该算法可以针对形状不规则的零件快速、有效的生成空间滑移约束曲面。     

采用轮廓识别法实现零件曲面重构

线性曲面反求算法的目的是根据原始数据点云反求得到能够正确反映原零件拓扑结构的线性曲面模型。该反求算法的核心思想是构造一个空间函数 ,该函数近似表示三维空间上任一点到所求曲面的距离 ,然后通过轮廓识别算法 ,可以由这个函数提取反求曲面的一个线性近似。本文所阐述的线性曲面反求算法结合网格优化算法可由原始数据点云 ,反求得到一个精确而简洁的具有任意拓扑类型的零件线性曲面。     

局部保形映射到整体能量优化的曲面展平

针对复杂网格曲面提出了一种局部保形映射到整体弹性能量优化的曲面展平算法。该方法基于局部到整体的思路,通过分析作用在局部三角形上的仿射变换雅可比矩阵的奇异值,得到三角形到平面参数域的保形映射。在此基础上,通过迭代优化由网格线弹性应变能组成的能量函数,使得整体网格的节点内力达到平衡状态,对局部保形映射后的网格进行整体拼接和优化。应用实例表明,该方法稳定可靠,能得到较好的网格曲面展平结果。     

复杂曲面的可展化及其展开方法

提出了一种复杂曲面可展化及其展开的新方法 ,在依附于复杂曲面的两条空间曲线之间 ,构造可展面 ,逼近复杂曲面 ,使复杂曲面可展化并展开。该方法以计算机辅助服装原型设计过程中的前片服装原型的可展化及其展开作为应用实例 ,证明其完全附和工业设计实际要求     

反求工程技术在复杂曲面重构系统中的应用

论述了针对注塑零件复杂曲面的反求设计,提出运用CCD白光光栅非接触工业相机采集点云数据,将点云数据加载到Geometric软件中,利用NURBS曲面重构方法和插值算法,进行点云数据筛选,构造点云特征网格和曲面拟合,得到点云曲面的三维重构.实践证明,基于Geometric系统的NURBS曲面重构方法,在复杂曲面为原型实体重构的反求设计中具有理想的应用价值.     

一种复杂曲面展开的通用算法

提出了一种基于几何展开/力学修正的复杂曲面展开的通用算法,实现复杂曲面的展开.首先,对三维曲面进行三角化,用三角片模型来表达三维曲面;然后,采用几何展开的方法将三维曲面展开为初始二维平面;最后,提出一种改进的能量法优化算法,建立能量模型,对初始展开平面进行优化,得到最终展开结果.由于采用了能量法对初始展开片面进行优化,曲面展开的精度较易控制,因此能够更有效地解决CAD/CAM中的曲面展开问题.     

板材三维曲面零件的坯料计算与变形逆分析

坯料计算是板材三维曲面零件成形工艺设计的重要问题之一。根据变形均匀原则及材料体积不变条件建立了一种基于三角形网格的坯料计算方法，该方法通过迭代格式使目标泛函极小化，得到零件的初始坯料。根据平面应变假定及三角形单元常应变条件，进行了由目标零件到坯料的变形逆分析。通过多点成形实验检验了坯料计算方法的精度与可靠性。     

基于三角网格模型的自由曲面自适应测点规划

测点自适应规划是复杂曲面类零件在加工质量数字化测量环节的关键。针对自由曲面自适应测点规划问题,开展曲面自适应布点研究。设置给定条件下的测点密度判定方法,生成样本集,再训练神经网络组合模型,构建测点密度预测模型,用于精简测点数量;按照给定的测点密度阈值自适应获取聚类中心,并采用区域生长算法将曲面划分为测点密度大致相等的子曲面;以子曲面为基础,根据其测点密度进行局部均匀布点,提出一种基于曲面划分的自适应测点规划算法。实验结果表明,在该算法的误差结果接近样本组的情况下,所需测点数量较迭代重构算法明显减少;在相同测点数量下,该算法的误差比均匀布点算法更接近样本组。根据测点密度,将曲面由一个复杂、非规则的模型分成若干测点密度相近的子曲面可以减少测点数量;所规划的测点能较好地描述自由曲面的加工质量。     

喷漆机器人空气喷枪的新模型

针对实际生产中喷漆机器人空气喷枪喷雾的形状及其附着在平面工件表面形成椭圆形喷漆区域的情况,进行喷枪静止的喷涂试验,得到漆膜厚度测量数据。采用BP神经网络方法进行漆膜表面函数拟合,通过比较拟合后的x、y方向的不同断面上的漆膜分布曲线,提出一种新的椭圆形区域的漆膜厚度分布函数——椭圆双b 分布模型,采用遗传算法及最小二乘法对椭圆双b 分布模型进行数学拟合,求得其参数。以此模型对一个喷枪行程进行仿真,并与实际的单行程喷漆试验结果进行比较,验证了所建模型的正确性。给出该模型用于一般曲面喷涂时工件表面上任意点的漆膜厚度计算公式,以及喷漆机器人为了保持喷枪姿态需要的喷涂运动方程,为喷漆机器人采用离线编程技术提供一个更为实用的空气喷枪模型。     

Optimal flattening of freeform surfaces based on energy model

Flattening of freeform surfaces (i.e., non-developable surfaces) is a difficult problem in engineering application. According to flattening distortions, a new development based on energy model is put forward in this paper. Given a doubly curved surface and using a triangle mesh subdivision, some triangles will be distorted when the surface is flattened. Generally, the developed plane will possess many splits. There are two kinds of developments: unconstrained flattening and constrained flattening, which are both analysed. In order to obtain a better pattern, the strain energy required to force a 3-D shape adopt the plane pattern should be minimised. At last a flattening algorithm is developed on the basis of theoretical analyses. Compared with the others, the proposed method can control the local precision easily, and is an effective method for flattening doubly curved surfaces.     

A method for planar development of 3D surfaces in shoe pattern design

This paper presents a new method for planar development of the 3D surfaces of a shoe upper. The 3D surface is first faceted into triangular elements and then roughly laid down on a 2D plane. Next, the nodal points of elements are repositioned by a refinement technique that minimizes the geometric errors. Even after elements have been refined by minimizing geometric errors, the resulting 2D shape still has some strain energy that needs to be reduced by a relaxation process. Hence, these elements are then used as an initial guess for further optimization during which the finite element inverse method is used to minimize the total strain energy. In fact, the two-step optimization technique not only can prevent the divergence of solutions (e.g., interferences between elements) but also yields a more reliable result. The method has been implemented as a module of the shoe design system by which a prototype shoe can be designed and manufactured more precisely and quickly.     

薄板等离子弧三维成形的工艺方法

平面薄板的等离子弧成形提出了一种有效实用的工艺方法.方法的重要特征是它首先计算成形一个特定形状所需要的应变场,利用应变场矢量和扫描路径方向垂直的关系设计扫描路径.等离子弧热参数通过应变场与等离子弧功率和扫描速度的关系确定.此方法在成形两种不同双曲形状上的有效性已经被仿真和试验所验证.     

Tool path planning for five-axis flank milling with developable surface approximation

This paper presents a novel approach that automatically generates an interference-free tool path for five-axis flank milling of a ruled surface. A boundary curve of the machined surface is subdivided into curve segments. Each segment works as a guide curve in the design method for developable Bézier surface that controls a developable patch for approximating the surface with available degrees of freedom. Geometric algorithms are proposed for calculating consecutive patches with G¹ continuity across the patch boundary. A tapered tool can move along the rulings of these patches without inducing local tool interference as a result of their developability. The machining deviation is controlled by the surface approximation error. A machining test is conducted with the generated CL data and the result verifies the feasibility of the proposed approach. This work successfully transforms avoidance of tool interference into a geometric modeling problem and provides a simple solution. It thus demonstrates a good potential for the developable surface theory of five-axis flank machining .     

窄间隙条件下基于光纤Bragg光栅的曲面位移测量

在充分利用光纤Bragg光栅既是敏感元件又是传光元件这一特点的基础上,提出一种在曲面空间间隙小于1 mm的窄间隙条件下,测量两曲面间相对位移的方法。设计一种矩形弹片式传感探头,利用其挠度与应变之间存在的对应关系,通过应变对光栅Bragg波长的调制,获得光栅Bragg波长偏移量与曲面位移之间的线性关系。通过双光纤光栅的应变差动成功消除了光纤Bragg光栅存在的温度干扰问题。结果表明,当曲面相对位移量在0.35～0.85 mm范围内时,测量系统的灵敏度达2.54 nm/mm,线性度优于1%。     

Investigations on the automatic precision polishing of curved surfaces using a five-axis machining centre

Polishing is usually indispensable process when better surface roughness is required for the parts such as injection mold. However, polishing process is often performed by manual operations. In this paper, an automatic polishing method for the metal parts with curved surfaces is proposed based on a machining centre. In order to realize the control of contact force, the relationship between the displacement of polishing disk and the force impacted on the polished part is first established. Then, within the contact zone between the polishing disk and the polished part, a pressure distribution model is derived for planar and curved surface polishing according to the specific process parameters. On this basis, the model of removal depth distribution along the vertical direction of feed is built for each polishing pass, and thus a suitable stepover size is further obtained so as to reduce the fluctuations of remove depth to most extent. Finally, an effective planning algorithm of cutter location data in polishing is proposed for a given CNC machine tools, and validation experiments are performed on planar and curved parts. The results show that the proposed automatic polishing scheme is able of achieving a mirror effect surface and keep a good global uniformity, at the same time it improves the polishing efficiency and realizes the integration with milling process.     

板式楔横轧接触区表面应力分布规律研究

楔横轧接触表面是形状复杂的空间曲面,接触表面应力分布变化规律相当复杂,对于其认识程度至今还局限于作较多假设的滑移线法分析结果,致使在模具设计和实际生产上主要依靠经验因素,阻碍楔横轧的应用和理论的发展。根据板式楔横轧的特点,在有限元ANSYS/DYNA软件基础上进行二次开发,编制模拟板式楔横轧轧制过程的命令流程序,模拟其轧制过程,获得接触区空间曲面形状,并较详细分析在楔横轧展宽段接触区的空间接触曲面上轧件接触表面应力的分布变化规律。研究结果为避免轧件表面产生缺陷、指导楔横轧模具设计和确定轧机力能参数等提供重要的理论依据。     

An adaptive uniform toolpath generation method for the automatic polishing of complex surfaces with adjustable density

During automatic polishing process, path trajectory is an important factor affecting the quality of machining. In this paper, a path generation algorithm based on adaptive Hilbert curves which can cover the curved surface evenly is proposed. The generated path not only makes the coverage density adjustable but also is able to pass through the points on the curved surface in more directions which is helpful to get a finished part without stripes. Using the proposed algorithm, the uniform distributed grid points are obtained in the parameter domain and then these node points with adjustable density can be calculated accordingly. Thus, according to the construction rule of adaptive Hilbert curve, the objective toolpaths are subsequently obtained. After that, by means of a mapping strategy, the path trajectory can be obtained on the physical space. To verify the proposed algorithm, uniform polishing paths with variable density are planned on two typical curved surfaces. The result of the machining experiment shows that the curved mirror-like surface can be achieved, and it also indicates the applicability of the proposed method.     

连续体结构综合优化设计

以连续体为对象的优化解法所求得的优化结果,经常只是反映最佳传力途径的具有锯齿状边界的某个区域。基于此,将拓扑优化、形状优化、有限元分析和计算机辅助几何设计有机地集成在一起,提出一种基于隐含边界描述的水平集连续体结构拓扑和形状渐进综合优化设计方法,将形状导数与拉格朗日乘子法引入到优化敏度分析中,控制水平集函数的动态运动,从而间接地实现结构边界的动态演化;用B样条曲线曲面逼近拓扑优化后的结构体边界,将前一优化过程所得到的反映传力途径的概念解上升为具有光顺边界,并被参数化了的物理解;在形状优化中,设计变量定义为B样条曲线或曲面的控制顶点的运动,建立边界节点移动速度场计算方法和边界形状调整方法,寻求较快的搜索方向,以合理速度分布,使结构变为最佳。通过一个典型算例证明所研究方法的有效性。