基于形状特征的自由曲面CAD重构理论及应用研究
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摘要
自由曲面的重构作为复杂工业产品设计、制造及检测的重要技术手段之一，深受CAD／CAM领域工程界的广泛重视。随着计算机技术，自动控制技术及CAD／CAM技术的发展，三坐标测量机(CMM)因其测量精度和智能化程度较高的特点，也被用于自由曲面的重建。但其测量效率问题常常约束了它在曲面重构中的广泛应用。本文基于自由曲面的形状特征，从提高三坐标测量机的测量效率入手，对曲面的重构理论及其工程应用进行了深入的研究分析。此外，由于得到的曲面都是以非均匀B样条或NURBS表示，故易于融入现有的CAD／CAM系统。
本文提出并建立了基于物体三维重心的自适应数字化模型，在此基础上对数字化模型中的弯曲度进行了深入的分析和研究，提出了表征曲面上一点弯曲程度的高斯弯曲度模型；同时，通过网格初始化方法，实现了数字化网格的加速形成。研究结果为自由曲面的离散采样规划奠定了理论基础。
根据接触测量的特点，为提高测量效率，本文提出了一种两次采样的曲面数字化规划方法。该方法通过初始曲面的引入，成功地把未知曲面转化为已知曲面，从而实现了曲面采样的自动化，为数据点的平滑曲面拟合提供了合理的信息支持。
本文从精度和外观形态两个方面对曲面的重构策略进行了研究。首先，针对重构曲面的精度问题，创新地将最小二乘技术、离散采样点参数化技术及约束非线性最小二乘优化技术等有机地结合起来，实现了重构曲面对采样点的精确而平滑的逼近；其次，从物理变形能量优化的角度出发，采用初始曲面参数化技术，以曲面拥有最小物理变形能量为目标函数，在外部约束条件下，构造了基于形状约束的曲面重构模型。
根据坐标测量需进行测头半径补偿的特点，研究了正则等距曲线曲面的有关性质。提出了测头半径的三维补偿方法，对测头半径的三维补偿精度进行了模拟仿真分析。分析结果表明，本文补偿方法是稳定可靠的。
根据以上研究，对实物模型进行了重构实验，并将曲面模型融入相关的CAD／CAM系统，进行了物体三维建模、NC路径生成、快速原型制造(RPM)及加工检测等方面的应用实验。实验表明，本文研究提出的曲面重构方法具有提高曲面数字化效率、重构精度高、集成性强等特点，因而具有工程应用价值。
As one of the important tools of design and manufacturing for complicated industrial products, it is very wide to attach great importance for the reconstruction of free-form surface on the engineering field of CAD/CAM. With the development of computer technology, automatic control technology and CAD/CAM technology etc., coordinate measuring machine(CMM) is also applied to reconstruction of surface because of measuring precision and intellectualized level. But CMM measuring efficiency usually becomes constraint to its wide application in the reconstruction of free-form surface. Starting with improving the measuring efficiency of CMM, the reconstruction theory of free-form surface and engineering application are profoundly studied on the basis of the shape characteristics of free-form surface in this dissertation. In addition, curves and surfaces constructed by the dissertation can be represented in the form of B SPLINE or NURBS, so it is easy to blend into current CAD/CAM systems.
The dissertation puts forward and sets up the adaptive sampling model based on the concept of gravity center. On the basis of the sampling model, the model of curvedness measure is analyzed deeply, and the gauss model of curvedness measure, which represents the curved magnitude on surface, is proposed. Meantime, the accelerating generation of sampling mesh is realized by the mesh-initialized method. The research result will establish a theoretical foundation for sampling planning of free-form surface.
According to the feature of contacting measurement, the dissertation first puts forward the twice-sampling planning method for free-form surface in order to improve measuring efficiency. This method makes a unknown surface become a known surface successfully by introducing a base surface. Then the automatic sampling of surface is realized, which provides reasonable information support for smooth fitting of sampling points.
Surface reconstruction approaches are studied at the same time from two aspects of precision and visual effect. First, in order to obtain the fitted surface with higher precision, the least-squares technology, the randomly points parameterization technology and the constraint non-linear least-squares optimization technology are combined together originally, and precise smooth approximation is realized for sampling points. Second, by applying the base surface parameterization, the surface reconstruction model based on shape constraint is constructed from physical deformation optimization model and geometric constraints.
In terms of the feature of radius compensation for coordinate measurement, the natures of offset curve and surface are studied in the dissertation. One three-dimensional compensation method on probe radium is put forward, and the three-dimensional compensation precision is probed by simulating computation. The simulating results show the compensation method is stable and reliable.
According to research results above, reconstruction experiments of object have been done. By blending reconstruction surface models into current CAD/CAM system, some applying experiments are carried into execution on CAD models of object, NC tool path generation, rapid prototyping manufacturing and machining inspection. The experiments indicate the proposed reconstruction method in the dissertation is characteristics of high sampling efficiency, fitting precision and integration, so it has engineering application value.
本文提出并建立了基于物体三维重心的自适应数字化模型，在此基础上对数字化模型中的弯曲度进行了深入的分析和研究，提出了表征曲面上一点弯曲程度的高斯弯曲度模型；同时，通过网格初始化方法，实现了数字化网格的加速形成。研究结果为自由曲面的离散采样规划奠定了理论基础。
根据接触测量的特点，为提高测量效率，本文提出了一种两次采样的曲面数字化规划方法。该方法通过初始曲面的引入，成功地把未知曲面转化为已知曲面，从而实现了曲面采样的自动化，为数据点的平滑曲面拟合提供了合理的信息支持。
本文从精度和外观形态两个方面对曲面的重构策略进行了研究。首先，针对重构曲面的精度问题，创新地将最小二乘技术、离散采样点参数化技术及约束非线性最小二乘优化技术等有机地结合起来，实现了重构曲面对采样点的精确而平滑的逼近；其次，从物理变形能量优化的角度出发，采用初始曲面参数化技术，以曲面拥有最小物理变形能量为目标函数，在外部约束条件下，构造了基于形状约束的曲面重构模型。
根据坐标测量需进行测头半径补偿的特点，研究了正则等距曲线曲面的有关性质。提出了测头半径的三维补偿方法，对测头半径的三维补偿精度进行了模拟仿真分析。分析结果表明，本文补偿方法是稳定可靠的。
根据以上研究，对实物模型进行了重构实验，并将曲面模型融入相关的CAD／CAM系统，进行了物体三维建模、NC路径生成、快速原型制造(RPM)及加工检测等方面的应用实验。实验表明，本文研究提出的曲面重构方法具有提高曲面数字化效率、重构精度高、集成性强等特点，因而具有工程应用价值。
As one of the important tools of design and manufacturing for complicated industrial products, it is very wide to attach great importance for the reconstruction of free-form surface on the engineering field of CAD/CAM. With the development of computer technology, automatic control technology and CAD/CAM technology etc., coordinate measuring machine(CMM) is also applied to reconstruction of surface because of measuring precision and intellectualized level. But CMM measuring efficiency usually becomes constraint to its wide application in the reconstruction of free-form surface. Starting with improving the measuring efficiency of CMM, the reconstruction theory of free-form surface and engineering application are profoundly studied on the basis of the shape characteristics of free-form surface in this dissertation. In addition, curves and surfaces constructed by the dissertation can be represented in the form of B SPLINE or NURBS, so it is easy to blend into current CAD/CAM systems.
The dissertation puts forward and sets up the adaptive sampling model based on the concept of gravity center. On the basis of the sampling model, the model of curvedness measure is analyzed deeply, and the gauss model of curvedness measure, which represents the curved magnitude on surface, is proposed. Meantime, the accelerating generation of sampling mesh is realized by the mesh-initialized method. The research result will establish a theoretical foundation for sampling planning of free-form surface.
According to the feature of contacting measurement, the dissertation first puts forward the twice-sampling planning method for free-form surface in order to improve measuring efficiency. This method makes a unknown surface become a known surface successfully by introducing a base surface. Then the automatic sampling of surface is realized, which provides reasonable information support for smooth fitting of sampling points.
Surface reconstruction approaches are studied at the same time from two aspects of precision and visual effect. First, in order to obtain the fitted surface with higher precision, the least-squares technology, the randomly points parameterization technology and the constraint non-linear least-squares optimization technology are combined together originally, and precise smooth approximation is realized for sampling points. Second, by applying the base surface parameterization, the surface reconstruction model based on shape constraint is constructed from physical deformation optimization model and geometric constraints.
In terms of the feature of radius compensation for coordinate measurement, the natures of offset curve and surface are studied in the dissertation. One three-dimensional compensation method on probe radium is put forward, and the three-dimensional compensation precision is probed by simulating computation. The simulating results show the compensation method is stable and reliable.
According to research results above, reconstruction experiments of object have been done. By blending reconstruction surface models into current CAD/CAM system, some applying experiments are carried into execution on CAD models of object, NC tool path generation, rapid prototyping manufacturing and machining inspection. The experiments indicate the proposed reconstruction method in the dissertation is characteristics of high sampling efficiency, fitting precision and integration, so it has engineering application value.
引文
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