复杂曲面零件数据拼合与精密加工技术研究
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摘要
复杂曲面零件在汽车精密覆盖件、舰船螺旋桨和航空发动机叶片等零件开发中广泛应用,研究复杂曲面零件的数据拼合与精密加工技术是提高具有复杂曲面特征的产品加工精度和效率的关键。本文研究了数据拼合、加工路径生成、曲面寻位等数据处理关键技术,主要研究工作和创新之处体现在：
研究测量数据粗拼合和精拼合算法。(1)针对当前粗拼合算法难以定义相似性度量和处理非重叠区域问题,提出基于降维形状标识(DRSD:Dimensionality-Reduction Shape Descriptions)的粗拼合算法。引入角度保形参数化理论对网格曲面在低维空间表述,应用调和映射和角度平化构造局部和全局DRSD,在低维空间搜索最近点、计算刚体变换参数、查询重叠区域和评价拼合误差。实验结果证明相比传统的粗拼合算法DRSD算法拼合效率高,对噪音、分辨率、固定点和缺失等外界因素的影响稳定性好。(2)针对当前精拼合算法的优缺点,提出基于自适应距离函数的精拼合算法。定义自适应距离函数(ADF:Adaptive Distance Function)描述点-曲面距离误差,同传统的点-点距离函数和点-切面距离函数的主要不同是ADF考虑了曲面曲率特征来量化点-曲面最近距离。使用该距离函数建立精拼合的非线性优化模型和求解策略,实验结果证明当初值较差且曲面具有高曲率特征时,ADF精拼合算法在收敛速度和收敛稳定性方面具有优势。
研究低维空间三轴加工路径生成算法。针对当前大部分路径生成算法只适应参数曲面的问题,应用网格参数化方法ABF(Angle Based Flattening)将网格曲面展开在平面参数区域,提出基于降维策略的三轴加工路径生成方法。一方面通过主成份分析提取单次最长走刀路径生成等平面加工路径,缓解传统算法在平坦区域产生冗余路径的问题；另一方面通过提取网格边界驱动曲线生成边界平移加工路径,避免在三维空间执行切片、平移、相交和投影等复杂的几何运算过程,提高计算效率。
研究点云-参数族曲面寻位与精度评估方法。提出点云-参数族曲面寻位ADF算法,建立产品质量检测、曲线拟合、对称特征寻位等多种情况下曲面寻位的非线性优化模型。此外,重点分析曲面寻位误差与几何误差的微分运动关系,推导测点位置偏差同几何误差的线性映射关系。在考虑加工、测量等制造误差影响的情况下,构造一个具有笛卡尔坐标变换不变性的数学统计量。应用该统计量提出基于t分布的寻位精度评估模型,并据此推导出刚体变换平移误差与旋转误差的理论上限。
应用本文提出的算法初步搭建一个基于逆向工程的数字化制造平台。在数字制造装备与技术国家重点实验室已有的软硬件基础上,将本文提出的数据处理算法进行应用,初步搭建一个集成“曲面测量-数据集成-加工制造-质量检测”功能的数字化制造平台。为验证该平台统的可行性,以典型的复杂曲面为例依次执行了数据采集、数据拼合、路径生成、铣削加工、曲面寻位、质量检测等处理过程,加工出满足精度要求的产品。
Complex surfaces have been widely applied into the products development, such as automobile precise panels, propeller of naval vessel and blade of aero-engine. The research on data registration and precision machining technologies towards complex surfaces is a key point to improve the machining accuracy and efficiency of such products. Based on ingoing analysis and summary of previous works, this thesis has investigated the key technologies of data processing, such as data registration, tool path generation and surface localization et al. The major research works and contributions of the thesis are introduced as follows:
Study the coarse and fine registration algorithms of measured data. (1) For the problem that most coarse registration algorithms have difficulty in defining similarity index and handling non-overlapping data, the thesis has proposed a new algorithm based on Dimensionality-Reduction Shape Descriptions, where Harmoinic Mapping and Angle Based Flattening are used to represent mesh surfaces in both local and global manners. Therefore, searching for closest point, calculating transformation parameters, verifying overlapping regions and evaluating error can be carried out in low-dimensional space. The experimental results indicate that DRSD algorithm is efficient and robust to Gaussian noise, resolution, fixed point and occlusion. (2) For the pros and cons of current fine registration algorithms, the thesis has proposed a new algorithm based on adaptive distance function (ADF), which is used to describe the point-surface distance error. The main difference between adaptive distance function and traditional distance functions is that the curvature feature is considered to quatify point-surface shortest distance. Non-linear optimization model is established to calculate the rigid transformation. The experimental result indicates that ADF algorithm has evident superiority in balancing convergent speed and stability, especially when the initial value is poor and the surfaces have high-curvature features.
Study the tool path generation algorithm of 3-axis machining in low dimensional space. For the problem that most of current tool path generation methods are only suitable for parametric surfaces, the thesis has presented a 3-axis tool path generation method with dimensionality-reduction strategy, by applying Angle Based Flattening to strech the overall surface on parametric plane. For one hand, iso-planar tool path is generated by employing Principal Component Analysis to obtain a maximal length of machining path. Hence, redundant tool paths of traditional iso-planar methods are relieved. For the other hand, contour-translation tool path is generated by extracting a boundary drive curve on meshes. This avoids complex calculations in 3D space such as slicing, offsetting, intersection, and projection, which increases the computational efficiency.
Study the surface localization and accuracy evaluation method between point cloud data and parametric family of surfaces. The thesis has proposed an ADF localization algorithm between point and parametric family of surfaces, established the non-linear optimization model for quality inspection, curve fitting and surface localization with symmetrical features. In addition, the thesis focuses on analyzing the differential relationship between localization error and geometric error, and deriving the linear mapping relationship from the geometric error, in order to construct a mathematical statistics with Cartesian frame-independence property. With the constructed statistics, the localization result can be determined by a criminative accuracy model based on t distribution, from which the uppers of translation and rotation errors are also derived.
Set up a reverse engineering-based digital manufacture platform by applying the proposed algorithms. Based on the existing software and hardware platforms in State Key Laboratory of Digital Manufacturing Equipment and Technology, we have developed the algorithms and basically set up a digital manufacture platform which integrates surface measurement, data processing, machining and quality inspection. To verify its feasibility, a typical complex surface has been employed to implement data acquirement, point cloud registration, tool path generation, milling, surface localization and quality inspection, from which a new product with specified accuracy is produced.
研究测量数据粗拼合和精拼合算法。(1)针对当前粗拼合算法难以定义相似性度量和处理非重叠区域问题,提出基于降维形状标识(DRSD:Dimensionality-Reduction Shape Descriptions)的粗拼合算法。引入角度保形参数化理论对网格曲面在低维空间表述,应用调和映射和角度平化构造局部和全局DRSD,在低维空间搜索最近点、计算刚体变换参数、查询重叠区域和评价拼合误差。实验结果证明相比传统的粗拼合算法DRSD算法拼合效率高,对噪音、分辨率、固定点和缺失等外界因素的影响稳定性好。(2)针对当前精拼合算法的优缺点,提出基于自适应距离函数的精拼合算法。定义自适应距离函数(ADF:Adaptive Distance Function)描述点-曲面距离误差,同传统的点-点距离函数和点-切面距离函数的主要不同是ADF考虑了曲面曲率特征来量化点-曲面最近距离。使用该距离函数建立精拼合的非线性优化模型和求解策略,实验结果证明当初值较差且曲面具有高曲率特征时,ADF精拼合算法在收敛速度和收敛稳定性方面具有优势。
研究低维空间三轴加工路径生成算法。针对当前大部分路径生成算法只适应参数曲面的问题,应用网格参数化方法ABF(Angle Based Flattening)将网格曲面展开在平面参数区域,提出基于降维策略的三轴加工路径生成方法。一方面通过主成份分析提取单次最长走刀路径生成等平面加工路径,缓解传统算法在平坦区域产生冗余路径的问题；另一方面通过提取网格边界驱动曲线生成边界平移加工路径,避免在三维空间执行切片、平移、相交和投影等复杂的几何运算过程,提高计算效率。
研究点云-参数族曲面寻位与精度评估方法。提出点云-参数族曲面寻位ADF算法,建立产品质量检测、曲线拟合、对称特征寻位等多种情况下曲面寻位的非线性优化模型。此外,重点分析曲面寻位误差与几何误差的微分运动关系,推导测点位置偏差同几何误差的线性映射关系。在考虑加工、测量等制造误差影响的情况下,构造一个具有笛卡尔坐标变换不变性的数学统计量。应用该统计量提出基于t分布的寻位精度评估模型,并据此推导出刚体变换平移误差与旋转误差的理论上限。
应用本文提出的算法初步搭建一个基于逆向工程的数字化制造平台。在数字制造装备与技术国家重点实验室已有的软硬件基础上,将本文提出的数据处理算法进行应用,初步搭建一个集成“曲面测量-数据集成-加工制造-质量检测”功能的数字化制造平台。为验证该平台统的可行性,以典型的复杂曲面为例依次执行了数据采集、数据拼合、路径生成、铣削加工、曲面寻位、质量检测等处理过程,加工出满足精度要求的产品。
Complex surfaces have been widely applied into the products development, such as automobile precise panels, propeller of naval vessel and blade of aero-engine. The research on data registration and precision machining technologies towards complex surfaces is a key point to improve the machining accuracy and efficiency of such products. Based on ingoing analysis and summary of previous works, this thesis has investigated the key technologies of data processing, such as data registration, tool path generation and surface localization et al. The major research works and contributions of the thesis are introduced as follows:
Study the coarse and fine registration algorithms of measured data. (1) For the problem that most coarse registration algorithms have difficulty in defining similarity index and handling non-overlapping data, the thesis has proposed a new algorithm based on Dimensionality-Reduction Shape Descriptions, where Harmoinic Mapping and Angle Based Flattening are used to represent mesh surfaces in both local and global manners. Therefore, searching for closest point, calculating transformation parameters, verifying overlapping regions and evaluating error can be carried out in low-dimensional space. The experimental results indicate that DRSD algorithm is efficient and robust to Gaussian noise, resolution, fixed point and occlusion. (2) For the pros and cons of current fine registration algorithms, the thesis has proposed a new algorithm based on adaptive distance function (ADF), which is used to describe the point-surface distance error. The main difference between adaptive distance function and traditional distance functions is that the curvature feature is considered to quatify point-surface shortest distance. Non-linear optimization model is established to calculate the rigid transformation. The experimental result indicates that ADF algorithm has evident superiority in balancing convergent speed and stability, especially when the initial value is poor and the surfaces have high-curvature features.
Study the tool path generation algorithm of 3-axis machining in low dimensional space. For the problem that most of current tool path generation methods are only suitable for parametric surfaces, the thesis has presented a 3-axis tool path generation method with dimensionality-reduction strategy, by applying Angle Based Flattening to strech the overall surface on parametric plane. For one hand, iso-planar tool path is generated by employing Principal Component Analysis to obtain a maximal length of machining path. Hence, redundant tool paths of traditional iso-planar methods are relieved. For the other hand, contour-translation tool path is generated by extracting a boundary drive curve on meshes. This avoids complex calculations in 3D space such as slicing, offsetting, intersection, and projection, which increases the computational efficiency.
Study the surface localization and accuracy evaluation method between point cloud data and parametric family of surfaces. The thesis has proposed an ADF localization algorithm between point and parametric family of surfaces, established the non-linear optimization model for quality inspection, curve fitting and surface localization with symmetrical features. In addition, the thesis focuses on analyzing the differential relationship between localization error and geometric error, and deriving the linear mapping relationship from the geometric error, in order to construct a mathematical statistics with Cartesian frame-independence property. With the constructed statistics, the localization result can be determined by a criminative accuracy model based on t distribution, from which the uppers of translation and rotation errors are also derived.
Set up a reverse engineering-based digital manufacture platform by applying the proposed algorithms. Based on the existing software and hardware platforms in State Key Laboratory of Digital Manufacturing Equipment and Technology, we have developed the algorithms and basically set up a digital manufacture platform which integrates surface measurement, data processing, machining and quality inspection. To verify its feasibility, a typical complex surface has been employed to implement data acquirement, point cloud registration, tool path generation, milling, surface localization and quality inspection, from which a new product with specified accuracy is produced.
引文
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