【作者】 彭悦；

【导师】 刘书桂；

【作者基本信息】 天津大学 ， 测试计量技术及仪器， 2013， 博士

【摘要】 包括航空发动机的叶盘和叶片等零件在内的复杂自由曲面，其扭曲角度较大，制造难度远大于一般的自由曲面，而这些零件往往决定着装备的总体性能和水平，甚至影响着一个国家的科技水平和国防实力。现有的自由曲面测量、数据处理、曲面拟合及误差评定等方法主要针对一般的自由曲面，虽然在点云数据建模及误差评定方面已有一些商业软件和文献报道，但对于扭曲的自由曲面来说，不少商业软件和文献方法的实际使用效果不佳，且极少针对具有较大扭曲转角和极薄边缘的自由曲面进行点云建模与评定。研究适用于扭曲自由曲面的测量数据处理与误差评定方法对于提高复杂零件的加工精度，提高我国科技水平都具有重要的意义。本论文针对扭曲自由曲面，对测量数据的预处理、自由曲面的连续性拼接、自由曲面的拟合技术和基于坐标系统一的误差评定方法进行了深入的研究。论文的主要工作包括：简单介绍了天津大学精密测试技术及仪器国家重点实验室自主开发、研制的在线原位高精度测量机的结构，及测量机基本参数与误差的标定和补偿原理。该测量机能够测量包括直径在1000mm以内、曲面片之间空隙可窄至10mm、扭转角可高达65°的扭曲自由曲面，且测量不确定度不超过0.01mm。对在线原位测量机所测得的扭曲自由曲面型值点数据进行了预处理。首先，对多次测量得到的数据进行坐标变换和坐标归一化的处理，使其成为统一的点云数据，并运用双正交小波实现点云数据的去噪，并提出了基于第二代小波变换上升格式的数据删减算法，此方法计算量小，计算速度快，适用于自适应、非线性的变换，而且可以确保变换的可逆性，文中用实验结果比较了此方法和其他数据删减方法的效果，表明其能更好的适应和实现扭曲自由曲面点云数据的删减。通过深入分析分片Bezier曲面的拼接理论，考虑到Bezier曲线是NURBS（非均匀有理B样条）曲线的特殊格式，提出了借助分片Bezier曲面的G1连续性条件进行NURBS曲面拼接的思想，推导并实现了NURBS曲面间的G1光滑拼接。通过求解多片NURBS曲面G1光滑连续的约束方程，获得了多片NURBS曲面G1光滑连续时角点处的控制顶点和两张相邻NURBS曲面片G1光滑连续约束方程的初始条件，为预处理后的数据点进行参数化和曲面拟合提供了基础。在对已有的数据参数化方法进行深入研究的基础上创立了一种数据参数化的算法。经过分析参数化的两种方案，选择直接在由折线围成的空间四边区域内进行参数化。通过坐标变换、点面投影把空间四边区域的数据参数化问题转化为了平面四边区域网格划分问题，通过提出平面四边区域两向弹性网格生成算法快速实现了由折线围成的空间区域的参数化；提出了基于B样条基函数快速计算和控制顶点数目优化的张量积双向NURBS拟合方法，通过NURBS曲面分片拟合可得到整体G1光滑连续的曲面，并通过比较本文的实验结果和文献中的结果，说明了本文方法针对扭曲自由曲面拟合的有效性和优势。对拟合所得到的G1光滑连续的扭曲自由曲面进行了测头半径补偿和误差评定。对测量数据直接进行测头半径补偿的办法会给测量带来负担，且误差较大，本文在得到曲面拟合模型之后再进行测头半径补偿，研究了求取已知模型上任意点法矢量的算法，在法矢量方向进行测头半径补偿。为了评定产品是否符合原始设计要求，需要与设计给定的数学模型进行比较，即进行误差的分析；经过测头半径补偿后的拟合曲面与理论数据间存在着位置误差，即二者的坐标系往往是不统一的，需要先进行坐标系的配准才能进行误差评定，本文认为每个理论数据到被测曲面的距离平方和为最小时，理论坐标系与测量坐标系就匹配到了一起，在此基础上根据点到曲面的法向最短距离可得到扭曲自由曲面的形状误差。更多还原

【Abstract】 The complex free-form surfaces, blisk and blade of aero engine included, arebig-twisted, they have more manufacture difficulties than the common free-formsurface, but the complex part decides the overall performance of the equipment, eveneffectes the technological level and national defense capabilities. Existing methods offree-form surface measurement、surface fitting and error evaluation mainly targetedthe common free-form surface, some methods in business software and literature wereineffective for twisted free-form surface, and barely studied for the surface withbig-twist and thin edge. So the study on data processing and evaluation for twistedfree-form surface is very important for improving the accuracy of complex part andtechnological level of our country.For the twisted free-form surface, this paper studied the data preprocessing, thecontinued montage of free-form surface, fitting and error evaluation under theuniform coordinate system, based on the point cloud measured by the on-line in-situhigh-precision machine. The main work is as follows:The structural design and error calibration of on-line in-situ measuring machinedeveloped by State Key Laboratory of precision measurement technology andinstruments in Tianjin University was described, and the error compensation ofthermal deformation and optical distortion was proposed the measuring machinecould measure all kinds of complex twisted free-form surfaces, including the surfacewas smaller than1000mm in diameter, with the gap between patches only10mm, thetorsion angle can be65°,and the measuring error was no more than0.01mm.The deleting method of abnormal noises is researched. Ineorporating the3δ lawof mathematical statistics, by means of calculating mean and standard error todeterminate threshold, the adaptive counting threshold method is putforward, whichhas well adaptivity. Denoising cloudy data based wavelet technology is researched.Using wavelet technology to denoise is the process of decomposing signal withwavelet, acquiring approximate coeffieients and detail coeffieients, acting detailedcoefficients with soft threshold to suppress noises, then reconstructing signal to getthe goal of denoising. The key of simplifying data technique is retaining originalfeatures of cloudy data utmost. On the basis of reseaching current simplification technique, new method using second generation wavelet based on lifting tosimplification data is proposed.TheG1smooth merging theory of the piecewise Bezier surface is analyzed, theBezier curve is a special NURBS curve is considered, the idea of resort to BeziersurfaceG1continuous condition for solving theG1continuous condition ofNURBS surfaces is presented.G1continuous condition of the NURBS is deducedand realized. Linear system ofG1continuous condition is solved, which providedthe basis for the following surface fitting.The existing grid generation theory is studied, incapability of grid generation thatthese theory to the four sided region constructed by four discontinuous broken line isfound. A rapid parametrization algorithm which is used to spatial four-sided region ontriangular mesh is presented in the paper. By comparing two kinds of parametrizationprojects of the spatial four-sided region, directly grid generation algorithm is chose. Aplanar two-directional flexing grid generation algorithm is presented which canquickly parametrizing the planar four-sided region, in fact, a spatial four-sided regionis parametrizated. Comparing two NURBS surface fitting methods, in order toenhance the fitting precision and obtain more detail information of the NURBSsurface fitting, two-directional fitting method is adopted to fitting the NURBS surface.For the points on the common boundaries and corners is restricted base on theG1smooth connection condition. So by fitting every patches and a wholeG1smoothsurface is obtained.Based on non-uniform B-splines, a new algorithm of calculating the normalvector at random position was deduced, and a formula with probe radius correctionwas proposed. An optimization algorithm named simplex method was applied in orderto eliminating the orientation error in the stage of workpiece measurement. It cansettle surfaces matching well by shifting and rotating the measuring coordinatesystem.更多还原