薄壁回转体几何尺寸测量的数据可视化研究
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摘要
某种薄壁回转体零件是高速飞行器的关键部件，其制造精度是影响高速飞行器性能的直接因素。对薄壁回转体的外廓形、壁厚等几何参数进行精密测量是检验其制造精度的有效手段。此类三维复杂曲面的薄壁回转体零件，深径比大，对几何参数的测量精度要求高(微米级)，现有的测量设备和测量技术在精度和效率上都无法满足高性能薄壁回转体零件的研制需求，因此本课题组研发了高精度、高效率的薄壁回转体几何尺寸检测设备。本文就该设备检测数据可视化的数学基础、方法与技术、软件编程实现等方面展开研究。
针对薄壁回转体几何形状特点以及几何尺寸测量精度要求，阐述了薄壁回转体外廓形和几何厚度测量原理，以及“一次装夹、两种测量、三轴联动”的总体设计方案。
分析总结了数据可视化的曲线、曲面重构技术数学基础。对本论文研究的测量数据可视化技术将要运用的NURBS曲面重构、三次样条拟合和插值算法等数学方法，进行了详尽的表述和分析，为实现薄壁回转体测量数据的可视化作了重要铺垫。
提出了一种薄壁回转体外廓型面数据可视化描述的NURBS曲面反求算法。根据该检测设备测得的外廓形数据，利用曲面型值点反求NURBS曲面控制点算法，并对节点矢量计算及边界条件构造进行了初步研究，给出了此种薄壁回转体外廓型面NURBS表达方法。
研究了基于三次样条曲线拟合及插值算法的壁厚测量数据可视化技术。针对壁厚区域检测方式得到的数据，利用三次样条拟合测量母线，并采用插值算法计算测量区域网格点坐标、壁厚等数据，构建壁厚测量区域曲面。
开发了测量数据可视化软件系统。基于VC++6.0开发平台，利用OpenGL编程技术，实现了测量数据预处理、薄壁回转体外廓型面可视化、壁厚误差三维云图和二维截面云图可视化。
配置本测量数据可视化系统的薄壁回转体几何尺寸检测设备已经交付某单位应用，解决了此类薄壁回转体几何参数精密测量的难题。应用结果表明，本测量数据可视化软件系统显示效果逼真，人机界面友好，输出数据准确，运行稳定。
A kind of thin wall revolving body is a key part in a high speed aircraft. Its machining precision could directly affect the stability of high speed aircrafts in flight. Measuring geometry parameters such as profile and thickness precisely is a effective instrument to test the machining precision of the thin wall revolving body. The thin wall revolving body is a kind of thin-wall part with complex three-dimension surface and large ratio of depth and radius. But the demand of measuring precise for the geometry parameters is very strict (0.001mm level). Researches on the high performance thin wall revolving body could not be addressed by existing measuring equipments and techniques in accuracy and efficiency. So our research team developed a high precision and high efficiency thin wall revolving body geometry dimension measuring facility. Math base, software programs and technology to visualize the data got by the facility are all researched in this paper.
Considering the geometry characters of the thin wall revolving body and measuring precision demand on profile and thickness, measuring principle and the total design scheme that installing once, measuring twice and three axis linkage are introduced.
Mathematic algorithms that visualize data into curves and surfaces are summed up and analyzed. Mathematics that will be used in data visualization such as NURBS surface re-construction, cubic spline fitting and interpolation arithmetic are expressed and analyzed in details. All prepares for the visualization of the thin wall revolving body's measuring data.
NURBS surface re-construction algorithm which is used to visualize profiles is put forward. According to the profile data measured by this facility, NURBS surface re-construction algorithm is used. And vector calculations of reference points and the constructions of boundary conditions are primarily researched in this paper. The NURBS algorithm which express the profile of thin wall revolving body is also given
The thickness data visualization technology which is basing on curve fitting of cubic spline and interpolation algorithm is researched. For the data got by regional measuring mode in thickness measure, cubic spline is used to measure generatrix. And not only is interpolation algorithm used to compute thickness data and the coordinates of reseau points in measuring region but also to construct the surface of thickness measuring region.
Measuring data visualization software system is developed. Data pretreatment, the profile visualization of the thin wall revolving body, three-dimension error nephogram of thickness and two-dimension section nephogram are all realized basing on the visual technology of OpenGL on VC++ 6.0 development platform.
The thin wall revolving body geometry dimension measuring facility which installs this data visualization system has been delivered to some war industry department. The difficult problem of thin wall revolving body geometry precise measurement is solved very well. Application result indicates that this data visualization software could display vividly besides its friendly human-machine interface, accurate output and stability.
针对薄壁回转体几何形状特点以及几何尺寸测量精度要求，阐述了薄壁回转体外廓形和几何厚度测量原理，以及“一次装夹、两种测量、三轴联动”的总体设计方案。
分析总结了数据可视化的曲线、曲面重构技术数学基础。对本论文研究的测量数据可视化技术将要运用的NURBS曲面重构、三次样条拟合和插值算法等数学方法，进行了详尽的表述和分析，为实现薄壁回转体测量数据的可视化作了重要铺垫。
提出了一种薄壁回转体外廓型面数据可视化描述的NURBS曲面反求算法。根据该检测设备测得的外廓形数据，利用曲面型值点反求NURBS曲面控制点算法，并对节点矢量计算及边界条件构造进行了初步研究，给出了此种薄壁回转体外廓型面NURBS表达方法。
研究了基于三次样条曲线拟合及插值算法的壁厚测量数据可视化技术。针对壁厚区域检测方式得到的数据，利用三次样条拟合测量母线，并采用插值算法计算测量区域网格点坐标、壁厚等数据，构建壁厚测量区域曲面。
开发了测量数据可视化软件系统。基于VC++6.0开发平台，利用OpenGL编程技术，实现了测量数据预处理、薄壁回转体外廓型面可视化、壁厚误差三维云图和二维截面云图可视化。
配置本测量数据可视化系统的薄壁回转体几何尺寸检测设备已经交付某单位应用，解决了此类薄壁回转体几何参数精密测量的难题。应用结果表明，本测量数据可视化软件系统显示效果逼真，人机界面友好，输出数据准确，运行稳定。
A kind of thin wall revolving body is a key part in a high speed aircraft. Its machining precision could directly affect the stability of high speed aircrafts in flight. Measuring geometry parameters such as profile and thickness precisely is a effective instrument to test the machining precision of the thin wall revolving body. The thin wall revolving body is a kind of thin-wall part with complex three-dimension surface and large ratio of depth and radius. But the demand of measuring precise for the geometry parameters is very strict (0.001mm level). Researches on the high performance thin wall revolving body could not be addressed by existing measuring equipments and techniques in accuracy and efficiency. So our research team developed a high precision and high efficiency thin wall revolving body geometry dimension measuring facility. Math base, software programs and technology to visualize the data got by the facility are all researched in this paper.
Considering the geometry characters of the thin wall revolving body and measuring precision demand on profile and thickness, measuring principle and the total design scheme that installing once, measuring twice and three axis linkage are introduced.
Mathematic algorithms that visualize data into curves and surfaces are summed up and analyzed. Mathematics that will be used in data visualization such as NURBS surface re-construction, cubic spline fitting and interpolation arithmetic are expressed and analyzed in details. All prepares for the visualization of the thin wall revolving body's measuring data.
NURBS surface re-construction algorithm which is used to visualize profiles is put forward. According to the profile data measured by this facility, NURBS surface re-construction algorithm is used. And vector calculations of reference points and the constructions of boundary conditions are primarily researched in this paper. The NURBS algorithm which express the profile of thin wall revolving body is also given
The thickness data visualization technology which is basing on curve fitting of cubic spline and interpolation algorithm is researched. For the data got by regional measuring mode in thickness measure, cubic spline is used to measure generatrix. And not only is interpolation algorithm used to compute thickness data and the coordinates of reseau points in measuring region but also to construct the surface of thickness measuring region.
Measuring data visualization software system is developed. Data pretreatment, the profile visualization of the thin wall revolving body, three-dimension error nephogram of thickness and two-dimension section nephogram are all realized basing on the visual technology of OpenGL on VC++ 6.0 development platform.
The thin wall revolving body geometry dimension measuring facility which installs this data visualization system has been delivered to some war industry department. The difficult problem of thin wall revolving body geometry precise measurement is solved very well. Application result indicates that this data visualization software could display vividly besides its friendly human-machine interface, accurate output and stability.
引文
[1] 敖辽辉．薄壁回转体技术的发展[J]．电讯技术，2000，40(2)：14-15．
[2] 彭望泽．防空薄壁回转体[M]．北京：宇航出版社，1993．
[3] 张谟杰．俄罗斯高速飞行器薄壁回转体研制情况介绍——赴俄罗斯考察报告[J]．制导与引信．1998(1)：17-18．
[4] 张国雄．三坐标测量机．天津：天津大学出版社，1999．
[5] 宋开臣，张国雄．空间自由曲面的非接触测量．中国机械工程，1999，10(6)：661-663．
[6] Stovicek D.R. Non-contact metrology. Tooling and Production, 1993(3): 13-15, 18.
[7] Kanji M, et al. Development of automatic non-contact measuring system of 3-D model shape of injection model (in Japanese). JSPE, 1989, 55(2): 393-399.
[8] Kanji M, et al. Development of non-contact profile sensor for 3-D free-form surface (second report)-properties of optical ring image sensor (in Japanese). JSPE, 1992, 58(12): 2087-2092.
[9] Kanji M, et al. Optical non-contact measuring instrument of 3-D shape (in Japanese). JSPE, 1993, 59(7): 1091-1096.
[10] T. Akuta, et al. Development of an automatic 3-D shape measuring system using a new auto-focusing method. Measurement, 1990, 9(3): 98-103.
[11] T. Akuta, Automatic 3-D shape measurement system by laser scanning control. Preprints of 29th Associate Conference of Automatic Control, 1986, Tokyo, Japan, 4002: 563-566.
[12] O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura and T. Kurosawa. Development of a coordinate measuring system with tracking laser-interferometer. Annals of the CIRP, 1991, 40(1): 523-526.
[13] Walter Zurcher, Raimund Loser. Improved reflector for interferometer tracking in three dimensions. Optical Engineering, 1995, 34(9).
[14] 宋甲午，张国正，安志勇等．圆度误差的激光扫描非接触测量方法[M]．兵工学报，2000，21(1)：61-63．
[15] 张春富，张军，唐文彦等．激光跟踪仪在大尺寸工件几何参数测量中的应用[M]．工具技术，2002，36(5)：26-28．
[16] 姚宝国．薄壁回转体几何参数测量原理及关键技术研究：(博士学位论文)．大连：大连理工大学，2003．
[17] 李东，孙长嵩，苏小红等．计算机图形学实用教程[M]．北京：人民邮电出版社，2004．
[18] 陈元琰，张睿哲，吴东等．计算机图形学实用技术[M]．北京：清华大学出版社，2007．
[19] 陈和平，邵平凡，汤惟．可视化编程技术及应用[M]．武汉：武汉理工大学出版社，2005．
[20] 李彪．薄壁回转体几何参数测量设备控制系统研究：(硕士学位论文)．大连：大连理工大学，2007．
[21] 施吉林，张宏伟，金光日．计算机科学计算[M]．北京：高等教育出版社，2005．
[22] 徐士良．数值分析与算法[M]．北京：机械工业出版社，2007．
[23] 施法中．计算机辅助设计与非均匀有理B样条．北京：高等教育出版社，2001．
[24] 吕丹，童创明，邓发升等．三次NURBS曲线控制点的计算[J]．弹箭与制导学报，26(4)：357-359．
[25] 张明霞，纪卓尚，林焰．面向计算的船体曲面NURBS造型[J]．船舶工程，2001(5)：11-12，40．
[26] B K Choi, W S Yoo, C S Lee. Matrix Representation for NURBS Curves and Surfaces [J]. Computer-Aided Design, 1990, 22(4): 235-240.
[27] 朱心雄．自由曲线曲面造型技术[M]．北京：科学出版社，2000．
[28] Nam J H, Parsons M G. A parametric approach for initial hull form modeling using NURBS representation [J]. Journal of Ship Production, 2000, 16(2): 76-89.
[29] 陈文略，王子羊．三次样条插值在工程拟合中的应用[J]．华中师范大学学报(自然科学版)．2004，38(4)：418-422．
[30] 姚宝国，徐志祥，王小明等．薄壁回转体几何参数测量仪软件系统研究[J]．大连理工大学学报，2000，40(4)：451-455．
[31] 娄鑫．薄壁回转体计算机辅助制造软件的研发：(硕士学位论文)．大连：大连理工大学，2001．
[32] Steven Holzner. Visual C++6轻松进阶[M]．王岚波等译．北京：电子工业出版社，1999．
[33] 郑阿奇，丁有和．Visual C++教程[M]．北京：清华大学出版社，2005．
[34] 李胜睿等．计算机图形学实验教程(OpenGL版)[M]．北京：机械工业出版社，2004．
[35] 费广正，芦丽丹，陈立新．可视化OpenGL程序设计[M]．北京：清华大学出版社，2001．
[36] (美)K．霍金，D．阿斯特．OpenGL游戏程序设计[M]．田昱川译．北京：科学出版社，2006．
[37] 潘贻亮．高速飞行器薄壁回转体精密修磨机床的CAM软件设计与开发：(硕士学位论文)．大连：大连理工大学，2003．
[38] 潘建华，卫跃文．C语言实用软件界面技术[M]．西安：西安电子科技大学出版社，1995．
[39] 乔林，费广正，林杜．OpenGL程序设计[M]．北京：清华大学出版社，2000．
[40] 史爱峰．薄壁回转体电厚度测量设备控制系统设计：(硕士学位论文)．大连：大连理工大学，2005．
[41] 石琼，沈春林，谭皓．基于OpenGL的三维建模实现方法．计算机工程与应用．2004(18)：122-124．
[42] 姚红革，李瀚山．基于OpenGL的三维实体的开发与控制．西安工业学院学报．2005．8，25(4)：335-339．
[43] 杨老师．Visual C++中操纵MS Word 123．http://www.vckbase.com/document/viewdoc/?id=1174
[2] 彭望泽．防空薄壁回转体[M]．北京：宇航出版社，1993．
[3] 张谟杰．俄罗斯高速飞行器薄壁回转体研制情况介绍——赴俄罗斯考察报告[J]．制导与引信．1998(1)：17-18．
[4] 张国雄．三坐标测量机．天津：天津大学出版社，1999．
[5] 宋开臣，张国雄．空间自由曲面的非接触测量．中国机械工程，1999，10(6)：661-663．
[6] Stovicek D.R. Non-contact metrology. Tooling and Production, 1993(3): 13-15, 18.
[7] Kanji M, et al. Development of automatic non-contact measuring system of 3-D model shape of injection model (in Japanese). JSPE, 1989, 55(2): 393-399.
[8] Kanji M, et al. Development of non-contact profile sensor for 3-D free-form surface (second report)-properties of optical ring image sensor (in Japanese). JSPE, 1992, 58(12): 2087-2092.
[9] Kanji M, et al. Optical non-contact measuring instrument of 3-D shape (in Japanese). JSPE, 1993, 59(7): 1091-1096.
[10] T. Akuta, et al. Development of an automatic 3-D shape measuring system using a new auto-focusing method. Measurement, 1990, 9(3): 98-103.
[11] T. Akuta, Automatic 3-D shape measurement system by laser scanning control. Preprints of 29th Associate Conference of Automatic Control, 1986, Tokyo, Japan, 4002: 563-566.
[12] O. Nakamura, M. Goto, K. Toyoda, Y. Tanimura and T. Kurosawa. Development of a coordinate measuring system with tracking laser-interferometer. Annals of the CIRP, 1991, 40(1): 523-526.
[13] Walter Zurcher, Raimund Loser. Improved reflector for interferometer tracking in three dimensions. Optical Engineering, 1995, 34(9).
[14] 宋甲午，张国正，安志勇等．圆度误差的激光扫描非接触测量方法[M]．兵工学报，2000，21(1)：61-63．
[15] 张春富，张军，唐文彦等．激光跟踪仪在大尺寸工件几何参数测量中的应用[M]．工具技术，2002，36(5)：26-28．
[16] 姚宝国．薄壁回转体几何参数测量原理及关键技术研究：(博士学位论文)．大连：大连理工大学，2003．
[17] 李东，孙长嵩，苏小红等．计算机图形学实用教程[M]．北京：人民邮电出版社，2004．
[18] 陈元琰，张睿哲，吴东等．计算机图形学实用技术[M]．北京：清华大学出版社，2007．
[19] 陈和平，邵平凡，汤惟．可视化编程技术及应用[M]．武汉：武汉理工大学出版社，2005．
[20] 李彪．薄壁回转体几何参数测量设备控制系统研究：(硕士学位论文)．大连：大连理工大学，2007．
[21] 施吉林，张宏伟，金光日．计算机科学计算[M]．北京：高等教育出版社，2005．
[22] 徐士良．数值分析与算法[M]．北京：机械工业出版社，2007．
[23] 施法中．计算机辅助设计与非均匀有理B样条．北京：高等教育出版社，2001．
[24] 吕丹，童创明，邓发升等．三次NURBS曲线控制点的计算[J]．弹箭与制导学报，26(4)：357-359．
[25] 张明霞，纪卓尚，林焰．面向计算的船体曲面NURBS造型[J]．船舶工程，2001(5)：11-12，40．
[26] B K Choi, W S Yoo, C S Lee. Matrix Representation for NURBS Curves and Surfaces [J]. Computer-Aided Design, 1990, 22(4): 235-240.
[27] 朱心雄．自由曲线曲面造型技术[M]．北京：科学出版社，2000．
[28] Nam J H, Parsons M G. A parametric approach for initial hull form modeling using NURBS representation [J]. Journal of Ship Production, 2000, 16(2): 76-89.
[29] 陈文略，王子羊．三次样条插值在工程拟合中的应用[J]．华中师范大学学报(自然科学版)．2004，38(4)：418-422．
[30] 姚宝国，徐志祥，王小明等．薄壁回转体几何参数测量仪软件系统研究[J]．大连理工大学学报，2000，40(4)：451-455．
[31] 娄鑫．薄壁回转体计算机辅助制造软件的研发：(硕士学位论文)．大连：大连理工大学，2001．
[32] Steven Holzner. Visual C++6轻松进阶[M]．王岚波等译．北京：电子工业出版社，1999．
[33] 郑阿奇，丁有和．Visual C++教程[M]．北京：清华大学出版社，2005．
[34] 李胜睿等．计算机图形学实验教程(OpenGL版)[M]．北京：机械工业出版社，2004．
[35] 费广正，芦丽丹，陈立新．可视化OpenGL程序设计[M]．北京：清华大学出版社，2001．
[36] (美)K．霍金，D．阿斯特．OpenGL游戏程序设计[M]．田昱川译．北京：科学出版社，2006．
[37] 潘贻亮．高速飞行器薄壁回转体精密修磨机床的CAM软件设计与开发：(硕士学位论文)．大连：大连理工大学，2003．
[38] 潘建华，卫跃文．C语言实用软件界面技术[M]．西安：西安电子科技大学出版社，1995．
[39] 乔林，费广正，林杜．OpenGL程序设计[M]．北京：清华大学出版社，2000．
[40] 史爱峰．薄壁回转体电厚度测量设备控制系统设计：(硕士学位论文)．大连：大连理工大学，2005．
[41] 石琼，沈春林，谭皓．基于OpenGL的三维建模实现方法．计算机工程与应用．2004(18)：122-124．
[42] 姚红革，李瀚山．基于OpenGL的三维实体的开发与控制．西安工业学院学报．2005．8，25(4)：335-339．
[43] 杨老师．Visual C++中操纵MS Word 123．http://www.vckbase.com/document/viewdoc/?id=1174