复杂曲面布点策略与误差评定方法研究
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摘要
随着现代制造业的快速发展,人们对零部件轮廓构造提出多元化要求的同时,对零部件表面质量的要求也相应提高。加工质量推动着几何量检测技术的发展。布点方法与误差评定算法对提高检测质量和效率有着直接的影响。本文主要对复杂曲面的布点策略和误差评定方法进行了研究。
本文首先对复杂曲面测点分布问题进行了研究,提出了一种基于距离的曲线、曲面布点方法。根据曲线-曲面的关系,在对曲线布点方法进行研究的基础上,将其扩展来解决曲面的采样问题。根据加工要求对曲线进行初始测点分割,然后逐层求精、迭代选点,实现了曲线的自适应布点。进而应用初始网格点与基于距离的迭代选点相结合的采样方法,实现了曲面测点的自适应分布。该方法使测点能够随曲面曲率变化进行疏密分布,有效的反映曲面的拓扑信息。
其次,对复杂曲面的误差评定方法进行了研究。利用最小二乘法构建误差评定的目标函数。通过对齐局部坐标系和构建点对约束条件,优化了初始条件,然后应用迭代最近点(ICP)算法,对影响曲面位移与旋转的六个参数进行优化,从而完成了复杂曲面轮廓度误差的评定工作。根据加工中的基准情况和曲面成型理论,针对大坡度以及曲率变化平缓的曲面提出了投影转换坐标、用平面度最小区域法求解的方法。
最后利用仿真实验对上述算法进行了相关验证。采用基于距离的曲面布点方法,对仿真曲面进行自适应布点,并通过添加误差项来模拟真实测点,然后应用ICP法和投影法分别对其进行了误差评价。实验表明,文中方法稳定有效,具有实用性。
With the rapid development of modern manufacturing industry, diversification requirements on the parts contour structure are promoted, while requirements of the surface quality are correspondingly increased. Development of geometric measurement is promoted by high processing quality. Improvement of inspection quality and efficiency is directly affected by point distribution method and error evaluation algorithm. The point distribution strategy and error evaluation on sculpture surface are mainly studied in this paper.
First of all, point distribution is studied based on surface processing sampling problems and a new method of sampling on curve and surface based on distance is approved. In view of curve-surface relationship, the method of point distribution on the curve is studied and then it is extended to address the issue of surface sampling. Curve is divided by initial measurement points according to processing requirement and then adaptive point distribution is achieved by refinement and iterative search. Adaptive point distribution on surface is realized by the method on combination of initial grid points and iterative points based on distance. Point density distribution can be varied with the change of surface curvature and surface topology information is effectively reflected.
Then, error evaluation method on surface is studied. The objective function is set up using least square method. The initial conditions are optimized by the alignment of local coordinate system and points constraint constructed. Profile error evaluation is completed by using iterative closest point (ICP) algorithm, while six parameters relative to surface pose are optimized. In view of reference and surface forming theory, an approach is promoted for surface with large scope and curvature changed slowly. Firstly coordinates are projected, and then the minimum zone method for flatness solving is used.
Finally, the algorithms mentioned are verified by simulation experiments. The adaptive point distribution on simulation surface is realized by the surface point distribution method based on distance. And the actual measuring points are simulated by adding error term. Then error evaluation is completed by ICP and projection method, respectively. The results of experiment show that the methods mentioned are effective and practical.
本文首先对复杂曲面测点分布问题进行了研究,提出了一种基于距离的曲线、曲面布点方法。根据曲线-曲面的关系,在对曲线布点方法进行研究的基础上,将其扩展来解决曲面的采样问题。根据加工要求对曲线进行初始测点分割,然后逐层求精、迭代选点,实现了曲线的自适应布点。进而应用初始网格点与基于距离的迭代选点相结合的采样方法,实现了曲面测点的自适应分布。该方法使测点能够随曲面曲率变化进行疏密分布,有效的反映曲面的拓扑信息。
其次,对复杂曲面的误差评定方法进行了研究。利用最小二乘法构建误差评定的目标函数。通过对齐局部坐标系和构建点对约束条件,优化了初始条件,然后应用迭代最近点(ICP)算法,对影响曲面位移与旋转的六个参数进行优化,从而完成了复杂曲面轮廓度误差的评定工作。根据加工中的基准情况和曲面成型理论,针对大坡度以及曲率变化平缓的曲面提出了投影转换坐标、用平面度最小区域法求解的方法。
最后利用仿真实验对上述算法进行了相关验证。采用基于距离的曲面布点方法,对仿真曲面进行自适应布点,并通过添加误差项来模拟真实测点,然后应用ICP法和投影法分别对其进行了误差评价。实验表明,文中方法稳定有效,具有实用性。
With the rapid development of modern manufacturing industry, diversification requirements on the parts contour structure are promoted, while requirements of the surface quality are correspondingly increased. Development of geometric measurement is promoted by high processing quality. Improvement of inspection quality and efficiency is directly affected by point distribution method and error evaluation algorithm. The point distribution strategy and error evaluation on sculpture surface are mainly studied in this paper.
First of all, point distribution is studied based on surface processing sampling problems and a new method of sampling on curve and surface based on distance is approved. In view of curve-surface relationship, the method of point distribution on the curve is studied and then it is extended to address the issue of surface sampling. Curve is divided by initial measurement points according to processing requirement and then adaptive point distribution is achieved by refinement and iterative search. Adaptive point distribution on surface is realized by the method on combination of initial grid points and iterative points based on distance. Point density distribution can be varied with the change of surface curvature and surface topology information is effectively reflected.
Then, error evaluation method on surface is studied. The objective function is set up using least square method. The initial conditions are optimized by the alignment of local coordinate system and points constraint constructed. Profile error evaluation is completed by using iterative closest point (ICP) algorithm, while six parameters relative to surface pose are optimized. In view of reference and surface forming theory, an approach is promoted for surface with large scope and curvature changed slowly. Firstly coordinates are projected, and then the minimum zone method for flatness solving is used.
Finally, the algorithms mentioned are verified by simulation experiments. The adaptive point distribution on simulation surface is realized by the surface point distribution method based on distance. And the actual measuring points are simulated by adding error term. Then error evaluation is completed by ICP and projection method, respectively. The results of experiment show that the methods mentioned are effective and practical.
引文
[1]甘永立,几何量公差与检测(第九版),上海:上海科学技术出版社,2010
[2]兰诗涛,自由曲面接触式测量方法研究与原型系统研制:[硕士学位论文],浙江:浙江大学,2004
[3]张国雄,三坐标测量机,天津:天津大学出版社, 1998
[4] Xie Zexiao,Wang Jiangguo,Jin Ming,Study On a full field of view laser scanning system,Machine Tools &Manufacture,2007(47):33~43
[5]王邦凯,杨辰龙,胡小辉等,大曲面工件超声检测技术研究,第十届全国无损检测新技术学术会议,20070522
[6]刘峥,自由曲线、自由曲面的误差评定软件的研制:[硕士学位论文],陕西:西安交通大学,2003
[7]何改云,形位误差的逼近原理与算法研究:[博士学位论文],天津:天津大学,22
[8] Cui C C,Che R Sh,Ye D et al,Sphericity error evaluation using the genetic algorithm,Optics and Precision Engineering,2002,10(4):333~339
[9] Guohua Jiang,Optimization approach for the evaluation of geometric errors in computer-aided inspection,Wichita :Wichita State University,2000
[10] ANSI Y14.5.1,Mathematical Definition of Dimensioning and Tolerancing Principles,1994
[11]单东日,柯映林,刘云峰,反求工程中复杂曲面测量规划研究,中国机械工程,2003,14(1):9~13
[12] Koster M,Curvature-dependent Parameterization of Curves and Surface, Computer-Aided Design,1991,23(8):569~579
[13] S Z Li,Adaptive Sampling and Mesh Generation,Computer-Aided Design,1995,27(3):235~240
[14]来新民,黄田,林忠钦等,数学模型已知的自由曲面数字化的自适应采样,计算机辅助设计与图形学学报,1999,11(4):359~362
[15] MENG C,YAN H,LAI G,Automated precision measurement of surface profile in CAD-directed inspection,IEEE Transactions on Robotics and Automation,1992,8(2):268~278
[16] Zhang Y F,Nee A Y C,Fuh J Y Hetal,A Neural Network Approach toDetermining Optimal Inspection Sampling Size for CMM,Computer Integated Manufacturing System,1996,9(3):161~169
[17] Merat F L,Radack G M,Automatic Inspection Planning within a Fcature-based CAD System,Robotics &Computer-Integrated Manufacturing,1992,19(1):61~69
[18]高国军,陈康宁,林志航等,用CMM检测自由曲面时检测点和路径的规划方法研究,西安交通大学学报,1996,30(7):57~63
[19]王平江,陈吉红,李作清等,空间自由曲面测量系统中的测点自动布置,计量技术,1995,12:10~13
[20]谢金,王文,李剑等,自由曲面测量中测点自适应规划方法研究,机电工程,2001,18(5):54~56
[21]陈丽萍,姜歌东,王小椿,一种高效的自由曲面求交算法,西安交通大学学报,2000,34(3):70~74
[22]方逵,谭元发,吴泉源,近似弧长参数化的一种数值算法,工程数学学报,2002,19(3):123~127
[23]王广彦,董继国,加工中心在线测头在自由曲线检测中的应用,组合机床与自动化加工技术,2003,7:60~62
[24]吴思源,周晓军,江健等,超声检测中曲面重构和路径规划方法研究,浙江大学学报(工学报),2006,40(5):763~767
[25]刘达新,赵韩,董玉德等,三坐标测量机无碰撞检测路径的生成,计算机辅助设计与图形学学报,2009,21(6):801~808
[26]王世刚,付宜利,数字化环境下在线检测路径优化技术的研究,组合机床与自动化加工技术,2009,5:52~56
[27]彭俊松,白作霖,李春波等,基于分布式协同求解技术的CMM检测路径神经网络优化,西安交通大学学报,1997,31(7):40~46
[28]邹刚,王亚平,李永刚,三坐标测量机测量路径自动生成的研究,航空计测技术,2004,24(3):6~8
[29]王世刚,基于CMM测量路径优化算法的研究,机械科学与技术,2005,24(5):606~608
[30]杨泽青,刘丽冰,谭志洪等,自适应遗传算法在柔性检测路径规划中的应用,Proceeding of the 27th Chinese Control Conference July 16-18,2008,Kunming,Yunnan,China
[31] Besl P J,McKay N D,A method for registration of 3-D shape,Trans Patt and Mach Intell,1992,14:239~255
[32]张结红,自由曲线、自由曲面的误差评定软件的研制:[硕士学位论文],陕西:西安交通大学,1993
[33]王旭蕴,张玉坤,轮廓度误差的精密测量和评定,计量学报,1995,16(1):12~16
[34]金小刚,马天驰,冯结青等,基于最佳圆弧样条逼近的快速距离曲面计算,中国图象图形学报,2001,6(5):486~490
[35]王伯平,曾建潮,一种自调整的空间面轮廓度误差的评定方法,计量学报,2002,23(2):106~108
[36]董明晓,郑康平,许伯彦等,一种快速求取空间点到曲面最短距离的算法,组合机床与自动化,2004,9:11~12
[37]刘浩,唐月红,NURBS曲面间的最短距离,南京理工大学学报,2002,26(4):420~425
[38] Tom Duff,Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry,Computer Graphics,1992,26(2):131~138
[39]叶晓平,龚友平,陈国金,快速求解点到自由曲面的距离的方法,工程图学学报,2008,4:91~95
[40] Wang Jianhua,Li Zhengyu,Offset Surface Generation of Bicubic B-spline and Fast Convergence Check,In:Zhou Zhaoying,The Proceedings of the Conference on MODMM,Beijing,1993;International Academic Publishers,1993:54~58
[41]朱心雄,自由曲线曲面造型技术,北京:科学出版社,2000:20~30
[42]李涛,贺勇军,刘志俭等,Mat lab工具箱应用指南-应用数学篇,北京:电子工业出版社,2000:160~162
[43]金涛,童水光等,逆向工程技术,北京:机械工业出版社,2003:48~53
[44]解则晓,冯国馨,张国雄,自由曲线曲面测量中的测点布置与准确度,计量技术,1999,12:21~23
[45]熊有伦,线轮廓度和面轮廓度的评定和判别,计量学报,1991,12(2):108~115
[46]范裕健,赵单贤,用最小区域法评定形状误差的数学模型,西安交通大学学报,1987(4):105~111
[47] Zhu L M,Xiong Z H,Ding H et al,A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface,Journal of Manufacturing Science and Engineering,2004,126(3):542~554
[48]石静,自由曲线、自由曲面误差评定系统的研究与开发:[硕士学位论文],上海:华东理工大学,2005
[49] Paul J. Besl,Neil D,McKay,A method for registration of 3-D shapes,IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239~256
[50]甘永立,何改云,几何误差检测问答,上海:上海科学技术出版社,2009,8:56~57
[2]兰诗涛,自由曲面接触式测量方法研究与原型系统研制:[硕士学位论文],浙江:浙江大学,2004
[3]张国雄,三坐标测量机,天津:天津大学出版社, 1998
[4] Xie Zexiao,Wang Jiangguo,Jin Ming,Study On a full field of view laser scanning system,Machine Tools &Manufacture,2007(47):33~43
[5]王邦凯,杨辰龙,胡小辉等,大曲面工件超声检测技术研究,第十届全国无损检测新技术学术会议,20070522
[6]刘峥,自由曲线、自由曲面的误差评定软件的研制:[硕士学位论文],陕西:西安交通大学,2003
[7]何改云,形位误差的逼近原理与算法研究:[博士学位论文],天津:天津大学,22
[8] Cui C C,Che R Sh,Ye D et al,Sphericity error evaluation using the genetic algorithm,Optics and Precision Engineering,2002,10(4):333~339
[9] Guohua Jiang,Optimization approach for the evaluation of geometric errors in computer-aided inspection,Wichita :Wichita State University,2000
[10] ANSI Y14.5.1,Mathematical Definition of Dimensioning and Tolerancing Principles,1994
[11]单东日,柯映林,刘云峰,反求工程中复杂曲面测量规划研究,中国机械工程,2003,14(1):9~13
[12] Koster M,Curvature-dependent Parameterization of Curves and Surface, Computer-Aided Design,1991,23(8):569~579
[13] S Z Li,Adaptive Sampling and Mesh Generation,Computer-Aided Design,1995,27(3):235~240
[14]来新民,黄田,林忠钦等,数学模型已知的自由曲面数字化的自适应采样,计算机辅助设计与图形学学报,1999,11(4):359~362
[15] MENG C,YAN H,LAI G,Automated precision measurement of surface profile in CAD-directed inspection,IEEE Transactions on Robotics and Automation,1992,8(2):268~278
[16] Zhang Y F,Nee A Y C,Fuh J Y Hetal,A Neural Network Approach toDetermining Optimal Inspection Sampling Size for CMM,Computer Integated Manufacturing System,1996,9(3):161~169
[17] Merat F L,Radack G M,Automatic Inspection Planning within a Fcature-based CAD System,Robotics &Computer-Integrated Manufacturing,1992,19(1):61~69
[18]高国军,陈康宁,林志航等,用CMM检测自由曲面时检测点和路径的规划方法研究,西安交通大学学报,1996,30(7):57~63
[19]王平江,陈吉红,李作清等,空间自由曲面测量系统中的测点自动布置,计量技术,1995,12:10~13
[20]谢金,王文,李剑等,自由曲面测量中测点自适应规划方法研究,机电工程,2001,18(5):54~56
[21]陈丽萍,姜歌东,王小椿,一种高效的自由曲面求交算法,西安交通大学学报,2000,34(3):70~74
[22]方逵,谭元发,吴泉源,近似弧长参数化的一种数值算法,工程数学学报,2002,19(3):123~127
[23]王广彦,董继国,加工中心在线测头在自由曲线检测中的应用,组合机床与自动化加工技术,2003,7:60~62
[24]吴思源,周晓军,江健等,超声检测中曲面重构和路径规划方法研究,浙江大学学报(工学报),2006,40(5):763~767
[25]刘达新,赵韩,董玉德等,三坐标测量机无碰撞检测路径的生成,计算机辅助设计与图形学学报,2009,21(6):801~808
[26]王世刚,付宜利,数字化环境下在线检测路径优化技术的研究,组合机床与自动化加工技术,2009,5:52~56
[27]彭俊松,白作霖,李春波等,基于分布式协同求解技术的CMM检测路径神经网络优化,西安交通大学学报,1997,31(7):40~46
[28]邹刚,王亚平,李永刚,三坐标测量机测量路径自动生成的研究,航空计测技术,2004,24(3):6~8
[29]王世刚,基于CMM测量路径优化算法的研究,机械科学与技术,2005,24(5):606~608
[30]杨泽青,刘丽冰,谭志洪等,自适应遗传算法在柔性检测路径规划中的应用,Proceeding of the 27th Chinese Control Conference July 16-18,2008,Kunming,Yunnan,China
[31] Besl P J,McKay N D,A method for registration of 3-D shape,Trans Patt and Mach Intell,1992,14:239~255
[32]张结红,自由曲线、自由曲面的误差评定软件的研制:[硕士学位论文],陕西:西安交通大学,1993
[33]王旭蕴,张玉坤,轮廓度误差的精密测量和评定,计量学报,1995,16(1):12~16
[34]金小刚,马天驰,冯结青等,基于最佳圆弧样条逼近的快速距离曲面计算,中国图象图形学报,2001,6(5):486~490
[35]王伯平,曾建潮,一种自调整的空间面轮廓度误差的评定方法,计量学报,2002,23(2):106~108
[36]董明晓,郑康平,许伯彦等,一种快速求取空间点到曲面最短距离的算法,组合机床与自动化,2004,9:11~12
[37]刘浩,唐月红,NURBS曲面间的最短距离,南京理工大学学报,2002,26(4):420~425
[38] Tom Duff,Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry,Computer Graphics,1992,26(2):131~138
[39]叶晓平,龚友平,陈国金,快速求解点到自由曲面的距离的方法,工程图学学报,2008,4:91~95
[40] Wang Jianhua,Li Zhengyu,Offset Surface Generation of Bicubic B-spline and Fast Convergence Check,In:Zhou Zhaoying,The Proceedings of the Conference on MODMM,Beijing,1993;International Academic Publishers,1993:54~58
[41]朱心雄,自由曲线曲面造型技术,北京:科学出版社,2000:20~30
[42]李涛,贺勇军,刘志俭等,Mat lab工具箱应用指南-应用数学篇,北京:电子工业出版社,2000:160~162
[43]金涛,童水光等,逆向工程技术,北京:机械工业出版社,2003:48~53
[44]解则晓,冯国馨,张国雄,自由曲线曲面测量中的测点布置与准确度,计量技术,1999,12:21~23
[45]熊有伦,线轮廓度和面轮廓度的评定和判别,计量学报,1991,12(2):108~115
[46]范裕健,赵单贤,用最小区域法评定形状误差的数学模型,西安交通大学学报,1987(4):105~111
[47] Zhu L M,Xiong Z H,Ding H et al,A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface,Journal of Manufacturing Science and Engineering,2004,126(3):542~554
[48]石静,自由曲线、自由曲面误差评定系统的研究与开发:[硕士学位论文],上海:华东理工大学,2005
[49] Paul J. Besl,Neil D,McKay,A method for registration of 3-D shapes,IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239~256
[50]甘永立,何改云,几何误差检测问答,上海:上海科学技术出版社,2009,8:56~57