形位误差测量的不确定度评定
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摘要
形位误差是评定机械零件的重要指标,它对产品的使用性能和装配质量有着很大的影响,在生产中要加以测量和控制。一个科学的测量结果需要包括其测量不确定度,但是目前对于形位误差测量结果的不确定度评定并没有系统深入的研究。因此,系统地研究形位误差的测量不确定度评定具有重要意义。
本文较为系统地对形位误差的测量不确定度评定进行了研究。对形位误差测量不确定度的国内外研究现状进行分析,并对各形位误差的测量方法、评定方法进行了系统的学习。以坐标测量法进行测量,并基于最小二乘原理进行形位误差的数学建模。结合上述方法,对形位误差的测量不确定度进行评定。
主要工作内容和研究成果如下:
(1)对形位误差的测量方法进行总结和分类,并对测量过程中的不确定度来源进行分析。
(2)依据最小二乘原理,在直角坐标系下建立各形位误差的数学模型,对于回转类的形位误差,如圆度误差和圆柱度误差,还建立了其在极坐标系下的最小二乘数学模型。
(3)根据不确定度评定表示指南(GUM)进行不确定度评定。计算了形位误差中各参数的单点不确定度、传递系数和参数间的相关性,最后利用不确定度合成公式求出形位误差的标准不确定度。
(4)根据蒙特卡罗方法的原理,产生随机数来构成一个概率分布来仿真测量值,然后进行不确定度的评定。
(5)实验验证所得到的理论结果。使用三坐标测量机和圆度仪等测量设备,对各形位误差进行测量,然后利用MATLAB编程对测量结果进行处理,得到不同方法下的测量不确定度,并比较不同方法的优缺点。
以上研究成果对计量学和测量误差理论的深入,具有重要的科学意义,在机械制造中的行为误差测量与控制领域,具有重要的实用价值。
The errors of form and position are parameters for the evaluation of mechanical components. It has great influence on the performance of products and the quality of assembly, which should be measurement and controlled. Measurement uncertainty should be contained in a scientific measurement result. However, today’s uncertainty evaluation methods to the results of position and form errors have not been deeply and systematically studied. Thus, a systematic research on that topic is of great significance.
More systematic research of the evaluation of measurement uncertainty in form and position errors was proposed in this paper. The research status of home and abroad on this subject were surveyed and analyzed. And the measurement methods and the evaluation methods of form and position errors were systematically studied. In this paper, based on least square principle a mathematic model was established from measurement results of coordinate measuring method. According to the mentioned results, the uncertainties of form and position errors were assessed.
The main results of work and achievement are as follows:
(1) The measurement methods of form error were summarized and classified. And the sources of measurement uncertainty were analysised.
(2) Based on the least-squares principle, the mathematical models of form and position errors were established in the Cartesian coordinate. To the form and position errors for the rotational, such as roundness error and cylindrical error, the mathematical models of form and position errors were also established in the polar coordinates.
(3) The uncertainty evaluation was based on Guide to the Expression of Uncertainty in Measurement (GUM). The uncertainty of the parameters of form and position errors, transmission coefficients and parameters of the correlation were Calculated. Then the standard uncertainty of form and position errors was evaluated based on GUM.
(4) A probability distribution was established from the random numbers generated based on the principle of Monte Carlo Method in order to simulate the measured values and the uncertainties were evaluated later.
(5) The theoretical results were verified by Experiments. Measuring the form and position errors and then using MATLAB programming to process the measurement results by different methods of measurement uncertainty. And the performance of different methods was compared
The results and achievements in this paper have important scientific significance for the metrology and measuring error theory, and would have practical worth for the measurement and control to the form and position error of machinery manufacturing.
本文较为系统地对形位误差的测量不确定度评定进行了研究。对形位误差测量不确定度的国内外研究现状进行分析,并对各形位误差的测量方法、评定方法进行了系统的学习。以坐标测量法进行测量,并基于最小二乘原理进行形位误差的数学建模。结合上述方法,对形位误差的测量不确定度进行评定。
主要工作内容和研究成果如下:
(1)对形位误差的测量方法进行总结和分类,并对测量过程中的不确定度来源进行分析。
(2)依据最小二乘原理,在直角坐标系下建立各形位误差的数学模型,对于回转类的形位误差,如圆度误差和圆柱度误差,还建立了其在极坐标系下的最小二乘数学模型。
(3)根据不确定度评定表示指南(GUM)进行不确定度评定。计算了形位误差中各参数的单点不确定度、传递系数和参数间的相关性,最后利用不确定度合成公式求出形位误差的标准不确定度。
(4)根据蒙特卡罗方法的原理,产生随机数来构成一个概率分布来仿真测量值,然后进行不确定度的评定。
(5)实验验证所得到的理论结果。使用三坐标测量机和圆度仪等测量设备,对各形位误差进行测量,然后利用MATLAB编程对测量结果进行处理,得到不同方法下的测量不确定度,并比较不同方法的优缺点。
以上研究成果对计量学和测量误差理论的深入,具有重要的科学意义,在机械制造中的行为误差测量与控制领域,具有重要的实用价值。
The errors of form and position are parameters for the evaluation of mechanical components. It has great influence on the performance of products and the quality of assembly, which should be measurement and controlled. Measurement uncertainty should be contained in a scientific measurement result. However, today’s uncertainty evaluation methods to the results of position and form errors have not been deeply and systematically studied. Thus, a systematic research on that topic is of great significance.
More systematic research of the evaluation of measurement uncertainty in form and position errors was proposed in this paper. The research status of home and abroad on this subject were surveyed and analyzed. And the measurement methods and the evaluation methods of form and position errors were systematically studied. In this paper, based on least square principle a mathematic model was established from measurement results of coordinate measuring method. According to the mentioned results, the uncertainties of form and position errors were assessed.
The main results of work and achievement are as follows:
(1) The measurement methods of form error were summarized and classified. And the sources of measurement uncertainty were analysised.
(2) Based on the least-squares principle, the mathematical models of form and position errors were established in the Cartesian coordinate. To the form and position errors for the rotational, such as roundness error and cylindrical error, the mathematical models of form and position errors were also established in the polar coordinates.
(3) The uncertainty evaluation was based on Guide to the Expression of Uncertainty in Measurement (GUM). The uncertainty of the parameters of form and position errors, transmission coefficients and parameters of the correlation were Calculated. Then the standard uncertainty of form and position errors was evaluated based on GUM.
(4) A probability distribution was established from the random numbers generated based on the principle of Monte Carlo Method in order to simulate the measured values and the uncertainties were evaluated later.
(5) The theoretical results were verified by Experiments. Measuring the form and position errors and then using MATLAB programming to process the measurement results by different methods of measurement uncertainty. And the performance of different methods was compared
The results and achievements in this paper have important scientific significance for the metrology and measuring error theory, and would have practical worth for the measurement and control to the form and position error of machinery manufacturing.
引文
[1]甘永立.形状和位置误差检测[M].国防工业出版社,1995
[2]国家质量技术监督局计量司,测量不确定度评定与表示指南[M].中国计量出版社,2000
[3]费业泰.误差理论与数据处理[M].机械工业出版社,2004
[4]刘智敏.不确定度及其实践[M].中国标准出版社,2001
[5]侯学锋,黄富贵,田树耀.形位误差测量不确定度研究状况[J].工具技术,2008(7):7~9
[6] Tohru kanada and Soichiroh Suzuki. Application of several computing techniques for minimum zone straightness[J]. Precision Engineering , 1993 (15) :135~149
[7] Chia-Hsiang Meng , Hong-Tzong Yau , Gwan-Ywan lai. Statistical evaluation of tolerance using discrete measurement date[J]. Advances In Integrated Product Design and Manufacturing , 1996 , 47 :1351
[8] P Bourdet , C Largue , F Leveaux. Effects of data point distribution and mathematical model on finding the best-fit sphere to data[J]. Precision Engineering , 1993 , 15 (31) :150~157
[9] S D Phillips , B Borchardt , W T Esteler et al . The estimation of measurement uncertainty of small circular features measured by coordinate measuring machine[J]. Precision Engineering , 1998 , 22 (2) :87~99
[10] Woncheol Choi , Thomas R Kurfess. Uncertainty of estreme fit evaluating for three-dimensional measurement data analysis[J]. Computer-aided Design , 1998 , 31 (7) :54~57
[11] E Cappello. The effect of sampling in circular substitute geometries evaluation[J]. International Journal of Machine Tool & Manufacture , 1999 (39) :55~85
[12] F M M Chan. The influence of sampling strategy on a circular feature in coordinate measurement[J]. Measurement ,Vo1. 19.No. 2 (1996) :73~81
[13] P.B.Dhanish, Jose Mathew. Effect of CMM point coordinate uncertainty on uncertainties in determination of circular features[J]. Measurement 39(2006):522~531
[14] Changcai Cui, Shiwei Fu, fugui Huang, Research on the uncertainties from different form error evaluation methods by CMM sampling[J]. Int J Adv ManufTechnol(2009)43:136~145
[15] Defen Zhang, Paul G.Maropoulos, Martyn Hill.Random uncertaintypropagation in estimates of sphere parameters from coordinate measurements[J], international journal of machine tools & manufacture, Volume 46,Issues 12-13,October 2006,Pages 1362-1368
[16]黄富贵,崔长彩.评定直线度误差的最小二乘法与最小包容区域法精度之比较[J].光学精密工程,Vol.15 No.6
[17]李淑娟.基于坐标测量数据的形状误差评定软件包的开发[D].西安理工大学位论文,2006
[18]迟彦孝,王守城.直线度误差的评定方法及其数学证明[J].机械制造与研究,2003,(5):14~16
[19]张昉.平面度误差的最小二乘法分析[J].机械制造与研究,2002,(3):17~19
[20]程飞月.计算圆度误差的几种方法[J].中国水运,2006(5)
[21] JJF 429-2000,圆度、圆柱度测量仪检定规程[S]
[22]侯宇.坐标测量机圆度评定的一种新算法[J].计量技术,1993,(10):1-3
[23]徐国旺,廖明潮.拟合圆的几种方法[J].武汉工业学院学报, 2002,(4):104~106
[24]陈立杰,张镭,张玉.直角坐标采样时的圆柱度误差数学模型[J].东北大学学报(自然科学版),2005,(7):677~679
[25]阎荫棠,王秀兰.平行度测量总不确定度的评估实例曹[J].计量技术,1996.2:37~38
[26]陈立杰,张镭,张玉.同轴度误差的数模研究[J].东北大学学报(自然科学版),2007,Vol.28 No.4:549~551
[27]杨金霞.基于坐标测量数据的位置误差评定软件包的开发[D].西安理工大学位论文,2008
[28]张国雄.三坐标测量机[M].天津大学出版社,1999
[29]王金星,蒋向前,徐振高,李柱.空间直线度坐标测量的不确定度计算[J].华中科技大学学报(自然科学版),2005,Vol.22 No.12:1~3
[30]杨将新,茅健,曹衍龙,徐旭松.基于新一代GPS体系的直线度不确定度研究[J].计量学报,2008,(1):14~16
[31]王金星,蒋向前,马利民,徐振高,李柱.平面度坐标测量的不确定度计算[J].中国机械工程,2005,Vol.16 No.19:1701~1703
[32]潘秀亮,王雨海.圆度仪在形状和位置误差测量中的应用[J].国防技术基础,2009,(3):24~30
[33]段留英,刘亚民,许勇.Talyrond 265圆度仪使用技巧[J].计量技术,2004,(10):55~56
[34]侯学锋,黄富贵,田树耀.圆度最小二乘评定结果的不确定度估计[J].工具技术,2008(42):102~104
[35]张根法.圆柱度的测量不确定度分析与评定[J].现代车用动力,2004(1):50~51
[36]阎荫棠,王秀兰.平行度测量总不确定度的评估实例[J].计量技术,1996(2):37~38
[37]田树耀,黄富贵,侯学锋.一种新的同轴度误差评定方法及其误差分析[J].工具技术,2008(42):82~85
[38]徐钟济.蒙特卡罗方法[M].上海科学技术出版社
[39]陈晓怀,薄晓静,王洪涛.基于蒙特卡罗方法的测量不确定度合成[J].仪器仪表学报,2005(suppl.1)
[40] Jean-Pierre Kruth, NickWan Gestel et al. Uncertainty determination for CMMs by Monte Carlo simulation integrating feature form deviations[J]. CIRP Annals–Manufacturing Technology 58(2009)
[41]苏金明,阮沈勇.Matlab实用教程[M].电子工业出版社,2005
[42]陈永鹏.基于MATLAB优化工具箱的机械产品形状误差评定系统研究[D].四川大学硕士学位论文,2003
[2]国家质量技术监督局计量司,测量不确定度评定与表示指南[M].中国计量出版社,2000
[3]费业泰.误差理论与数据处理[M].机械工业出版社,2004
[4]刘智敏.不确定度及其实践[M].中国标准出版社,2001
[5]侯学锋,黄富贵,田树耀.形位误差测量不确定度研究状况[J].工具技术,2008(7):7~9
[6] Tohru kanada and Soichiroh Suzuki. Application of several computing techniques for minimum zone straightness[J]. Precision Engineering , 1993 (15) :135~149
[7] Chia-Hsiang Meng , Hong-Tzong Yau , Gwan-Ywan lai. Statistical evaluation of tolerance using discrete measurement date[J]. Advances In Integrated Product Design and Manufacturing , 1996 , 47 :1351
[8] P Bourdet , C Largue , F Leveaux. Effects of data point distribution and mathematical model on finding the best-fit sphere to data[J]. Precision Engineering , 1993 , 15 (31) :150~157
[9] S D Phillips , B Borchardt , W T Esteler et al . The estimation of measurement uncertainty of small circular features measured by coordinate measuring machine[J]. Precision Engineering , 1998 , 22 (2) :87~99
[10] Woncheol Choi , Thomas R Kurfess. Uncertainty of estreme fit evaluating for three-dimensional measurement data analysis[J]. Computer-aided Design , 1998 , 31 (7) :54~57
[11] E Cappello. The effect of sampling in circular substitute geometries evaluation[J]. International Journal of Machine Tool & Manufacture , 1999 (39) :55~85
[12] F M M Chan. The influence of sampling strategy on a circular feature in coordinate measurement[J]. Measurement ,Vo1. 19.No. 2 (1996) :73~81
[13] P.B.Dhanish, Jose Mathew. Effect of CMM point coordinate uncertainty on uncertainties in determination of circular features[J]. Measurement 39(2006):522~531
[14] Changcai Cui, Shiwei Fu, fugui Huang, Research on the uncertainties from different form error evaluation methods by CMM sampling[J]. Int J Adv ManufTechnol(2009)43:136~145
[15] Defen Zhang, Paul G.Maropoulos, Martyn Hill.Random uncertaintypropagation in estimates of sphere parameters from coordinate measurements[J], international journal of machine tools & manufacture, Volume 46,Issues 12-13,October 2006,Pages 1362-1368
[16]黄富贵,崔长彩.评定直线度误差的最小二乘法与最小包容区域法精度之比较[J].光学精密工程,Vol.15 No.6
[17]李淑娟.基于坐标测量数据的形状误差评定软件包的开发[D].西安理工大学位论文,2006
[18]迟彦孝,王守城.直线度误差的评定方法及其数学证明[J].机械制造与研究,2003,(5):14~16
[19]张昉.平面度误差的最小二乘法分析[J].机械制造与研究,2002,(3):17~19
[20]程飞月.计算圆度误差的几种方法[J].中国水运,2006(5)
[21] JJF 429-2000,圆度、圆柱度测量仪检定规程[S]
[22]侯宇.坐标测量机圆度评定的一种新算法[J].计量技术,1993,(10):1-3
[23]徐国旺,廖明潮.拟合圆的几种方法[J].武汉工业学院学报, 2002,(4):104~106
[24]陈立杰,张镭,张玉.直角坐标采样时的圆柱度误差数学模型[J].东北大学学报(自然科学版),2005,(7):677~679
[25]阎荫棠,王秀兰.平行度测量总不确定度的评估实例曹[J].计量技术,1996.2:37~38
[26]陈立杰,张镭,张玉.同轴度误差的数模研究[J].东北大学学报(自然科学版),2007,Vol.28 No.4:549~551
[27]杨金霞.基于坐标测量数据的位置误差评定软件包的开发[D].西安理工大学位论文,2008
[28]张国雄.三坐标测量机[M].天津大学出版社,1999
[29]王金星,蒋向前,徐振高,李柱.空间直线度坐标测量的不确定度计算[J].华中科技大学学报(自然科学版),2005,Vol.22 No.12:1~3
[30]杨将新,茅健,曹衍龙,徐旭松.基于新一代GPS体系的直线度不确定度研究[J].计量学报,2008,(1):14~16
[31]王金星,蒋向前,马利民,徐振高,李柱.平面度坐标测量的不确定度计算[J].中国机械工程,2005,Vol.16 No.19:1701~1703
[32]潘秀亮,王雨海.圆度仪在形状和位置误差测量中的应用[J].国防技术基础,2009,(3):24~30
[33]段留英,刘亚民,许勇.Talyrond 265圆度仪使用技巧[J].计量技术,2004,(10):55~56
[34]侯学锋,黄富贵,田树耀.圆度最小二乘评定结果的不确定度估计[J].工具技术,2008(42):102~104
[35]张根法.圆柱度的测量不确定度分析与评定[J].现代车用动力,2004(1):50~51
[36]阎荫棠,王秀兰.平行度测量总不确定度的评估实例[J].计量技术,1996(2):37~38
[37]田树耀,黄富贵,侯学锋.一种新的同轴度误差评定方法及其误差分析[J].工具技术,2008(42):82~85
[38]徐钟济.蒙特卡罗方法[M].上海科学技术出版社
[39]陈晓怀,薄晓静,王洪涛.基于蒙特卡罗方法的测量不确定度合成[J].仪器仪表学报,2005(suppl.1)
[40] Jean-Pierre Kruth, NickWan Gestel et al. Uncertainty determination for CMMs by Monte Carlo simulation integrating feature form deviations[J]. CIRP Annals–Manufacturing Technology 58(2009)
[41]苏金明,阮沈勇.Matlab实用教程[M].电子工业出版社,2005
[42]陈永鹏.基于MATLAB优化工具箱的机械产品形状误差评定系统研究[D].四川大学硕士学位论文,2003