数控机床精度保持性的定量评价与误差敏感度分析
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摘要
针对数控机床精度保持性定量评价难题,分析精度保持性基本内涵,提出精度保持度的概念,并给出精确数学描述;在此基础上,建立基于多体理论的机床空间位置精度保持性评价模型,形成机床精度保持能力的刻画与表达。采用SOBOL全局敏感度分析法,分析各误差项时变状态对机床空间位置精度保持度的影响,实现误差溯源。以某三轴立式加工中心为实验对象,对机床的9项关键精度指标进行了为期400天的长期跟踪检测,计算分析各单项精度保持度与机床空间位置精度保持度随时间的变化规律,完成机床精度保持性的误差敏感度定量评估,验证了所提出方法及模型的有效性。
Aiming at the problem of quantitative evaluation of accuracy retentivity of CNC machine tools. Basic connotation of accuracy retentivity is analyzed. The conception of accuracy retentivity degree is put forward and its accurate mathematical description is also given. On the basis of mathematical description, evaluation model of volumetric accuracy retentivity of machine tools is established based on multi-body theory whereby forming the characterization and expression of accuracy retentivity ability of machine tools. In order to realize error tracing, influence of time varying state of each error term on the volumetric accuracy retentivity degree of machine tools is analyzed by using SOBOL global sensitivity theory. Taking a three-axis vertical machining center as the experimental object, nine kinds of accuracy index were detected for a period of 400 days of long-term tracking test. The variation laws of individual accuracy retentivity degree and volumetric accuracy retentivity degree with time are calculated and analyzed. The sensitivity of error on the accuracy retentivity of machine tool is quantitative evaluated. The effectiveness of proposed method and model are verified.
Aiming at the problem of quantitative evaluation of accuracy retentivity of CNC machine tools. Basic connotation of accuracy retentivity is analyzed. The conception of accuracy retentivity degree is put forward and its accurate mathematical description is also given. On the basis of mathematical description, evaluation model of volumetric accuracy retentivity of machine tools is established based on multi-body theory whereby forming the characterization and expression of accuracy retentivity ability of machine tools. In order to realize error tracing, influence of time varying state of each error term on the volumetric accuracy retentivity degree of machine tools is analyzed by using SOBOL global sensitivity theory. Taking a three-axis vertical machining center as the experimental object, nine kinds of accuracy index were detected for a period of 400 days of long-term tracking test. The variation laws of individual accuracy retentivity degree and volumetric accuracy retentivity degree with time are calculated and analyzed. The sensitivity of error on the accuracy retentivity of machine tool is quantitative evaluated. The effectiveness of proposed method and model are verified.
引文
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[15]李春林,陈旭红.应用多元统计分析[M].北京:清华大学出版社,2013.LI Chunlin,CHEN Xudong.Applied multivariate statistical analysis[M].Beijing:Tsinghua University Press,2013.
[2]CHENG Qiang,ZHANG Ziling,ZHANG Guojun,et al.Geometric accuracy allocation for multi-axis CNCmachine tools based on sensitivity analysis and reliability theory[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2015,229(6):1134-1149.
[3]TIAN Wenjie,GAO Weiguo,CHANG Wenfen,et al.Error modeling and sensitivity analysis of a five-axis machine tool[J].Mathematical Problems in Engineering,2014,2014(8).
[4]赵强强,洪军,刘志刚,等.任意拓扑结构机床运动轴误差传递链建模方法[J].机械工程学报,2016,52(21):130-137.ZHAO Qiangqiang,HONG Jun,LIU Zhigang,et al.Modeling method on motive axes error transfer chain for machine tool of arbitrary topological structure[J].Journal of Mechanical Engineering,2016,52(21):130-137.
[5]韩飞飞,赵继,张雷,等.数控机床几何精度综合解析与试验研究[J].机械工程学报,2012,48(21):141-148.HAN Feifei,ZHAO Ji,ZHANG Lei,et al.Synthetical analysis and experimental study of the geometric accuracy of CNC machine tools[J].Journal of Mechanical Engineering,2012,48(21):141-148.
[6]褚宁,张为民.基于模式搜索法的数控机床空间误差溯源[J].中国工程机械学报,2015,13(3):202-205.CHU Ning,ZHANG Weimin.Spatial error tracing on NCmachines based on pattern searching[J].Chinese Journal of Construction Machinery,2015,13(3):202-205.
[7]程强,刘广博,刘志峰,等.基于敏感度分析的机床关键性几何误差源识别方法[J].机械工程学报,2012,48(7):171-179.CHENG Qiang,LIU Guangbo,LIU Zhifeng,et al.An identification approach for key geometric error sources of machine tool based on sensitivity analysis[J].Journal of Mechanical Engineering,2012,48(7):171-179.
[8]黄强,张根保,张新玉.机床位姿误差的敏感性分析[J].机械工程学报,2009,45(6):141-146.HUANG Qiang,ZHANG Genbao,ZHANG Xinyu.Sensitivity analysis of the pose error of machine tool[J].Journal of Mechanical Engineering,2009,45(6):141-146.
[9]HUANG Qiang,ZHANG Genbao.Precision design for machine tool based on error prediction[J].Chinese Journal of Mechanical Engineering,2013,26(1):151-157.
[10]CHEN Guoda,LIANG Yingchun,SUN Yazhou,et al.Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool[J].The International Journal of Advanced Manufacturing Technology,2013,68(9):2525-2534.
[11]CHENG Qiang,ZHAO Hongwei,ZHANG Guojun,et al.An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis[J].The International Journal of Advanced Manufacturing Technology,2014,75(1-4):107-121.
[12]GUO Shijie,ZHANG Dongsheng,XI Yang.Global quantitative sensitivity analysis and compensation of geometric errors of CNC machine tool[J].Mathematical Problems in Engineering,2016,2016(1):1-10.
[13]CHENG Qiang,FENG Qiunan,LIU Zhifeng,et al.Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and morris method[J].The International Journal of Advanced Manufacturing Technology,2016,84(9):2301-2318.
[14]马军旭,赵万华,张根保.国产数控机床精度保持性分析及研究现状[J].中国机械工程,2015,26(22):3108-3115.MA Junxu,ZHAO Wanhua,ZHANG Genbao.Research status and analyses on accuracy retentivity of domestic CNC machine tools[J].China Mechanical Engineering,2015,26(22):3108-3115.
[15]李春林,陈旭红.应用多元统计分析[M].北京:清华大学出版社,2013.LI Chunlin,CHEN Xudong.Applied multivariate statistical analysis[M].Beijing:Tsinghua University Press,2013.