数控机床几何误差相关性分析方法研究
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摘要
为提高数控机床的精度,降低装配、制造过程产生的几何误差的影响,基于多体系统理论建立几何误差模型,在误差相关性分析的基础上,提出了一种辨识关键性几何误差元素的方法。首先,基于多体系统理论及齐次坐标变换方法建立了三轴数控机床几何误差模型,构建了几何误差元素相关性分析模型。其次,采用拉丁超立方抽样方法在整个参数空间内抽样,有效避免了单因素分析的缺陷。最后,通过计算拉丁立方抽样确定的误差元素引起的空间几何误差,进行相关性分析并辨识影响机床精度的关键几何误差元素。误差补偿后的圆测试对比结果表明,该方法可判别影响数控机床空间精度的重要误差元素,并能够定量辨识误差元素对几何误差向量的作用效果,可为机床误差补偿及精度分配提供重要的理论参考。
In order to improve the accuracy of NC machine tool and reduce the influence of geometric errors caused by assembly and manufacturing process,the geometric error model was established based on multi-body system theory,and a new method of identifying key elements of the geometric errors was proposed on the basis of geometric errors correlation analysis. Firstly,geometric errors model of three-axis vertical CNC machine tools was derivated by using multi-body system theory and homogeneous coordinate transformation method,and correlation analysis model of the geometric error elements was established,which contained 21 geometric errors of three-axis NC machine tools. Secondly,to avoid the defects of single factor analysis,and considering the coupling effects of geometric error elements,Latin hypercube sampling method was used in the whole parameter space sampling. Finally,based on the geometric error model and correlation analysis model,spatial error was calculated by using geometric errors element which was determined by Latin cube sample. And the key geometric error elements that affected the accuracy of machine tool were analyzed. Before error compensation,the twelve-line method was applied to identify the geometric error elements for each axis based on Renishaw XL-80 laser interferometer measuring system. The comparison result of circular tests after error compensation showed that the method can effectively and quantificationally identify the key factors that affecting the precision of machine tool space and the effects of error elements of total space error,thus important theoretical foundation was provided for accuracy allocation and error compensation of machine tool reasonably.
In order to improve the accuracy of NC machine tool and reduce the influence of geometric errors caused by assembly and manufacturing process,the geometric error model was established based on multi-body system theory,and a new method of identifying key elements of the geometric errors was proposed on the basis of geometric errors correlation analysis. Firstly,geometric errors model of three-axis vertical CNC machine tools was derivated by using multi-body system theory and homogeneous coordinate transformation method,and correlation analysis model of the geometric error elements was established,which contained 21 geometric errors of three-axis NC machine tools. Secondly,to avoid the defects of single factor analysis,and considering the coupling effects of geometric error elements,Latin hypercube sampling method was used in the whole parameter space sampling. Finally,based on the geometric error model and correlation analysis model,spatial error was calculated by using geometric errors element which was determined by Latin cube sample. And the key geometric error elements that affected the accuracy of machine tool were analyzed. Before error compensation,the twelve-line method was applied to identify the geometric error elements for each axis based on Renishaw XL-80 laser interferometer measuring system. The comparison result of circular tests after error compensation showed that the method can effectively and quantificationally identify the key factors that affecting the precision of machine tool space and the effects of error elements of total space error,thus important theoretical foundation was provided for accuracy allocation and error compensation of machine tool reasonably.
引文
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2 FAN K G,YANG J G,YANG L.Unified error model based spatial error compensation for four types of CNC machining center:part II-unified model based spatial error compensation[J].Mechanical Systems and Signal Processing,2014,49(1-2):63-76.
3余文利,姚鑫骅,孙磊,等.基于PLS和改进CVR的数控机床热误差建模[J].农业机械学报,2015,46(2):357-364.YU Wenli,YAO Xinhua,SUN Lei,et al.Thermal error modeling of CNC machine tool based on partial least squares and improved core vector regression[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(2):357-364.(in Chinese)
4 FRENCH D,HUMPHRIES S H.Compensation for backlash and alignment errors in a numerically controlled machine tool by a digital computer program[C]∥Proceedings of the 8th International MTDR Conference,1967:167-172.
5 FERREIRA P M,LIU C R.An analytical quadratic model for the geometric error of a machine tool[J].Journal of Manufacturing Systems,1986,5(1):51-63.
6郭然,付国强,孙磊,等.基于切比雪夫多项式的数控机床几何误差参数化建模[J].农业机械学报,2015,46(5):336-343.GUO Ran,FU Guoqiang,SUN Lei,et al.Chebyshev polynomials based parametric modeling of geometric errors for CNC machine tools[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(5):336-343.(in Chinese)
7 KIRIDENA V,FERREIRA P.Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools[J].International Journal of Machine Tools and Manufacture,1993,33(3):417-437.
8 YAO X,FU J,XU Y,et al.Synthetic error modeling for NC machine tools based on intelligent technology[J].Procedia CIRP,2013,10:91-97.
9 FU G,FU J,XU Y,et al.Accuracy enhancement of five-axis machine tool based on differential motion matrix:geometric error modeling,identification and compensation[J].International Journal of Machine Tools and Manufacture,2015,89:170-181.
10 WANG W,ZHANG Y,YANG J,et al.Geometric and thermal error compensation for CNC milling machines based on Newton interpolation method[J].Proc IMech E,Part C:Journal of Mechanical Engineering Science,2013,227(4):771-778.
11杜柳青,周武.基于图形识别的数控机床误差溯因方法[J].农业机械学报,2015,46(10):391-396.DU Liuqing,ZHOU Wu.Method for machine tool's motion error abduction based on graphic recognition[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(10):391-396.(in Chinese)
12 TSUTSUMI M,SAITO A.Identification and compensation of systematic deviations particular to 5-axis machining centers[J].International Journal of Machine Tools and Manufacture,2003,43(8):771-780.
13余文利,付国强,孙磊,等.数控加工中心空间误差场建模与仿真软件开发[J].农业机械学报,2016,47(4):382-390.YU Wenli,FU Guoqiang,SUN Lei,et al.Error field modeling and simulation software developing for CNC machining center[J].Transactions of the Chinese Society for Agricultural Machinery,2016,47(4):382-390.(in Chinese)
14 CHEN G,LIANG Y,SUN Y,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(9-12):2525-2534.
15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 Q,LIU G B,LIU Z F,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.(in Chinese)
16韩飞飞,赵继,张雷,等.数控机床几何精度综合解析与实验研究[J].机械工程学报,2012,48(21):141-148.
17余治民,刘子建,艾彦迪,等.大型数控龙门导轨磨床几何误差建模与基于可靠性理论的精度分配[J].机械工程学报,2013,49(17):142-151.YU Zhimin,LIU Zijian,AI Yandi,et al.Geometric error model and precision distribution based on reliability theory for large CNC gantry guideway grinder[J].Journal of Mechanical Engineering,2013,49(17):142-151.(in Chinese)
18高猛,李铁民,尹文生,等.一种基于相关性分析的并联机床标定方法[J].机械工程学报,2005,41(1):88-92.
19 CHEN J S.Computer-aided accuracy enhancement for multi-axis CNC machine tool[J].International Journal of Machine Tools and Manufacture,1995,35(4):593-605.
20 FENG B,ZHANG D,YANG J,et al.A novel time-varying friction compensation method for servomechanism[J].Mathematical Problems in Engineering,2015(2015):1-16.
21粟时平,李圣怡,王贵林.基于空间误差模型的加工中心几何误差辨识方法[J].机械工程学报,2002,38(7):121-125.
22 ISO 230-4 Test code for machine tools-part 4:circular tests for numerically controlled machine tools[S].2005.
2 FAN K G,YANG J G,YANG L.Unified error model based spatial error compensation for four types of CNC machining center:part II-unified model based spatial error compensation[J].Mechanical Systems and Signal Processing,2014,49(1-2):63-76.
3余文利,姚鑫骅,孙磊,等.基于PLS和改进CVR的数控机床热误差建模[J].农业机械学报,2015,46(2):357-364.YU Wenli,YAO Xinhua,SUN Lei,et al.Thermal error modeling of CNC machine tool based on partial least squares and improved core vector regression[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(2):357-364.(in Chinese)
4 FRENCH D,HUMPHRIES S H.Compensation for backlash and alignment errors in a numerically controlled machine tool by a digital computer program[C]∥Proceedings of the 8th International MTDR Conference,1967:167-172.
5 FERREIRA P M,LIU C R.An analytical quadratic model for the geometric error of a machine tool[J].Journal of Manufacturing Systems,1986,5(1):51-63.
6郭然,付国强,孙磊,等.基于切比雪夫多项式的数控机床几何误差参数化建模[J].农业机械学报,2015,46(5):336-343.GUO Ran,FU Guoqiang,SUN Lei,et al.Chebyshev polynomials based parametric modeling of geometric errors for CNC machine tools[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(5):336-343.(in Chinese)
7 KIRIDENA V,FERREIRA P.Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools[J].International Journal of Machine Tools and Manufacture,1993,33(3):417-437.
8 YAO X,FU J,XU Y,et al.Synthetic error modeling for NC machine tools based on intelligent technology[J].Procedia CIRP,2013,10:91-97.
9 FU G,FU J,XU Y,et al.Accuracy enhancement of five-axis machine tool based on differential motion matrix:geometric error modeling,identification and compensation[J].International Journal of Machine Tools and Manufacture,2015,89:170-181.
10 WANG W,ZHANG Y,YANG J,et al.Geometric and thermal error compensation for CNC milling machines based on Newton interpolation method[J].Proc IMech E,Part C:Journal of Mechanical Engineering Science,2013,227(4):771-778.
11杜柳青,周武.基于图形识别的数控机床误差溯因方法[J].农业机械学报,2015,46(10):391-396.DU Liuqing,ZHOU Wu.Method for machine tool's motion error abduction based on graphic recognition[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(10):391-396.(in Chinese)
12 TSUTSUMI M,SAITO A.Identification and compensation of systematic deviations particular to 5-axis machining centers[J].International Journal of Machine Tools and Manufacture,2003,43(8):771-780.
13余文利,付国强,孙磊,等.数控加工中心空间误差场建模与仿真软件开发[J].农业机械学报,2016,47(4):382-390.YU Wenli,FU Guoqiang,SUN Lei,et al.Error field modeling and simulation software developing for CNC machining center[J].Transactions of the Chinese Society for Agricultural Machinery,2016,47(4):382-390.(in Chinese)
14 CHEN G,LIANG Y,SUN Y,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(9-12):2525-2534.
15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 Q,LIU G B,LIU Z F,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.(in Chinese)
16韩飞飞,赵继,张雷,等.数控机床几何精度综合解析与实验研究[J].机械工程学报,2012,48(21):141-148.
17余治民,刘子建,艾彦迪,等.大型数控龙门导轨磨床几何误差建模与基于可靠性理论的精度分配[J].机械工程学报,2013,49(17):142-151.YU Zhimin,LIU Zijian,AI Yandi,et al.Geometric error model and precision distribution based on reliability theory for large CNC gantry guideway grinder[J].Journal of Mechanical Engineering,2013,49(17):142-151.(in Chinese)
18高猛,李铁民,尹文生,等.一种基于相关性分析的并联机床标定方法[J].机械工程学报,2005,41(1):88-92.
19 CHEN J S.Computer-aided accuracy enhancement for multi-axis CNC machine tool[J].International Journal of Machine Tools and Manufacture,1995,35(4):593-605.
20 FENG B,ZHANG D,YANG J,et al.A novel time-varying friction compensation method for servomechanism[J].Mathematical Problems in Engineering,2015(2015):1-16.
21粟时平,李圣怡,王贵林.基于空间误差模型的加工中心几何误差辨识方法[J].机械工程学报,2002,38(7):121-125.
22 ISO 230-4 Test code for machine tools-part 4:circular tests for numerically controlled machine tools[S].2005.