六自由度并联地震模拟振动台全误差分析及标定研究
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摘要
地震工程研究中通常会使用地震模拟振动台重现天然的地震纪录波或产生指定的振动,通过检验建筑模型在不同振动输出下的反应来鉴定建筑物的抗震性能,或加强建筑的抗震结构设计。但是在模拟振动台的制造与安装过程中难免会产生各种误差,这些误差将会影响模拟运动精度。因此,为了精确重现自然地震波形或产生指定运动,需要对平台进行全误差分析,增加对系统结构误差的认识,以指导机构的设计与综合。同时,还需要进行机构参数的标定研究,用以提高机构的模拟运动精度。
本文针对一种新型的具有冗余输入的并联地震模拟振动台,以提高运动精度为出发点,对模拟振动台进行了误差模型的建立、分析与优化,并对其标定方法进行了理论研究。
首先,本文对系统的冗余支链进行简化,并建立相应的D-H坐标系。借助于辅助坐标系的设置,本文成功地将支链固连点安装位置等常被忽略的误差包含进误差模型内,保证了误差分析的结果更为全面与有效。
然后,借助于蒙特卡洛模拟,在全工作空间范围内,对系统进行了全误差参数分析,研究了单个结构误差所造成运动末端运动误差的值域范围,并统计其概率分布。根据分析结果归纳出系统的敏感误差参数,并提出可供标定研究参考的测量位姿选取策略。由于参数及位姿选取较为全面,分析结果能够进一步促进了对模拟振动台机构误差的认识。
再次,为了使标定模型能够考察更多的误差参数,本文利用由敏感误差构成的误差模型构建系统的标定模型。采用Levenberg-Marquardt算法编制出模拟振动台基于最小二乘法的参数辨识程序,并进行了仿真验证。仿真结果证实了算法的有效性以及基于敏感D-H参数的标定模型的完整性。
最后,为降低标定复杂度、提高标定效率,本文使用分析辨识矩阵的秩与测量点数的关系,从敏感误差参数中挑选最小数量的独立误差参数。这一独立误差参数的选取策略既保证系统误差能够得到辨识,又避免了标定必需的独立误差参数的缺失。另外根据参数的互换性,这一策略为其它并联机构的标定提供了极为有益的借鉴。
Earthquake simulator is often used in the research of earthquake to generate the simulated seismic waves or specified vibration. Building models should be tested under different vibration waves in order to identify the seismic performance, or strengthen the structure design. However, the process of manufacturing and installation of earthquake simulator, will inevitably generate a variety of errors, these errors will affect simulated kinematic accuracy. Therefore, in order to reproduce the seismic wave accurately or generate specified vibration, the total errors need to be analyzed, so the errors could be understood better. Total errors analysis could also guide the design integration. At the same time, the parameters need to be calibrated so that the kinematic accuracy can be improved.
In this paper, a new type of parallel redundancy earthquake simulator is introduced. In order to improve the kinematic accuracy, the total error model of earthquake simulator is built, analyzed and optimized, the calibration method is studied as well.
First of all, this redundantly actuated branched-chain need to be simplified, and a corresponding D-H co-ordinate system should be built. With the setting of auxiliary coordinate system, this model successfully contains neglected errors in previous publications, such as branched-chain installation location etc., which could ensure the results of error analysis more comprehensive and effective.
Second, by means of Monte-Carlo simulation, the total error parameter is analyzed in the whole workspace, study the range of the kinematic error cause by single error and its distribution probability is studied. Based on the results, sensitive error parameters are summarized, and position and posture selection strategy of calibration is proposed. As the parameters and pose is selected more comprehensively, the error could be understood more deeply by the results of analysis.
Then, this paper build the calibration model with sensitive error parameters, in order that the calibration model could examine more error parameters. Levenberg-Marquardt algorithm is adopted in parameter identification procedure which based on least squares method. Simulation results show the effectiveness of the algorithm and the integrity of calibration model which based on sensitive error parameters.
Finally, in order to reduce complexity of calibration, improve efficiency of calibration, this paper analyzes the relationship between the rank of identification matrix and the number of measurement points, so that the least independent parameters can be selected from the sensitive error parameters. The selection strategy of independent error parameters could not only ensure identification of the system error, but also avoid omission of independent parameters in calibration. According to parameters interchangeability, this strategy provides a very useful reference for the calibration of other parallel mechanism.
本文针对一种新型的具有冗余输入的并联地震模拟振动台,以提高运动精度为出发点,对模拟振动台进行了误差模型的建立、分析与优化,并对其标定方法进行了理论研究。
首先,本文对系统的冗余支链进行简化,并建立相应的D-H坐标系。借助于辅助坐标系的设置,本文成功地将支链固连点安装位置等常被忽略的误差包含进误差模型内,保证了误差分析的结果更为全面与有效。
然后,借助于蒙特卡洛模拟,在全工作空间范围内,对系统进行了全误差参数分析,研究了单个结构误差所造成运动末端运动误差的值域范围,并统计其概率分布。根据分析结果归纳出系统的敏感误差参数,并提出可供标定研究参考的测量位姿选取策略。由于参数及位姿选取较为全面,分析结果能够进一步促进了对模拟振动台机构误差的认识。
再次,为了使标定模型能够考察更多的误差参数,本文利用由敏感误差构成的误差模型构建系统的标定模型。采用Levenberg-Marquardt算法编制出模拟振动台基于最小二乘法的参数辨识程序,并进行了仿真验证。仿真结果证实了算法的有效性以及基于敏感D-H参数的标定模型的完整性。
最后,为降低标定复杂度、提高标定效率,本文使用分析辨识矩阵的秩与测量点数的关系,从敏感误差参数中挑选最小数量的独立误差参数。这一独立误差参数的选取策略既保证系统误差能够得到辨识,又避免了标定必需的独立误差参数的缺失。另外根据参数的互换性,这一策略为其它并联机构的标定提供了极为有益的借鉴。
Earthquake simulator is often used in the research of earthquake to generate the simulated seismic waves or specified vibration. Building models should be tested under different vibration waves in order to identify the seismic performance, or strengthen the structure design. However, the process of manufacturing and installation of earthquake simulator, will inevitably generate a variety of errors, these errors will affect simulated kinematic accuracy. Therefore, in order to reproduce the seismic wave accurately or generate specified vibration, the total errors need to be analyzed, so the errors could be understood better. Total errors analysis could also guide the design integration. At the same time, the parameters need to be calibrated so that the kinematic accuracy can be improved.
In this paper, a new type of parallel redundancy earthquake simulator is introduced. In order to improve the kinematic accuracy, the total error model of earthquake simulator is built, analyzed and optimized, the calibration method is studied as well.
First of all, this redundantly actuated branched-chain need to be simplified, and a corresponding D-H co-ordinate system should be built. With the setting of auxiliary coordinate system, this model successfully contains neglected errors in previous publications, such as branched-chain installation location etc., which could ensure the results of error analysis more comprehensive and effective.
Second, by means of Monte-Carlo simulation, the total error parameter is analyzed in the whole workspace, study the range of the kinematic error cause by single error and its distribution probability is studied. Based on the results, sensitive error parameters are summarized, and position and posture selection strategy of calibration is proposed. As the parameters and pose is selected more comprehensively, the error could be understood more deeply by the results of analysis.
Then, this paper build the calibration model with sensitive error parameters, in order that the calibration model could examine more error parameters. Levenberg-Marquardt algorithm is adopted in parameter identification procedure which based on least squares method. Simulation results show the effectiveness of the algorithm and the integrity of calibration model which based on sensitive error parameters.
Finally, in order to reduce complexity of calibration, improve efficiency of calibration, this paper analyzes the relationship between the rank of identification matrix and the number of measurement points, so that the least independent parameters can be selected from the sensitive error parameters. The selection strategy of independent error parameters could not only ensure identification of the system error, but also avoid omission of independent parameters in calibration. According to parameters interchangeability, this strategy provides a very useful reference for the calibration of other parallel mechanism.
引文
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[31] T. Huang, D. G. Chetwynd, D. J. Whitehouse and J. Wang. A general and novel approach for parameter identification of 6-DOF parallel kinematic machines [J].Mechanism and Machine Theory:2005,40(2):219-239
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[2]松泽武雄.地震理论及其应用[M].北京:地震出版社,1980
[3]国家地震局.地震[M].北京:科学出版社,1981
[4]地震预报与减灾技术国际讨论会.地震预报与减灾技术[M].北京:地震出版社,1994
[5] Pollard W. L. G. Spray painting machine: USA, 2,213,108[P]. August 26, 1940
[6] Gough V.E. Whitehall S.G. Universal type test machine. Proceedings of the FISITA Ninth International Technical Congress.1962
[7] D. Stewart. A Platform with Six Degrees of Freedom[J].Proceedings of the Institution of Mechanical Engineers:1965,180(1):371-386
[8] K. H. Hunt. Kinematic geometry of mechanisms[M].Cambridge: Cambridge Univ Press,1978
[9] H. MacCallion, D. T. Pham. The Analysis of a Six degree of Freedom Workstation for Mechanized Assembly. Proceedings of the 5th World Congress on Theory of Machines and Mechanisms.1978
[10]黄浩华.3×3m模拟地震振动台[J].地震学报:1986,8(1):72-78
[11]董莹.全国最大地震模拟振动台通过部级鉴定[J].世界地震工程:1989,(2):41
[12]董莹.全国最大地震模拟振动台收效良好[J].世界地震工程:1990,(2):45
[13]陈龙飞.振动台基础预埋件的施工测量[J].工程勘察:1984,(2):27-31
[14]余安东,王天龙.同济大学地震模拟振动台基础设计[J].同济大学学报:1986,14(2):118-125
[15]吕西林,朱伯龙.五层砌块模型房屋的振动台试验研究[J].同济大学学报:1986,14(1):18-31
[16]杨佳梅,李德玉.三峡溢流坝段动力模型试验研究[J].水力发电:1995,(5):45-49
[17]苏克忠,常廷改.地球物理技术在大坝抗震研究中的应用[J].地球物理学进展:2005,20(3):834-842
[18]韩俊伟,胡宝生,徐文德等.三向地震模拟振动台竖向激振系统分析[J].地震工程与工程振动:1996,16(2):114-122
[19]胡宝生.我国自行研制的第一个大型三向地震模拟振动台[J].世界地震工程:1995,(4):44-46
[20]韩俊伟,李玉亭,胡宝生.大型三向六自由度地震模拟振动台[J].地震学报:1998,20(3):104-108
[21]韩亮.桥墩结构模型与水相互作用的水下振动台试验研究[D].[硕士论文].大连理工大学,2011
[22]何小妹,丁洪生,付铁等.并联机床运动学标定研究综述[J].机床与液压:2004,(10):9-11,31
[23]彭斌彬,高峰,王冰等.五轴并联机床的标定仿真[J].组合机床与自动化加工技术:2005,(10):13-15
[24]王东署,迟健男.机器人运动学标定综述[J].计算机应用研究:2007,24(9):8-11
[25] T. Ropponen, Arai T. Accuracy analysis of a modified Stewart platform manipulator. Robotics and Automation, 1995. Proceedings., 1995 IEEE International Conference on 1995
[26] J. Wang and O. Masory. On the accuracy of a Stewart platform. I. The effect of manufacturing tolerances. IEEE International Conference on Robotics and Automation.1993
[27]黄田,唐国宝,李思维等.一类少自由度并联构型装备运动学标定方法研究[J].中国科学E辑:技术科学:2003,33(09):829-838
[28] K. A. P. Maurine, M. Uchiyama. Towards More Accurate Parallel Robots.15th World Congress of Int. Measurement Confederation.1999
[29] J. W. Zhao, K. C. Fan, T. H. Chang etc. Error Analysis of a Serial–Parallel Type Machine Tool [J].The International Journal of Advanced Manufacturing Technology:2002,19(3):174-179
[30] J. Ryu and J. Cha. Volumetric error analysis and architecture optimization for accuracy of HexaSlide type parallel manipulators [J].Mechanism and Machine Theory:2003,38(3):227-240
[31] T. Huang, D. G. Chetwynd, D. J. Whitehouse and J. Wang. A general and novel approach for parameter identification of 6-DOF parallel kinematic machines [J].Mechanism and Machine Theory:2005,40(2):219-239
[32] R. Yao, X. Tang, T. Li and C. Lin. Error Analysis and Distribution of 6-SPS and 6-PSS Reconfigurable Parallel Manipulators[J].2010,15(547-554
[33]李凌云.Stewart机构的误差建模与参数标定方法研究[D].[硕士论文].燕山大学,2006
[34]吕崇耀.Stewart并行机构位姿误差分析[J].华中理工大学学报:1999,27(8):4-6
[35]刘伟.冗余电机驱动的正交并联模拟台误差分析[J].机床与液压:2009,37(7):1-4
[36] T. Huang, J. Wang, DG. Chetwynd. Identifiability of geometric parameters of 6-DOF PKM systems using a minimum set of pose error data. Robotics and Automation, 2003. Proceedings. ICRA '03. IEEE International Conference on.2003
[37] J.A. Soons, F.C. Theuws, P.H. Schellekens. Modeling the errors of multi-axis machines: a general methodology [J].Precision Engineering:1992,14(1):5-19
[38] S. Besnard, W. Khalil. Robotics and Automation, 1995. Proceedings., 1995 IEEE International Conference on 1999
[39]刘得军,艾清慧,王建林等.3自由度并联坐标测量机运动学参数标定与计算机仿真[J].机械工程学报:2004,40(03):15-19
[40] H. Zhuang, L. Liu. Self Calibration of a Class of Parallel Manipulators. Robotics and Automation, 1996. Proceedings., 1996 IEEE International Conference on 1996
[41] H. Zhuang. Self Calibration of Parallel Mechanisms with a Case of Study on Stewart Platforms. Robotics and Automation, 1996. Proceedings., 1996 IEEE International Conference on 1997
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