利用结构等效转换的空间可展机构装配误差建模与灵敏度分析
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摘要
为解决空间可展机构装配过程中无法对杆件进行精准定量调整的难题,针对杆件耦合与环约束复杂等特点,提出了一种空间可展机构装配误差建模与灵敏度分析的方法。首先,通过结构等效转换将空间可展机构分为两部分,并分别基于闭环矢量与虚位移法,推导出上述两部分的几何精度模型,然后利用线性叠加,建立了空间可展机构整体装配误差模型。在此基础上,运用偏微分法完成了空间可展机构误差灵敏度分析,实现了关键误差源识别。最后,以星载SAR卫星天线空间可展机构为数值算例进行了计算,结果表明:在杆长误差和铰链安装位置误差范围相同的情况下,单独调整支撑杆件能更好地满足装配精度要求,且星体连接杆尺寸误差对天线面板指向精度的影响尤为显著。
The precise and quantitative link adjustment of the spatial deployable mechanism cannot be implemented in the assembly shop nowadays. Considering the characteristics like coupled links and complex loop constraints, an approach of assembly error modeling is proposed and the corresponding sensitivity analysis is carried out. The spatial deployable mechanism is divided into two parts via structural equivalent transformation, and the geometric accuracy models of these two parts are established with the methods of closed-loop vector and virtual displacement respectively. Then the whole assembly accuracy model of the spatial deployable mechanism is derived from the linear superposition, and the error sensitivity is analyzed with partial differential method to accordingly identify the key error source. A spatial deployable mechanism of space borne SAR antenna is taken as a numerical example. If link length deviations and assembly position misalignments of joints are in the same range respectively, it indicates that merely adjusting the support links can better meet the requirement of assembly accuracy, and the link connected with payload module has a particularly significant impact on the pointing accuracy of antenna panels.
The precise and quantitative link adjustment of the spatial deployable mechanism cannot be implemented in the assembly shop nowadays. Considering the characteristics like coupled links and complex loop constraints, an approach of assembly error modeling is proposed and the corresponding sensitivity analysis is carried out. The spatial deployable mechanism is divided into two parts via structural equivalent transformation, and the geometric accuracy models of these two parts are established with the methods of closed-loop vector and virtual displacement respectively. Then the whole assembly accuracy model of the spatial deployable mechanism is derived from the linear superposition, and the error sensitivity is analyzed with partial differential method to accordingly identify the key error source. A spatial deployable mechanism of space borne SAR antenna is taken as a numerical example. If link length deviations and assembly position misalignments of joints are in the same range respectively, it indicates that merely adjusting the support links can better meet the requirement of assembly accuracy, and the link connected with payload module has a particularly significant impact on the pointing accuracy of antenna panels.
引文
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[25]ZHAO Qiangqiang,GUO Junkang,HONG Jun.Assembly precision prediction for planar closed-loop mechanism in view of joint clearance and redundant constraint[J].Journal of Mechanical Science and Technology,2018,32:3395-3405.
[26]赵强强,郭俊康,洪军.基于连杆机构旋转法则的平面单环闭链结构装配误差不确定性分析[J].机械工程学报,2018,54(11):29-38.ZHAO Qiangqiang,GUO Junkang,HONG Jun.Uncertainty analysis of assembly error of planar singleloop mechanisms based on the rotatability laws of linkages[J].Journal of Mechanical Engineering,2018,54(11):29-38.
[27]丁建中,王春洁.含铰链间隙板式卫星天线展开精度分析[J].北京航空航天大学学报,2016,42(12):2625-2631.DING Jianzhong,WANG Chunjie.Deployment accuracy analysis of planar satellite antenna with joint clearances[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(12):2625-2631.
[28]张武翔,杨毅,罗均,等.多环闭链可展机构尺寸调整方法[J].机械工程学报,2015,51(19):11-20.ZHANG Wuxiang,YANG Yi,LUO Jun,et al.Size adjustment of multi-closed-loop deployable mechanisms[J].Journal of Mechanical Engineering,2015,51(19):11-20.
[29]洪林.并联机器人精度分析与综合研究[D].天津:天津大学,2004:16-19.
[30]PAUL R P.Robot manipulators:mathematics,programming,and control:the computer control of robot manipulat[M].Cambridge,Massachusetts,USA:MIT Press,1981:82-90.
[2]GRALEWSKI M R,ADAMS L,HEDGEPETH J M.Deployable extendable support structure for the RA-DARSAT synthetic aperture radar antenna[C]∥International Astronautical Federation Congress.Washington,DC,USA:International Astronautical Federation,1992:18-24.
[3]LUHMANN H J,ETZLER C C,WAGNER R.Design and verification of mechanisms for a large foldable antenna[C]∥23rd Aerospace Mechanisms Symposium.Huntsville,USA:NASA,1989:113-126.
[4]JORDAN R L.The Seasat:a synthetic aperture radar system[J].IEEE Journal of Oceanic Engineering,1979,5(2):154-164.
[5]WANG H,WANG C J,LI X,et al.Large SAR antenna deployable structure design and optimization[J].Applied Mechanics&Materials,2012,163:62-65.
[6]XU Y,LIN Q,WANG X,et al.Mechanism design and dynamic analysis of a large-scale spatial deployable structure for space mission[C]∥Seventh International Conference on Electronics and Information Engineering.Washington,USA:International Society for Optics and Photonics,2017:1032226.
[7]胡凯.星载可展桁架机构Radarsat-2的基础问题研究[D].上海:上海交通大学,2015:48-51.
[8]SHEN Y,MONTMINY S,ZHENG W,et al.Large SAR membrane antenna deployable structure design and dynamic simulation[C]∥AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.New York,USA:AIAA,2013:1-11.
[9]王丹丹.可展开平面天线支撑机构展开运动学及动力学分析[D].哈尔滨:哈尔滨工业大学,2013:15-20.
[10]SHEN Y,MONTMINY S,ZHENG W.Design and dynamical analysis of a SAR membrane antenna deployable structure[C]∥ASME 2006International Mechanical Engineering Congress and Exposition.New York,USA:ASME,2006:613-619.
[11]SONG S G,WANG C J,WANG H,et al.Dynamic analysis of extendible support structure deployment[J].Applied Mechanics&Materials,2012,163:91-94.
[12]CAMPBELL B E,HAWKINS W.An 11-METER deployable truss for the Seasat radar antenna[C]∥12th Aerospace Mechanisms Symposium.Santa Barbara,USA:NASA,1979:77-88.
[13]ALI Z,KROUPNIK G,MATHARU G,et al.RA-DARSAT-2space segment design and its enhanced capabilities with respect to RADARSAT-1[J].Canadian Journal of Remote Sensing,2004,30(3):235-245.
[14]NETO M A,AMBRSIO J A C,LEAL R P.Composite materials in flexible multibody systems[J].Computer Methods in Applied Mechanics&Engineering,2006,195(50/51):6860-6873.
[15]李波,梁宝柱,周鑫,等.一种星载平面天线支撑桁架:CN106129578A[P].2016-11-16.
[16]EVANS D L,ALPERS W,CAZENAVE A,et al.Seasat-A 25-year legacy of success[J].Remote Sensing of Environment,2005,94(3):384-404.
[17]FRANCIS C R,GRAF G,EDWARDS P G,et al.The ERS-2 spacecraft and its payload[EB/OL].[2018-07-23].http:∥www.esa.int/esapub/bulletin/bullet83/fran83.htm.
[18]VANT M,LIVINGSTONE C,REY M.Canadian experience on Radarsat 1and Radarsat 2/GMTI for surveillance[C]∥AIAA International Air and Space Symposium and Exposition.New York,USA:AIAA,2013:2820:1-11.
[19]ROSENQVIST A,SHIMADA M,ITO N,et al.ALOS PALSAR:apathfinder mission for global-scale monitoring of the environment[J].IEEE Transactions on Geoscience&Remote Sensing,2007,45(11):3307-3316.
[20]国家航天局对地观测与数据中心.高分三号卫星介绍[EB/OL].[2018-07-23].http:∥gfplatform.cnsa.gov.cn/n6084429/n6084446/n6084504/n6759687/index.html.
[21]HEDGEPETH J M.Influence of fabrication tolerances on the surface accuracy of large antenna structures[J].AIAA Journal,1982,20(5):680-686.
[22]GREENE W H.Effects of random member length errors on the accuracy and internal loads of truss antennas[J].Journal of Spacecraft&Rockets,1985,22(5):554-559.
[23]MOBREM M.Methods of analyzing surface accuracy of large antenna structures due to manufacturing tolerances[C]∥AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.New York,USA:AIAA,2013:1-10.
[24]吴建云,王春洁,汪瀚.基于蒙特卡洛法的卫星天线板展开精度分析[J].航天返回与遥感,2013,34(6):89-94.WU Jianyun,WANG Chunjie,WANG Han.Accuracy analysis of satellite antenna plate deployment based on Monte Carlo method[J].Spacecraft Recovery&Remote Sensing,2013,34(6):89-94.
[25]ZHAO Qiangqiang,GUO Junkang,HONG Jun.Assembly precision prediction for planar closed-loop mechanism in view of joint clearance and redundant constraint[J].Journal of Mechanical Science and Technology,2018,32:3395-3405.
[26]赵强强,郭俊康,洪军.基于连杆机构旋转法则的平面单环闭链结构装配误差不确定性分析[J].机械工程学报,2018,54(11):29-38.ZHAO Qiangqiang,GUO Junkang,HONG Jun.Uncertainty analysis of assembly error of planar singleloop mechanisms based on the rotatability laws of linkages[J].Journal of Mechanical Engineering,2018,54(11):29-38.
[27]丁建中,王春洁.含铰链间隙板式卫星天线展开精度分析[J].北京航空航天大学学报,2016,42(12):2625-2631.DING Jianzhong,WANG Chunjie.Deployment accuracy analysis of planar satellite antenna with joint clearances[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(12):2625-2631.
[28]张武翔,杨毅,罗均,等.多环闭链可展机构尺寸调整方法[J].机械工程学报,2015,51(19):11-20.ZHANG Wuxiang,YANG Yi,LUO Jun,et al.Size adjustment of multi-closed-loop deployable mechanisms[J].Journal of Mechanical Engineering,2015,51(19):11-20.
[29]洪林.并联机器人精度分析与综合研究[D].天津:天津大学,2004:16-19.
[30]PAUL R P.Robot manipulators:mathematics,programming,and control:the computer control of robot manipulat[M].Cambridge,Massachusetts,USA:MIT Press,1981:82-90.