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
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摘要
影响平面单环闭链结构装配精度的主要误差源有杆件加工偏差、装配约束误差以及铰链间隙。而铰链间隙的随机性导致平面单环闭链结构装配误差具有不确定性。为了能够实现装配精度预测和获得装配误差边界,通过分析平面单环四杆结构装配特点,提出单杆件固定和双杆件连接两种装配单元,并建立两种单元的误差模型。在此基础上,完成了无间隙平面单环闭链结构装配误差建模。然后通过引入连杆机构旋转法则,以虚拟杆件表征铰链间隙并将其视为"短杆",从而基于杆件旋转不变性建立了考虑间隙的平面单环闭链结构装配误差不确定性分析模型,并给出了装配误差边界计算方法。最后以平面五杆单环结构作为数值案例,验证了所提出方法与模型的可行性与实用性。
The link deviation, assembly constraint error and joint clearance are the major error sources, which affect the assembly accuracy of planar single-closed-loop mechanisms. However, the randomness of joint clearance results in the accuracy uncertainty of the planar single-closed-loop mechanism. In order to predict the assembly accuracy and obtain the error bound, two assembly components, single-fixed link and two-connected link, are proposed and their error models are established by analyzing the assembly property of a planar four-bar single-loop mechanism. And accordingly, the error modeling of assembly error of the single-loop mechanism without considering joint clearance is firstly completed. Then the uncertainty analysis model of assembly error of the planar single-loop mechanism is built by introducing the rotatability law of the linkage, in which the joint clearance is regarded as a ‘short link'. In addition, the method of calculating the bound of assembly error is given. At last, the feasibility and utility of the method proposed above are verified by a numerical example of the planar five-bar single-loop mechanism.
The link deviation, assembly constraint error and joint clearance are the major error sources, which affect the assembly accuracy of planar single-closed-loop mechanisms. However, the randomness of joint clearance results in the accuracy uncertainty of the planar single-closed-loop mechanism. In order to predict the assembly accuracy and obtain the error bound, two assembly components, single-fixed link and two-connected link, are proposed and their error models are established by analyzing the assembly property of a planar four-bar single-loop mechanism. And accordingly, the error modeling of assembly error of the single-loop mechanism without considering joint clearance is firstly completed. Then the uncertainty analysis model of assembly error of the planar single-loop mechanism is built by introducing the rotatability law of the linkage, in which the joint clearance is regarded as a ‘short link'. In addition, the method of calculating the bound of assembly error is given. At last, the feasibility and utility of the method proposed above are verified by a numerical example of the planar five-bar single-loop mechanism.
引文
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[22]AGHABEIGI M,MOVAHHEDY M R.An algorithm for geometrical uncertainty analysis in planar truss structures[J].Structural&Multidisciplinary Optimization,2014,49(2):225-238.
[23]LUO K,DU X.Probabilistic mechanism analysis with bounded random dimension variables[J].Mechanism&Machine Theory,2013,60(1):112-121.
[24]刘伟东,宁汝新,刘检华,等.基于偏差有向图和D-H方法的产品装配精度预测技术[J].机械工程学报,2012,48(7):125-140.LIU Weidong,NING Ruxin,LIU Jianhua,et al.Precision predicting based on directed deviation graph modeling and D-H methodology[J].Journal of Mechanical Engineering,2012,48(7):125-140.
[25]LIU J,JIN J,SHI J.State space modeling for 3-D variation propagation in rigid-body multistage assembly processes[J].IEEE Transactions on Automation Science&Engineering,2010,7(2):274-290.
[26]张黎,聂宏,魏小辉,等.飞机起落架收放机构静态装配的误差灵敏度分析方法[J].兵工自动化,2012,31(4):17-20.ZHANG Li,NIE Hong,WEI Xiaohui,et al.Analysis method of static assembly error sensitivity of aircraft landing gear retraction mechanism[J].Ordnance Industry Automation,2012,31(4):17-20.
[27]唐健钧,田锡天,耿俊浩,等.基于多维矢量环的装配偏差源敏感度分析[J].机械工程学报,2015,51(17):156-161.TANG Jianjun,TIAN Xitian,GENG Junhao,et al.Sensitivity analysis of assembly deviation source based on multidimensional vector loop[J].Journal of Mechanical Engineering,2015,51(17):156-161.
[28]李冬英,李梦奇,张根保,等.元动作装配单元误差源及误差传递模型研究[J].机械工程学报,2015,51(17):146-155.LI Dongying,LI Mengqi,ZHANG Genbao,et al.Mechanism analysis of deviation sourcing and propagation for meta-action assembly unit[J].Journal of Mechanical Engineering,2015,51(17):146-155.
[29]YAN K,WANG N,ZHAI Q,et al.Theoretical and experimental investigation on the thermal characteristics of double-row tapered roller bearings of high speed locomotive[J].International Journal of Heat&Mass Transfer,2015,84:1119-1130.
[30]SHYU J H,TING K L.Invariant link rotatability of N-Bar kinematic chains[J].Journal of Mechanical Design,1994,116(1):343-347.
[31]ZHU J,TING K L.Uncertainty analysis of planar and spatial robots with joint clearances[J].Mechanism&Machine Theory,2000,35(9):1239-1256.
[32]TING K L,HSU K L,YU Z,et al.Clearance-induced output position uncertainty of planar linkages with revolute and prismatic joints[J].Mechanism&Machine Theory,2017,111:66-75.
[2]TING K L,LIU Y W.Rotatability laws for N-bar kinematic chains and their proof[J].ASME Journal of Mechanical Design,1991,113(1):32-39.
[3]TSAI M J,LAI T H.Accuracy analysis of a multi-loop linkage with joint clearances[J].Mechanism&Machine Theory,2008,43(9):1141-1157.
[4]LI X,DING X,CHIRIKJIAN G S.Analysis of angular-error uncertainty in planar multiple-loop structures with joint clearances[J].Mechanism&Machine Theory,2015,91:69-85.
[5]MENG J,LI Z.A general approach for accuracy analysis of parallel manipulators with joint clearance[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems.IEEE,2005:889-894.
[6]PARENTI C V,VENANZI S.Clearance influence analysis on mechanisms[J].Mechanism&Machine Theory,2005,40(12):1316-1329.
[7]LI J,HUANG H,YAN S,et al.Kinematic accuracy and dynamic performance of a simple planar space deployable mechanism with joint clearance considering parameter uncertainty[J].Acta Astronautica,2017,136:34-45.
[8]TSAI M J,LAI T H.Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality[J].Mechanism&Machine Theory,2004,39(11):1189-1206.
[9]FLORES P.A methodology for quantifying the kinematic position errors due to manufacturing and assembly tolerances[J].Strojniski Vestnik,2011,57(6):457-467.
[10]KROGER R,BINDER S.Accuracy analysis of 3-DOF planar parallel robots[J].Mechanism&Machine Theory,2008,43(4):445-458.
[11]YU A,BONEV I A,ZSOMBOR-MURRAY P.Geometric approach to the accuracy analysis of a class of 3-DOF planar parallel robots[J].Mechanism&Machine Theory,2008,43(3):364-375.
[12]ZHANG J,DU X.Time-dependent reliability analysis for function generation mechanisms with random joint clearances[J].Mechanism&Machine Theory,2015,92:184-199.
[13]GENG X,WANG X,WANG L,et al.Non-probabilistic time-dependent kinematic reliability assessment for function generation mechanisms with joint clearances[J].Mechanism&Machine Theory,2016,104:202-221.
[14]HAFEZIPOUR M,KHODAYGAN S.An uncertainty analysis method for error reduction in end-effector of spatial robots with joint clearances and link dimension deviations[M].Abingdon:Taylor&Francis,Inc.,2017.
[15]王卓识,陈根良,王皓,等.基于误差区域映射的并联机构精度设计研究[J].机械设计与研究,2016(4):10-14.WANG Zhuoshi,CHEN Genliang,WANG Hao.A study on precision design of parallel mechanisms based on mapping of error space[J].Machine Design and Research,2016(4):10-14.
[16]刘大炜,王立平,关立文.一个特殊3自由度并联机构的精度分析及标定[J].机械工程学报,2010,46(9):46-51.LIU Dawei,WANG Liping,GUAN Liwen.Accuracy analysis and calibration of a special 3-dof parallel mechanism[J].Journal of Mechanical Engineering,2010,46(9):46-51.
[17]BRIOT S,BONEV I A.Accuracy analysis of 3T1R fully-parallel robots[J].Mechanism&Machine Theory,2010,45(5):695-706.
[18]LIN P D,CHEN J F.Accuracy analysis of planar linkages by the matrix method[J].Mechanism&Machine Theory,1992,27(5):507-516.
[19]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.Deployable accuracy analysis of planar satellite antenna with joint clearacnes[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(12):2625-2631.
[20]常鹏,李铁民,刘辛军.基于集合理论的并联机构精度分析方法[J].清华大学学报,2007,47(11):1984-1988.CHANG Peng,LI Tiemin,LIU Xinjun.Accuracy analysis of parallel mechanisms based on set theory[J].Journal of Tsinghua University,2007,47(11):1984-1988.
[21]WITTWER J W,CHASE K W,HOWELL L L.The direct linearization method applied to position error in kinematic linkages[J].Mechanism&Machine Theory,2004,39(7):681-693.
[22]AGHABEIGI M,MOVAHHEDY M R.An algorithm for geometrical uncertainty analysis in planar truss structures[J].Structural&Multidisciplinary Optimization,2014,49(2):225-238.
[23]LUO K,DU X.Probabilistic mechanism analysis with bounded random dimension variables[J].Mechanism&Machine Theory,2013,60(1):112-121.
[24]刘伟东,宁汝新,刘检华,等.基于偏差有向图和D-H方法的产品装配精度预测技术[J].机械工程学报,2012,48(7):125-140.LIU Weidong,NING Ruxin,LIU Jianhua,et al.Precision predicting based on directed deviation graph modeling and D-H methodology[J].Journal of Mechanical Engineering,2012,48(7):125-140.
[25]LIU J,JIN J,SHI J.State space modeling for 3-D variation propagation in rigid-body multistage assembly processes[J].IEEE Transactions on Automation Science&Engineering,2010,7(2):274-290.
[26]张黎,聂宏,魏小辉,等.飞机起落架收放机构静态装配的误差灵敏度分析方法[J].兵工自动化,2012,31(4):17-20.ZHANG Li,NIE Hong,WEI Xiaohui,et al.Analysis method of static assembly error sensitivity of aircraft landing gear retraction mechanism[J].Ordnance Industry Automation,2012,31(4):17-20.
[27]唐健钧,田锡天,耿俊浩,等.基于多维矢量环的装配偏差源敏感度分析[J].机械工程学报,2015,51(17):156-161.TANG Jianjun,TIAN Xitian,GENG Junhao,et al.Sensitivity analysis of assembly deviation source based on multidimensional vector loop[J].Journal of Mechanical Engineering,2015,51(17):156-161.
[28]李冬英,李梦奇,张根保,等.元动作装配单元误差源及误差传递模型研究[J].机械工程学报,2015,51(17):146-155.LI Dongying,LI Mengqi,ZHANG Genbao,et al.Mechanism analysis of deviation sourcing and propagation for meta-action assembly unit[J].Journal of Mechanical Engineering,2015,51(17):146-155.
[29]YAN K,WANG N,ZHAI Q,et al.Theoretical and experimental investigation on the thermal characteristics of double-row tapered roller bearings of high speed locomotive[J].International Journal of Heat&Mass Transfer,2015,84:1119-1130.
[30]SHYU J H,TING K L.Invariant link rotatability of N-Bar kinematic chains[J].Journal of Mechanical Design,1994,116(1):343-347.
[31]ZHU J,TING K L.Uncertainty analysis of planar and spatial robots with joint clearances[J].Mechanism&Machine Theory,2000,35(9):1239-1256.
[32]TING K L,HSU K L,YU Z,et al.Clearance-induced output position uncertainty of planar linkages with revolute and prismatic joints[J].Mechanism&Machine Theory,2017,111:66-75.
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