ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Precision analysis of deployable structures based on dimension reduction method and effective link length
Received date: 2016-07-06
Revised date: 2016-10-26
Online published: 2016-11-10
Supported by
National Natural Science Foundation of China (51635002)
The uncertainties of joint clearances and link length errors are studied by the method of probability and statistics. A precision analysis method for deployable structure is proposed based on Univariate Dimension Reduction Method (UDRM) and effective link length model. Using the UDRM, the precision function for the deployable structure is decoupled into a combination of independent effects of multiple link length errors to establish the precision analysis model for the structure. The effective link length model is applied to replace the original link length for precision calculation. The effective model converts the joint clearances and link length errors into effective link length errors, which are proved to follow normal distributions. An example of deployable antenna is given to calculate the means and variances in the deployable state with the Gauss quadrature based on the error distributions of link lengths and joint clearances. The correctness and effectiveness of the precision analysis method is verified by comparing the results of Monte Carlo Simulation (MCS) and First Order Second Moment (FOSM) method.
QI Junwei , WANG Chunjie , DING Jianzhong . Precision analysis of deployable structures based on dimension reduction method and effective link length[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017 , 38(6) : 220590 -220590 . DOI: 10.7527/S1000-6893.2016.0273
[1] 刘荣强, 田大可, 邓宗全. 空间可展开天线结构的研究现状与展望[J]. 机械设计, 2010, 27(9): 1-10. LIU R Q, TIAN D K, DENG Z Q. Research actuality and prospect of structure for space deployable antenna[J]. Journal of Machine Design, 2010, 27(9): 1-10 (in Chinese).
[2] 刘明治, 高桂芳. 空间可展开天线结构研究进展[J]. 宇航学报, 2003, 24(1): 82-87. LIU M Z, GAO G F. Advances in the study on structure for space deployable antenna[J]. Journal of Astronautics, 2003, 24(1): 82-87 (in Chinese).
[3] CHEN G L, WANG H, LIN Z Q. A unified approach to the accuracy analysis of planar parallel manipulators both with input uncertainties and joint clearance[J]. Mechanism & Machine Theory, 2013, 64(6): 1-17.
[4] MERLET J P. Computing the worst case accuracy of a PKM over a workspace or a trajectory[C]//5th Chemnitzer Parallel Kinematic Seminar. Zwickau: Verlag Wissenschaftliche Scripten, 2006.
[5] SUN D Y, CHEN G P. Kinematic accuracy analysis of planar mechanisms with clearance involving random and epistemic uncertainty[J]. European Journal of Mechanics—A/Solids, 2016, 58: 256-261.
[6] LI X, DING X L, CHIRIKJIAN G S. Analysis of angular-error uncertainty in planar multiple-loop structures with joint clearances[J]. Mechanism & Machine Theory, 2015, 91: 69-85.
[7] 姚泽良, 李宝平, 周雪峰. 结构可靠度分析的一次二阶矩方法与二次二阶矩方法[J]. 西北水力发电, 2005, 21(3): 20-23. YAO Z L, LI B P, ZHOU X F. Simple and quadratic of the two ranks quadrature of the structure reliability[J]. Journal of Northwest Hydroelectric Power, 2005, 21(3): 20-23 (in Chinese).
[8] 陈胜军, 贾方. 曲柄滑块机构运动精度的概率分析与计算[J]. 机械设计与制造, 2013(7): 203-206. CHEN S J, JIA F. Probability analysis and calculation of kinematic accuracy for slider-crank mechanism[J]. Machinery Design & Manufacture, 2013(7): 203-206 (in Chinese).
[9] PADMANABHAN D, AGARWAL H, RENAUD J E, et al. A study using Monte Carlo simulation for failure probability calculation in reliability-based optimization[J]. Optimization & Engineering, 2006, 7(3): 297-316.
[10] 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 J Y, WANG C J, WANG H. Accuracy analysis of satellite antenna plate deployment based on Monte Carlo method[J]. Spacecraft Recovery & Remote Sensing, 2013, 34(6): 89-94 (in Chinese).
[11] 彭茂林, 杨自春, 曹跃云, 等. 基于响应面法的可靠性稳健设计优化[J]. 航空动力学报, 2013, 28(8): 1784-1790. PENG M L, YANG Z C, CAO Y Y, et al. Reliability robust design optimization based on response surface method[J]. Journal of Aerospace Power, 2013, 28(8): 1784-1790 (in Chinese).
[12] 刘成立, 吕震宙. 结构可靠性分析中考虑高次项修正的组合响应面法[J]. 航空学报, 2006, 27(4): 594-599. LIU C L, LV Z Z. Response surface combination improved by high order term for structure reliability analysis[J]. Acta Aeronautica et Astronautica Sinica, 2006, 27(4): 594-599 (in Chinese).
[13] RAHMAN S, XU H. A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics[J]. Probabilistic Engineering Mechanics, 2004, 19(4): 393-408.
[14] ZHANG X F, PANDEY M D, ZHANG Y M. A numerical method for structural uncertainty response computation[J]. Science China Technological Sciences, 2011, 54(12): 3347-3357.
[15] WANG J G, ZHANG J F, DU X P. Hybrid dimension reduction for mechanism reliability analysis with random joint clearances[J]. Mechanism & Machine Theory, 2011, 46(10): 1396-1410.
[16] 孟广伟, 冯昕宇, 李锋,等. 基于降维算法和Edgeworth级数的结构可靠性分析[J]. 北京航空航天大学学报, 2016, 42(3): 421-425. MENG G W, FENG X Y, LI F, et al. Structural reliability analysis based on dimensionality reduction and Edgeworth series[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(3): 421-425 (in Chinese).
[17] EARLES S W E, WU C L S. Motion analysis of rigid-link mechanism with clearance at a bearing using Lagrangian mechanics and digital computation[C]//Conference on Mechanisms. London: Institution of Mechanical Engineers, 1972.
[18] LEE S J, GILMORE B J. The determination of the probabilistic properties of velocities and accelerations in kinematic chains with uncertainty[J]. Journal of Mechanical Design, 1991,113(1): 84-90.
[19] BLOZNELIS M. An Edgeworth expansion for studentized finite population statistics[J]. Acta Applicandae Mathematicae, 2003, 78(1): 51-60.
[20] 张义民, 贾敬存, 黄贤振. 基于Edgeworth级数法和数据包络分析法的数控车床可靠性分配[J]. 机械强度, 2016(1): 69-73. ZHANG Y M, JIA J C, HUANG X Z. Reliability allocation of CNC lathe based on Edgeworth series method and date envelopment analysis[J]. Journal of Mechanical Strength, 2016(1): 69-73 (in Chinese).
[21] 叶江水, 王仲刚, 陈友良, 等. 基于前四阶矩的非高斯响应概率密度函数逼近方法研究[J]. 后勤工程学院学报, 2010, 26(1): 12-16. YE J S, WANG Z G, CHEN Y L, et al. Research on approximate methods of non-Gaussian probability density function based on the first four moments of the response[J]. Journal of Logistical Engineering University, 2010, 26(1): 12-16 (in Chinese).
[22] 刘彦明. 基于四阶矩的机械可靠性相关研究[D]. 太原: 太原科技大学, 2011: 23-38. LIU Y M. Research on mechanical reliability based on the four order moment[D]. Taiyuan: Taiyuan University of Science & Technology, 2011: 23-38 (in Chinese).
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