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Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (9): 1647-1655    DOI: 10.3785/j.issn.1008-973X.2019.09.002
Mechanical Engineering     
Assembly variation prediction for compliant aeronautical structures using fuzzy interval analysis
Li DU1,3,4(),Biao MEI2,3,4,*(),Wei-dong ZHU1,3,4,Zhen-zheng KE2,3
1. School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
2. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
3. Institute of Advanced Technology, Zhejiang University, Hangzhou 310027, China
4. Zhejiang Province Key Laboratory of Advanced Manufacturing Technology, Hangzhou 310027, China
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Abstract  

Variation sources’ distributions were described as discrete fuzzy numbers under the condition that only the ranges of variation sources were known. An assembly variation model for compliant aeronautical structures was built based on the theory of elastic mechanics and finite element analysis (FEA). The variation sources described by discrete fuzzy numbers were treated as the inputs of the assembly variation model, the fuzzy distribution of assembly variation was obtained with the aid of fuzzy interval analysis, and the effectiveness of proposed assembly variation model and prediction method were verified with the case of simulated wing-box skeleton assembly. The experimental results show that the predicted intervals based on the proposed assembly variation prediction method contains the measured assembly variation, which can estimate the assembly variation with poor information of the variation sources. Meanwhile, the proposed method provides the assembly variation intervals under different confidence levels. This method is a complement to the traditional assembly variation analysis method base on the Monte Carlo simulation (MCS).



Key wordsassembly variation prediction      compliant aeronautical structures      discrete fuzzy number      variation source estimation      influence coefficient method      fuzzy interval analysis     
Received: 13 March 2019      Published: 12 September 2019
CLC:  TU 111  
Corresponding Authors: Biao MEI     E-mail: 610714464@qq.com;biaomei@zju.edu.cn
Cite this article:

Li DU,Biao MEI,Wei-dong ZHU,Zhen-zheng KE. Assembly variation prediction for compliant aeronautical structures using fuzzy interval analysis. Journal of ZheJiang University (Engineering Science), 2019, 53(9): 1647-1655.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.09.002     OR     http://www.zjujournals.com/eng/Y2019/V53/I9/1647


采用模糊区间分析的柔性航空结构件装配偏差预测

在仅知偏差源区间的条件下,将偏差源分布描述为离散模糊数;基于弹性力学原理,通过有限元仿真分析,建立柔性航空结构件的装配偏差模型;以离散模糊数表达的偏差源作为装配偏差模型的输入,结合模糊区间分析得到装配偏差的模糊分布;通过模拟翼盒骨架装配试验验证建立的装配偏差模型以及提出的装配偏差预测方法的有效性. 试验结果表明:基于模糊区间分析的装配偏差分析方法预测的装配偏差区间包含了实测的装配偏差,可解决偏差源信息匮乏时的装配偏差预测问题,并给出了不同置信水平下的装配偏差区间,是传统基于蒙特卡洛模拟(MCS)的装配偏差分析方法的一种补充.


关键词: 装配偏差预测,  柔性航空结构件,  离散模糊数,  偏差源估计,  影响系数法,  模糊区间分析 
Fig.1 Variation analysis for assembly of compliant aeronautical structures
Fig.2 Warping deformation and torsion deformation of rib depicted by angles
Fig.3 Model of simulation wing-box skeleton
Fig.4 Obtain sensitivity matrix of assembly through finite element analysis (FEA)
Fig.5 Calculation process of fuzzy interval distribution of simulation wing-box skeleton
观测点编号 ${U_{{\rm{fuz}}}}$/m ${U_{{\rm{int}}}}$/m ${U_{{\rm{mea}}}}$/m
λ=0 λ=0.2 λ=0.4 λ=0.6 λ=0.8 λ=1
1 [?0.579 8,0.579 8] [?0.580 6,0.580 6] [?0.581 4,0.581 4] [?0.582 2,0.582 2] [?0.583 0,0.583 0] [?0.583 7,0.583 7] [?0.583 7,0.583 7] ?0.544
2 [?0.554 4,0.554 4] [?0.554 4,0.554 4] [?0.554 5,0.554 5] [?0.554 5,0.554 5] [?0.554 6,0.554 6] [?0.554 6,0.554 6] [?0.554 6,0.554 6] ?0.407
3 [?0.535 9,0.535 9] [?0.536 0,0.536 0] [?0.536 0,0.536 0] [?0.536 1,0.536 1] [?0.536 1,0.536 1] [?0.536 2,0.536 2] [?0.536 2,0.536 2] ?0.269
4 [?0.518 4,0.518 4] [?0.518 5,0.518 5] [?0.518 6,0.518 6] [?0.518 7,0.518 7] [?0.518 8,0.518 8] [?0.518 9,0.518 9] [?0.518 9,0.518 9] ?0.131
5 [?0.507 6,0.507 6] [?0.507 7,0.507 7] [?0.507 7,0.507 7] [?0.507 7,0.507 7] [?0.507 7,0.507 7] [?0.507 7,0.507 7] [?0.507 7,0.507 7] 0.007
6 [?0.581 2,0.581 2] [?0.581 9,0.581 9] [?0.582 7,0.582 7] [?0.583 5,0.583 5] [?0.584 2,0.584 2] [?0.585 0,0.585 0] [?0.585 0,0.585 0] 0.305
7 [?0.557 0,0.557 0] [?0.557 1,0.557 1] [?0.557 1,0.557 1] [?0.557 2,0.557 2] [?0.557 2,0.557 2] [?0.557 3,0.557 3] [?0.557 3,0.557 3] 0.259
8 [?0.539 1,0.539 1] [?0.539 1,0.539 1] [?0.539 1,0.539 1] [?0.539 1,0.539 1] [?0.539 1,0.539 1] [?0.539 1,0.539 1] [?0.539 1,0.539 1] 0.214
9 [?0.519 3,0.519 3] [?0.519 4,0.519 4] [?0.519 4,0.519 4] [?0.519 5,0.519 5] [?0.519 6,0.519 6] [?0.519 6,0.519 6] [?0.519 6,0.519 6] 0.168
10 [?0.500 8,0.500 8] [?0.500 8,0.500 8] [?0.500 8,0.500 8] [?0.500 8,0.500 8] [?0.500 8,0.500 8] [?0.500 8,0.500 8] [?0.500 8,0.500 8] 0.122
11 [?1.414 2,1.414 2] [?1.514 2,1.514 2] [?1.614 2,1.614 2] [?1.714 2,1.714 2] [?1.814 2,1.814 2] [?1.914 2,1.914 2] [?1.914 2,1.914 2] 0.657
12 [?1.051 9,1.051 9] [?1.151 9,1.151 9] [?1.251 9,1.251 9] [?1.351 9,1.351 9] [?1.451 9,1.451 9] [?1.551 9,1.551 9] [?1.551 9,1.551 9] 0.581
13 [?0.690 4,0.690 4] [?0.690 4,0.690 4] [?0.790 4,0.790 4] [?0.890 4,0.890 4] [?0.990 4,0.990 4] [?1.090 4,1.090 4] [?1.190 4,1.190 4] 0.505
14 [?0.810 3,0.810 3] [?0.814 0,0.814 0] [?0.817 6,0.817 6] [?0.821 3,0.821 3] [?0.825 0,0.825 0] [?0.828 6,0.828 6] [?0.828 6,0.828 6] 0.429
15 [?0.533 5,0.533 5] [?0.533 5,0.533 5] [?0.533 5,0.533 5] [?0.533 5,0.533 5] [?0.533 5,0.533 5] [?0.533 6,0.533 6] [?0.533 6,0.533 6] 0.353
16 [?1.409 8,1.409 8] [?1.509 8,1.509 8] [?1.609 8,1.609 8] [?1.709 8,1.709 8] [?1.809 8,1.809 8] [?1.909 8,1.909 8] [?1.909 8,1.909 8] ?0.869
17 [?1.049 0,1.049 0] [?1.149 0,1.149 0] [?1.249 0,1.249 0] [?1.349 0,1.349 0] [?1.449 0,1.449 0] [?1.549 0,1.549 0] [?1.549 0,1.549 0] ?0.728
18 [?0.686 7,0.686 7] [?0.786 7,0.786 7] [?0.886 7,0.886 7] [?0.986 7,0.986 7] [?1.086 7,1.086 7] [?1.186 7,1.186 7] [?1.186 7,1.186 7] ?0.588
19 [?0.806 8,0.806 8] [?0.810 4,0.810 4] [?0.814 1,0.814 1] [?0.817 7,0.817 7] [?0.821 4,0.821 4] [?0.825 1,0.825 1] [?0.825 1,0.825 1] ?0.447
20 [?0.536 7,0.536 7] [?0.536 7,0.536 7] [?0.536 7,0.536 7] [?0.536 7,0.536 7] [?0.536 7,0.536 7] [?0.536 7,0.536 7] [?0.536 7,0.536 7] ?0.307
Tab.1 Comparison between measured and predicted assembly variation by fuzzy interval analysis and interval analysis based on assembly variation analysis methods
Fig.6 Platform for assembly variation measurement of simulant wing-box skeleton
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