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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (9): 1647-1655    DOI: 10.3785/j.issn.1008-973X.2019.09.002
机械工程     
采用模糊区间分析的柔性航空结构件装配偏差预测
杜丽1,3,4(),梅标2,3,4,*(),朱伟东1,3,4,柯臻铮2,3
1. 浙江大学 机械工程学院，浙江 杭州 310027
2. 浙江大学 先进技术研究院，浙江 杭州 310027
3. 浙江大学 流体动力及机电系统国家重点实验室，浙江 杭州 310027
4. 浙江大学 浙江省先进制造技术重点实验室，浙江 杭州 310027
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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摘要：

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    
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 words: assembly variation prediction    compliant aeronautical structures    discrete fuzzy number    variation source estimation    influence coefficient method    fuzzy interval analysis
收稿日期: 2019-03-13 出版日期: 2019-09-12
CLC:  TU 111  
通讯作者: 梅标     E-mail: 610714464@qq.com;biaomei@zju.edu.cn
作者简介: 杜丽（1994—），女，硕士生，从事飞机数字化装配/弱刚度结构装配研究. orcid.org/0000-0001-5029-8085. E-mail： 610714464@qq.com
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引用本文:

杜丽,梅标,朱伟东,柯臻铮. 采用模糊区间分析的柔性航空结构件装配偏差预测[J]. 浙江大学学报(工学版), 2019, 53(9): 1647-1655.

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.

链接本文:

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

图 1  柔性航空结构件装配偏差分析
图 2  采用角度表征肋翘曲和扭转变形示意图
图 3  模拟翼盒骨架模型
图 4  基于有限元分析(FEA)获取装配敏感度矩阵
图 5  模拟翼盒骨架装配偏差的模糊分布计算过程
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
表 1  基于模糊区间分析和区间分析的装配偏差分析方法的预测结果以及装配偏差实测数据比较
图 6  模拟翼盒骨架装配偏差测量平台
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