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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 (8): 1582-1593    DOI: 10.3785/j.issn.1008-973X.2019.08.017
电气工程、机械工程     
机械装配过程的偏差传递网络建模与误差溯源
祝鹏1(),余建波1,*(),郑小云1,王永松2,孙习武2
1. 同济大学 机械与能源工程学院，上海 201804
2. 上海航天设备制造总厂，上海 201100
Variation propagation network-based modeling and error tracing in mechanical assembling process
Peng ZHU1(),Jian-bo YU1,*(),Xiao-yun ZHENG1,Yong-song WANG2,Xi-wu SUN2
1. School of Mechanical Engineering, Tongji University, Shanghai 201804, China
2. Shanghai Aerospace Equipment Manufacturing Factory, Shanghai 201100, China
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摘要：

为了保证机械产品及其装配过程符合规范，须对产品装配过程的偏差传递流进行建模，识别关键装配特征并对相应误差装配节点进行溯源及控制. 提出基于复杂网络的自调节偏差传递网络建模方法与误差溯源方法，结合装配过程中的实测数据、特征表面信息以及装配工艺流程构建加权自调节偏差传递网络. 利用改进的加权半局部中心性排序算法识别偏差传递网络中的关键特征. 提出逆向回溯算法以及重要度排名（IR）指标，在加权自调节偏差传递网络中识别出关键特征的误差源，以确定须进行重点监控的装配面. 以锥齿轮轴组件的多阶段装配过程为研究对象进行验证，结果表明利用所提出的方法可对多阶段装配过程中的偏差流进行有效建模，识别关键装配面，实施误差溯源.
关键词： 多阶段装配;  偏差流;  复杂网络;  关键装配特征;  误差溯源    
Abstract:

To ensure the quality of mechanical products and the assembling process, it is necessary to model the variation propagation flow of the assembly process, identify the key assembly characteristics and control the corresponding error assembling nodes and the error source. A method of modeling and error tracing based on the complex network was proposed. The method was used to construct a self-regulated weighted variation propagation network, taking into account the measured data, the information of characteristic surfaces and the assembly technology in the assembly process. The improved weighted semi-local centrality sorting algorithm was used to identify the key characteristics of the constructed variation propagation network. The backtracking algorithm and the importance rank (IR) index were proposed to identify the error source of the key characteristics in the constructed self-regulated weighted variation propagation network, after which the assembly surfaces which need to be monitored could be distinguished. With the multistage assembly process of a gear shaft as a study case, the proposed method was verified. The method can be used to effectively model the variation flow, as well as identify the key assembly surface and the error source in the multistage assembly process.
Key words: multistage assembly    variation flow    complex network    key assembly characteristics    error source identification
收稿日期: 2018-07-21 出版日期: 2019-08-13
CLC:  TH 16  
通讯作者: 余建波     E-mail: paray@foxmail.com;jbyu@tongji.edu.cn
作者简介: 祝鹏（1995—），男，硕士生，从事多工序加工、装配过程的质量控制研究. orcid.org/0000-0002-2645-8998. E-mail： paray@foxmail.com
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引用本文:

祝鹏,余建波,郑小云,王永松,孙习武. 机械装配过程的偏差传递网络建模与误差溯源[J]. 浙江大学学报(工学版), 2019, 53(8): 1582-1593.

Peng ZHU,Jian-bo YU,Xiao-yun ZHENG,Yong-song WANG,Xi-wu SUN. Variation propagation network-based modeling and error tracing in mechanical assembling process. Journal of ZheJiang University (Engineering Science), 2019, 53(8): 1582-1593.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.08.017    或    http://www.zjujournals.com/eng/CN/Y2019/V53/I8/1582

图 1  自调节赋权偏差传递网络的建模与误差溯源方案
图 2  网络加权映射图及赋权偏差传递网络建模过程图
网络特性 定义 计算方法
复杂网络 赋权偏差传递网络
节点出（强）度 节点误差对邻居节点的影响效应 ${\rm{ES}}_i^{{\rm{out}}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ij}}} $ ${\rm{ES}}_i^{{\rm{out}}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ij}}{\omega _{ij}}} $
节点入（强）度 节点受邻居节点误差的影响效应 ${\rm{AS}}_i^{\rm{in}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ji}}} $ ${\rm{AS}}_i^{\rm{in}} = \displaystyle\sum\limits_{j \in {N_i}} {{a_{ji}}{\omega _{ji}}} $
节点（强）度 节点在网络中的重要性 ${S_{{i}}} = {\rm{AS}}_i^{\rm{in}} + {\rm{ES}}_i^{\rm{out}}$ ${S_{{i}}} = {\rm{AS}}_i^{\rm{in}} + {\rm{ES}}_i^{\rm{out}}$
聚集系数 节点间的误差传递效应 ${c_i}{\rm{ = }}\displaystyle\frac{{\displaystyle\sum\limits_{r = 1}^{{k}} {\displaystyle\sum\limits_{s = 1}^k {d\left( {{n_r},{n_s}} \right)} } }}{{k\left( {k - 1} \right)}}$ $c_{_B}^\omega {\rm{ = }}\displaystyle\frac{1}{{{s_i}\left( {{k_i} - 1} \right)}}\sum\limits_{j,k} {\frac{{{\omega _{_{ij}}} + {\omega _{ik}}}}{2}{a_{ij}}{a_{jk}}{a_{ki}}} $
平均聚集系数 网络节点的聚集程度 $C = \displaystyle\sum\limits_{i = 1}^N {{c_i}} /N$ $C =\displaystyle\sum\limits_{i = 1}^N {c_{_B}^\omega } /N$
平均最短路径 任意两节点间最短路径的平均值 $L = \displaystyle\sum\limits_{i,j \in {\bf N},i \ne j}^N {{d_{ij}}} /M$ $L = \displaystyle\frac{2}{{N(N - 1)}}\displaystyle\sum\limits_{i > j} {\frac{{{\omega _{ik}}{\omega _{kj}}}}{{{\omega _{ik}} + {\omega _{ik}}}}} $
介数 节点在网络传播中的重要性 $B = \displaystyle\sum\limits_{j,l,j \ne l \ne i}^n {{{{N_{jl}}(i)}}/{{{N_{jl}}}}} $
表 1  偏差传递网络的网络特性及计算方法
图 3  关键节点的误差溯源过程
图 4  锥齿轮轴组件装配工艺示意图
图 5  锥齿轮轴组件多阶段装配过程的偏差传递网络拓扑结构
图 6  偏差传递网络的节点度分布
图 7  偏差传递网络的节点度和节点强度分布图
图 8  网络特性分析与加权半局部算法分析结果
图 9  加权半局部算法与PageRank算法、LeaderRank算法的计算结果的对比
路径 关键节点 回溯第1步节点 第2步节点 第3步节点
路径1 ZCG-3 Z-2 Z-1 Z-0
路径2 ZCG-3 Z-2 Z-1 VT1
路径3 ZCG-3 Z-2 Z-1 TZ1
路径4 ZCG-3 Z-2 Z-1 CD1
路径5 ZCG-3 Z-2 Z-1 TZ2
路径6 ZCG-3 Z-2 Z-1 ZN-11
路径7 ZCG-3 Z-2 Z-1 TZ3
路径8 ZCG-3 Z-2 Z-1 GQ-1
路径9 ZCG-3 Z-2 Z-1 ZN-3
路径10 ZCG-3 Z-2 Z-1 TZ4
路径11 ZCG-3 Z-2 Z-1 TZ5
路径12 ZCG-3 ZCG-2 ZCT-3 ZCT-12
路径13 ZCG-3 ZCG-2 ZCG-1 ZCT-4
路径14 ZCG-3 ZCG-2 ZCG-1 ZN-22
路径15 ZCG-3 ZCG-2 ZCG-1 ZW-22
路径16 ZCG-3 MZ PJ ?
表 3  节点ZCG-3的逆向误差源回溯路径
节点 ZCT-12 ZCT-3 VT3 TZ2 TZ4 DS-2 ZW-21 ZW-22 VT5 Z-2 TZ-5 ZCG-1 ZCG-2 ZCG-3
CD3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ZCT-11 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0
ZCT-12 0 0.001 0 0 0 0 0 0 0 0 0 0 0 0
ZCT-3 0 0 0 0 0 0 0 0 0 0 0 0 0.571 0
VT3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TZ2 0.050 0 0 0 0 0 0 0 0 0 0 0 0 0
ZCT-4 0 0 0 0 0 0 0 0 0 0 0 0.030 0 0
ZW-11 0.810 0 0 0 0 0 0 0 0 0 0 0 0 0
ZN-21 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ZN-22 0 0 0 0 0 0 0 0 0 0 0 0.050 0 0
ZN-3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TZ4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
DS-2 0 0 0 0 0 0 0.060 0 0 0 0 0 0 0
ZW-21 0.905 0 0 0 0 0 0 0 0 0 0 0 0 0
ZW-22 0 0 0 0 0 0 0 0 0 0 0 0.070 0 0
VT5 0 0 0 0 0 0 0.020 0.020 0 0 0 0 0 0
Z-2 0 0 0 0 0 0 0 0 0 0 0 0 0 0.762
TZ5 0 0 0 0 0 0 0 0 0 0.060 0 0 0 0
ZCG-1 0 0 0 0 0 0 0 0.040 0 0 0 0 0.001 0
ZCG-2 0 0.952 0 0 0 0 0 0 0 0 0 0 0 0.001
ZCG-3 0 0 0 0 0 0 0 0 0 0.870 0 0 0 0
ZCGK-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
表 2  部分自调节赋权偏差传递网络的误差溯源过程
路径节点 IR 路径节点 IR
Z-2 0.816 TZ2 0.043
ZCG-2 1.020 ZN-11 0.365
MZ 0.002 TZ3 0.043
Z-1 1.245 GQ-1 0.223
ZCT-3 1.020 ZN-3 0.364
ZCG-1 0.144 TZ4 0.026
PJ 0.012 TZ5 0.051
Z-0 0.033 ZCT-12 1.122
VT1 0.043 ZCT-4 0.029
TZ1 0.017 ZN-22 0.049
CD1 0.183 ZW-22 0.067
表 4  节点ZCG-3的误差传播路径中各节点的误差影响力
关键节点 误差源
Z-1 Z-0
ZCT-11 Z-1，CD2
ZCT-12 ZCT-11，CD2
ZN-3 Z-1
Z-2 Z-1
表 5  关键节点及对应的误差源
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