北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (5): 802-810.doi: 10.13700/j.bh.1001-5965.2014.0372

• 论文 • 上一篇    下一篇

基于动态规划的飞机多交点装配离散公差优化

谭昌柏1, 匡衡2   

  1. 1. 南京航空航天大学 机电学院, 南京 210016;
    2. 密歇根大学 机械工程系, 安娜堡 48109
  • 收稿日期:2014-06-20 修回日期:2014-09-26 出版日期:2015-05-20 发布日期:2015-06-02
  • 通讯作者: 谭昌柏(1978—),男,重庆人,副教授,tcbnuaa@nuaa.edu.cn,主要研究方向为飞机装配准确度与容差设计、计算机辅助设计与制造. E-mail:tcbnuaa@nuaa.edu.cn
  • 基金资助:

    国家自然科学基金(51275236);航空科学基金(2012ZE66016)

Discrete tolerance optimization for aircraft multi-joint assembly based on dynamic programming

TAN Changbai1, KUANG Heng2   

  1. 1. School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    2. Department of Mechanical Engineering, University of Michigan, Ann Arbor 48109, USA
  • Received:2014-06-20 Revised:2014-09-26 Online:2015-05-20 Published:2015-06-02

摘要:

针对飞机多交点装配公差设计的多阶段决策特点,提出了基于动态规划的离散公差优化方法.首先,给出了典型的3交点和4交点装配协调误差表达式;然后,引入装配性能和成本指标,建立了公差设计的动态规划有向图模型,其中图节点表示可选的公差配合,并存储其后部子过程的最优装配性能和成本指标值,有向边表示相邻移形环节间的公差取值约束;最后,采用两阶段图遍历算法求解最优的公差设计,其中,“回溯”阶段逆序求解各节点和边的二元指标属性值,“前溯”阶段根据节点的二元指标属性值进行最优路径的启发式搜索.以某直升机尾梁及斜梁装配为例进行验证,结果表明该方法可求取公差的全局最优解,同时避免各环节成本和装配性能的重复计算、有效减小公差搜索空间、提高公差优化效率.

关键词: 公差优化, 飞机多交点装配, 动态规划, 启发式搜索, 有向图

Abstract:

According to the nature of multi-stage decision of tolerance design for aircraft multi-joint assembly, a novel method of discrete tolerance optimization was proposed based on dynamic programming. First, coordination error models of typical three-joint assembly and four-joint assembly were presented. Second, a dynamic programming-based directed graph was built by introducing assembly quality indicator and cost indicator. Each individual graph node denoted an optional tolerance and contained optimal assembly quality index and cost index of rear sub-process. The constraint of tolerance selection between adjacent dimensional links was depicted by a directed edge linking two correspondent graph nodes. Finally, a two-phrase graph traversal algorithm was developed to make the optimal tolerance selection. The binary-indicator attribute of each graph node and edge were evaluated by inverse sequence method in the “backtracking” phase, and then a heuristic search algorithm was proposed to find the optimal route based on the binary-indicator attribute of each graph node in the following “forwarding” phase. This method was verified by a case study of helicopter tail beam and inclined beam assembly. The results show that the global optimal tolerance selection can be attained. Meanwhile, the efficiency of tolerance optimization is improved significantly by elimination of repetitive cost and assembly quality evaluations as well as diminishment of tolerance search space.

Key words: tolerance optimization, aircraft multi-joint assembly, dynamic programming, heuristic search, directed graph

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