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

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.