Optimum tolerance design for complex assemblies using hierarchical interval constraint networks

• Published in: Computers & industrial engineering Vol. 45; no. 3; pp. 511 - 543
• Main Authors: Yang, Christopher C, Achutha Naikan, V.N
• Format: Journal Article
• Language: English
• Published: Seoul Elsevier Ltd 01.10.2003; Oxford Pergamon Press; New York, NY Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Exact sciences and technology; Flows in networks. Combinatorial problems; Hierarchical interval constraint networks; Hierarchies; Lagrange multiplier; Operational research and scientific management; Operational research. Management science; Operations research; Sensitivity analysis; Studies; Theory of constraints; Tolerance design; Tolerance intervals; Hierarchical interval constraint networks; Tolerance design; Sensitivity analysis; Optimal algorithm; Optimal allocation; Tolerance analysis; Objective function; Algorithm analysis; Storage tank
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/S0360-8352(03)00072-X

In this paper, we propose two efficient algorithms for optimal allocation of tolerance among the components of complex assembly with large number of constraints and entities. Basic concepts of hierarchical interval constraint networks have been used for deriving the objective functions and constraint functions of the problem. The optimization problem is then solved by two different algorithms and the results are compared. The first algorithm is based on Lagrange multipliers and the second one is developed based on an iterative relative sensitivity analysis procedure. The relative sensitivity analysis algorithm can practically handle any number of constraints and entities with required level of accuracy, whereas the Lagrange multiplier algorithm is more suitable for simple problems. The proposed algorithms accept any type of cost-tolerance relationship for modeling. The algorithms are illustrated using two examples. The first example is the tolerance design of a tank, which is solved by both algorithms, and the results are compared. A second example of a movable double bearing assembly has been discussed to show that the relative sensitivity analysis algorithm can handle complex tolerance design problems, which is difficult or inaccurate to solve by Lagrange multiplier algorithm.