Optimum tolerance design for complex assemblies using hierarchical interval constraint networks

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.