Optimum design of component tolerances of assemblies using constraint networks

This paper proposes an efficient algorithm for optimum allocation of tolerances among components of an assembly with an objective to minimize the total cost of manufacturing while meeting the tolerance specifications of the assembly. The assembly is first represented as a two-layer constraint network by describing its functions, attributes and then entities. Forward propagation of entity tolerances is carried out to see whether the present tolerances will meet the assembly tolerances. Backward propagation (BP) is carried out to find out the dependence of incremental change of any assembly function tolerance with that of the associated attributes and the entities. Constraints for the optimization problem are obtained from the two-stage BP of the contraint networks of the assembly for the required tolerances. The objective function of the optimization problem is obtained as an algebraic sum of the cost of manufacturing of individual entities with required tolerances. Lagrange multiplier method is then applied to obtain the optimum tolerances of the entities or components. This algorithm will provide an exact, closed-form solution. Example is provided for illustration of the algorithm.