Study of an assembly tolerance allocation model based on Monte Carlo simulation

Abstract The traditional design methods of assembly tolerance allocation are usually based on engineers' experience, or the worst on worst tolerance analysis (WOW) method, or the root sum square tolerance analysis (RSS) method. However, the above-mentioned methods, whilst used frequently in the analysis of a single-dimensional chain, are not suitable for the analysis of geometrical tolerance and multi-dimensional chains. Also, the relationship between tolerance and manufacturing cost is not considered and a suitable tolerance allocation based on minimum manufacturing cost can not be obtained. Some research works have applied linear or non-linear programming methods to optimize the tolerance allocation of each part in an assembly. However, the convergence of the solution is not ensured. The purpose of this study is to provide an integrated approach, including tolerance design, manufacturing cost analysis and multiple chains consideration, using the Monte Carlo method to optimize the tolerance allocation with minimum cost. The Monte Carlo method, a statistical simulation method, was used to simulate the dimension variance of each part and each dimensional chain. The contribution percentage of each part on each dimensional chain was calculated. Tolerance cost was chosen as an object function and the tolerance allocation model as a constraint condition, the optimum tolerances of each part being obtained by the iteration method. Results of computer simulation for several examples were compared with published data for demonstrating the feasibility of the proposed method. It can be concluded that the tolerance-allocation model combined with a tolerance-cost relationship can provide a very practical and useful approach for design engineers.

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