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A framework for tolerance design considering systematic and random uncertainties due to operating conditions

S. Khodaygan (Department of Mechanical Engineering, Sharif University of Technology, Tehran, Islamic Republic of Iran)

Assembly Automation

ISSN: 0144-5154

Article publication date: 25 July 2019

Issue publication date: 18 October 2019




The purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties.


In the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions.


The proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results.

Research limitations/implications

The proposed method is limited to the dimensional tolerances of components with the normal distribution.

Practical implications

The proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications.


In conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.



Khodaygan, S. (2019), "A framework for tolerance design considering systematic and random uncertainties due to operating conditions", Assembly Automation, Vol. 39 No. 5, pp. 854-871.



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