# Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic

## Abstract

In mechanical assemblies, individual components are placed together to deliver a certain function. The performance, quality, and cost of the mechanical assembly are significantly affected by its tolerances. Toleranced dimensions inherently generate an uncertain environment in a mechanical assembly. This paper presents a proper method for tolerance analysis of mechanical assemblies with asymmetric tolerances based on an uncertainty model. This mathematical approach is based on fuzzy logic and tolerance accumulation models such as worst-case and root-sum-square methods. A fuzzy-based tolerance representation is developed to model uncertainty of tolerance components in the mechanical assemblies. According to this scheme, toleranced components are described as fuzzy numbers with their membership functions constructed using the statistical distributions of manufactured variables. In this way, the uncertainty of assembly requirements and accumulation of tolerances are represented in the form of fuzzy number. In this paper, a new factor, the fuzzy factor, is introduced that helps converting the membership functions into fuzzy intervals that can be used for modal interval analysis. Equations for estimation of percent contributions of individual tolerances are introduced in terms of uncertainty parameter. These equations yield percent contributions of upper and lower bounds of independent variables (manufactured dimensions) on the upper and lower bounds of dependent variables (assembly dimensions). The proposed method is applied to an example, and its results are discussed.

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Correspondence to M. R. Movahhedy.

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Khodaygan, S., Movahhedy, M.R. Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic. Int J Adv Manuf Technol 53, 777–788 (2011). https://doi.org/10.1007/s00170-010-2855-4

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### Keywords

• Tolerance analysis
• Tolerance accumulation
• Fuzzy logic
• Modal interval analysis
• Asymmetric tolerances