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Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts


Tolerance analysis is a key analytical tool for estimation of accumulating effects of the individual part tolerances on the design specifications of a mechanical assembly. This paper presents a new feature-based approach to tolerance analysis for mechanical assemblies with geometrical and dimensional tolerances. In this approach, geometrical and dimensional tolerances are expressed by small degrees of freedom (SDOF) of geometric entities (faces, feature axes, edges, and features of size) that are described by tolerance zones. The uncertainty of dimensions and geometrical form of features due to tolerances is mathematically described using modal interval arithmetic. The two concepts of modal interval analysis and SDOF are combined to describe the tolerance specifications. The algorithm is presented which explains the steps and the procedure of tolerance analysis. The proposed method is compatible with the current GD&T standards and can incorporate GD&T concepts such as various material modifiers (maximum material condition, least material condition, and regardless of feature size), envelope requirement, and bonus tolerances. This method can take into account multidimensional effects due to geometrical tolerances in tolerance analysis. The application of the proposed method is illustrated through presenting an example problem and comparing results with tolerance charting method.

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Correspondence to M. R. Movahhedy.

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Khodaygan, S., Movahhedy, M.R. & Saadat Fomani, M. Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts. Int J Adv Manuf Technol 50, 1041–1061 (2010).

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  • Tolerance analysis
  • Tolerance zone
  • Modal interval arithmetic
  • Small degrees of freedom