A comparison of tolerance analysis models for assembly

Mechanical products are usually made by assembling many parts. The dimensional and geometrical variations of each part have to be limited by tolerances so that it can ensure both a standardized production and a certain level of quality defined to satisfy functional requirements. The appropriate allocation of tolerances among the different parts is the fundamental tool to ensure that assemblies work correctly at lower costs. Therefore, to ensure their functionality, assembly designers have to apply tolerance analysis. A model based on either worst case or statistical type analysis may be used. Actually, there are some different models used or proposed by the literature to make the tolerance analysis of an assembly constituted by rigid parts, but none of them is completely and univocally accepted. None of them has done an objective and complete comparison for analyzing the advantages and the weaknesses and furnishing a criterion for the choice and application. This paper briefly introduces three of the main models for tolerance analysis, the Jacobian, the vector loop, and the torsor. These models are briefly described and then compared to show their analogies and differences. Some guidelines are provided as well, with the purpose of developing a novel approach which is aimed at overcoming some of the limitations of these models.

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