Abstract
The notion of tolerance zone is fundamental for geometric tolerance analysis and synthesis. In this paper, a definition is proposed for the tolerance zones, slightly different from the ISO standard definition, but leading to a non ambiguous model. The tolerance zones are represented by inequations between the real variables that represent relative admissible displacements from the theoretical nominal positions. In the limit case of equality, the equations obtained are those of boundaries that limit a domain in the displacement space.
Some properties of these relations and of the corresponding volumes are investigated from their mathematical or geometrical representations, particularly the symmetry and transitivity.
The mathematical representation of tolerance zones allows to translate the standard concepts of projected tolerance zone and maximal material condition, and to analyse a given toleranced mechanism.
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© 1999 Springer Science+Business Media Dordrecht
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Giordano, M., Pairel, E., Samper, S. (1999). Mathematical representation of Tolerance Zones. In: van Houten, F., Kals, H. (eds) Global Consistency of Tolerances. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1705-2_18
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DOI: https://doi.org/10.1007/978-94-017-1705-2_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5198-1
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