Allocation Tolerance by Jacobian-Torsor Model

W. Ghie, L. Laperrirre, D. Nadeau, and A. Desrochers (Canada)


Tolerancing, Jacobian, torsor, synthesis and design.


This paper describes a novel method for implementing tolerance synthesis by decoupled inversion of the Jacobian-torsor tolerance analysis model. Earlier work showed that a coupled pseudo inversion of the non-square Jacobian matrix implements an equal repartition of the functional requirement interval over all part tolerances involved in the chain, which is not representative of the way tolerances are usually assigned. Purchased parts become particularly problematic: bearings, fasteners, etc, that are bought externally come with their own manufactured tolerances which might not comply with such an equal repartition strategy. To correct this, we need a way to maintain independent tolerance values for each part that make up the functional chain. Doing so would give designers all the freedom necessary to determine tolerance values for each part depending where it comes from or from which process it was manufactured. The paper presents a decoupled Jacobian inversion strategy that implements such a more realistic way of performing tolerance synthesis. Example of using the model to design a totally functional mechanism is also provided..

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