Stratégies de mise en oeuvre des polytopes en analyse de tolérance

Abstract : In geometric tolerancing analysis area, a classical approach consists in handling polyhedrons coming from sets of linear constraints. The relative position between any two surfaces of a mechanism is determined by operations (Minkowski sum and intersection) on these polyhedrons. The polyhedrons are generally unbounded due to the inclusion of degrees of invariance for surfaces and degrees of freedom for joints defining theoretically unlimited displacements.In a first part are introduced the cap half-spaces to limit these displacements in order to transform the polyhedron into polytopes. This method requires controlling the influence of these additional half-spaces on the topology of calculated polytopes. This is necessary to ensure the traceability of these half-spaces through the tolerancing analysis process.A second part provides an inventory of the issues related to the numerical implementation of polytopes. One of them depends on the choice of a computation configuration (expression point and base, homogenization coefficients) to define a polytope. After proving that the modification of a computation configuration is an affine transformation, several simulation strategies are listed in order to understand the problems of numerical precision and computation time.
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Lazhar Homri. Stratégies de mise en oeuvre des polytopes en analyse de tolérance. Mécanique [physics]. Université de Bordeaux, 2014. Français. ⟨NNT : 2014BORD0156⟩. ⟨tel-01133691⟩

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