Tolerance Analysis and Synthesis by Means of Deviation Domains, Axi-Symmetric Cases

The small displacement torsors are generally used for the representation of the geometrical deviations. The standardised tolerances can then be translated by a set of inequalities between the components of a deviation torsor. In the case of cylindrical tolerance zones, and surfaces of revolution, the inequalities are quadratic and the stack up tolerances are more difficult to calculate. But the axi-symmetric case makes it possible to reduce the space to three dimensions at the maximum instead of six in the general case. Topological operations like the Minkowski sum to carry out the domains for stack up analyse of tolerances are then reduced to operations on polyhedrons. Moreover, we propose a way of taking into account the size tolerances. The first presented application relates to metro-logic inspection for a specification with maximum material condition on both the toleranced surface and the datum. The second example makes it possible to determine the deviation between two surfaces belonging to two different parts after mating them by two contact features.