Statistical tolerance analysis applied on overconstrained mechanisms with form deviations

Abstract

One method for modeling geometric variations in hyperstatic (i.e. overconstrained) systems is to use sets of constraints. Different models have been developed in this way, e.g. domains, T-maps, and polytopes. In general, if the intersection of the contact constraints between two parts potentially in contact is nonempty, the parts can be assembled without interference, and their relative positions determined. In this study, the polytope method is used with a statistical approach to define the behavior of an assembly. In the first part, geometric variations including form deviations of individual parts are defined. The relations between these variations resulting from the architecture of a mechanism are then defined. In the second part, contact constraints are introduced and the general method to conform the constraints into double description polytopes is presented. The general process to simulate the compliance of the mechanism with respect to functional conditions is described. A failure rate is obtained for a simulated population of manufactured parts using the Monte Carlo method. In the third part, an application to a flange is described, an example from an industrial case study. We show how to take advantage of double description of polytopes when simulating the assembly and the misalignment of the two parts that make up the flange. Finally, we present our conclusions and prospects for future studies.

Imprecise Probabilities as an Answer to the Indeterminacy Inherent to Mechanical Tolerances

“…Considerable research efforts have been put into the simulation of over-constrained mechanisms with geometrical defects and gaps [6,10], on the development of spatial mathematical models representing the deviation space [2,17], and on statistical methods to either determine the ideal tolerance values [11], or to assess the effect of a specific tolerance choice on the metric of interest [9]. All these considerations are part of the more general field of tolerance analysis.…”