Statistical Analysis of Assemblies Having Dependent Fitting Conditions

Analysis of the propagation of geometric variability through assemblies is used to estimate the probability that randomly selected components will, in fact, assemble. This process is known as Statistical Tolerance Analysis. One-dimensional analyses utilize a direct root-sum-square composition of the contributing part dimensions (the dimension stack) to estimate the probability that appropriate clearances will be maintained in the assembled configuration. Higher dimensional analyses frequently use the sensitivities of the clearances to dimensional changes based on the kinematics of the assembly. However, commercial tolerance analysis software does not support the analysis of assemblies where more than one dependent variable (a clearance) appears in each dimension stack. This paper describes the extension of a novel modeling method to accommodate statistical variability in assemblies. Assemblies are modeled in terms of their clearance conditions between mating surfaces, and parts are allowed to “float” with respect to one another, rather than being required to have all degrees of freedom removed in the final assembly. Variability in part dimensions is transformed to variation in the clearances, allowing inter-dependent dimension stacks sharing multiple, dependent clearances. The differences in predicted yield — will the parts fit together as designed? — for assemblies whose components can float with respect to one another is compared to similar assemblies where relative motion is fixed by a specified condition of contact or alignment.