Identification of Correlated Characteristics in a Linear Statistical Tolerance Design

Abstract:- In order to study the variations of mechanical components of an assembly, the accumulation of tolerances may be calculated using two major approaches: the Worst Case method and the Statistical (or probabilistic) method. The Worst Case method is very simple and well known. It must be applied only for simple assemblies where a larger allowance of the available space is granted for the tolerances. The statistical approach allows us to assign bigger tolerances for each component by taking advantage of random phenomena, which may occur during the manufacturing and assembly. On the other hand, this approach implies several hypotheses which may not always be respected in reality. This article proposes a case study to model a mechanical assembly of electrochemical cells whereby each cell consists of multiple layers of various materials. The first part of the study describes our main working hypothesis that encompasses the variability of environmental conditions (such as temperature, charge, pressure, shape defects, etc.) that necessitated the introduction of corrective semi-empirical factors. The second part contains the mathematical model, which describes the stochastic behavior of the thickness of cells once they are assembled. This model integrates the variance of each of the materials and the resulting effects of correlation between the materials, as well as the effects of the auto correlation into the case of several layers of the same material. The study demonstrates that the correlation and the auto correlation combine with different capability indices allows more precise predictions during the modeling stage. This allows the designer to optimize the parameters of the design to maximize the mechanical and energy performances of the electric cells