Statistical Tolerance Analysis of Flexible Assemblies with Contact Effects

One of the most important characteristics of industrial products, especially mechanical set-ups, is considering the tolerances of production and assembly of these set-ups, which directly influences the products’ operations. In sheet metal structures, due to the high flexibility of the sheets, the errors appeared while assembly will be as highly influential as the errors due to the production tolerance of the sheets. As a result, having a comprehensive model which could analyze the assembly process of these structures and also clarifies the relation between the tolerance of the parts and the ultimate changes of the set-up will be of considerable importance. During the assembly process, the contact effect between the components is inevitable. If such effect is not considered, the contact surfaces will permeate. The purpose of this paper is to present a method to analyze the tolerance of flexible sheet structures, considering the contact effect between surfaces. It is performed by the Method of Modified Influence Coefficients (MMIC) for calculating the outcome error appeared in the assembly set-up. To do so, the method has also been applicable for nonlinear contact problems by modifying the sensitivity matrix and proposing a statistical solution for the errors of the assembly setup. Finally the capabilities of the presented method have been investigated through analyzing an example of assembling two panels of an automobile body and the authenticity of the results has been validated by comparing with Monte Carlo simulation results.