Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precisions assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account form errors. When we analyze a batch of assemblies, the problem is to compute the Non-Conformity Rate (NCR) of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared to the functional requirements. The pilot production can then be validated or not.