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

TL;DR

This paper presents a new method for modeling 2D and 3D assemblies that incorporates form errors of surfaces, enabling more accurate analysis of high-precision assemblies through a geometrical and static equilibrium approach.

Contribution

It introduces a novel approach to parameterize and solve assemblies with form errors using modal shapes and static equilibrium, improving accuracy over traditional methods.

Findings

Accurate evaluation of assembly performance considering form errors.

Comparison of results with and without form errors shows significant differences.

Method enables assessment of nonconformity rate in batch production.

Abstract

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 precision 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 of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of 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 for 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 the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate 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 with the functional requirements. The pilot production then can or cannot be validated.