A variational model for 3D tolerance analysis with manufacturing signature and operating conditions

The purpose of this work is to present a variational model able to deal with form tolerances and assembly conditions. The variational model is one of the methods proposed in literature for tolerance analysis, but it cannot deal with form tolerances and assembly conditions that may influence the functional requirements of mechanical assemblies.

This work shows how to manage the actual surfaces generated by the manufacturing process and the operating conditions inside the variational model that has been modified to integrate the manufacturing signature left on the surfaces of the parts and the operating conditions that arise during an actual assembly, such as gravity and friction. Moreover, a geometrical model was developed to numerically simulate what happens in a real assembly process and to give a reference value.

The new variational model was applied to a three-dimensional case study. The obtained results were compared to those of the geometrical model and to those of the variational model to validate the new model and to show the improvements.

The proposed approach may be extended to other models of literature. However, its limitation is that it is able to deal with a sphere–plane contact.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease in the manufacturing costs.

The main contributions of the study are the insertion of a systematic pattern characterizing the features manufactured by a process, assembly operating conditions and development of a geometrical model to reproduce what happens in a real assembly process.