Geometric tolerance analysis through Jacobian model for rigid assemblies with translational deviations

The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements.

This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed.

The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational.

In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies.

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 of the manufacturing costs.

The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.