  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.
