How geometrical tolerances affect the measurement of reciprocal alignment of two different assemblies: a case study

Often a designer has the problem to apply a suitable system of
geometrical and dimensional tolerances to an assembly. The
right solution is not unique, in fact it depends on the chosen
parameters. If the tolerances have to be optimized, some
important parameters have to be taken into account, e.g. the
efficiency of each prescription, or if this last is reachable, or it
can be verified and how much the realization costs.
The authors opinion is that a statistical approach based on the
Monte Carlo Method is very useful when the tolerances chains
are complex.
This paper shows an application of this method in order to
verify the functional alignment between two assemblies and a
critical analysis of the uncertainty in phase both of the
component design and test.
This study has been developed thanks to the strict requirements
imposed by ESA (European Space Agency) on the components
that Thales Alenia Space has to realize within the LISA
Pathfinder experiment.
The very critical aspect of this work is to reciprocally align two
cylindrical elements of two different assemblies. The
specifications require 100 μm as maximum linear displacement
and 300 μrad as maximum angular displacement. Moreover this
prescriptions have to be verified also when the two elements are
independently moving.
To be able to reach such strict accuracy level the components
have been assembled in an ISO 100 class cleanroom and the
work space was a 3D Coordinate-Measuring Machine (CMM).
The cylindrical elements have a 10 mm diameter, so the value
of the measurement uncertainty associated with the alignment
check is fundamental.
Starting from the different uncertainty sources, the
measurability and verifiability of the alignment have been
considered and evaluated.
The overall uncertainty has been assessed by numerical
simulations which have taken into account the dimensional,
geometrical and form tolerances as well as the instrumental
uncertainty of the 3D CMM. This estimation has been
positively validated by a session of repeated measurements.
Numerical simulations have also allowed performing a
sensitivity analysis, in order to give information about which
sources more contribute to the overall uncertainty.