The geometrical interaction of the stylus and the measured surface in 3D roughness measurements
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Abstract
The target of this work is to study the effect of the stylus tip geometry on the
surface roughness measurements by the stylus methods. A computer simulation
of the measuring process in 3D using arbitrary tip shapes has been undertaken. A
novel feature of this simulation is that it determines and reports the contact
distribution of the contact points on the stylus when scanning each surface.
Following analysis of fully simulated data to establish the fidelity of the simulation
process, it was applied to data set from real surfaces. First these were examined
using ideal (sometimes truncated) pyramid, conical and spherical tips. Then tip
shapes determined from the measurement of real styli were used. Relatively large
tips (of the order of 10 μm) were used in order to ease the need for measurement
resolution. The simulation results were evaluated against real measurements of
the surfaces. A bespoke measuring system was developed for this, adding X-Y
scanning and a means of interchanging styli while maintaining micrometer lateral
positioning between measurements. The shape of each stylus tip has been
determined using a technique based on the replication by indentation into a soft
substrate (typically lead).
The roughness values of the real surfaces when scanned (theoretically) by the real
tips have been compared to the roughness values of the same surfaces when
measured by the measuring system with different tips. This comparison has shown
a good compliance of both the theoretical and the practical results. This provides a
degree of confidence for interpreting details of the simulation as having practical
relevance.
Both computer simulation and real measurements confirm the trends that would be
expected from earlier studies. For example, amplitude parameters tend to drop in
value as stylus size increases. The distribution of stylus contacts in simulation
suggests that it is rarely to be found near the nominal centre of the tip. It is also
clearly demonstrated that real worn tips do not necessary act as if blunt, contacts
concentration in small regions when local features dominate. These results have
significant implementations for the uncertainty in topographic measurements