The geometrical interaction of the stylus and the measured surface in 3D roughness measurements
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.