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The time-dependent evolution of an abrasive jet micro-machined surface is described by a partial differential equation which is difficult to solve using traditional analytical or numerical techniques. As a result, traditional surface advancement models can give incorrect predicted profile depths. In this work, level set methods were used to develop novel models of the abrasive jet machined surface evolution of unmasked and masked channels and holes in glass and polymethylmethacrylate. The level set-predicted eroded profiles were compared to those experimentally obtained, as well as to those predicted by existing analytical and computer models. For the majority of cases, the level set-predicted surface advancement was closer to the measured profiles than those predicted by existing analytical and computer models. The work demonstrates the potential of the level set methodology as a generally applicable tool for the prediction of abrasive jet machined surface profiles, and provides a foundation for future simulation of more complex abrasive jet micro-machining operations.

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Novel experimental techniques for obtaining the particle spatial distribution and the velocity distribution across a micro-abrasive jet were presented and tested. The spatial distribution of particles within the jet was found by using a direct particle capture technique, and was found to depend on the nozzle diameter, following either a Weibull or a piecewise Weibull distribution. In general, the jet was found to be more focused when more particles were present across the nozzle opening. It was demonstrated how the measured particle spatial distribution could be used with a measurement of the eroded profile to extract an estimate of the non-dimensional particle velocity distribution within the jet. Using this technique, a linear or nonlinear velocity distribution was obtained, depending on the particle type and the nozzle diameter used. The results for the velocity distribution were compared to particle tracking velocimetry (PTV) results and were found to be within the acceptable measurement error ranges.

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A previous implementation of narrow-band level set methodology developed by the authors was extended to allow for the modelling of mask erosive wear in abrasive jet micro-machining (AJM). The model permits the prediction of the surface evolution of both the mask and the target simultaneously, by representing them as a hybrid and continuous mask-target surface. The model also accounts for the change in abrasive mass flux incident to both the target surface and, for the first time, the eroding mask edge, that is brought about by the presence of the mask edge itself. The predictions of the channel surface and eroded mask profiles were compared with measurements on channels machined in both glass and poly-methyl-methacrylate (PMMA) targets at both normal and oblique incidence, using tempered steel and elastomeric masks. A much better agreement between the predicted and measured profiles was found when mask wear was taken into account. Mask wear generally resulted in wider and deeper glass target profiles and wider PMMA target profiles, respectively, when compared to cases where no mask wear was present. This work has important implications for the AJM of complex MEMS and microfluidic devices that require longer machining times.

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