Level set methods for the modelling of surface evolution in the abrasive jet micromachining of features used in MEMS and microfluidic devices

Abstract

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.

A level set methodology for predicting the surface evolution of inclined masked micro-channels resulting from abrasive jet micro-machining at oblique incidence

“…LSM are especially useful for predicting the propagation of surfaces that experience irregular or complex motion in two dimensions (2D) and higher. They have been used to track interfaces in many applications in material science, fluid mechanics, image processing, wet and ion beam etching [15,16], and very recently, AJM [14].…”

“…Most recently, Burzynski and Papini [14] developed an LSM [15,16] based model for the prediction of the surface evolution of masked glass and PMMA micro-channels and micro-holes machined using AJM at normal incidence. To account for the effect of decreasing particle flux near the mask edge, the analytical technique of [11] was used.…”

“…To be consistent with the LSM formulation, using the geometry of Fig. 3, the local x 0 and z 0 coordinates can be expressed in terms of the global x and z coordinates as follows [14]:…”

“…For the AJM of brittle targets such as glass, the velocity of the surface in the direction of the local normal in (1) can be written as [14] F b ðx,y,z,tÞ ¼…”

Investigation of machining accuracy of micro-dimples fabricated by modified microscale pattern transfer without photolithography of substrates

“…Various techniques have been developed to produce surface texturing, such as abrasive jet machining [3], micro-milling [4], electrical discharge machining [5], laser beam machining [6], and electrochemical micromachining (EMM) [7].…”