Surface evolution models for abrasive jet micromachining of holes in glass and polymethylmethacrylate (PMMA)

Abstract

Models are presented to predict the shape and size of masked and unmasked holes machined in glass and polymethymethacrylate (PMMA) using abrasive jet micromachining (AJM). An existing AJM surface evolution model for brittle materials was modified by introducing a curvature-dependent smoothing (viscosity) term to the surface velocity function, greatly improving the prediction of hole shape in cases where the erosive power creates a sharp corner. The modified model predicts hole profiles that agree well with both experiments and a computer simulation. The profiles of holes machined in PMMA using a mask are also compared with the predictions of a recently developed theoretical model for the AJM of ductile materials. There is good agreement in both shape and depth with a maximum error of 13% up to an aspect ratio of 0.6 in PMMA.

Abrasive jet micro-machining of planar areas and transitional slopes in glass using target oscillation

“…In previous work (Ghobeity et al, 2007a(Ghobeity et al, , b, 2008, the etch rate from a single pass calibration channel, defined as the channel center depth, was measured and used in analytical models of profile development. An analogous expression for the case of an oscillating target would be useful in determining the scan speed required to etch the surface to a desired depth.…”

“…Based on this assumption, Slikkerveer and in't Veld (1999) developed a partial differential equation governing the surface profile evolution. Ten Thije Boonkkamp and Jansen (2002) extended the model by Slikkerveer and in't Veld (1999), and later Ghobeity et al (2008Ghobeity et al ( , 2007a developed it further to the following form:…”

“…E * (x * ) = * (x * )V * (x * ) k is defined as the normalized erosive power distribution seen by the exposed target surface, where * (x * ) is the spatial powder mass distribution across the jet, V * (x * ) is the normalized velocity distribution across the jet, and k is the velocity exponent of the erosion which describes the dependency of erosion rate on the normal impact velocity (Ghobeity et al, 2008). The term (1 − εÄ) is a smoothing expression used when the erosive power distribution creates unrealistically sharp corners in the predicted surface profile (Ghobeity et al, 2007a). Guidelines for the selection of the nondimensional constant ε are presented in Ghobeity et al (2007a).…”

“…The term (1 − εÄ) is a smoothing expression used when the erosive power distribution creates unrealistically sharp corners in the predicted surface profile (Ghobeity et al, 2007a). Guidelines for the selection of the nondimensional constant ε are presented in Ghobeity et al (2007a). The term (1 + z * 2 ,x * ) −k/2 in Eq.…”

Thermal analysis of cryogenically assisted abrasive jet micromachining of PDMS

“…In previous papers, the model was modified and surface evolution equations were obtained that quite accurately predict the machined profile evolution in masked and unmasked micro-channels in both ductile and brittle erosive systems [8,9,39,[45][46][47]. For example, in Ref.…”