An analytical model of the effect of particle size distribution on the surface profile evolution in abrasive jet micromachining

An analytical model to estimate the spatial distribution of erosive efficacy across the mask opening in the abrasive jet micromachining (AJM) of substrates is presented. A closed form analytical expression is derived which allows the erosive efficacy in the vicinity of the mask edge to be estimated as a function of the measured abrasive particle size distribution and the width of the mask opening. This analytical expression was used in a previously developed analytical surface evolution model to predict the time dependent eroding surface profiles of micro-holes and micro-channels of various sizes in glass and polymethylmethacrylate (PMMA), using aluminum oxide abrasive powders of different sizes. Use of the measured powder size distributions in the analytical models resulted in excellent agreement between the measured and model predicted channel profiles. The results of the study demonstrate that the particle size distribution and mask opening width can greatly affect the shape and depth of micro-channel profiles. A major improvement over previously developed models is ease-of-application since the erosive efficacy is given by an analytical expression rather than by the use of a computer simulation or a semi-empirical approach.