An inverse method for the abrasive jet micro-machining of high aspect ratio channels of desired topography – Part I, theory.

Control of the cross-sectional shape of micro-channels may be of interest in micro-heat-sinks, microfluidic particle sorting, and micro-machine lubrication applications. It has been previously shown that inverse methods can be used to determine the abrasive jet micromachining (AJM) traverse speed and path required to sculpt desired micro-channel topographies, as long as the aspect ratios (AR, ratio of depth to width) are low (<0.06), such that the channel sidewall slopes are negligible. However, for many applications, higher AR channels with steep sidewalls are required. This paper introduces an iterative inverse method which allows prediction of the machining procedure required to sculpt higher (AR up to 1) micro-channels of prescribed cross-sectional shape using mask-less AJM. The method is developed for AJM in both ductile and brittle erosive systems, its robustness and limitations are discussed, and the iterative methodology is compared to the General Reduced Gradient optimization technique. Part II of the paper will experimentally verify the procedure for a wide variety of desired topographies machined in borosilicate glass and Poly(methyl methacrylate) (PMMA). • Inverse algorithm predicts the machining requirements for high AR cross-sections. • Most challenging topographies are semicircles in glass and ramps in PMMA. • Machining requirements are unique, a minimum radius of curvature is required. • Inverse algorithm converges faster than GRG-nonlinear optimization. [ABSTRACT FROM AUTHOR]