Numerical simulation of surface roughness and erosion rate of abrasive jet micro-machined channels

Abrasive jet micro-machining (AJM) utilizes the impact of particles in high-speed air jets to erode ductile or brittle target surfaces and produce micro-scale features such as channels and holes, as well as planar areas of controlled depth. The roughness of micro-channels for micro-fluidic applications made using AJM can affect fluid flow phenomena such as separation efficiency, electro-osmotic mobility and solute dispersion. Moreover, surface roughness plays a major role in microscale adhesion contact in MEMS and light scattering in optoelectronics devices. A numerical model was developed to simulate the brittle erosion process leading to the creation of unmasked channels as a function of particle size, velocity, dose, impact angle and target material properties. For the first time, erosion was simulated using models of two damage mechanisms: crater removal due to the formation and growth of lateral cracks, and edge chipping. Accuracy was further enhanced by simulating the actual relationship between particle size, velocity and radial location within the jet using distributions measured with high-speed laser shadowgraphy. Comparisons with experimental data showed that the model can predict the average roughness of the centerline of channels machined on borosilcate glass with 9% average error over a wide range of particle kinetic energies. The simulation also allowed for the first time the prediction of surface profile waviness and the transient roughness leading to a steady-state. The numerical model predicted the glass erosion rate with an average error of 29% for a broad range of AJM process conditions. The results indicated that the main erosion mechanism in the AJM of borosilicate glass was chip removal by lateral cracking. Edge chipping normally occurred when the impact angle was small and a particle impact occurred on an eroded surface near the apex of a peak, resulting in the removal of a relatively small portion of the peak. Thus, edge chipping contributed to profile smoothing and less so to erosion.