Erosion and Roughness Modeling in Abrasive JetMicro-machining of Brittle MaterialsbyReza Haj Mohammad JafarA thesis submitted in conformity with the requirementsfor the degree of Doctor of PhilosophyGraduate Department of Mechanical and Industrial EngineeringUniversity of Toronto Copyright by Reza Haj Mohammad Jafar (2013)
iiErosion and Roughness Modeling in Abrasive JetMicro-machining of Brittle MaterialsReza Haj Mohammad JafarDoctor of PhilosophyMechanical and Industrial EngineeringUniversity of Toronto2013AbstractThe effect of particle size, velocity, and angle of attack was investigated on the roughness anderosion rate of unmasked channels machined in borosilicate glass using abrasive jet micromachining (AJM). Single impact experiments were conducted to quantify the damage due to theindividual alumina particles.Based on these observations, an analytical model from theliterature was modified and used to predict the roughness and erosion rate.A numerical model was then developed to simulate the brittle erosion process leading to thecreation of unmasked channels as a function of particle size, velocity, dose, impact angle andtarget material properties. For the first time, erosion was simulated using models of two damagemechanisms: crater removal due to the formation and growth of lateral cracks, and edgechipping. Accuracy was further enhanced by simulating the actual relationship between particlesize, velocity and radial location within the jet using distributions measured with high-speedlaser shadowgraphy.The process of post-blasting AJM channels with abrasive particles at a relatively low kineticenergy was also investigated in the present work by measuring the roughness reduction of areference unmasked channel in borosilicate glass as a function of post-blasting particle size,velocity, dose, and impact angle. The numerical model was modified and used to simulate thepost-blasting process leading to the creation of smooth channels as a function of particle size,velocity, dose, impact angle, and target material properties.
iiiFinally, the effect of alumina particle kinetic energy and jet impact angle on the roughness anderosion rate of channels machined in borosilicate glass using abrasive slurry jet micro-machining(ASJM) was investigated. The analytical and numerical models derived for AJM, were found topredict reasonably well the roughness and the erosion rate of ASJM channels, despite the largedifferences in the fluid media, flow patterns, and particle trajectories in AJM and ASJM.
ivThis thesis is dedicated to my dear parents.
vAcknowledgmentsI sincerely appreciate the invaluable guidance, consistent encouragement and great assistance ofmy supervisors, Professors Marcello Papini and Jan Spelt, without their support, the completionof this work would be impossible.I owe special thanks to my lovely wife, Samira, whose continuous love, moral support andencouragement made this thesis possible within a four-year time frame.
viTable of ContentsDedication . vAcknowledgments . vTable of Contents . viiList of Tables . ixList of Figures . x1Introduction . 11.1Overview. 11.2Literature review . 18.104.22.168.21.2.32Effect of process parameters on roughness . 3Roughness modeling . 3Roughness reduction . 41.3Objectives . 61.4Thesis outline . 61.5References . 7Analytical Modeling. 102.1Introduction . 102.2Experiments . 112.2.1Apparatus and target material. 112.2.3Target damage due to single impacts . 182.2.2Particle characterization . 122.2.4Modeling . 192.3.1Roughness modeling . 192.3Roughness and erosion measurement . 182.3.2Results and discussion . 252.4.1Surface roughness . 252.4.3Comparison of the models with experiments. 322.214.171.124Erosion rate modeling . 25Single impact experiments . 28
vii32.5Conclusions. 362.6References . 37Numerical Simulation. 403.1Overview of modeling in AJM . 403.2Target damage due to particle impacts .4126.96.36.199.24Glass edge chipping . 433.3Experiments . 443.4Erosion simulation. 453.5Results and discussion . 503.6Conclusion. 563.7References . 57Simulation of Erosive Smoothing . 594.1Overview of smoothing AJM channels. 594.2Experiments . 614.2.1Apparatus and target material. 6188.8.131.52Erosion simulation . 634.4Results and Discussion . 644.4.1Experimental results . 644.4.25Crater removal. 42Particle size, velocity and mass flux characterization. 62Numerical simulation . 754.5Conclusions. 794.6References . 80Erosion Modeling in Abrasive Slurry Jet Micro-machining . 825.1Introduction . 825.2Experiments . 845.2.1ASJM setup . 845.2.3Effect of water on the erosion of glass. 87Modeling . 885.3.1Estimation of particle velocity in ASJM . 8184.108.40.206.220.127.116.11Machining of channels and single particle impact tests . 85Analytical modeling of roughness and erosion rate . 91Numerical erosion simulation. 93
viii18.104.22.168Single impact experiments . 945.4.3Comparison of the analytical models with experiments. 922.214.171.124.46Results and discussion . 94Oblique blasting . 95Numerical simulation . 1005.5Conclusions. 1035.6References . 104Conclusions . 107Appendix ARoughness and erosion models of  in Chapter 2 . 110Appendix BSelection of Cut-off length . 111References . 116Appendix CA MATLAB code for numerical erosion simulation . 117
ixList of TablesTable #DescriptionPageTable 2 – 1Measured particle size distribution parameters for the four abrasive powders.15Table 2 – 2Measured particle velocities at the jet center and 10 mm from the nozzle exit, and15nozzle focus coefficients. Velocity range corresponds to 95% of population.Table 2 – 3Measured average equivalent radius (rc) and average depth (dc) of craters due to30individual particle impacts with standard deviations in parentheses, and correspondingcalculated impact zone dimensions 𝑎𝑎, 𝑏𝑏, 𝑐𝑐𝐿 (Fig. 2-3; Eqs. (2-4)-(2-6)). Impact anglewas 90 .Table 4 – 1Measured particle mean diameter, nozzle focus coefficients, particle velocities at the63jet center 10 mm from the nozzle exit, and mass flow rates. Velocity range correspondsto 95% of population.Table 4 – 2Average roughness, Ra, root-mean-square roughness, Rq, skewness, Rsk, kurtosis, Rku,77and waviness, Wa, of the initial glass reference channel centerline profile and themeasured and predicted profilesat the onset of steady-state for different blastingconditions. ( %) is the percentage error between the predicted and measured values.Table 5 – 1Process parameters used in the machining of the channels and the measurement of86erosion rates.Table 5 – 2CFD predictions of the normal component of impact velocity for particles with90diameter between 5 and 45 µm at the 6 pressures used in the experiments. The kineticenergy due to the normal component of the impact velocity is given in parentheses.Table 5 – 3Measured and predicted profile roughness, waviness, shape parameters and depth ofthe centerline channels machined at different pressures and scan speeds.102
xList of FiguresFigure #DescriptionPageFigure 1 – 1AJM experimental apparatus 1Figure 1 – 2Scanning electron micrographs of typical channels machined using AJM with erosion2resistant masks .Figure 2 – 1Schematic of AJM blasting configuration.12Figure 2 – 2(a) Particle diameter and (b) velocity distribution in the jet center. (c) Particle velocity17as a function of particle size at the jet center normalized by the average velocity at thejet center. (d) Average particle velocity variation across the jet normalized by thevelocity at the jet center Data points are the measurements for 50 μm aluminum oxideparticles blasted at 300 kPa, solid lines indicate the least-squares fit to a log-normaldistribution, and the dashed line shows the linear least-squares fit.Figure 2 – 3(a) Cross-section of indentation (hemisphere of radius 𝑎𝑎) and plastic deformation zone21(hemisphere of radius 𝑏𝑏), and cross-section of circular lateral crack (radius 𝑐𝑐𝐿 ) due tosingle particle impact in brittle erosion. (b) Spherical cap representing the chipremoved (crater) from a single impact in a brittle target.Figure 2 – 4(a) Cross-sections of a spherical cap representing a removed chip, (b) 2D roughness23profile through randomly located neighboring chips.Figure 2 – 5(a) A random 2D roughness scan across a model rough surface with a close-packed24array of craters, and (b) the resulting 2D roughness profile.Figure 2 – 6Measured average steady-state roughness of borosilicate glass versus average particle26kinetic energy for aluminum oxide particles (25 µm, 50 µm, 100 µm, 150 µm) atnormal incidence. The scatter bars show the range of measured roughness over threechannels, and the solid curve is the least-squares power law fit.Figure 2 – 7(a) Measured roughness of borosilicate glass as a function of impact angle for 50 µmaluminum oxide particles at P 200 kPa, and (b) Ra vs the average particle kineticenergy due to the velocity component normal to the surface for the data of (a). Thescatter bars show the range of measured roughness over three channels. The solidcurves show the least-squares power law fit and the dashed curve represents the fit for50 µm aluminum oxide particles blasted at 90 at different pressures (data of Fig. 2-6).28
xiFigure 2 – 8Individual craters on borosilicate glass after blasting 150 µm particles at 100 kPa with30a low mass flux.Figure 2 – 9Measured steady-state roughness of borosilicate glass compared to predictions of Eq.32(2-9), Eq. (2-13) and Eq. (A.1)  at various average particle kinetic energies. Thelines indicate the least-squares power law fit of data. Experimental conditions: aluminaparticles (25-150 µm) blasted at 100-300 kPa and at an impact angle of 90 .Figure 2 – 10(a) Erosion rate, 𝐸𝑟 , (b) erosion efficiency, 𝐸𝑓 , and (c) mass of removed material per36particle, 𝐸𝑝 , as a function of average particle kinetic energy compared to predictions ofEqs. (2-16)-(2-18) and Eqs. (A2)-(A4) . The lines indicate the least-squares powerlaw fit of data. Experimental conditions: alumina particles (50-150 µm) blasted at 100300 kPa and impact angle of 90 .Figure 3 – 1Two-dimensional edge indentation model .44Figure 3 – 2(a) Simulated jet footprint that passes over the target to machine a channel. Darker46shades correspond to greater erosive energy within each annular. (b) Projected areas ofrandom particles impacting the target within a band of width 3 times the nominalparticle diameter on either side of the channel centerline.Figure 3 – 3Numerical simulation algorithm.47Figure 3 – 4(a) Particle impact on a centerline profile resulting in a crater removal event, and (b)49the modified profile after the impact. (c) Particle impact on a centerline profile for anedge chipping event, and (d) the modified profile after the impact. Note that thevertical scale has been exaggerated relative to the horizontal scale.Figure 3 – 5(a) Measured and (b) simulated centerline profiles of a 5 mm long channel machined51with 50 µm Al2O3 (100 kPa, θ 90 ) after 40,000 particle impacts.Figure 3 – 6Variation of predicted roughness after the passage of jet annular bands (50 µm Al2O3,52300 kPa, θ 90 , 10,000 total particle impacts).Figure 3 – 7Measured and predicted steady-state channel centerline roughness versus particlekinetic energy over a wide range of alumina particle sizes (25-150 µm) and velocities(corresponding to 100, 200 and 300 kPa at 90 nozzle angle). The solid line representsthe least-squares power law fit of the measured data while the dashed line indicates thatof the predicted data.53
xiiFigure 3 – 8Measured and pred
erosion rate of unmasked channels machined in borosilicate glass using abrasive jet micro-machining (AJM). Single impact experiments were conducted to quantify the damage due to the individual alumina particles. Based on these observations, analytical model from the an literature was modified and used to predict the roughness and erosion rate. A numerical model was developed to simulate the .
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