The Development of Surface Profile Models in Abrasive Slurry Jet … · 2016. 7. 19. · the jet in slurry jet (Emamifar [35]; Guha et al. [37]) and air jet (Dehnadfar et al. [27])

The Development of Surface Profile Models in Abrasive Slurry Jet Micro-machining of Brittle and Ductile materials

by

Hooman Nouraei

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Hooman Nouraei, 2016

ii

The Development of Surface Profile Models in Abrasive Slurry Jet Micro-machining of Brittle and Ductile materials

Hooman Nouraei

2016

Doctor of Philosophy

Department of Mechanical and Industrial Engineering University of Toronto

Abstract

In low-pressure abrasive slurry jet micro-machining (ASJM), a slurry jet of fine abrasive

particles is used to erode micro-sized features such as holes and channels in a variety of brittle

and ductile materials with a high degree of accuracy and repeatability without the need for a

patterned mask. ASJM causes no tool wear and thermal damage, applies small forces on the

workpiece, allows multilevel etching on a single substrate and is relatively quick and

inexpensive.

In this study for the first time, the mechanics of micro-slurry jet erosion and its relation to the

fluid flow of the impinging jet was investigated using a newly developed ASJM system. Existing

surface evolution models, previously developed for abrasive air jet machining (AJM), were

evaluated and modified through the use of computational fluid dynamic (CFD) models for

profile modeling of micro-channels and micro-holes machined with ASJM in brittle materials. A

iii

novel numerical-empirical model was also developed in order to compensate for the shortcoming

of existing surface evolution models and provide a higher degree of accuracy in predicting the

profiles of features in ductile materials machined with ASJM. In addition, the effect of process

parameters on the minimum feature size attainable with ASJM as a maskless process was also

examined and it was shown that the size of machined features could be further reduced.

iv

Acknowledgements

I would like to express my most sincere appreciation and gratitude to my supervisors, Professors

Jan K. Spelt and Marcello Papini, for their continuous guidance and support throughout the

course of my research. They were especially caring and generous with their time and knowledge.

I also wish to acknowledge the help and technical advice of Mehdi Emamifar and Dr. Babak

Samareh. Furthermore, I would like to acknowledge the assistance and support of my dear friend

and colleague, Kavin Kowsari, during the past five years of my studies. Thanks are also due to

my thesis advisory committee, Professor Benhabib and Professor Sullivan for their constructive

suggestions and recommendations during my Ph.D. qualifying exam and seminar. As well, I

would like to thank my lab mates, Dr. Reza Haj Mohammad Jafar, Dr. Kamyar Hashemnia,

Saeed Akbari and Amir Nourani for always being cooperative and helpful and Thais Regina

Dotto, Jonathan Smith, Shiksha Rai, Zahin Rahman, Eric Chong, Lin Sen Mu, Leonardo

Menezes de Faria and Qiaozhi Liu who did a great job as summer research assistants. Last and

foremost, I am indebted to my parents, my brother and my wife for their help, encouragement

and patience. This thesis is dedicated to my family.

v

Table of Contents

Abstract........... ............................................................................................................................... ii

Acknowledgements ...................................................................................................................... iv

Table of Contents .......................................................................................................................... v

List of Tables. ............................................................................................................................. viii

List of Figures ............................................................................................................................... ix

Chapter 1: Introduction and Justification ............................................................................. 1 1.1 Introduction ................................................................................................................................1 1.1.1 Background and motivation ....................................................................................................1 1.1.2 Literature review .....................................................................................................................3

1.1.2.1 AWJ Cutting Experiments and Models ...................................................................4 1.1.2.2 AWJ Milling Experiments and Models ...................................................................5 1.1.2.3 ASJM Experiments and Models ..............................................................................6

1.1.3 Abrasive Slurry Jet Micro-machining Setup ...........................................................................7 1.2 Objectives ...................................................................................................................................8 1.3 Thesis outline .............................................................................................................................9 1.4 References ................................................................................................................................ 11

Chapter 2: Characteristics of Abrasive Slurry Jet Micro-machining: A Comparison with Abrasive Air Jet Micro-machining............................................................................................ 14

2.1 Introduction .............................................................................................................................. 14 2.2 Experiments .............................................................................................................................. 16

2.2.1 ASJM setup .............................................................................................................. 16 2.2.2 Machining tests......................................................................................................... 18 2.2.3 Measurement of particle crushing force ................................................................. 21

2.3 Results and Discussion ............................................................................................................. 22 2.3.1 Effect of water on the crushing strength of aluminum oxide particles ..................... 22 2.3.2 Slurry jet diameter .................................................................................................... 23 2.3.3 Estimation of particle velocity in ASJM .................................................................. 24 2.3.4 Single impact craters ................................................................................................ 31 2.3.5 Machining of micro-holes with ASJM ..................................................................... 35 2.3.6 Machining of micro-channels with ASJM ............................................................... 38 2.3.7 Erosion rate of ASJM ............................................................................................... 43

vi

2.3.8 Effect of process parameters on material removal ................................................... 46 2.4 Conclusions .............................................................................................................................. 52 2.5 References ................................................................................................................................ 54

Chapter 3: Surface Evolution Models for Abrasive Slurry Jet Micro-machining of Channels and Holes in Glass ...................................................................................................... 59


3.2.1 ASJM setup .............................................................................................................. 62 3.2.2 Characterization of performance of ASJM setup ..................................................... 66 3.2.3 Machining tests......................................................................................................... 68

3.3 Modeling of ASJM channels and holes .................................................................................... 71 3.3.1 Erosion rate due to ASJM ........................................................................................ 71 3.3.2 Surface evolution modeling of micro-channels ........................................................ 72 3.3.3 Surface evolution modeling of micro-holes ............................................................. 75

3.4 Results and discussion .............................................................................................................. 75 3.4.1 Prediction of ASJ micro-channel profiles using the first-pass results ...................... 75 3.4.2 Prediction of ASJ micro-hole profiles ...................................................................... 80

3.5 Conclusions .............................................................................................................................. 84 3.6 References ................................................................................................................................ 85

Chapter 4: Combined Numerical-analytical Modeling of Abrasive Slurry Jet Micro-machined Holes ........................................................................................................................... 87


4.2.1 ASJM system ............................................................................................................ 89 4.2.2 Micro-hole machining tests ...................................................................................... 90

4.3 Modeling .................................................................................................................................. 92 4.3.1 Surface evolution modeling of micro-holes ............................................................. 92 4.3.2 CFD modeling of micro-holes .................................................................................. 94

4.4 Conclusions ............................................................................................................................. 99 4.5 References .............................................................................................................................. 100

Chapter 5: Operating Parameters to Minimize Feature Size in Abrasive Slurry Jet Micro-machining ....................................................................................................................... 102

5.1 Introduction ............................................................................................................................ 102 5.2 Experiments ............................................................................................................................ 105

5.2.1 ASJM setup ............................................................................................................ 105 5.2.2 Machining tests....................................................................................................... 107 5.2.3 Erosion rate vs. impact angle ................................................................................. 110 5.2.4 CFD modeling ........................................................................................................ 111

5.3 Results and discussion ............................................................................................................ 112 5.3.1 Measurement of jet footprint .................................................................................. 112

vii

5.3.2 Mechanism of channel formation in glass and PMMA .......................................... 114 5.3.3 Effect of operating parameters on channel depth and width .................................. 118 5.3.3.1 CFD results .......................................................................................................... 120 5.3.3.2 Effect of particle density, diameter and velocity at θ = 90° ................................ 121 5.3.3.3 Effect of slurry jet temperature............................................................................ 125 5.3.3.4 Effect of scan speed ............................................................................................. 127 5.3.3.5 Effect of jet angle ................................................................................................ 132 5.3.3.6 Effect of scan direction ........................................................................................ 133 5.3.3.7 Effect of orifice size ............................................................................................ 136 5.3.3.8 Effect of sacrificial coatings ................................................................................ 137 5.3.4 Summary of findings .............................................................................................. 139

5.4 Conclusions ............................................................................................................................ 140 5.5 References .............................................................................................................................. 141

Chapter 6: Calibrated CFD Erosion Modeling of Abrasive Slurry Jet Micro-machining of Channels in Ductile Materials ............................................................................................. 145

6.1 Introduction ............................................................................................................................ 145 6.1.1 Abrasive slurry jet micro-machining (ASJM) ........................................................ 145 6.1.2 Existing profile modeling in abrasive jet processes ............................................... 146 6.1.3 Motivation for a CFD approach ............................................................................. 147

6.2 Experiments ............................................................................................................................ 149 6.2.1 ASJM setup and machining tests ............................................................................ 149

6.3. Modeling ............................................................................................................................... 150 6.3.1 CFD modeling ........................................................................................................ 151 6.3.1.1 Domain, boundary conditions and assumptions used for the CFD models ......... 152 6.3.1.2 Calculation of the erosive efficacy distribution during ASJM ............................ 156 6.3.2 Micro-channel profile development ....................................................................... 159

6.4 Results and discussion ............................................................................................................ 161 6.4.1 Target erosion characterization: Velocity exponent at perpendicular incidence derived from specific erosion rate measurements and Model 1 ...................................... 161 6.4.2 Target erosion characterization: Erosion constants for oblique impact derived from specific erosion rate measurements and CFD Model 2 ................................................... 165 6.4.3 Comparison of channel shapes in acrylic and metallic targets ............................... 167 6.4.4 Characterization of jet erosion pattern: Erosive efficacy distribution .................... 172 6.4.5 Profile modeling of multi-pass micro-channels in ASJM of ductile materials ...... 175

6.5 Conclusions ............................................................................................................................ 178 6.6 References .............................................................................................................................. 179

Chapter 7: Conclusions and Future Work ......................................................................... 182 7.1 Conclusions ..................................................................................................................... 182 7.2 Directions for Future Work ............................................................................................. 185

Thesis References ...................................................................................................................... 186

viii

List of Tables Table 2.1: Process parameters used in the machining of holes, channels and the measurement of erosion rates..............................................................................................................................................................19

Table 2.2: Crushing loads of dry and wet 150 µm Al2O3 particles...........................................................23

Table 2.3: Calculated centerline 25 µm Al2O3 particle and water velocities in the jet upstream of the stagnation zone and estimated centerline particle impact velocities (20 mm standoff)...............................30

Table 3.1: Process parameters used in the machining of holes, channels and the measurement of erosion rates..............................................................................................................................................................68

Table 5.1: Ranges of operating parameters used for channel machining and measurements of erosion rate as a function of jet angle for glass and PMMA..........................................................................................108

Table 5.2: Measured slurry flow rates and corresponding jet velocities...................................................108

Table 5.3: CFD predictions of average kinetic energy and impact angle of particles in zones I and II for specified operating parameters holding everything else constant. With increases in the parameter (↑) indicates an increase, (↓) indicates a decrease and (-) indicates no change...............................................120

Table 5.4: Percentage change in channel width for the specified changes in the ASJM parameter for a given depth; (↑) indicates an increase, (↓) indicates a decrease.................................................................140

Table 6.1: Properties of the target materials.............................................................................................150

Table 6.2: Process parameters used in channel machining, velocity exponent and erosion rate measurements.............................................................................................................................................150

Table 6.3: CFD predictions (Model 1) of the range of local particle impact velocities over the jet footprint along the centerline for the specified jet velocity......................................................................................164

Table 6.4: Best-fit constants (Eq. (1)) for the impact velocity dependence of erosion.............................164

Table 6.5: CFD predictions (Model 2) of the local particle impact angles along the centerline for the specified jet impact angle...........................................................................................................................166

Table 6.6: Best-fit constants (Eq. (10)) for the impact angle dependence of the specific erosion rates...167

Table 6.7: Best fit coefficients of erosion data to 9th order polynomial fit...............................................175

Table 6.8: Best fit coefficients of the first-pass channel profiles to 9th order polynomial fit...................176

ix

List of Figures Figure 1.1: Schematic of the first abrasive slurry jet prototype [30]. ...........................................................8

Figure 1.2: Schematic of the abrasive slurry jet apparatus [31]. ..................................................................8

Figure 2.1: (a) Schematic of the abrasive slurry jet apparatus (Nouraei et al. [20]), and (b) orientation of orifice installation (not to scale). ........................................................................ 18

Figure 2.2: Schematic of jet orientation during erosion rate measurements (not to scale). ....................... 20

Figure 2.3: Definition of channel depth and width. .................................................................................... 20

Figure 2.4: Schematic of the single particle crushing apparatus. ............................................................... 22

Figure 2.5: (a) Photograph of the jet 1 mm from the 254 µm orifice (scale bar is 100 µm), and (b) jet diameter versus distance from the orifice. ........................................................................... 24

Figure 2.6: Structure of free water jet flow in air (not to scale) (Leu et al. [30]). ...................................... 26

Figure 2.7: Calculated centerline velocity of 25 µm Al2O3 particles (2 MPa) and water: (a) flowing through the orifice, (b) after orifice exit, and (c) within the 600 µm thick stagnation zone (20 mm standoff). ............................................................................................................. 29

Figure 2.8: Comparison of normalized (with respect to centerline) particle velocity profiles across the jet in slurry jet (Emamifar [35]; Guha et al. [37]) and air jet (Dehnadfar et al. [27]) at 20 mm from exit. AJM: 760 µm nozzle, air centerline velocity 300 m/s at 200 kPa, and 25 µm Al2O3 particle centerline velocity of 160 m/s. ASJM: 254 µm orifice, water centerline velocity 62 m/s at 2 MPa, and 25 µm Al2O3 particle centerline velocity of 62 m/s. ............................................................................................................................................ 31

Figure 2.9: (a) SEM image of unblasted borosilicate glass surface; (b) four different types of single impact sites: (i) brittle chipping, (ii) brittle fracture with no chip removal, (iii) ductile ploughing, and (iv) plastically deformed craters without cracking; and (c) higher magnification image of type (iii) impact sites. Conditions: 254 µm orifice, 0.1 wt % 25 µm Al2O3, 2 MPa, 50 mm/s traverse speed, 20 mm standoff. ................................................... 34

Figure 2.10: Cross-sectional profiles of holes machined with ASJM as a function of blasting time. Conditions: 254 µm orifice, 0.25 wt % 25 µm Al2O3, 2 MPa, 20 mm standoff. ...................... 35

Figure 2.11: (a) Depth, and (b) volume of holes machined with ASJM versus blasting time. Conditions: 254 µm orifice, 0.25 wt % 25 µm Al2O3, 2 MPa, 20 mm standoff. Solid lines are least-squares best fits. ................................................................................................. 36

Figure 2.12: Comparison of the normalized profiles of machined holes in ASJM and masked AJM (Ghobeity et al. [45]). The dimensions were normalized by dividing by the diameter of each hole. ASJM: 254 µm orifice, 2 MPa, 0.625 g/min 25 µm Al2O3, 20 mm standoff. Maximum diameter and depth of 530 µm and 286 µm, respectively (aspect ratio of 0.53). AJM: 760 µm nozzle, 2.83 g/min ± 0.12 g/min of 25 µm Al2O3, 200 kPa, 20 mm standoff. Maximum mask opening and depth of 900 µm and 560 µm, respectively (aspect ratio of 0.62). ................................................................................................................ 37

x

Figure 2.13: (a) Scanning electron micrograph of blasted channel, and (b) depth and width of the channel along its length. Conditions: 254 µm orifice, 1 wt % 25 µm Al2O3, 4 MPa, 0.1 mm/s traverse speed, 20 mm standoff. Solid lines are to guide the eye. ................................... 38

Figure 2.14: Comparison of the normalized profiles of a hole and channel machined with ASJM. The dimensions were normalized by dividing by the hole diameter or channel width. Channel: 254 µm orifice, 1 wt % 25 µm Al2O3, 4 MPa, 0.1 mm/s traverse speed, 20 mm standoff. Maximum channel width and depth of 430 µm and 221 µm. Hole: 254 µm orifice, 0.25 wt % 25 µm Al2O3, 2 MPa, 20 mm standoff. Maximum hole diameter and depth of 530 µm and 186 µm. ................................................................................................... 39

Figure 2.15: Comparison of the normalized profile of machined channels in ASJM and masked AJM (Ghobeity et al. [25]). The dimensions of the machined channels were normalized by dividing by the channel width. ASJM: 180 µm orifice, 4 MPa, 2.5 g/min 25 µm Al2O3, 20 mm standoff. Maximum width and depth of 350 µm and 200 µm, respectively (aspect ratio of 0.57). AJM: 760 µm nozzle, 2.83 g/min ± 0.12 g/min of 25 µm Al2O3, 200kPa , 20 mm standoff with maximum mask opening and depth of 250 µm and 160 µm, respectively (aspect ratio of 0.64). ....................................................................... 40

Figure 2.16: Cross-sectional profiles of multi-pass channels. Conditions: 180 µm orifice, 1 wt % of 10 µm Al2O3, 4 MPa, 0.1 mm/s traverse speed, 25 mm standoff. ........................................ 41

Figure 2.17: Profile of machined channel at 1 mm standoff distance. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 2 MPa, 0.5 mm/s traverse speed. .................................................. 43

Figure 2.18: Normalized erosion rate of ASJM and AJM (Ghobeity et al. [25]) as a function of impact angle. Error bars represent ±1 standard deviation for 3 measurements. ASJM: 254 µm orifice, 4 MPa (particle centerline velocity of 89 m/s), 2.5 g/min 25 µm Al2O3, 20 mm standoff. AJM: 760 µm nozzle, 2.83 g/min ± 0.12 g/min of 25 µm Al2O3, 200 kPa (particle centerline velocity of 160 m/s) , 20 mm standoff. Note that the erosion rates in ASJM and AJM were normalized by their respective 90° values. ............................... 46

Figure 2.19: Effect of orifice standoff distance on depth and width of ASJM channel. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 2 MPa, 0.5 mm/s traverse speed. Solid lines are least-squares best fits. .......................................................................................................... 47

Figure 2.20: Effect of slurry pressure on depth and width of channel. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 0.5 mm/s traverse speed and 20 mm standoff. Solid lines are least-squares best fits. ................................................................................................................ 47

Figure 2.21: Effect of particle concentration on depth and width of channel. Conditions: 254 µm orifice, 2 MPa, 0.5 mm/s traverse speed and 20 mm standoff. Solid lines are least-squares best fits. ........................................................................................................................ 48

Figure 2.22: Effect of traverse speed on depth and width of channel. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 2 MPa, 20 mm standoff. Solid lines are to guide the eye. ............ 49

Figure 2.23: Channel depth as a function of particle dose that was varied by either changing (a) traverse speed, or (b) concentration. Error bars represent ±1 standard deviation for 3 measurements. Conditions: 254 µm orifice, 2 MPa, 10 mm standoff. ...................................... 50

Figure 2.24: Schematic of the local front geometry (side view) of channel (not to scale). ........................ 51

xi

Figure 2.25: Corrected depth versus dose varied by traverse speed assuming the local and global impact angles are equal. Error bars represent ±1 standard deviation for 3 measurements. Conditions: 254 µm orifice, 2 MPa, 20 mm standoff. ............................................................... 52

Figure 3.1: (a) Schematic of the abrasive slurry jet apparatus, (b) orientation of orifice installation, and (c) orientation of orifice in micro-hole machining experiments (not to scale) [18]. .......... 65

Figure 3.2: Flow rates of water, 10 and 25 µm nominal diameter Al2O3 slurries of various concentrations as a function of pump stroke frequency. Each point is the average of 5 measurements, amongst which the variability was less than 8% of the mean. ......................... 66

Figure 3.3: Schematic of the suction and discharge ports of the slurry pump illustrating leakage due to a trapped particle (not to scale). ..................................................................................... 67

Figure 3.4: Scanning electron micrographs, and depth and width along the length of blasted channels: (a) and (c) without pulsation damper; and (b) and (d) with pulsation damper. Experimental conditions: 0.765 g/min 10 µm Al2O3, 1.7 mL/s flow rate, 0.1 mm/s traverse speed, 15 mm standoff. Solid and dashed lines are to guide the eye. .......................... 68

Figure 3.5: Schematic of jet orientation during erosion rate measurements (not to scale; depth of channel exaggerated for clarity) [5]. ......................................................................................... 70

Figure 3.6: Schematic of channel or hole cross-sectional profile showing the definition of channel centerline depth and width (Cd, Cw), hole depth and diameter (Hd, Hw), and side wall slope. ......................................................................................................................................... 71

Figure 3.7: Normalized erosion rate (erosion rate at θ /erosion rate at 90°) as a function of impact angle. Error bars represent ±1 standard deviation for 3 measurements. Experimental conditions: 1 g/min 10 and 25 µm Al2O3. ................................................................................. 72

Figure 3.8: Comparison of predicted (solid lines) and measured (symbols) channel cross-sectional profiles for aspect ratio <1.5. Half of the symmetric profile is shown. Experimental conditions: 1 g/min 10 µm Al2O3, traverse speed of 0.5 mm/s, number of nozzle passes shown above each curve. ........................................................................................................... 77

Figure 3.9: (a) Comparison of first-pass channels machined at various traverse speeds, and (b) depth of single-pass channel versus traverse speed. Solid line is to guide the eye. Half of the symmetric profile is shown. Experimental conditions: 1 g/min 10 µm Al2O3. ............... 78

Figure 3.10: Comparison of measured single-pass profile at 0.05 mm/s, 10-pass channel and corrected 10 pass channel machined at 0.5 mm/s. Half of the symmetric profile shown. Experimental conditions: 1 g/min 10 µm Al2O3. ...................................................................... 79

Figure 3.11: Comparison of predicted (solid lines) and measured channel profiles for aspect ratios >1. Half of the symmetric profile is shown. Experimental conditions: 1 g/min 10 µm Al2O3, traverse speeds of 0.05 mm/s. The non-dimensional erosive efficacy function, E*(x*), measured at 0.05 mm/s was modified to account for the reduced erosion caused by the large slope at the leading edge of the jet. ....................................................................... 80

Figure 3.12: (a) Profile development and (b) depth of micro holes, at various exposure times. Experimental conditions: 0.23 g/min 10 µm Al2O3. Line represents linear erosion rate based on depth of 30 s hole. ...................................................................................................... 81

xii

Figure 3.13: (a) Depth of machined holes versus exposure time and (b) Comparison of predicted (solid lines) and measured hole profiles. The 60 s profile was used to infer erosive efficacy. Half of the symmetric profile shown. Experimental conditions: 0.23 g/min 25 µm Al2O3. A 60 s micro-machined hole was used to fit E*(r*) = 3.03×10

15 r* 9-1.75×10

14

r* 8+2.98×1012

r* 7 +8.04×10

8 r* 6-3.88×10

8 r* 5+9.46×10

5 r* 4+1.94×10

4 r* 3 +1.52×10

1 r*

2- 9.16×10

-2 r*-7.33×10

-3, R2 ≈ 0.99. ......................................................................................... 83

Figure 4.1: (a) Schematic of the ASJM system and (b) three-point level used to connect the orifice to specimen (not to scale). ......................................................................................................... 90

Figure 4.2: Typical profile of ASJ machined hole in borosilicate glass after 10 min of machining. ......... 92

Figure 4.3: Depth of micro-machined holes at various machining time. Error bars represent ±1 standard deviation for 3 measurements. .................................................................................... 95

Figure 4.4: Incoming jet volume fraction for a 30 s machined hole. ......................................................... 97

Figure 4.5: Pressure distribution for a 30 s machined hole. ....................................................................... 97

Figure 4.6: Particle trajectories during the jet impingement for 10 µm Al2O3 particles. ........................... 97

Figure 4.7: Centerline particle impact velocity at various machining times. ............................................. 98

Figure 4.8: Comparison of predicted (solid lines) and measured hole profiles. Half of the symmetric profile shown. .......................................................................................................... 99

Figure 5.1: Schematic of (a) the ASJM apparatus, (b) sapphire orifice, (c) heating elements and (d) jet orientation at various impact angles. .................................................................................. 106

Figure 5.2: Scanning electron micrographs of 20 µm nominal diameter (a) Al2O3 and (b) WO3 particles. .................................................................................................................................. 109

Figure 5.3: Scanning electron micrographs of the typical channels machined with ASJM in: (a) glass and (b) PMMA using 5 passes of the jet under identical experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. .................................................................................... 110

Figure 5.4: Normalized erosion rate as a function of slurry jet impact angle of (a) borosilicate glass [9], and (b) PMMA. Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, do = 15 mm. Solid lines were added to guide the eye. .................................................................................................................................... 111

Figure 5.5: Domains and boundary conditions of the CFD model for the 3D simulation of the particle trajectories within a channel. ...................................................................................... 112

Figure 5.6: CFD predictions of particle trajectories during jet impingement of 10 µm (P1) and 20 µm (P2) Al2O3 particles. Modeling conditions: P = 4 MPa (water velocity of 90 m/s), dorifice =180 µm (jet diameter of 150 µm) , C = 1 wt%, Q = 1.7 mL/s, θ = 90°, do = 15 mm. ......................................................................................................................................... 113

xiii

Figure 5.7: Scanning electron micrograph of the ASJ footprint on glass. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 10 mm/s, D = 1.7 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. .................................................................................... 114

Figure 5.8: Profiles of channels machined with ASJM in glass and PMMA under identical experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. ............................................. 116

Figure 5.9: CFD predictions of initial (in zone I) and secondary particle impact (in zone II) during jet impingement of 10 µm Al2O3 particles. Modeling conditions: P = 4 MPa (water velocity of 90 m/s), dorifice =180 µm (jet diameter of 150 µm) , C = 1 wt%, Q = 1.7 mL/s, θ = 90° and do = 15 mm. ............................................................................................... 116

Figure 5.10: Increase of local impact angle of particles near jet centerline in (a) AJM [26] compared with (b) ASJM [10]. ............................................................................................... 118

Figure 5.11: Effect of particle density on channel profiles in: (a) glass and (b) PMMA using 3 and 5 passes (P) of the jet. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. .................................. 122

Figure 5.12: Effect of particle diameter on channel profiles in: (a) glass and (b) PMMA. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. ........................................................................... 124

Figure 5.13: Channel profiles machined in a single pass at 8 MPa and 4 MPa slurry pressures in: (a) glass and (b) PMMA. Experimental conditions: dorifice =180 µm, dp = 10 µm Al2O3, T = 15°C, θ = 90°, do = 15 mm. 8 MPa: C = 0.75 wt%, vs = 0.7 mm/s, D = 24 mg/mm, Q = 2.3 mL/s. 4 MPa: C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, Q = 1.7 mL/s. ..................... 125

Figure 5.14: Effect of slurry temperature on width and depth of 5 pass channel machined in glass. Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, θ = 90°, do = 15 mm. ............................................................................ 126

Figure 5.15: Effect of scan speed on depth, width, volume removed and aspect ratio (depth/width) during a single pass in: (a), (c), (e) glass, and (b), (d), (f) PMMA. Dashed lines show expected values if depth and volume were linearly proportional to the10 fold increase in dose from 0.5 to 0.05 mm/s (i.e. vs = 0.5 mm/s: D = 34 mg/mm, vs = 0.05 mm/s: D = 340 mg/mm). Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. .............................................................................................. 128

Figure 5.16: Scanning electron micrograph of the local front geometry of a channel in glass (side view). Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.2 mm/s, D = 85 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. .......................... 129

xiv

Figure 5.17: Streamlines in ASJM of PMMA: (a) relatively slow scan speed (e.g. 0.05 mm/s) developing a high aspect-ratio (depth/width) channel, and (b) relatively fast scan speeds (e.g. 0.5 mm/s) developing a low aspect-ratio channel. .......................................................... 130

Figure 5.18: Channel profiles machined using a fixed abrasive dose delivered in two ways: 5 passes at 0.5 mm/s or 50 passes at 5 mm/s. (a) glass and (b) PMMA. Experimental conditions: dorifice =180 µm, C = 1 wt%, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. vs = 0.5 mm/s: D = 34 mg/mm, vs = 5 mm/s: D = 3.4 mg/mm. ................... 131

Figure 5.19: Effect of slurry jet angle on depth and width of 5-pass channels in: (a) glass and (b) PMMA. Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, do = 15 mm. .......................................................................... 133

Figure 5.20: Scanning electron micrographs of the surface quality at the bottom of a 5-pass channel along centerline in: glass (a) backward (Ra = 0.4 µm), (b) forward (Ra = 0.54 µm) and PMMA (c) backward (Ra = 0.1 µm), (d) forward (Ra = 0.17 µm) as a function of jet orientation. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 30°, do = 15 mm. .............. 135

Figure 5.21: Channel width as a function of orifice size in (a) glass (11-pass, depth: 20 µm) and (b) PMMA (6-pass, depth: 30 µm). Experimental conditions: dp = 3 µm Al2O3, T = 15°C, θ = 90°, vs = 0.5 mm/s, D = 17 mg/mm; dorifice = 180 µm - Q = 2.0 mL/s , C = 0.4 wt%, do= 15 mm; dorifice = 100 µm - Q = 0.6 mL/s , C = 1.4 wt%, do=12 mm; dorifice = 75 µm - Q = 0.4 mL/s , C = 2.0 wt%, do=8 mm; dorifice = 50 µm - Q = 0.2 mL/s , C = 4.2 wt%, do = 5 mm. Error bars represent the standard deviation for 3 measurements. Solid lines added to guide the eye. ................................................................................................... 137

Figure 5.22: (a) Channel profiles, (b) microscope image (top view) of 5-pass micro-channel machined in glass without sacrificial layer, and(c) with 1 mm thick epoxy coating (coating removed for photograph). Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. ..................................................................................................................... 139

Figure 6.1: Domains and boundary conditions of the CFD models for the 3D simulation of the particle trajectories within: (a) a channel at θ = 90° incidence and (b) a flat target at oblique incidence (θ = 45°; half the channel modelled). ......................................................... 155

Figure 6.2: CFD predictions of Model 3 for: (a) particle trajectories during jet impingement of 10 µm Al2O3 particles and (b) the resulting erosion pattern on the target surface of a shallow (35 µm deep) channel machined in PMMA. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 90°. ........................................................................................................... 158

Figure 6.3: Schematic of the propagation of a given point on an eroding two-dimensional channel profile. ..................................................................................................................................... 160

Figure 6.4: (a) CFD predictions of Model 1 for 10 µm nominal diameter particle trajectories at normal jet impingement and (b) comparison of the particle impact velocities on the

xv

centerline (P1) and periphery of the jet (P2). Particles P1 and P2 illustrate change in impact angle and velocity with position in the jet. The ''o’s" indicate the particle impact velocity at the target. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 90°. ................ 163

Figure 6.5: Specific erosion rate as a function of particle impact velocity for PMMA, Al6061-T6, 316L SS and Ti-6Al-4V. Error bars represent the standard deviation for 3 cross-sectional profile measurements 1 mm apart on a given channel. Solid lines represent the best-fit of erosion data to Eq. (6.1). Experimental conditions: D = 1 mg/mm, vs = 0.5 mm/s. ....................................................................................................................................... 164

Figure 6.6: CFD predictions of Model 2 for 10 µm nominal diameter particle trajectories at oblique jet impingement. Particles P1 and P2 illustrate variation in local impact angle across footprint. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 45°. ...................... 166

Figure 6.7: Normalized erosion rate along the centerline as a function of average particle impact angle of PMMA, Al6061-T6, 316L SS and Ti-6Al-4V. Error bars represent the standard deviation for 3 cross-sectional profile measurements 1 mm apart on a given channel. Solid lines represent the best-fit of erosion data to Eq. (6.10). Experimental conditions: P = 4 MPa (vjet = 90 m/s), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s, vs = 0.5 mm/s. ........... 167

Figure 6.8: Comparison of the profiles of shallow, single-pass channels in PMMA, AL6061-T6, 316L SS and Ti–6Al–4V. Experimental conditions: P = 4 MPa (vjet = 90 m/s), dorifice =180 µm, C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s. Scan speeds adjusted to give approximately equal depths. .................................................................................................... 168

Figure 6.9: (a) Width and (b) depth of micro-channels at a function of number of machined passes in PMMA, AL6061-T6, 316L SS and Ti–6Al–4V. Error bars represent the standard deviation for 3 cross-sectional profile measurements 1 mm apart on a given channel. Solid lines added to guide the eye. Experimental conditions: P = 4 MPa (vjet = 90 m/s), dorifice =180 µm, C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s. ................................................... 169

Figure 6.10: Comparison of (a) the size of stagnation zone in shallow (NP =1, 35 µm depth) and (b) deep (NP =10, 342 µm depth) machined channels in PMMA and (c) the 10 µm nominal diameter particle velocities on jet centerline. The ''x" indicates the particle impact velocity along the centerline. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), Q = 1.7 mL/s and θ = 90°. ................................... 171

Figure 6.11: Normalized erosive efficacy distribution of slurry jet (symbols) across channel width in (a) PMMA (o –first pass approach; ×-CFD approach), (b) AL6061-T6 (CFD approach), (c) 316L SS (CFD approach) and (d) Ti–6Al–4V (CFD approach). Half of the symmetric erosion data is shown. Solid lines represent the best-fit of data to 9th order polynomial. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 90°. ...................... 174

Figure 6.12: Comparison of predicted (solid lines) and measured (symbols) channel cross-sectional profiles in (a) PMMA, (b) AL6061-T6, (c) 316L SS and (d) Ti–6Al–4V for aspect ratios of up to approximately 1. Half of each symmetric profile is shown.

xvi

Experimental conditions: P = 4 MPa (vjet = 90 m/s), dorifice =180 µm, C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s.

........................................................................................................... 177

1

Chapter 1: Introduction and Justification

1.1 Introduction

1.1.1 Background and motivation

In recent years, the demand for fabricating micro-fluidic and micro-electro-mechanical components

has increased the need for efficient micro-fabrication technologies [1]. Due to the small sizes,

complex details, and high demands for surface integrity, traditional mechanical cutting processes can

be limited in their applications [2, 3].

Traditional micro-machining techniques such as micro-milling [2, 3], chemical etching [1], electrical

discharge machining (EDM) [4] and laser [5] require relatively expensive equipment, employ

hazardous chemicals and are time-consuming. These fabrication techniques have limitations such as

thermal damage to the material and poor surface texture [6]. In micro-milling, the chips have

submicron-level dimensions, which makes the removal of chips difficult even under flooded

conditions. Micro-milling is also associated with sudden tool failure due to its highly unpredictable

cutting action. The tool deflection influences the chip formation and accuracy of the desired feature.

In addition, the run-out of the tool tip even within a few microns greatly affects the accuracy of the

end milling operations at the micro-scale [2, 3]. EDM has a slow rate of material removal with

excessive tool wear and requires high power. Cracking on the workpiece may occur and reproducing

sharp corners and fillets on the workpiece is difficult due to electrode wear. Also, EDM is mostly

effective in machining of conductive materials and electrically non-conductive materials can be

machined with extra conductive assisting electrode [7]. CO2 laser could leave a pile-up around the

2

hole perimeter that obstructs plate bonding and device assembly [8]. In practice, these limitations

make it uneconomical to fabricate the larger micro-fluidic chips required for chemical analysis [5].

Abrasive jet machining (AJM), which is an erosion based material removal process, has been

implemented in recent years to make MEMS devices such as inertial sensors [9, 10], and micro-

fluidic components for capillary electrophoresis chips [11, 12]. One of the disadvantages of AJM is

that the air jet used to propel the particles diverges significantly after the nozzle exit, lowering the

resolution of the process considerably. As a result, AJM must be used in conjunction with patterned

erosion resistant masks in order to define the micro-feature edges [13]. Another weakness of AJM is

the high surface roughness of machined features, although some progress has been made in recent

years to minimize it [14].

Abrasive water jet (AWJ) is similar to AJM, except that water, instead of air, is used to accelerate the

abrasive particles such as garnet or aluminum oxide (Al2O3). The abrasive particles are accelerated to

sufficiently high speeds in order to erode a target substrate and cut the desired pattern on the target

work piece. The material removal occurs without interfering with the inherent structure of the

material as there is no "heat-affected zone", allowing the material to be machined without changing

its intrinsic properties [15]. Water jets have higher viscosity, lower Reynolds numbers and much

lower divergence angle than air jets used for the same dimensions and flow speed in AJM [16].

The developments so far have been limited to the use of ultrahigh pressure abrasive water jets (170-

400 MPa) mostly for cutting applications on ductile or brittle materials (e.g. metals, ceramics,

polymers, and composite materials) [17]. In high-pressure systems, the water jet removes workpiece

material by the cutting action of small diameter (70-500 µm), and high velocity (350-1000 m/s) jet of

water or water with abrasive particle additives [18]. The abrasive media is added to the water through

3

a feed port immediately prior to the nozzle. Consequently, the abrasive particles do not reach the

speed of the water when impacting the target surface [19]. In order to overcome the limitations of

AWJ, abrasive slurry-jet (ASJ) machining was introduced by Miller in 2004 [19]. In ASJ systems,

the water and abrasive are pre-mixed in a chamber, rather than continuously fed in to the system. Due

to superior effectiveness of the suspension method for generating the slurry, similar jet cutting energy

densities as entrainment systems at much lower pressure (70 MPa) was achieved [19].

Miller demonstrated the use of an abrasive suspension (slurry) jet for micro-slot cutting operation on

metals, glass, ceramics, polymers and composite materials. He also found that abrasive slurry jet

micro-machining (ASJM) has more variables (e.g. slurry concentration, dispersion and suspension

stability) that can be controlled and optimized than AWJs generated by the entrainment method [19].

The initial studies of ASJM [6, 19 and 20] have shown that low pressure ASJ erosion is a practical

process not only for cutting, but also for milling/etching of materials. However, relevant knowledge

in this newly developed field is limited to preliminary experimental work. Relatively little is known

about the relationship between ASJM operating parameters and the resulting erosion rates, machined

surface profile and roughness [20]. There has not been any previous attempt to model the erosion

mechanisms or surface profile evolution of ASJM. Moreover, the capability of ASJM to perform

maskless machining has not been fully explored.

1.1.2 Literature review

ASJM systems have a lot in common with AWJ in terms of operating principle and process

parameters. Accordingly, reviewing the developments in experimental and modeling aspects AWJ

indentifies the knowledge gaps and potential areas for further research in ASJM.

4

A major breakthrough in water jet technology was made in 1980s by adding garnet as an abrasive to

the water jet system, allowing for the cutting of material such as steel over 8 cm and concrete up to

30 cm thick. AWJ systems were introduced commercially in 1982. Since then the process was being

improved and applications of this technology have been expanded [21].

1.1.2.1 AWJ Cutting Experiments and Models

The need for two different approaches for modeling the erosion of ductile and brittle material under

AWJ cutting based on the differences in the micro-mechanism of material removal was indicated by

Zeng and Kim [22]. In ductile materials, the mechanism of material removal in AWJ cutting is

micro-cutting by free-flowing abrasive particles along with gross plastic deformation and ploughing.

In brittle materials along with micro-cutting and plastic deformation, intergranular cracking of the

target material plays a significant role in material removal [22, 23].

Paul et al. [24] presented an analytical model of predicting the depth of cut in AWJ machining of

polycrystalline ceramics with the consideration of the shape and size of abrasive particles. It was

assumed that there was no particle fragmentation within the jet at the time of impact. The energy and

mass flow rate of the abrasive particles were uniformly distributed and the velocity of the particle

does not change due to groove wall drag. They developed their model based on the hypothesis that

the material removal took place in to two distinctive zones: In the first zone (closer to the top surface

of target workpiece), the mode of material removal was micro-cutting and fracture. However, the

mode of material removal in the second region (away from the top surface) was altered to plastic

deformation and fracture due to the change in impact angle of abrasive particles. They obtained a

good correlation between the experimental data and their predictions [24].

5

Domiaty et al. [25] developed a material removal model which was capable of predicting the

maximum depth of cut for different types of materials. In their model, only one property of the target

material (modulus of elasticity) was considered and calibration coefficients were determined from

experimental results. They observed that the maximum depth of cut could be further improved if the

jet diameter decreases. They concluded that in order to increase the accuracy of the model, other

target material properties such as the dynamic hardness and the dynamic fracture toughness as well

as the classical mechanical properties should be included [25].

1.1.2.2 AWJ Milling Experiments and Models

Alberdi et al. [26] investigated the effect of process parameters on the jet footprint of AWJ during the

machining of channels between 3 to 5 mm in width. They introduced a model to predict the kerf

profile in AWJ channel milling in aluminum. Their experimentation modeled the maximum cutting

depth and width in terms of four process parameters: pressure, abrasive mass flow rate, stand-off

distance, and traverse feed rate. They also showed that the introduction of the maximum depth and

width in a Gaussian function is suitable to describe the kerf profile [26].

Paul et al. [27] studied the effect of different parameters on rectangular pocket milling with AWJ in

order to control the variation in the depth of pockets between 0.15 and 7 mm deep. They used a

simple milling process consisting of a longitudinal pass and a transverse pass. They studied the

effect of different parameters on the variation in the depth, material removal rate, erosion rate and

depth of material removal per machining cycle of the pocket. They developed empirical models

using experiments and regression analysis and concluded that the variation in the depth of the

pocket can be controlled with precision of 0.04mm with a satisfactory surface finish quality [27].

Maniadaki et al. [28] developed a non-linear FE model (using LS-DYNA 3D), which simulated the

6

water flow and the erosion of the target material caused by a high-velocity water jet. Through their

simulation model, they calculated the von-Mises stresses in an aluminum target at the impact time

[28]. Axinte et al. [29] developed an analytical model for predicting the profile of maskless

channels (1.4 mm width and between 0.3 to 2 mm in depth) machined with high pressure

controlled-depth AWJ. Their model was calibrated based on the experimentally obtained erosion

rate of silicon carbide (SiC) ceramic target workpiece. It was assumed that only the kinetic energy

transfer normal to the target surface contributed to the development of the eroded surface. This

assumption limited the usage of their model only for brittle materials. They managed to predict the

channel shape (including width and depth) over a wide range of jet traverse speed accurately (error

was less than 5%) [29]. AWJ simulation models require a number of calibration coefficients which

results in limiting the range of applicability of the models.

1.1.2.3 ASJM Experiments and Models

Wang et al. [6, 20] investigated the formation mechanisms of micro-holes and channels

experimentally on soda-lime glass with an in-house ASJM apparatus. They indicated that a low

pressure jet (less than 10 MPa), at the instant of the jet impinging on the target surface, did not have

sufficient energy to immediately form a cut and eroded the material at a small rate. They discussed

that the jet flow was divided into two regions: a potential flow that had the velocity aligning with

the jet direction and a viscous flow that was generated from the jet expending in the direction

aligned with the target surface. The viscous flow caused greater erosion than did the potential flow

of the jet. In addition, they observed that the machined features on the target material were free of

visible cracks and concluded that the predominant mode of erosion was ductile. They determined

that deeper channels can be machined by increasing the jet pressure and particle concentration.

7

However, the surface quality was reduced by the formation of pit fragments on the target material

[6, 20].

1.1.3 Abrasive Slurry Jet Micro-machining Setup

For the purpose of the preliminary investigation, an abrasive slurry jet apparatus was designed,

prototyped, and put through basic tests of functionality†. Figure 1.1 illustrates a schematic of the test

apparatus. In this apparatus, compressed air was used to drive the slurry toward the target [30].

However, due to the small size (i.e. 500 mL) of the pressurized cylinder used as the slurry tank, the

total continuous machining time was less than 5 min. Moreover, the spring-loaded seals in the setup

were not rated for pressures higher than 5 MPa, and as a result, micro-machining at higher kinetic

energies was not feasible. Consequently, a second prototype was designed and developed‡

in order to

overcome the shortcomings of the initial apparatus [31]. Figure 1.2 shows a schematic of the second

low-pressure ASJM system. The apparatus was constructed utilizing an open reservoir mixing tank,

positive displacement slurry pump and pulsation damper connected to an orifice to propel the

premixed slurry toward the target substrate. The specimens were mounted on a computer-controlled

linear stage.

† This initial work was in cooperation with Mr. A. Wodoslawasky who began the design and fabrication as part of his M.Eng. report. ‡ This work was in cooperation with Mr. K. Kowsari who participated in the design and fabrication as part of his M.A.Sc. report.

8

Pressurized air cylinder

Pressure regulator

Slurry tankSlurry

Exit tube

Propeller

Stirring shaft

DC motorRefilling port and plug

Orifice

Target material Linear stage

Figure 1.1: Schematic of the first abrasive slurry jet prototype [30].

Slurry

Propeller

Pulsation damper

Pressure gauge

Safety valve

Flexible pipe Orifice

Target Linear stage

Drainage

DC motor

Diaphragm pump

Exit tube

AC motor

Figure 1.2: Schematic of the abrasive slurry jet apparatus [31].

1.2 Objectives

The PhD research investigated the interaction between relatively low-pressure abrasive slurry jets

and brittle and ductile target materials in order to understand and model the erosion mechanisms and

the resulting cross-sectional profiles of eroded features such as channels and holes. A secondary

9

objective in this work was to study the effect of particle, target, and process parameters on the

minimum feature size attainable with ASJM as a maskless process.

1.3 Thesis outline

The first chapter gives an introduction to ASJM, while Chapter 2 presents the experimental study of

the micro-machining of holes and channels in borosilicate glass with ASJM, and compares the

machined features with those produced by abrasive air-jet micro-machining (AJM).This work has

been published as:

H. Nouraei, A. Wodoslawsky, M. Papini, J.K. Spelt, Characteristics of abrasive slurry jet micro-

machining: a comparison with abrasive air jet micro-machining, Journal of Materials Processing

Technology Vol. 213, (2013) 1711-1724.

Chapter 3 includes the surface evolution modeling of micro-holes and channels in borosilicate glass

machined with ASJM. It includes the consideration of the effect of multi-pass machining, traverse

speed and the local erosion front geometry on the accuracy of the surface evolution models. This

work has been published as:

H. Nouraei, K. Kowsari, J.K. Spelt, M. Papini, Surface evolution models for abrasive slurry jet

micro-machining of channels and holes in glass. Wear Vol. 309, (2014) 65–69.

Chapter 4 presents a combined numerical-analytical methodology to characterize the changes in the

flow field and particle trajectories within the impinging jet as function of machining time using

computational fluid dynamics (CFD) models. This work has been published as:

10

H. Nouraei, K. Kowsari, B. Samareh, M. Papini, J.K. Spelt, Combined numerical-analytical

modeling of abrasive slurry jet micro-machining of holes. ICOMM 2015-10th International

Conference on Micro-manufacturing, Milan, 2015.

Chapter 5 examines the effects of ASJM operating parameters such as jet traverse speed and

orientation, number of machining passes, particle density and diameter, orifice size, slurry

temperature and velocity on the minimum size of features made with ASJM in brittle and ductile

materials. The results were explained in terms of differences in the impacting particle energies and

trajectories as predicted using CFD models. This work has been submitted for publication as:

H. Nouraei, K. Kowsari, B. Samareh, M. Papini, J.K. Spelt, Operating parameters to minimize

feature size in abrasive slurry jet micro-machining, Journal of Precision Engineering, 2015

(submitted).

Chapter 6 presents the development of a comprehensive numerical-empirical profile prediction

model using three-dimensional CFD models to account for the effect of flow fields on particle

trajectories within an eroded feature and predict the shape and size of micro-channels machined

with ASJM. This work has been submitted for publication as:

H. Nouraei, K. Kowsari, B. Samareh, J.K. Spelt, M. Papini, Calibrated CFD-erosion modeling of

abrasive slurry jet micro-machining of channels in ductile materials, Journal of Materials

Processing Technology, 2015 (submitted).

Finally, the main conclusions of this dissertation and recommendations for future work are summarized

in Chapter 7.

11

1.4 References

[1] C. Iliescu, B. Chen, F.E.H. Tay, G. Xu, J. Miao, Characterization of deep wet etching of glass, Proc. of SPIE Vol. 6037 (2003) 60370A-2.

[2] X. Cheng, A. Wang, K. Nakamoto, K. Yamazaki, A study on the micro tooling for micro/nano milling, International Journal of Advanced Manufacturing Technology 53 (2011) 523-533.

[3] O. Iordan, C. Burlacu, The main factors of influence in the micro-milling field, Academic Journal of Manufacturing Engineering 48 (2010) 43-49.

[4] C. T. Yang, S.S. Ho, B.H. Yan, Micro-hole machining of borosilicate glass through electro mechanical discharge machining, Key Engineering Materials 196 (2001) 149- 166.

[5] H. Ogura, Y. Yoshida, Hole drilling of glass substrates with a CO2 laser, Japanese Journal of Applied Physics 42 (2003) 2881–2886.

[6] K. Pang, T. Nguyen, J. Fan , J. Wang, Machining of micro-channels on brittle glass using an abrasive slurry jet, Key Engieering Materials 443 (2010) 639-644.

[7] G. Kucukturk, C. Cogun, A new method for machining electrically nonconductive work piece using electric discharge machining technique, International Journal of Machining Science and Technology 14 (2010) 189-207.

[8] A. Abgrall, A-M Gu'e, Lab-on-chip technologies: making a micro-fluidic network and coupling it into a complete micro system-a review, Journal of Micro-mechanics and Micro-engineering 1 (2007) 15-49.

[9] E. Blloy, S. Thurre, E. Walchiers, A. Sayah, M.A.M. Gijs, The introduction of powder blasting for sensor and micro system applications, Sensors and Actuators 84 (2000) 330-337.

[10] D.S. Park, M.W. Cho, H. Lee, W.S. Cho, Micro-grooving of glass using micro-abrasive jet machining, Journal of Materials Processing Technology 146 (2004) 234-240.

[11] S. Schlautmann, H. Wensink, R. Schasfoort, M. Elwenspoek, A. Vandenberg, Powder-blasting technology as an alternative tool for micro fabrication of capillary electrophoresis chips with integrated conductivity sensor, Journal of Micro-mechanics and Micro-engineering 11 (2001) 386-389.

[12] R. M. Guijt, E. Baltussen, G. Van Der Steen, R.B.M. Schasfoort, S. Schlautmann, H.A.H. Billet, F. Frank, G.W.K. van Dedem, A. Van Den Berg, New approaches for fabrication of micro-fluidic capillary electrophoresis devices with on-chip conductivity detection, Electrophoresis 22 (2001) 235–241.

[13] L. Zhang, T. Kuriyagawa, Y. Yasutomi, J. Zhao, Investigation into micro abrasive intermittent jet machining, International Journal of Machine Tools and Manufacture 45 (2005) 873–879.

12

[14] H. Wensink, S. Schlautmann, M. H. Goedbloed, M. C. Elwenspoek, Fine tuning the roughness of powder blasted surfaces, Journal of Micro-mechanics and Micro-engineering 12 (2002) 616-620.

[15] H. T. Liu, Water jet technology for machining fine features pertaining to micro-machining, Journal of Manufacturing Processes 12 (2010) 8-18.

[16] A. Wodoslawsky, Focusing of Maskless Abrasive Jets, Master of Engineering Report, Department of Mechanical and Industrial Engineering, University of Toronto 2011.

[17] J. Wang, T. Nguyen, K. L. Pang, Mechanisms of micro-hole formation on glasses by an abrasive slurry jet, Journal of Applied Physics 105 (2009) 044906.

[18] R.K. Miller, Water jet Cutting: Technology and Industrial Applications. Lilburn,GA: The Fairmont Press, Inc. (1991).

[19] D.S. Miller, Micro-machining with abrasive water jets, J. of Materials Processing Technology 149 (2004) 37-42.

[20] T. Nguyen, K. Pang, J. Wang, A preliminary study of the erosion process in micro-machining of glasses with a low pressure slurry jet, Key Engineering Materials 389-390 (2009) 378-380.

[21] C. Burnham, Abrasive water jets come of age, Machine Design, (1990) 93-97.

[22] J. Zeng, T.J. Kim, An erosion model for abrasive water jet milling of polycrystalline ceramics, Wear 199 (1996) 275–282.

[23] M. Hashish, A model for abrasive water jet (AWJ) machining, Journal of Engineering Materials and Technology 111 (1989) 154–162.

[24] S. Paul, A.M. Hoogstrate, C.A. van Luttervelt, H.J.J Kals, Analytical modelling of the total depth of cut in the abrasive water jet machining of polycrystalline brittle material, Journal of Material Processing Technology 73 (1998) 206-212.

[25] A.A.E. Domiaty, M.A. Shabara, A.A. Abdel-Rahman, A.K. Al-sabeeh, On the modelling of abrasive water jet cutting, International Journal of Advanced Manufacturing Technology 12 (1996) 255-265.

[26] A. Alberdi, A. Rivero, L.N. Lopez de Lacalle, I. Etxeberria, A. Suarez, Effect of process parameter on the kerf geometry in abrasive water jet milling, International Journal of Advanced Manufacturing Technology 51 (2010) 467-480.

[27] S. Paul, A.M. Hoogstrate, C.A. van Luttervelt, H.J. Kals, An experimental investigation of rectangular pocket milling with abrasive water jet, Journal of Material Processing Technology 73 (1998) 179-188.

13

[28] K. Maniadaki, T. Kestis, N. Bilalis, A. Antoniadis, A finite element-based model for pure water jet process simulation, International Journal of Advanced Manufacturing Technology 31 (2007) 933–940.

[29] D. A. Axinte, D. S. Srinvasu, J. Billingham, M. Cooper, Geometrical modelling of abrasive water jet footprints: A study for 90º jet impact angle, CIRP Annals-Manufacturing Technology 59 (2010) 341-346.

[30] H. Nouraei, A. Wodoslawsky, M. Papini, J.K. Spelt, Characteristics of abrasive slurry jet micro-machining: A comparison with abrasive air jet micro-machining, Journal of Materials Processing Technology 213 (2013) 1711-1724.

[31] H. Nouraei, K. Kowsari, J.K. Spelt, M. Papini, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in glass, Wear 309 (2014) 65–69.

14

Chapter 2: Characteristics of Abrasive Slurry Jet

Micro-machining: A Comparison with Abrasive Air Jet

Micro-machining

2.1 Introduction

Traditional micro-machining techniques such as micro-milling, chemical wet etching, electrical

discharge machining (EDM) and laser micro-machining require relatively expensive equipment, can

be time-consuming, and can suffer from a number of other limitations. For example, chemical wet

etching requires hazardous chemicals such as hydrogen fluoride (HF) as described by Huang et al.

[1]. Micro-milling tool failure is difficult to predict, and tool deflection and radial errors in the tool

tip trajectory (run-out) affect the accuracy of the desired features as illustrated by Iordan and

Burlacu [2] and Cheng et al. [3]. Iordan and Burlacu [2] and Cheng et al. [3] have also found that

micro-milling creates machined chips that have submicron-level dimensions, making their removal

difficult. Micro-machining with EDM suffers from electrode wear which makes it difficult to

reproduce sharp corners and fillets on the workpiece. As shown by Kucukturk and Cogun [4], EDM

can also produce large temperature variations, increasing the magnitude of compressive and tensile

stresses, ultimately leading to crack formation in the workpiece. Ogura and Yoshida [5] found that

micro-machining with a laser causes local melting and a heat-affected zone, as well as material pile-

up adjacent to the cut that can obstruct subsequent bonding and device assembly.

15

Belloy et al. [6] used abrasive jet micro-machining (AJM) to fabricate components for micro-

electro-mechanical systems (MEMS) such as inertial sensors. Schlautmann et al. [7] and Guijt et al.

[8] used AJM to produce micro-fluidic components for capillary electrophoresis chips. One of the

disadvantages of AJM is that the compressed air jet used to propel the erodent particles against the

target material diverges significantly after the nozzle exit, lowering the resolution of the process

considerably. Zhang et al. [9] suggested that AJM must be used in conjunction with patterned

erosion resistant masks in order to define the micro-feature edges. Wensink et al. [10] found

another potential weakness of AJM, which is the relatively high surface roughness of the micro-

machined features and made some progress in improving the surface quality.

Abrasive slurry jet micro-machining (ASJM) is similar to AJM except that pressurized water

instead of air is used to accelerate the suspended abrasive particles such as garnet or aluminum

oxide (Al2O3). As reported by Liu [11] in both AJM and ASJM, material removal occurs by erosion

with little heating that can alter material properties. Wodoslawsky [12] found that for the same jet

dimension and flow speed, slurry jets have a much lower divergence angle than air jets, allowing

for the micro-machining of smaller features without the use of patterned masks.

High pressure ASJM was investigated by Miller [13], who used a slurry at a pressure of 70MPa to

cut micro-slots into metals, glass, ceramics, polymers and composite materials. Nguyen et al. [14]

and Wang et al. [15] studied the mechanisms of micro-hole formation in glass with ASJM. Based

on the crack free surfaces of machined holes, it was concluded that ductile erosion mechanisms

dominated. Also, it was shown that increasing the pressure and erosion time increased the hole

depth, with an insignificant effect on the hole diameter. The holes were characterized by a "W"

shaped cross-section, which was explained in terms of the variation in particle trajectories near the

target. It was illustrated that as the slurry jet flow expands along the target surface, three zones

16

develop, each with a different erosion rate. A direct impact zone results from the initial impact of

the slurry jet on the target. An adjacent wavy zone is due to the subsequent slurry flow along the

target surface spreading out from the impact zone. And an accumulation zone develops as the slurry

flow momentum decreases and particles accumulate at the bottom of the machined holes in a

turbulent mixture. Wang et al. [16] studied the effect of operating parameters such as slurry

pressure, jet exposure time, standoff distance and particle concentration on the machining of micro-

holes in glass. It was observed that the material removal rate was approximately proportional to the

applied pressure, jet exposure time and particle concentration. The hole depth and material removal

rate decreased with increasing standoff distance. Pang et al. [17, 18] modeled the erosion rate,

opening width and wall slope of machined channels in glass using dimensional analysis and multi-

variable regression of experimental data. They found that the machined channels suffered from

severe waviness due to the mechanical vibration of the equipment.

The present study examined the micro-machining of holes and channels in borosilicate glass with a

new ASJM system, and compared the machined features with those produced by abrasive air jet

micro-machining (AJM). This enabled an improved understanding of the mechanics of micro-slurry

jet erosion and its relation to the fluid flow of the impinging jet.

2.2 Experiments

2.2.1 ASJM setup

Hashish [19] and Miller [13] suggested that the ASJM process parameters that control the quality of

machined features fall into three categories: (i) hydraulic parameters such as the water jet pressure

and nozzle geometry; (ii) machining parameters including principally the traverse speed, standoff

17

distance and global impact angle; and (iii) the abrasive material, its flow rate, and the particle shape

and size.

Figure 2.1(a) shows a schematic of the low-pressure ASJM system that was developed for the

present study. Air from a pressurized cylinder was used to propel the premixed slurry from a 500

mL tank (Swagelok, Mississauga, ON, Canada) through a sapphire orifice toward the target

material. A 100 mm long stainless steel exit tube with 4 mm I.D. was positioned within the slurry

tank so that it butted against the orifice, in order to maintain a slurry flow rate adequate to prevent

particle sedimentation and clogging of the orifice. The specimens were mounted on a computer-

controlled linear stage (KT- LSM100A, Zaber Technologies Inc., Vancouver, BC, Canada) that

could be moved at various speeds up to 7 mm/s. In order to ensure the repeatability and uniformity

of the machined features, an adjustable speed DC motor attached to a four-blade, 10 mm diameter

folding propeller was used to continuously mix the water and Al2O3 particles (10 and 25 μm,

Comco Inc., CA, USA) in the pressurized slurry tank. The motor shaft passed through a spring-

loaded seal that prevented leaks at pressures up to 5 MPa. The global impact angle was controlled

by rotating the linear stage around the z-axis (Fig. 2.1(a)) while maintaining a constant orifice to

target standoff distance as measured along the orifice centerline. Operating pressures, P, were 1-4

MPa, producing flow rates, Q, of 1-5 mL/s through 0.3 mm thick sapphire orifices (KMT Waterjet,

KS, USA) with internal diameters of either 180 or 254 µm. In order to adapt the orifice to the exit

tube and prevent any sudden contraction, the orifice was installed backwards relative to its normal

orientation in abrasive water jets, as shown in Fig. 2.1(b).

18

Pressurized air cylinder

Pressure regulator

Slurry tankSlurry

Exit tube

Propeller

Stirring shaft

DC motorRefilling port and plug

Orifice

Target material Linear stage

y

x

z

(a)

(b)

Figure 2.1: (a) Schematic of the abrasive slurry jet apparatus (Nouraei et al. [20]), and (b) orientation of orifice installation (not to scale).

2.2.2 Machining tests

All machining experiments were conducted on 100×50×3 mm thick borosilicate glass plates

(Borofloat®, Schott Inc., NY, USA) having Young’s modulus of 63 GPa, Poisson’s ratio of 0.2,

fracture toughness of 0.76 MPa m1/2

, and a Vickers hardness of 5.4 GPa.

In addition to the pressure and the orifice diameter, the primary variables in the machining

experiments were the target traverse speed, vs, orifice standoff distance, do, particle concentration,

C, and jet impact angle, θ, which were varied as shown in Table 2.1. The orientation of jet impact

angle during the erosion rate measurements is illustrated in Fig. 2.2.

19

The abrasive slurry was prepared by mixing water with the 10 or 25 µm nominal diameter Al2O3

particles (Comco Inc., CA, USA). The required amount was taken from the original container using

a standard quartering technique to ensure an unbiased sampling of the powder sizes (ASTM C702-

98 [21]). The uniformity and repeatability of the slurry concentration was measured by collecting

10 samples of 50 mL of the slurry from the orifice in a container. The slurry was passed through

filter paper and then the water was evaporated in a drying oven prior to being weighed. For nominal

particle concentrations of 5 g/mL the variability in the concentration within a single experiment

utilizing a full 500 mL tank was less than 4%.

An optical profilometer (ST400, Nanovea Inc., CA, USA) and scanning electron microscope (SEM)

were used to measure the width, depth, cross-sectional area, and total target volume removed of the

machined holes and channels. Each measurement was repeated three times on each specimen using

different cross-section locations. The repeatability of the results was assessed by replicating some

of the holes and channels three times. It was found that the variation in the measured dimensions of

the replicate features was less than approximately 5%.

Table 2.1: Process parameters used in the machining of holes, channels and the measurement of erosion rates.

Micro-hole Micro-channel Erosion rate Traverse speed, vs (mm/s) 0 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 1 Slurry pressure, P (MPa) 2 1, 2, 3, 4 4 Particle concentration, C (wt %) 0.25 0.25, 0.5, 0.75, 1 1 Orifice standoff distance, do(mm) 20 1, 5, 10, 20, 25 20 Jet impact angle, θ (deg) 90 90 15, 30, 45, 60, 75, 90

The channel depth was measured at the centerline, while the width was defined using the

intersection of a tangent line passing through the half depth on the sidewall profile with the free

surface datum level, as shown in Fig 2.3. The slope of the line was calculated using a linear fit of

20

the first 6 digitized profile points on the sidewall above the half-depth. The calculated width was

found to be insensitive to the number of points used, as long as at least 4 were used (less than 2%

difference between 5 and 10 points). Similar approach was also used in order to measure the hole

depth and diameter.

θ

Orifice

Target

θ=90°

yx

z do =20 mm

Figure 2.2: Schematic of jet orientation during erosion rate measurements (not to scale).

-25-20-15-10-505

10152025

0 100 200 300 400 500 600 700

Dep

th,D

c(µ

m)

Width,Wc (µm)

Dc

1/2 Dc

Wc

Figure 2.3: Definition of channel depth and width.

21

2.2.3 Measurement of particle crushing force

In order to compare features machined using ASJM and AJM, it was necessary to determine

whether the fracture strength of the Al2O3 erodent was affected by water. This was guided by a

study by Nahvi et al. [22] who measured the crushing strength of silica abrasive and bottom-ash

particles in a combustion chamber by loading them between hard steel plates using a 50 N load cell

to record the sudden load drop that accompanied fracture. The average value of 10 particle force

measurements was reported as the particle strength. Nahvi et al. [22] found that the bottom-ash

particles exhibited multiple fractures during compression, but the silica particles fragmented

suddenly at a higher load. In the present study, the crushing loads of single dry and wet Al2O3

particles were measured using a specially-designed apparatus (Fig. 2.4) that crushed single 150 µm

(nominal diameter) Al2O3 particles between two 5 mm diameter tungsten carbide (WC) spheres.

The upper sphere could be lowered using a rack and pinion drive with a vertical positioning

accuracy of 100 µm so that it was just above the particle placed on the fixed lower ball. A release

mechanism then permitted the upper sphere assembly to move into contact with the particle along

guide rails. The applied load was then increased by slowly adding 6 mm diameter steel balls (7.2

mg) to a loading box attached to the upper ball assembly until particle fragmentation was observed

through a horizontally-mounted optical microscope having a field of view of 3.2×2.4 mm.

22

Cast iron base

Tungsten

Figure 2.4: Schematic of the single particle crushing apparatus.

Dry, nominally 150 µm Al2O3 particles were prepared by conditioning them in an oven at 80°C for

30 min immediately before the experiment. Wet particles were soaked in water for 24 h, removed

and tested immediately. A total of 60 crushing tests were conducted for each group of wet and dry

Al2O3 particles.

2.3 Results and Discussion

2.3.1 Effect of water on the crushing strength of aluminum oxide particles

Feng and Ball [23] showed that the fracture strength of the erodent has a substantial effect on the

solid particle erosion rate (mass of removed material per mass of abrasive particles). Van der Laag

et al. [24] investigated the effect of humidity on fracture toughness of aluminum oxide, lead

zirconate titanate (PZT) and magnesium. Although it has been reported by Van der Laag et al. [24]

that increasing humidity decreases the fracture toughness of aluminum oxide, the data of Table 2.2

23

show that the difference between the average crushing force of the wet and dry Al2O3 particles was

less than 1%, which was statistically insignificant (t test, 95% confidence). It was expected that in

larger, possibly multi-grain particles, the effect of moisture would be greater than in smaller

particles. Since the present data indicated that the crushing strength of the larger particles was not

affected by moisture, it can be reasonably concluded that moisture would have no effect on the

smaller 10 and 25 µm particles used in the machining experiments. Accordingly, differences in the

shape and erosion rate of features machined with ASJM and AJM could be attributed directly to the

differences in the fluid flow and particle impact conditions.

Table 2.2: Crushing loads of dry and wet 150 µm Al2O3 particles.

Dry particles Wet particles Number of particles 60 60 Maximum load (N) 9.17 9.90 Average load (N) 7.82 7.86 Minimum load (N) 4.51 5.00 Standard deviation 1.58 1.39

2.3.2 Slurry jet diameter

The diameter of the ASJM jet at a pressure of 2 MPa using the 254 µm orifice was measured

optically using a microscope with a field of view of 2.3×2.3 mm. Figure 2.5(a) shows a

representative image taken with diffuse backlighting, 1 mm from the orifice. The uncertainty in the

diameter measurements was approximately ±2%. The jet diameter increased slowly and

approximately linearly with standoff distance as seen in Fig. 2.5(b). The jet divergence angle was

0.015°, which was much smaller than the 10° jet divergence typically seen with the air jets used in

AJM as noted by Ghobeity et al. [25]. As mentioned previously, this increased resolution of ASJM

makes maskless machining feasible for a range of applications.

24

The orifice discharge coefficient (ratio of the actual mass flow rate at the orifice exit to that of an

ideal orifice) was estimated to be approximately 0.98 based on the jet diameter measurement at 1

mm standoff (255 µm). This was consistent with the flow rate measurements obtained by collecting

the jet output over a 90 s period in separate experiments. The flow rate variability within a single

experiment was less than 7%.

Djet = 0.509x + 255R² = 0.983

250

260

270

280

290

300

0 5 10 15 20 25

Jet d

iam

eter

, Dje

t(µ

m)

Distance from orifice, x (mm) (a) (b) Figure 2.5: (a) Photograph of the jet 1 mm from the 254 µm orifice (scale bar is 100 µm), and (b) jet diameter versus distance from the orifice.

2.3.3 Estimation of particle velocity in ASJM

With the assumption of insignificant friction and contraction losses in the ASJM prototype, the

average water jet velocity, vw, at the orifice exit is given by

( )2 i atmw

w

P Pv

ρ−

≈ (2.1)

Jet

25

where Pi is the hydrostatic pressure at the orifice entrance, Patm is the atmospheric pressure, and ρw

is the water density.

Li et al. [26] developed an analytical model of spherical particle velocity within an air jet, assuming

that the abrasive particles were uniformly distributed at each cross-section throughout the orifice,

and that the interaction of particles with the inner orifice wall and the rotation and Brownian motion

of the particles were negligible. The particles were assumed to be spherical in calculating the

accelerating drag force developed by the relative velocity between the fluid and the particles.

Dehnadfar et al. [27] modified this slightly to better represent the drag force on angular particles,

and validated it using laser shadowgraphy measurements of particle velocity.

In the present work, this model was adapted for use in ASJM by changing the properties of the

accelerating fluid from air to those of water. Following Dehnadfar et al. [27], the drag force

coefficient, CD for angular particles, which depends on the particle relative Reynolds number, Re,

and sphericity of the particle, φ, was obtained from Haider and Levenspiel [28] as

( ) ( )

( )

( )

5.07484.0655 0.0964 0.5565

6.2122

73.6924 1 8.17165.378DRe eC e Re

Re Re e

ϕϕ ϕ

ϕ

−− + × = + × × + + × (2.2)

where the particle relative Reynolds number, Re, is given by Wadell [29] as

w pd vRe

ρµ

∆=

(2.3)

and ρw is the water density, dp is the particle diameter, ∆v is the relative water/particle velocity, µ is

the dynamic viscosity of water and the particle sphericity is given by Wadell [29] as

26

1 23 3(6 )p

s

VA

πϕ =

(2.4)

in which Vp is the particle volume and As is the measured particle surface area. For the nominal 25

µm Al2O3 particles used in the present study, the average sphericity was measured by Dehnadfar et

al. [27] to be 0.76.

As shown by Li et al. [26] and Leu et al. [30], after the slurry exits the orifice, the structure of a free

slurry jet in air can be divided into three regions, as illustrated in Fig. 2.6: (i) the initial region, in

which the velocity in the potential core remains constant at its value at the orifice exit; (ii) the main

region in which the mean velocity of the flow decreases with distance from the orifice, and a

surrounding mist region grows; and (iii) the diffused droplet region, a relatively low velocity region

associated with the disintegration of the jet into droplets.

Orifice

lorifice

dorifice

Initial region Main region Diffused droplet

region

Water mist Potential

core

xpc

xm x

y

Figure 2.6: Structure of free water jet flow in air (not to scale) (Leu et al. [30]).

In order to estimate the centerline particle velocity in the free jet, it was required to determine the

length of the potential core, xpc, and the centerline velocity of the free jet. Rajaratnam et al. [31, 32]

suggested that the length of the potential core, xpc, is independent of the jet exit velocity and

27

proportional to the orifice diameter, dorifice. According to Rajaratnam et al. [31, 32], the length of

this region for a water jet passing through air is about 100 times the orifice diameter, which, as

discussed by Rajaratnam [33], is considerably longer than that of an air jet in air (6.2 times the

orifice diameter). Rajaratnam et al. [31, 32] also showed that the centerline velocity of the jet in the

main region decreases linearly to about 0.25 times the orifice outlet velocity at a distance of 2,500

orifice diameters from the outlet. As a result, the centerline velocity of the free water jet, vw-x, at an

axial distance, x, can be approximated as

( )

for 100

0.75100 for 100

2400

orifice

w x

orifice orificeorifice

v x dwv vw x d v x dwd

−

≤

= − − + >

(2.5)

In order to estimate the particle velocity, following Li et al. [26], the axial distance, x, was divided

into small identical segments in which the increment of particle acceleration, assumed constant over

the length of each segment, was calculated based on the drag force inferred from an iterative

solution of Eqs. (2.2) and (2.3). The particle velocity was then updated for the subsequent segment,

and the relative water/particle velocity was calculated using the particle velocity at the starting point

of each segment.

The predicted centerline velocities of 25 µm Al2O3 particles (density ρp=3,900 kg/m3) inside and

outside (i.e. in the free jet) the 0.3 mm long 254 µm orifice at 2 MPa pressure are shown in Fig.

2.7(a) and (b), respectively. Figure 2.7(a) and (b) show that the centerline particles accelerate

rapidly within the orifice and for a short distance after they exit, reaching their maximum velocity

after approximately 10 mm where they reach the water velocity. The centerline particle velocity is

28

then constant for approximately another 20 mm before it decreases linearly at distances greater than

30 mm from the orifice. The potential core exists up to approximately 25 mm (100 times of the

orifice diameter).

Immediately upstream of the target, the water velocity in the axial direction falls quickly to zero in

the stagnation zone. The rapid deceleration of the fluid causes a difference in the relative

water/particle velocity that in turn decelerates the particles approaching the target in the stagnation

zone. Clark [34] investigated the effect of the flow field on the impinging particles in slurry erosion.

He also concluded that the impact velocity of the particles on the target was smaller than their

velocity in the free jet. This effect is negligible in an AJM air jet, where it can be assumed that the

particle impact velocity is almost the same as the particle velocity directly upstream of the target.

However, in ASJM the effect of the stagnation zone is significant, because the viscosity of water is

about 100 times that of air. In order to estimate the impact velocities of particles in ASJM, the water

jet velocity profile in the stagnation zone was obtained from a two-dimensional axis-symmetric

computational fluid dynamics model of a free water jet striking a wall at 90° impingement angle

developed by Emamifar [35]. It was found that the centerline axial water velocity decelerated in a

stagnation zone extending about 600 µm from the plate (Fig. 2.7(c)). With this velocity profile, the

modified numerical approach of Li et al. [26] was used to predict the particle impact velocities by

calculating their deceleration through the stagnation zone. Figure 2.7(c) illustrates the estimated

velocity of 25 µm Al2O3 centerline particles just before impact with the target for a case where the

orifice standoff distance was 20 mm. The impact velocity of these 25 µm Al2O3 particles (28 m/s)

was found to be 54% lower than the centerline velocity far from the plate (62 m/s) due to the effect

of the stagnation zone. This is a significant difference with AJM, where particle are not slowed

appreciably immediately prior to impact. The calculated centerline particle and water velocities at

29

the upstream as well as the particle impact velocities (in the stagnation zone) for the operating

pressures of 1-4 MPa are presented in Table 2.3.

0

10

20

30

40

50

60

70

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Cen

terli

ne v

eloc

ity (m

/s)

Distance from the orifice entrance (mm)

Particle Water

50

52.5

55

57.5

60

62.5

65

0 10 20 30 40 50

Cen

terli

ne v

eloc

ity (m

/s)

Distance from the orifice exit (mm)

Particle Water

(a) (b)

0

10

20

30

40

50

60

70

0.00.20.40.60.81.0

Cen

terli

ne v

eloc

ity (m

/s)

Distance from the target (mm)

Particle Water

(c) Figure 2.7: Calculated centerline velocity of 25 µm Al2O3 particles (2 MPa) and water: (a) flowing through the orifice, (b) after orifice exit, and (c) within the 600 µm thick stagnation zone (20 mm standoff).

30

Table 2.3: Calculated centerline 25 µm Al2O3 particle and water velocities in the jet upstream of the stagnation zone and estimated centerline particle impact velocities (20 mm standoff).

Pressure (MPa) Upstream water and particle velocity (m/s) Particle impact velocity (m/s) 1 42 19 2 62 28 3 77 35 4 89 41

Figure 2.8 compares the normalized particle velocity profiles across the jet at 20 mm from the

orifice in ASJM and AJM. As discussed by Rajaratnam [33] and Ashforth-Frost and Jambunathan

[36], in ASJM, because of the very low drag exerted by the surrounding air, the water velocity is

nearly constant across the jet. Accordingly, the particle velocity can also be assumed to be uniform

(Fig. 2.8). However, in AJM, Li et al. [26] and Dehnadfar et al. [27] found that the air and particle

velocities are a strong function of the radial distance from the centerline. This particle velocity

distribution causes unmasked channels and holes made with AJM to be much wider and shallower

than those made with ASJM, which have relatively steep sidewalls.

31

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

par

ticle

vel

ocity

( v

p /v

p-0)

Normalized radial distance (y/rjet)

ASJM AJM

Figure 2.8: Comparison of normalized (with respect to centerline) particle velocity profiles across the jet in slurry jet (Emamifar [35]; Guha et al. [37]) and air jet (Dehnadfar et al. [27]) at 20 mm from exit. AJM: 760 µm nozzle, air centerline velocity 300 m/s at 200 kPa, and 25 µm Al2O3 particle centerline velocity of 160 m/s. ASJM: 254 µm orifice, water centerline velocity 62 m/s at 2 MPa, and 25 µm Al2O3 particle centerline velocity of 62 m/s.

2.3.4 Single impact craters

Brittle erosion occurs by the formation of cracks that cause the removal of fragmented chips in the

impact zone, while ductile erosion removes the material in the fully-developed plastic zone by

cutting and ploughing, as described by Ali and Wang [38]. During the impact of a hard sharp

particle on a brittle material such as glass, the contact area is plastically deformed due to the high

compressive and shear stresses, and radial cracks are formed. The plastic deformation zone also

causes tensile stresses that result in lateral cracks that remove material when they reach the surface.

Slikkerveer et al. [39] assumed that the brittle erosion associated with glass is controlled by the

normal component of the impact velocity. However, Sheldon and Finnie [40] showed that as the

particle speed and size decrease, a ductile-brittle transition is reached, where the contact stress

becomes too small to initiate cracks and the target only yields. Sheldon and Finnie [40] also found

32

that the resulting ductile erosion tends to increase to a maximum at an impact angle in the range of

approximately 20-30°.

Slikkerveer et al. [39] used data from air jets to develop the following relation for the threshold

value of the kinetic energy, Uth, at the ductile-brittle transition of eroding particles at normal

incidence:

362

132

23225 cth

E KUH

=

(2.6)

where E is the Young's modulus, Kc the fracture toughness and H the hardness of the target

material. Thus the threshold depends only on the properties of the target material and is the same

for air and slurry jets. In another study, Wensink and Elwenspoek [41] examined the brittle to

ductile transition range for brittle materials such as Pyrex glass (borosilicate), silicon and soda-lime

glass. It was concluded that the Slikkerveer et al. [39] model overestimated the threshold value of

the kinetic energy by up to 50%. For borosilicate glass, the ductile-brittle transition occurred at

kinetic energies less than 17 nJ, which corresponds to a normal component of impact velocity of

approximately 32 m/s for Al2O3 particles with an equivalent spherical diameter of 25 µm. In AJM

according to the measurements of Dehnadfar et al. [27], the impact velocity of particles is normally

three to four times higher than this threshold velocity; however in ASJM, the surface-normal

velocity components can be in this range, leading to ductile erosion. This has the potential

advantage of machining features of lower roughness, as noted by Mineta et al. [42] and Matsumura

et al. [43].

33

To gain an understanding of the material removal mechanisms due to low-pressure slurry jets,

single impact sites were produced at 2 MPa using the 254 µm orifice with 25 µm Al2O3 particles at

a 20 mm standoff distance. A very sparse jet was obtained by using a relatively low particle

concentration (0.1 wt %) and a high traverse speed (50 mm/s). Figure 2.9(a), (b) and (c) show the

unblasted and blasted borosilicate glass, where four types of impact sites can be recognized: (i) chip

removal from lateral crack formation, (ii) brittle fracture site with no chip removal, because lateral

cracks did not spread to the surface, (iii) scratch marks with raised plastically deformed edges

resulting from ductile erosive ploughing, and (iv) plastically deformed craters without cracking

typical of ductile erosive behavior resulting from smaller particles and low kinetic energy impacts.

These impact sites indicated that the glass surface was subject to both brittle and ductile erosion

mechanisms.

The impact velocity for centerline Al2O3 particles with an equivalent spherical diameter of 25 µm at

2 MPa pressure according to Fig. 2.7(c) was 28 m/s which is less than the 32 m/s threshold value,

implying a ductile erosion process. Particles travelling off the centerline can be expected to have

slightly lower impact velocities. However, the particle size distribution data from Ghobeity et al.

[44] for these same particles showed that approximately 27% of the particles had an equivalent

spherical diameter larger than 25 µm. These larger particles had kinetic energies above the ductile

to brittle threshold and could cause brittle erosion damage. As seen from Fig. 2.9(b) and (c), the

sizes of the removed craters due to lateral cracking were much larger than the scratch marks on the

glass due to ductile erosion. It is therefore likely that brittle erosion governed the material removal

process, while the ductile erosion mechanism mainly reduced the roughness and waviness of the

channels. At pressures of 3 and 4 MPa, Table 2.3 shows that the average particle size of 25 µm

34

would have velocities giving kinetic energies above the brittle-ductile threshold and would

therefore generate brittle chipping.

(ii)

(i)

(i) (iii)

(iii)

(iv)

(a) (b)

(c)

Figure 2.9: (a) SEM image of unblasted borosilicate glass surface; (b) four different types of single impact sites: (i) brittle chipping, (ii) brittle fracture with no chip removal, (iii) ductile ploughing, and (iv) plastically deformed craters without cracking; and (c) higher magnification image of type (iii) impact sites. Conditions: 254 µm orifice, 0.1 wt % 25 µm Al2O3, 2 MPa, 50 mm/s traverse speed, 20 mm standoff.

(iii)

(iii)

35

2.3.5 Machining of micro-holes with ASJM

Typical two-dimensional profiles of holes machined at 90° for different exposure times are shown

in Fig. 2.10. The aspect ratio (ratio of depth to average diameter) of the holes after 120 s of slurry

jet blasting was approximately 1.3. The hole cross-sections were "U" shaped, with a relatively flat

bottom and steep sidewalls.

-600

-500

-400

-300

-200

-100

00 100 200 300 400 500 600

Dep

th o

f hol

e (µ

m)

Diameter of hole (µm)

20 s 40 s 60 s 80 s 100 s 120 s Figure 2.10: Cross-sectional profiles of holes machined with ASJM as a function of blasting time. Conditions: 254 µm orifice, 0.25 wt % 25 µm Al2O3, 2 MPa, 20 mm standoff.

The depth and volume of the micro-machined holes as a function of machining time are shown in

Fig. 2.11(a) and (b), respectively. Both the depth and the removed volume increased linearly with

blasting time indicating that the material removal rate was proportional to the particle dose incident

to the surface. The average material removal rate (MRR) was 7×10-4 mm

3/s.

dorifice = 254 µm

36

Dh = 4.72tR² = 0.999

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140

Dep

th, D

h(µ

m)

Exposure time, t (s)

Vh = 0.700x10-3 tR² = 0.998

0

0.02

0.04

0.06

0.08

0.1

0 20 40 60 80 100 120 140

Volu

me,

Vh

(mm

3 )

Exposure time, t (s) (a) (b) Figure 2.11: (a) Depth, and (b) volume of holes machined with ASJM versus blasting time. Conditions: 254 µm orifice, 0.25 wt % 25 µm Al2O3, 2 MPa, 20 mm standoff. Solid lines are least-squares best fits.

The resolution of the machined holes, defined as the ratio of the orifice diameter to the hole

diameter, was approximately 0.57. Although the relatively small jet divergence angle contributed to

a greater hole resolution than is possible in unmasked AJM as shown by Ghobeity et al. [45], the

machined holes became slightly enlarged by the secondary erosion due to the slurry flowing

radially outward after impacting the bottom of the hole. As the hole deepened, the radial flow at the

bottom had to turn and flow back up toward the surface. However, these upward secondary flows

parallel to the side walls apparently did not cause significant additional erosion, since it is seen

from Fig. 2.10 that the hole diameter did not change appreciably with depth. This is similar to the

observations of Nguyen et al. [14] and Wang et al. [15].

Figure 2.12 compares the normalized profiles of holes machined using ASJM and masked AJM

developed by Ghobeity et al. [45]. The cross-sections of masked holes in glass machined with AJM

are typically "V" shaped, with side walls that are not as steep as those machined using ASJM. The

difference in the shape of the holes in ASJM and AJM is caused by the difference in the distribution

of particle mass flux and velocity across the jet which, in turn, affects the erosive power of the jet.

37

As discussed previously, in the region of fully developed turbulent flow in an air jet, the air axial

velocity decreases continuously with radial distance from its maximum at the jet centerline to

essentially zero at the periphery of the flow. As a result, as shown by Ghobeity et al. [45], the

particle velocity in unmasked AJM, and thus the erosive power, also decreases sharply from the

center to the jet periphery (Fig. 2.8). When used with erosion resistant masks with openings that are

relatively narrow compared with the nozzle diameter, this velocity distribution becomes negligible

across the hole, however, the distribution of particle flux nevertheless decreases as the edges of the

mask openings are approached due to particle collisions with the mask edges. As discussed earlier,

slurry jets have a more uniform distribution of impacting velocities across the jet, thereby leading to

more uniform machining, much flatter bottoms and steeper side walls ("U" shaped) without the use

of erosion resistant masks.

-1

-0.8

-0.6

-0.4

-0.2

00.0 0.2 0.4 0.6 0.8 1.0

Nor

mal

ized

dep

th

Normalized width

ASJM AJM

Figure 2.12: Comparison of the normalized profiles of machined holes in ASJM and masked AJM (Ghobeity et al. [45]). The dimensions were normalized by dividing by the diameter of each hole. ASJM: 254 µm orifice, 2 MPa, 0.625 g/min 25 µm Al2O3, 20 mm standoff. Maximum diameter and depth of 530 µm and 286 µm, respectively (aspect ratio of 0.53). AJM: 760 µm nozzle, 2.83 g/min ± 0.12 g/min of 25 µm Al2O3, 200 kPa, 20 mm standoff. Maximum mask opening and depth of 900 µm and 560 µm, respectively (aspect ratio of 0.62).

38

2.3.6 Machining of micro-channels with ASJM

Figure 2.13(a) shows a 10 mm long channel machined in a single pass of the abrasive slurry jet at

0.1 mm/s. Figure 2.13(b) indicates that the depth of 221 µm and the width of 430 µm varied along

the channel length by less than 5% and 2%, respectively. This illustrates the uniformity of the slurry

abrasive concentration produced by the mixing system which was delivering 50 mg/s of 25 µm

Al2O3 at a 1 wt % concentration.

The "U" shaped channel with a relatively flat bottom shown in Fig. 2.13(a) is in agreement with the

observations of Pang et al. [17], except that no evidence of the extreme waviness or striation

patterns seen in their work was observed in the present channels.

250

300

350

400

450

200

225

250

275

300

0 2.5 5 7.5 10 12.5W

idth

(µm

)

Dep

th (

µm)

Distance (mm)

Depth Width

(a) (b)

Figure 2.13: (a) Scanning electron micrograph of blasted channel, and (b) depth and width of the channel along its length. Conditions: 254 µm orifice, 1 wt % 25 µm Al2O3, 4 MPa, 0.1 mm/s traverse speed, 20 mm standoff. Solid lines are to guide the eye.

Figure 2.14 shows that the normalized cross-sectional profiles of a hole and channel machined

using ASJM are both U-shaped. The resolution of the channel, defined as the ratio of the orifice

39

diameter to the channel opening width, was approximately 0.59 (i.e. nearly identical to the value for

holes). This is consistent with the hypothesis that the radial flow after jet impact erodes and

steepens the channel side walls, but does not produce significant erosion once the slurry flow has

deflected to be more parallel to the channel surfaces.

-0.70

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.000.0 0.2 0.4 0.6 0.8 1.0

Nor

mal

ized

dep

th

Normalized width

Hole Channel

Figure 2.14: Comparison of the normalized profiles of a hole and channel machined with ASJM. The dimensions were normalized by dividing by the hole diameter or channel width. Channel: 254 µm orifice, 1 wt % 25 µm Al2O3, 4 MPa, 0.1 mm/s traverse speed, 20 mm standoff. Maximum channel width and depth of 430 µm and 221 µm. Hole: 254 µm orifice, 0.25 wt % 25 µm Al2O3, 2 MPa, 20 mm standoff. Maximum hole diameter and depth of 530 µm and 186 µm.

Figure 2.15 compares the normalized profiles of the machined channels in ASJM and masked AJM

developed by Ghobeity et al. [25]. As was seen in Fig. 2.12 for holes, the typical "V" shaped cross-

section of channels machined using AJM changes to a more "U" shaped cross-section in ASJM,

because of the more uniform erosive power distribution delivered to the surface. The development

of steep sidewalls in unmasked machined channels with ASJM causes the edge resolution

(sharpness of transition from channel wall to adjacent flat glass surface) to be comparable with that

of masked AJM.

40

-1.0

-0.8

-0.6

-0.4

-0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

Nor

mal

ized

dep

th

Normalized width

ASJM AJM

Figure 2.15: Comparison of the normalized profile of machined channels in ASJM and masked AJM (Ghobeity et al. [25]). The dimensions of the machined channels were normalized by dividing by the channel width. ASJM: 180 µm orifice, 4 MPa, 2.5 g/min 25 µm Al2O3, 20 mm standoff. Maximum width and depth of 350 µm and 200 µm, respectively (aspect ratio of 0.57). AJM: 760 µm nozzle, 2.83 g/min ± 0.12 g/min of 25 µm Al2O3, 200kPa , 20 mm standoff with maximum mask opening and depth of 250 µm and 160 µm, respectively (aspect ratio of 0.64).

Higher aspect ratio (depth/width) channels were made by scanning the jet repeatedly over the target.

The profiles of multi-pass channels machined with a 180 µm orifice and 10 µm Al2O3 particles are

shown in Fig. 2.16. As with the machined holes, the center depth was directly proportional to the

increase in particle dose delivered by increasing the number of passes. Consistent with the

observation that only the outward radial flow after impact produces additional side-wall erosion, the

number of passes did not significantly affect the width or resolution of the machined channels. For

all the passes, the top width of the channel was approximately 1.95 times the orifice diameter for a

resolution of 0.51. This was slightly smaller than the resolution of the 221 µm deep single-pass

channel of Fig. 2.13, although the standoff, abrasive and orifice were different in that case.

41

-600

-500

-400

-300

-200

-100

00 75 150 225 300 375 450

Dep

th (µ

m)

Width (µm)

Pass#1 Pass#5 Pass#10

Figure 2.16: Cross-sectional profiles of multi-pass channels. Conditions: 180 µm orifice, 1 wt % of 10 µm Al2O3, 4 MPa, 0.1 mm/s traverse speed, 25 mm standoff.

The material removal process in solid particle impact is affected by not only particle size and

velocity, but also by the mass flux and local impact angle distribution incident to the surface,

which, in turn, depends on the particle trajectories. Particles with sufficient kinetic energy to cause

brittle erosion (i.e. above the ductile to brittle threshold level) remove larger chips than those

causing ductile erosion, and chip size will increase with the cube of particle size. Hence, at

relatively large standoff distances, where the particles have accelerated to their maximum values,

the erosion rate of glass was most influenced by the impact of these larger particles. In contrast, Fig.

2.17 illustrates the profile of a channel machined using a relatively small standoff distance of 1 mm,

where the particles were still accelerating (Fig. 2.7(b)); i.e. the particle velocity in the free jet was

50 m/s while the water velocity was approximately 62 m/s. Taking into account the deceleration

through the stagnation zone, the particle impact velocity was approximately 17 m/s, which was well

below the ductile-brittle threshold velocity of 32 m/s (Section 2.3.4). Consequently, at this very low

42

velocity ductile erosion mechanisms were likely dominant, and Wang et al. [15] proposed that the

"W" shaped profile was a result of this ductile erosion and two additional factors related to the size

distribution and impact angle of the particles. As indicated by Fan et al. [46], the slurry jet

streamlines change direction from normal to parallel to the target surface in the vicinity of the

stagnation point. The abrupt change of streamline direction affects the trajectory of particles with

relatively low Stokes number, St, given by Humphrey [47] as

D

Stfλ

= (2.7)

where λ is the ratio of two time scales that characterize the dynamics of the solid and fluid phases,

and fD is the quantity relating St and λ specified by Humphrey [47] as

( )( )

2

p p jet

orifice

d v

18 d

ρλ

µ=

(2.8)

( )23

11 0 5006Df Re Re= + ≤ ≤

(2.9)

where ρp is the particle density, vjet is the jet velocity at the orifice exit, and Re is the particle

relative Reynolds number (Eq. (2.3)). Humphrey [47] reported that particles with St < 1 tend to

follow the jet streamlines and are carried away from the initial jet impact zone (center of the jet).

For Al2O3 particles with an average equivalent spherical diameter of 25 µm travelling at 17 m/s, the

St is approximately 9, suggesting that their momentum carries them to the target. However,

assuming that particle size does not influence velocity in the jet, for the same 25 µm nominal size

Al2O3 particles used in the present study, the particle size distribution measurements performed by

43

Ghobeity et al. [44] indicate that 34% of the particles are sufficiently small (dp<16 µm) to result in

St < 1. Therefore, a significant fraction of the particle trajectories incident perpendicular to the

surface would be deflected radially, causing these smaller particles to strike the surface further from

the centerline and at a shallower angle. The net result is that the striking particle flux is relatively

low in the center of the jet, and the local impact angle varies across the jet, being nearly 90° (i.e.

perpendicular) in the central region, but becoming increasingly shallow at larger distances from the

jet centerline where the secondary flows move more parallel to the surface. Since the erosion rate

for a ductile erosive system is generally higher at these shallower impact angles, the local erosion

rate is lower near the jet center than away from it, thus resulting in the "W" shaped profile.

-15-12-9-6-30

0 50 100 150 200 250 300 350 400 450

Dep

th (µ

m)

Width (µm)

Figure 2.17: Profile of machined channel at 1 mm standoff distance. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 2 MPa, 0.5 mm/s traverse speed.

2.3.7 Erosion rate of ASJM

The erosion rate, Er, of brittle materials (target mass loss/mass of erodent) is usually assumed to be

a function of the normal component of the impact velocity, given by Slikkerveer et al. [39] as

( )( )k

r pE N v sin α= (2.10)

44

where vp is the particle impact velocity and α is the local impact angle. N and k (the velocity

exponent) are constant for a given particle-target system. Normalizing by the erosion rate at α =

90°, gives

( )( )* krE sin α= (2.11)

Following the work of Ghobeity et al. [25] in AJM, the erosion rate of the borosilicate glass as a

function of the impact angle was measured using ASJM channels by using a relatively high traverse

speed of 1 mm/s, in order to maintain the aspect ratio of machined channels at approximately 0.06,

thus ensuring that the local and global particle impact angles were approximately equal; i.e. α =θ.

The global impact angle of the jet, θ, was varied in the plane perpendicular to the direction of linear

stage motion, resulting in shallow, asymmetrical channels. This configuration eliminated the effect

of secondary erosion of the slurry flow on the channel side walls since the dominant flow was

perpendicular to the channel axis and the channels were very shallow.

Figure 2.18 shows the normalized ASJM erosion rate as function of impact angle compared with

earlier AJM results developed by Ghobeity et al. [25]. The trend of increasing normalized erosion

rate with increasing impact angle suggests that brittle erosion was dominant under these conditions.

The best fit velocity exponent k for ASJM was 1.30, compared to k =1.43 obtained from Ghobeity

et al. [25]. The value of k as reported by Uuemǒis and Kleis [48] is generally considered to be a

function of particle size, impact velocity, and also the mechanical properties of the target material

and particles. The obtained k values were less than 2 for both the ASJM and AJM setups, thus, as

suggested by Uuemǒis and Kleis [48] , particle deformation and breakage may have occurred in

both cases. Although the impact velocities were significantly different in the ASJM and AJM

45

setups, it is not surprising that the k values were relatively close. A previous AJM study performed

by Burzynski and Papini [49] showed that, for the presently utilized 10 and 25 µm Al2O3 particles

impacting on borosilicate glass substrate, k was only a weak function of velocity, varying between

1.44 and 1.59 for velocities between 130 and 260 m/s. Moreover, the crushing experiments showed

that water did not alter the particle strength.

The N value (Eq. (2.10)) of 8×10-6

m-1.43

s1.43

measured by Shafiei et al. [50] using AJM allows a

calculation of the erosion rate at perpendicular incidence of 11 mg/g for AJM, whereas for ASJM,

the erosion rate at perpendicular incidence was measured as 0.6 mg/g. This difference in erosion

rate is attributed to the much higher particle impact velocities in AJM (160 m/s) compared to ASJM

(41 m/s), and to the differences in the local particle impact angles due to the different air and water

jet flows at the surface.

46

Er*AJM = 0.955sin(α)1.43

R² = 0.987

Er*ASJM = 1.04sin (α)1.3

R² = 0.995

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Nor

mal

ized

ero

sion

rate

, Er*

sin(α)

ASJM AJM

Figure 2.18: Normalized erosion rate of ASJM and AJM (Ghobeity et al. [25]) as a function of impact angle. Error bars represent ±1 standard deviation for 3 measurements. ASJM: 254 µm orifice, 4 MPa (particle centerline velocity of 89 m/s), 2.5 g/min 25 µm Al2O3, 20 mm standoff. AJM: 760 µm nozzle, 2.83 g/min ± 0.12 g/min of 25 µm Al2O3, 200 kPa (particle centerline velocity of 160 m/s) , 20 mm standoff. Note that the erosion rates in ASJM and AJM were normalized by their respective 90° values.

2.3.8 Effect of process parameters on material removal

The channel depth and width was measured for a series of shallow channels machined using ASJM

under various process conditions. Figure 2.19 illustrates that the effect of standoff distance on the

depth and width of the channels was quite small, indicating that the abrasive particles reached their

maximum speed within 5 mm of the orifice exit, and did not decelerate appreciably up to 20 mm

(Fig. 2.7(b)).

The effect of pressure and hence jet velocity on channel depth and width for a given traverse speed

is shown in Fig. 2.20. An increase in the slurry pressure resulted in deeper and wider channels per

unit machining time (i.e. a higher material removal rate, MRR, mm3/s), so that the channel

47

resolution (orifice diameter/channel opening width) was reduced from 0.67 to 0.63 as the pressure

increased from 1 MPa to 4 MPa.

200

250

300

350

400

0

10

20

30

40

0 5 10 15 20 25

Wid

th (µ

m)

Dep

th (µ

m)

Standoff distance (mm)

Depth Width

Figure 2.19: Effect of orifice standoff distance on depth and width of ASJM channel. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 2 MPa, 0.5 mm/s traverse speed. Solid lines are least-squares best fits.

0 1 2 3 4 5

300

325

350

375

400

425

0

10

20

30

40

50

0 1 2 3 4 5

Wid

th (µ

m)

Dep

th ( µ

m)

Slurry pressure (MPa)

Depth Width

Slurry velocity (m/s)42 62 76 88 100

Figure 2.20: Effect of slurry pressure on depth and width of channel. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 0.5 mm/s traverse speed and 20 mm standoff. Solid lines are least-squares best fits.

48

Figure 2.21 shows the linear dependence of erosion on abrasive dose, changed by varying the

abrasive particle concentration. Higher slurry concentrations increased the particle dose delivered to

the channel, resulting in deeper and slightly wider channels, and a higher MRR. These observations

are in agreement with the findings of Pang et al. [17] and Fan et al. [51]. As in Fig. 2.10 (holes) and

Fig. 2.16 (channels), the depth was linearly proportional to the dose of abrasive delivered to the

channel and the channel width did not vary much.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

300

325

350

375

400

425

0

20

40

60

80

100

0 30 60 90 120 150 180

Particle concentration, C (wt %)

Wid

th (µ

m)

Dep

th (µ

m)

Particle dose (mg/mm2)

Depth Width

Figure 2.21: Effect of particle concentration on depth and width of channel. Conditions: 254 µm orifice, 2 MPa, 0.5 mm/s traverse speed and 20 mm standoff. Solid lines are least-squares best fits.

The effect of the traverse speed on the depth and width of the channel is shown in Fig. 2.22.

Increasing the traverse speed from 0.1 to 0.5 mm/s decreased the depth in a nonlinear manner

without significantly affecting the width of channel. This is in contrast with the trend seen in Figs.

2.15 and 2.21 where the channel depth varied linearly with dose.

49

0 0.1 0.2 0.3 0.4 0.5 0.6

300

320

340

360

380

400

0

20

40

60

80

0 0.1 0.2 0.3 0.4 0.5 0.6

Particle dose (mg/mm2)

Wid

th (µ

m)

Dep

th (µ

m)

Traverse speed (mm/s)

Depth Width

216 108 72 54 43

Figure 2.22: Effect of traverse speed on depth and width of channel. Conditions: 254 µm orifice, 0.25 wt % of 25 µm Al2O3, 2 MPa, 20 mm standoff. Solid lines are to guide the eye.

Figure 2.23 examines this further by comparing the effect of particle dose on depth of channel as

result of varying the traverse speed compared with that due to varying the particle concentration. It

is evident that depth-dose relation may be regarded as similarly linear for doses less than about 150

mg/mm2. However, at a dose of 216 mg/mm

2 (delivered at the slowest traverse speed of 0.1 mm/s),

the depth was smaller than predicted by the linear trend, probably due to the change of the leading

edge slope and its effect on the local impact angle, α.

50

Dc = 0.305BR² = 0.971

Dc = -0.600x10-3B2 + 0.380BR² = 0.973

0

20

40

60

80

0 30 60 90 120 150 180 210 240

Dep

th, D

c(µ

m)

Particle dose, B (mg/mm2)

ConcentrationTraverse speed

Figure 2.23: Channel depth as a function of particle dose that was varied by either changing (a) traverse speed, or (b) concentration. Error bars represent ±1 standard deviation for 3 measurements. Conditions: 254 µm orifice, 2 MPa, 10 mm standoff.

Fowler et al. [52] found similar behavior in the high-pressure water jet milling of a titanium alloy.

The leading edge angle, β, as shown in Fig. 2.24 can be approximated as

1tan c

jet

DD

β −

= (2.12)

where Dc, and Djet are the channel depth and jet diameter. Reducing the traverse speed from 0.5 to

0.1 mm/s increased the leading edge slope approximately from 3° to 12°. The increase in the

leading edge slope reduced the local impact angle of particles (from α =87° to 78°). As a result, the

erosion rate was reduced slightly at the lower traverse speeds, leading to the nonlinear behavior. In

AJM however, the jet foot print is usually much larger than in ASJM due to the larger nozzles and

much higher jet divergence. In that case, as reported by Ghobeity et al. [25], the leading edge slope

is usually negligible and the change in the depth of channel remains directly proportional to the

dose delivered regardless of the traverse speed.

51

θ = 90°

Dc

Djet

β

Target

Traverse direction

Particle

Orifice

Datum level α

Figure 2.24: Schematic of the local front geometry (side view) of channel (not to scale).

The normalized erosion rate as a function of the impact angle (α) using ASJM shown in Fig. 2.18

can be used to correct for the effect of the leading edge slope by introducing a correction coefficient

1/sin (α)1.3

. In other words, the actual erosion rates (reflected in the depths) can be converted to the

corresponding values for α = 90°. For the data presented in Fig. 2.23, values of α for traverse

speeds of 0.5, 0.4, 0.3, 0.2 and 0.1 mm/s are 87°, 85.3°, 84.6°, 83° and 78°, respectively. Since the

effect of leading edge angle at traverse speeds above 0.1 mm/s are negligible, only the channel

depth at this speed was corrected in Fig. 2.25, which illustrates the expected linear trend of depth

with respect to dose.

52

Dc = -0.600x10-3B2 + 0.380BR² = 0.973

Dc = 0.283B R² = 0.922

0

20

40

60

80

0 30 60 90 120 150 180 210 240

Dep

th, D

c(µ

m)

Particle dose, B (mg/mm2)

Traverse speedCorrected depth at 0.1 mm/s

Figure 2.25: Corrected depth versus dose varied by traverse speed assuming the local and global impact angles are equal. Error bars represent ±1 standard deviation for 3 measurements. Conditions: 254 µm orifice, 2 MPa, 20 mm standoff.

2.4 Conclusions

The mechanics of erosion in ASJM were studied and modeled by comparing the micro-machining

of holes and channels in borosilicate glass with the performance of AJM, a process that is simpler

and relatively well understood. The differences in the shapes and erosion rates of features machined

with ASJM and AJM could be attributed directly to the differences in the fluid flow and particle

impact conditions since it was found that the crushing strength of the abrasive Al2O3 particles was

not affected by water. In contrast to ASJM systems previously used in the literature, the new low

pressure ASJM system utilized in this study was found to produce smooth channels of relatively

uniform depth that did not suffer from significant waviness. The depth of both holes and channels

machined using the ASJM system were found to be linearly proportional to the dose of abrasive

delivered, with the exception of single pass channels machined at lower traverse speeds, where

differences in the slope of the leading machined edge led to a nonlinear relationship resulting from

a decrease in the local impact angle. This effect is rarely evident in AJM due to the much greater

53

radius of the blast zone impinging on masked or unmasked channels. The resolution (ratio of orifice

diameter to feature width; i.e. channel width or hole diameter) of the holes and channels produced

using ASJM without a mask was found to be approximately 0.5, which remained constant as the

depth of these features was increased by repeated passes of the slurry jet. This important

observation supports the potential of unmasked ASJM as a direct-write machining tool in contrast

to AJM that typically requires the use of masks to achieve adequate feature definition. The

behaviour was explained in terms of the slurry flow field which became parallel to the side walls,

minimizing erosion after turning at the bottom of the hole or channel.

In ASJM, particles had a nearly constant velocity across the free slurry jet, and had a very small

divergence angle from the centerline. These characteristics increase the resolution of unmasked

ASJM compared with unmasked AJM jets where particles diverge and are slowed near the jet

periphery relatively quickly. These differences in the distribution of particle mass flux and velocity

delivered to the surface, also explain why the holes and channels machined using ASJM were

characterized by relatively steep sidewalls and flat bottoms compared with those machined using

masked AJM which were more "V" shaped. Thus micro-channels and holes machined using ASJM

have a larger volume for a given depth than those made with AJM.

Examination of individual particle impact sites indicated that the borosilicate glass experienced

both brittle and ductile erosion in the range of ASJM operating conditions utilized in the present

study. However, brittle erosion was found to lead to most of the bulk material removal, with ductile

erosion playing mainly a role in reducing the roughness and waviness of the channels. A typically

brittle erosive response characterized by an increasing normalized erosion rate with increasing

impact angle was found for both ASJM and AJM.

54

The particle impact velocity in AJM can be assumed to be equal to that of the carrier air stream.

However, in ASJM it was necessary to develop a model to predict the particle impact velocity due

to the strong decelerating effect of the water stagnation zone near the target. Due to the higher

impact velocity of particles in AJM, the measured ASJM erosion rates were much smaller than

those in AJM under comparable conditions. Nevertheless, the similarity of the velocity exponents in

the respective erosion rate correlations confirmed that the erosion mechanisms in ASJM and AJM

were similar with this borosilicate glass.

2.5 References

[1] C.Y. Huang, C.H. Kuo, W.T. Hsiao, K.C. Huang, S.F. Tseng, C.P. Chou, Glass biochip fabrication by laser micromachining and glass-molding process, Journal of Materials Processing Technology 212 (2011) 633-639.


[3] X. Cheng, Z. Wang, K. Nakamoto, K. Yamazaki, A study on the micro tooling for micro/nano milling, The International Journal of Advanced Manufacturing Technology 53 (2011) 523-533.

[4] G. Kucukturk, C. Cogun, A new method for machining electrically nonconductive work piece using electric discharge machining technique, Machining Science and Technology: An International Journal 14 (2010) 189-207.

[5] H. Ogura, Y. Yoshida, Hole drilling of glass substrates with a CO2 laser, Japanese Journal of Applied Physics 42 (2003) 2881-2886.

[6] E. Belloy, S. Thurre, E. Walckiers, A. Sayah, M. Gijs, The introduction of powder blasting for sensor and micro-system applications, Sensors and Actuators A: Physical 84 (2000) 330-337.

[7] S. Schlautmann, H. Wensink, R. Schasfoort, M. Elwenspoek, A. Berg, Powder-blasting technology as an alternative tool for micro-fabrication of capillary electrophoresis chips with integrated conductivity sensors, Journal of Micromechanics and Micro-engineering 11 (2001) 386-389.

[8] R.M. Guijt, E. Baltussen, G. Van der Steen, R. Schasfoort, S. Schlautmann, H.A.H. Billiet, J. Frank, G.W.K. Van Dedem, A. Van den Berg, New approaches for fabrication

55

of micro-fluidic capillary electrophoresis devices with on-chip conductivity detection, Electrophoresis 22 (2001) 235-241.

[9] L. Zhang, T. Kuriyagawa, Y. Yasutomi, J. Zhao Investigation into micro abrasive intermittent jet machining, International Journal of Machine Tools and Manufacture 45 (2005) 873-879.

[10] H. Wensink, S. Schlautmann, M.H. Goedbloed, M.C. Elwenspoek, Fine tuning the roughness of powder blasted surfaces, Journal of Micro-mechanics and Micro-engineering 12 (2002) 616-620.

[11] H.T. Liu, Water jet technology for machining fine features pertaining to micro-machining, Journal of Manufacturing Processes 12 (2010) 8-18.


[13] D.S. Miller, Micro-machining with abrasive water jets, Journal of Materials Processing Technology 149 (2004) 37-42.

[14] T. Nguyen, K. Pang, J. Wang, A preliminary study of the erosion process in micro-machining of glasses with a low pressure slurry jet, Key Engineering Materials 389 (2009) 375-380.

[15] J. Wang, T. Nguyen, K.L. Pang, Mechanisms of micro-hole formation on glasses by an abrasive slurry jet, Journal of Applied Physics 105 (2009) 044906 1-4.

[16] C.Y. Wang, M. Chen, P. Yang, J.M. Fan, Hole machining of glass by micro abrasive suspension Jets, Key Engineering Materials 389 (2009) 381-386.

[17] K.L. Pang, T. Nguyen, J.M. Fan, J. Wang, Machining of micro-channels on brittle glass using an abrasive slurry Jet, Key Engineering Materials 443 (2010) 639-644.

[18] K. Pang, T. Nguyen, J. Fan, J. Wang, Modeling of the micro-channeling process on glasses using an abrasive slurry jet, International Journal of Machine Tools and Manufacture 53 (2012) 118-126.

[19] M. Hashish, Optimization factors in abrasive-water jet machining, Journal of Engineering for Industry 113 (1991) 29-37.

[20] H. Nouraei, A. Wodoslawsky, J.K. Spelt, M. Papini, Micro-machining using an Abrasive Slurry Jet, Wear of Materials, 18th International Conference, Philadelphia, USA, Poster, 2011.

[21] ASTM C702-98 (2003): Standard Practice for Reducing Samples of Aggregate to Testing Size.

56

[22] S. Nahvi, P. Shipway, D. McCartney, Effects of particle crushing in abrasion testing of steels with ash from biomass-fired power plants, Wear 267 (2009) 34-42.

[23] Z. Feng, A. Ball, The erosion of four materials using seven erodents: towards an understanding, Wear 233 (1999) 674-684.

[24] N.J. Van der Laag, L.J.M.G. Dortmans, G. de With, Influence of relative humidity on mechanical properties of Alumina, PZT, Ziconia, Key Engineering Materials, Euro Ceramics VII (2002) 751-754.

[25] A. Ghobeity, T. Krajac, T. Burzynski, M. Papini, J.K. Spelt, Surface evolution models in abrasive jet micromachining, Wear 264 (2008) 185-198.

[26] H. Li, J. Wang, J. Fan, Analysis and modeling of particle velocities in micro-abrasive air jet, International Journal of Machine Tools and Manufacture 49 (2009) 850-858.

[27] D. Dehnadfar, J. Friedman, M. Papini, Laser shadowgraphy measurements of abrasive particle spatial, size and velocity distributions through micro-masks used in abrasive jet micro-machining, Journal of Materials Processing Technology 212 (2011) 137-149.

[28] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and non-spherical particles, Powder Technology 58 (1989) 63-70.

[29] H. Wadell, Volume, shape, and roundness of quartz particles, Journal of Geology 43 (1935) 250-280.

[30] M.C. Leu, P. Meng, E.S. Geskin, L. Tismeneskiy, Mathematical modeling and experimental verification of stationary water jet cleaning process, Journal of Manufacturing Science and Engineering 120 (1998) 571-579.

[31] N. Rajaratnam, S. Rizvi, P. Steffler, P. Smy, An experimental study of very high velocity circular water jets in air, Journal of Hydraulic Research 32 (1994) 461-470.

[32] N. Rajaratnam, C. Albers, Water distribution in very high velocity water jets in air, Journal of Hydraulic Engineering 124 (1998) 647-650.

[33] N. Rajaratnam, Turbulent Jets, Elsevier Scientific Publishing Company, Amsterdam, 1976.

[34] H.M.I. Clark, The influence of the flow field in slurry erosion, Wear 152 (1992) 223-240.

[35] M. Emamifar, CFD modelling of low pressure slurry jet, Master of Engineering Report, Department of Mechanical and Industrial Engineering, University of Toronto, 2012.

[36] S. Ashforth-Frost, K. Jambunathan, Effect of nozzle geometry and semi-confinement on the potential core of a turbulent axisymmetric free jet, International Communications in Heat Mass Transfer 23 (1996) 155-162.

57

[37] A. Guha, R.M. Barron, R. Balachandar, Numerical simulation of high-speed turbulent water jets in air, Journal of Hydraulic Research 48 (2010) 119-124.

[38] Y.M. Ali, J. Wang, Impact Abrasive Machining. In: M.J. Jackson, J.P. Davim (Eds.), Machining with Abrasives, Springer, West Lafayette (2011) 385-422.

[39] P. Slikkerveer, P. Bouten, H. Scholten, Erosion and damage by sharp particles, Wear 217 (1998) 237-250.

[40] G. Sheldon, I. Finnie, On the ductile behavior of nominally brittle materials during erosive cutting, Journal of Engineering for Industry 88 (1966) 387-392.

[41] H. Wensink, M.C. Elwenspoek, A closer look at the ductile-brittle transition in solid particle erosion, Wear 253 (2002) 1035-1043.

[42] T. Mineta, T. Takada, E. Makino, T. Kawashima, T. Shibata, 2009. A wet abrasive blasting process for smooth micromachining of glass by ductile-mode removal, Journal of Micro-mechanics and Micro-engineering 19 (2009) 015031 1-9.

[43] T. Matsumura, T. Muramatsu, S. Fueki, Abrasive water jet machining of glass with stagnation effect, CIRP Annals-Manufacturing Technology 60 (2011) 355-358.

[44] A. Ghobeity, D. Ciampini, M. Papini, An analytical model of the effect of particle size distribution on the surface profile evolution in abrasive jet micromachining, Journal of Materials Processing Technology 209 (2009) 6067-6077.

[45] A. Ghobeity, H. Getu, M. Papini, J.K. Spelt, Surface evolution models for abrasive jet micromachining of holes in glass and polymethylmethacrylate (PMMA), Journal of Micromechanics and Micro-engineering 17 (2007) 2175-2185.

[46] J.M. Fan, C.M. Fan, J. Wang, Flow dynamic simulation of micro abrasive water jet, Solid State Phenomena 175 (2011) 171-176.

[47] J. Humphrey, Fundamentals of fluid motion in erosion by solid particle impact, International Journal of Heat and Fluid Flow 11 (1990) 170-195.

[48] H. Uuemǒis, I. Kleis, A critical analysis of erosion problems which have been little studied, Wear 31 (1975) 359-371.

[49] T. Burzynski, M. Papini, Measurement of the particle spatial and velocity distributions in micro-abrasive jets, Measurement Science and Technology 22 (2011) 025104 1-15.

[50] N. Shafiei, H. Getu, A. Sadeghian, M. Papini, Computer simulation of developing abrasive jet machined profiles including particle interference, Journal of Materials Processing Technology 209 (2009) 4366-4378.

[51] J.M. Fan, C.M. Fan, J. Wang, Modeling the material removal rate in micro abrasive water jet machining of glasses, Advanced Materials Research 135 (2010) 370-375.

58

[52] G. Fowler, P.H. Shipway, I.R. Pashby, Abrasive water-jet controlled depth milling of Ti6A14V alloy-an investigation of the role of jet-workpiece traverse speed and abrasive grit size on the characteristics of the milled material, Journal of Materials Processing Technology 161 (2005) 407-414.

59

Chapter 3: Surface Evolution Models for Abrasive

Slurry Jet Micro-machining of Channels and Holes in

Glass

3.1 Introduction

Abrasive slurry jet micro-machining (ASJM) utilizes pressurized water to accelerate suspended

abrasive particles such as garnet or aluminum oxide (Al2O3). Material removal occurs by

mechanical erosion with little of the heating that can alter material properties [1]. Slurry jets have

relatively high resolution machining capabilities [2], allowing for the fabrication of features such as

micro-holes and channels without the use of patterned masks. Furthermore, the ready control of the

erosion rate through the operating parameters such as slurry jet flow rate or pressure, concentration,

impact angle and traverse speed simplifies the geometrical control of micro-machined features, such

as, for example, channels of varying depth or width.

A high pressure (70 MPa) abrasive slurry jet (ASJ) system for cutting metals, glass, ceramics,

polymers and composite materials was developed by Miller [3]. The system consisted of a pair of

plunger water pumps powered by compressed air connected to an abrasive storage vessel filled with

abrasive suspensions. The abrasive mixture was added to the pressurized water from the pumping

unit before the slurry exited the orifice. It was found that the particle mass flux was not constant in

the apparatus due to the development of a layer of unmixed particles at the bottom of the storage

60

vessel. Pang et al. [4] developed a similar ASJ apparatus for low pressure (2-14 MPa) micro-

machining applications using an air-driven water pump, an abrasive slurry tank and a shaker to

control the abrasive concentration. The micro-channels machined with this apparatus were found to

be wavy due to mechanical vibration.

Nouraei et al. [5] developed a low pressure (1-4 MPa) ASJ prototype utilizing compressed air to

drive the slurry and a slurry tank with a mixing propeller. However, due to the small size (i.e. 500

mL) of the pressurized cylinder used as the slurry tank, the total continuous machining time was

less than 5 min. Moreover, the spring-loaded seals in the setup were not rated for pressures higher

than 5 MPa, and as a result, micro-machining at higher kinetic energies was not feasible. The ASJ

system used in the present work overcomes the shortcomings of these previous devices.

Pang et al. [6] modeled the erosion rate, opening width and wall slope of ASJ machined channels in

glass using dimensional analysis and multi-variable regression of experimental data. While this

approach is practically very useful, it relies on data obtained from a relatively large set of

experimental trials. For the further development of ASJM technology, it is desirable to develop

models capable of predicting the shape and size of micro-machined features without recourse to

extensive testing. Surface evolution models have been developed primarily to predict the shapes of

masked features fabricated by abrasive air jets in brittle materials such as glass by ten Thije

Boonkkamp and Jansen [7], and Slikkerveer and in’t Veld [8]. Ghobeity et al. [9, 10] improved the

accuracy of these evolution models by using a "first-pass profile", and later, an analytical model

[11] to characterize the erosive efficacy across the mask opening when performing abrasive air jet

micro-machining (AJM). The surface evolution models were later modified by Getu et al. [12, 13]

to predict the profile of masked and unmasked AJM features in ductile materials.

61

Axinte and coworkers [14, 15] used the water jet footprint, similar to the first-pass profile described

above, and a surface evolution model in order to model abrasive high-pressure abrasive water jet

milling (AWJM) processes. The cross-sectional profile of the jet footprint was predicted for a wide

range of scan speeds. The velocity exponent, k, which relates the etching rate to the impact velocity,

was obtained from the shallow single pass profile of the jet foot print rather than from fundamental

measurements of erosion rate. Correction coefficients accounting for changes in etch rate with

depth were implemented in order to predict the jet foot print up to aspect ratios (channel centerline

depth/width) of 1.1. Such correction coefficients are not necessary in the case of ASJM, since the

standoff distance does not affect the depth and width of such micro-machined features [5].

Although brittle erosion is a common mode of material removal in the AJM, AWJM and ASJM of

glass, the fluid flow of the impinging jet and the particle trajectories and interactions with the target

substrate differ considerably among these three methods. In comparison with previous modeling

based on dimensional analysis [6], the use of the "first-pass profile" in conjunction with the surface

evolution model has the advantage of being independent of the properties of the machining

apparatus and target material. The applicability of such models to the ASJM of holes and channels

has not yet been investigated.

The present study examines the surface evolution modeling of micro-holes and channels in

borosilicate glass machined with ASJM. In particular, the effect of multi-pass machining, traverse

speed and the local front geometry on the accuracy of the surface evolution model were

investigated. To the knowledge of the author, this is the first application of surface evolution

models in ASJM.

62

3.2 Experiments

3.2.1 ASJM setup

As mentioned above, previous low pressure ASJM setups suffered from either a limited machining

time, a non-uniform particle mass flow rate, or problems associated with vibrations that resulted in

channels with a high waviness. Figure 3.1(a) shows a schematic of the low-pressure ASJM system

that was developed for the present study. The main components were an open-reservoir slurry

mixing tank (20 L, 280 mm diameter, 330 mm deep), a positive displacement slurry pump with

pulsation damper, and a sapphire orifice. The glass specimens were mounted on a computer-

controlled linear stage (KT- LSM100A, Zaber Technologies Inc., Vancouver, BC, Canada) that

could be moved at speeds of up to 7 mm/s. The main difference of the new ASJM setup compared

to the one presented previously by Nouraei et al. [5] is the replacement of the air driven system with

a slurry pump. The use a slurry pump in the new setup overcomes the shortcoming of the previous

setup, enhance the continuous machining time up to 1 h and allows a much greater control over the

operating parameters and experimental conditions.

The repeatability and uniformity of the particle concentration in the slurry was maintained by

continuously mixing the water and Al2O3 particles (10 and 25 μm nominal diameter, Comco Inc.,

CA, USA) using a DC motor attached to a three-blade, 100 mm diameter propeller turning at 180

rpm. The propeller was installed approximately 110 mm above the tank bottom in order to

maximize the mixing uniformity [16]. The positive displacement diaphragm slurry pump

(LCA/M9/11-DC, LEWA Inc., Leonberg, Germany) had an adjustable stroke length up to 15 mm

and a frequency of up to 3.5 Hz producing flow rates, Q, of 1-5 mL/s with a maximum pressure of 8

MPa. The pump is specially designed to resist erosion from highly abrasive slurries. During the

experiments, the flow rate was adjusted to within ±0.1% using a variable frequency drive (CFW-10,

63

WEG, Jaraguá do Sul, Brazil) while setting the stroke length to its maximum value of 15 mm. In

order to reduce the pressure and flow pulsations to within ±1% peak-to-peak, a pulsation damper

(FG 44969/01-9, Flowguard Ltd., Houston, TX, U.S.A.) was installed after the pump discharge

valve and pre-pressurized at up to 80% of the slurry pump’s operating pressure (1-8 MPa). To

minimize the transfer of vibrations, the orifice was mounted on a separate table and connected to

the pump with a flexible pipe (Fig. 3.1(a)). The orifice consisted of a 300 μm thick sapphire disk

with a hole diameter of 180 µm, mounted in a steel housing (KMT Waterjet, KS, USA; Fig. 3.1(b)).

In the earlier work of Nouraei et al. [5], for ease of assembly and to prevent any sudden contraction

in the flow field, the orifice was installed backwards relative to the orientation suggested by the

manufacturer for AWJs. The orientation was adjusted to forwards for the present study, since it

provides a narrower jet diameter under comparable conditions, thus decreasing the minimum

feature size that could be machined. In the backwards configuration, the orifice discharge

coefficient (ratio of the actual mass flow rate at the orifice exit to that of an ideal orifice) was

approximately 0.98 [5], while in the forwards configuration it was measured to be 0.60±0.03 using

a microscope attached to a digital camera (field of view of 1.71×1.71 mm). Thus the actual slurry

jet diameter was 140 µm in the present, while it was 180 µm in [5].

In order to minimize particle sedimentation, the Reynolds number of the flow approaching the

orifice was maintained above 1200 using a stainless steel exit tube (1.7 mm inner diameter, 300 mm

long) positioned within the flexible pipe so that it butted against the orifice as shown in Fig. 3.1(b)

[17]. Nevertheless, a relatively small amount of particle sedimentation did occur within the piping

system, particularly at junctions between fittings. As a result, the mean concentration exiting the jet

was consistently 8% less than the nominal slurry concentration of 7.5 g/L in the mixing tank.

64

Nevertheless, this reduction was constant over operating periods of up to 1 h, and thus did not

negatively affect the repeatability of the micro-machined features.

In contrast to the evolution of channel profiles, the evolution of the hole profiles was extremely

sensitive to minute deviations in the incident angle of the jet. This sensitivity extended to the

symmetry of the drainage flow from the hole, and it was impossible to machine symmetric holes

unless the target was mounted horizontally. The arrangement of Fig. 3.1 was thus modified for the

hole machining experiments using a 90° elbow so that the slurry jet was vertical (Fig. 3.1(c)). In

addition, a three-point level was used to connect the target substrate directly to the orifice-end cap

unit in order to minimize misalignment.

65

Slurry

Propeller

Pulsation damper

Pressure gauge

Safety valve

Flexible pipe Orifice

Target Linear stage

Drainage

DC motor

Diaphragm pump

z

x

y

Exit tube

AC motor

(a)

Exit tube

Orifice

Tube end cap

Flow direction

Flexible pipe

(b)

(c)

Figure 3.1: (a) Schematic of the abrasive slurry jet apparatus, (b) orientation of orifice installation, and (c) orientation of orifice in micro-hole machining experiments (not to scale) [18].

66

3.2.2 Characterization of performance of ASJM setup

Figure 3.2 shows that the flow rate was a linear function of the pump frequency as expected, but

that it varied with the Al2O3 particle size and was independent of slurry concentration for a given

particle size. The flow rate was measured as the average of 5 60-second samples, taken at 2 min

intervals. The flow rate of the 10 μm slurry was 28% less than that of water at any stroke frequency,

while it was 59% less in the case of the 25 μm slurry. As illustrated in Fig. 3.3, this was due to

leakage during the suction and discharge cycles of the pump, caused by abrasive particles deposited

at the interface between the ball and the seat. It was found that the particle concentration in the

slurry had no effect on the amount of leakage, and that the flow rate remained constant for the

duration of all the experiments and was highly repeatable (Fig. 3.2).

Qwater = 1.44fsR² = 0.99

Q10 µm-slurry = 1.03fsR² = 0.98

Q25 µm-slurry = 0.59fsR² = 0.97

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Flow

rate

, Q(m

l/s)

Stroke frequency , fs (Hz)

Water 0.25 wt% 0.5 wt% 0.75 wt% 1 wt%

Figure 3.2: Flow rates of water, 10 and 25 µm nominal diameter Al2O3 slurries of various concentrations as a function of pump stroke frequency. Each point is the average of 5 measurements, amongst which the variability was less than 8% of the mean.

67

Leakage

z

x

y

Valve seat

Diaphragm

Ball valve

Valve chamber

Particle deposition site

Suction port

Discharge port

Flow Direction

Figure 3.3: Schematic of the suction and discharge ports of the slurry pump illustrating leakage due to a trapped particle (not to scale).

The effect of the pulsation damper on the uniformity of the channel cross-sectional profiles was

investigated by machining 20 mm long single-pass channels under similar operating conditions, as

illustrated in Fig. 3.4. At a nominal slurry flow rate of 1.7 mL/s without the damper, the pump

operating pressure fluctuated considerably between 3.5 and 7.5 MPa during each stroke cycle, and

the apparatus suffered from substantial vibration. However, with the damper pre-pressurized to 3.2

MPa, the pump pressure was measured to be 4±0.1 MPa and no noticeable pump or orifice

vibration was detected. Without the damper, the higher average and peak pressures (and particle

velocities) increased the channel depth and width by 64% and 16%, respectively, and the channel

edge definition (i.e. at the transition from the channel wall to the unmachined flat surface) was not

as sharp as that of the machined channel with the damper, as shown in Fig. 3.4(a) and (b). The

poorer channel edge resolution was probably due to the pump and orifice vibration caused by the

pressure and flow fluctuations. The variation in the depth and width of the channels along their

68

length was less than 3%, as shown in Fig. 3.4(c) and (d), both with and without the damper,

indicating that the pressure fluctuation frequency was sufficiently low as to not cause waviness in

the channel depth.

(a) (b)

225

250

275

300

325

80

100

120

140

160

180

0 5 10 15 20 25

Wid

th (µ

m)

Dep

th (

µm)

Length along scanning direction (mm)

Depth Width

200

220

240

260

280

300

0

20

40

60

80

100

0 5 10 15 20 25

Wid

th (µ

m)

Dep

th (

µm)

Length along scanning direction (mm)

Depth Width

(c) (d)

Figure 3.4: Scanning electron micrographs, and depth and width along the length of blasted channels: (a) and (c) without pulsation damper; and (b) and (d) with pulsation damper. Experimental conditions: 0.765 g/min 10 µm Al2O3, 1.7 mL/s flow rate, 0.1 mm/s traverse speed, 15 mm standoff. Solid and dashed lines are to guide the eye.


All machining experiments were conducted on 100×50×3 mm thick borosilicate glass plates

(Borofloat®, Schott Inc., NY, USA) having a Young’s modulus of 63 GPa, Poisson’s ratio of 0.2,

69

fracture toughness of 0.76 MPa m1/2

, and a Vickers hardness of 5.4 GPa [19]. The experiments were

conducted at varying slurry flow rate, Q, target traverse speed, vs, particle concentration, C, and jet

impact angle, θ (Fig. 3.5), as shown in Table 3.1. The orifice to target standoff distance, do, along

the orifice centerline was maintained constant at 15 mm.

Table 3.1: Process parameters used in the machining of holes, channels and the measurement of erosion rates.

Micro-hole Micro-channel Erosion rate Slurry flow rate, Q (mL/s) 1.5 2.2 2.2 Traverse speed, vs (mm/s) 0 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 1 Mixing tank particle concentration, C (wt %) 0.25, 1 0.75 0.75

Jet impact angle, θ (deg) 90 90 15, 30, 45, 60, 75, 90

The required amount of abrasive for each experiment was taken from the original container using a

standard quartering technique to ensure an unbiased sampling of the powder sizes (ASTM C702-98,

[20]). The slurry concentration was measured before each set of experiments by collecting 10 slurry

samples of 50 mL each from the orifice at 15 s intervals. The samples were passed through filter

paper in order to collect the abrasive particles and then the remaining water was evaporated in a

drying oven prior to being weighed. For a nominal particle concentration of 7.5 g/L in the mixing

tank (i.e. 0.75 wt %), the variability in the particle dose delivered to the target substrate within a

given experiment utilizing 10 L of slurry was less than 3% (after about 75 min of machining).

An optical profilometer having a lateral resolution of 426 nm and depth resolution of 16 nm

(ST400, Nanovea Inc., CA, USA) was used to measure the cross-sectional profiles of the machined

holes and channels. The centerline depths of the channels, Cd, and holes, Hd, were measured at the

centerline, while the locations of the channel and hole edges, used to define channel width, Cw, and

70

the hole diameter, Hw, were defined as the points corresponding to a 10% decrease in the absolute

slope measured using five consecutive digitized profile points, each 2 µm apart, as shown in Fig.

3.6. The channel wall slope was calculated using a linear fit of the first 5 digitized profile points on

the sidewall above the half-depth, each 2 µm apart (Fig. 3.6). Both the location of the channel edge

and the calculated side wall slope were found to be insensitive to the number of points used in this

linear fit (less than 4% difference between 4 and 10 points).

As mentioned previously, Fig. 3.4(c) and (d) indicate that the depth and width of the channels

typically varied by less than 3% along the channel length. The channel-to-channel repeatability was

assessed by replicating some of the holes and channels three times. It was found that the variation in

the measured dimensions of the replicate features was always less than approximately 5%.

θ

Orifice

Target

θ = 90°

do = 15 mm

z

x y

Figure 3.5: Schematic of jet orientation during erosion rate measurements (not to scale; depth of channel exaggerated for clarity) [5].

71

Dep

th

Cw , Hw

(0,0)

x, ry

z

(-Hw /2,0) (Hw /2,0)Cd ,HdCd /2

(0,0)

x, r

(-Cw /2,0) (Cw /2,0)

y

z(0,Cd)(0,Hd)

Figure 3.6: Schematic of channel or hole cross-sectional profile showing the definition of channel centerline depth and width (Cd, Cw), hole depth and diameter (Hd, Hw), and side wall slope.

3.3 Modeling of ASJM channels and holes

3.3.1 Erosion rate due to ASJM

The erosion rates (mass of removed material per dry mass of abrasive particles) of the borosilicate

glass as a function of the impact angles shown in Table 3.1 were measured by machining channels

using a relatively high traverse speed of 1 mm/s in order to maintain the resulting channel aspect

ratios (depth/width) below 0.06. Such shallow channels and sidewall slopes ensured that the local

and global particle impact angles were approximately equal. The global impact angle of the jet, θ,

was varied in the plane perpendicular to the direction of linear stage motion as shown in Fig. 3.5,

resulting in asymmetrical channels. Figure 3.7 shows the normalized erosion rate as function of

impact angle using 10 and 25 µm nominal diameter Al2O3 particles; i.e. the erosion rate at a given

angle divided by that at θ = 90°. The trend of increasing normalized erosion rate with increasing

impact angle suggests that brittle erosion was dominant under these conditions. The erosion rate as

a function of impact angle relation was obtained previously for 25 µm particles [5]. However the

experiments were repeated in the present study since the orifice orientation and jet flow rate was

different from that of the previous work.

72

E*r = (sin (θ))1.69

R² = 0.98

E*r = (sin (θ))1.55

R² = 0.97

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Nor

mal

ized

ero

sion

rate

, E* r

sin (θ)

10 25

µm Al2O3µm Al2O3

Figure 3.7: Normalized erosion rate (erosion rate at θ /erosion rate at 90°) as a function of impact angle. Error bars represent ±1 standard deviation for 3 measurements. Experimental conditions: 1 g/min 10 and 25 µm Al2O3.

3.3.2 Surface evolution modeling of micro-channels

Ten Thije Boonkkamp and Jansen [7] developed an analytical surface evolution model for

predicting the cross-sectional profile of features micro-machined in brittle materials using air driven

abrasive jets. Their model expressed the speed of surface erosion at a given point on the profile in

terms of the incident particle flux and the component of particle velocity in the direction of the local

normal to the surface at that point. Ghobeity et al. [9] introduced the use of a shallow "first-pass

profile" as a means for characterizing the erosive efficacy distribution, E(x), across the air-abrasive

jet, i.e. the total erosive power delivered to a given point on the channel cross-section over one pass

of the jet. Although there are significant differences in the distribution of particles and local impact

angles in the blast zone of air jets and slurry jets, it was of interest to assess the applicability to

ASJM of the approach used by Ghobeity et al. [9] to predict the cross-sectional profiles of channels

made with unmasked air abrasive jet machining.

73

Briefly, for brittle materials, the profile evolution of a two-dimensional channel by an abrasive jet

was expressed as [9]

( ) 2 2, ,1 0

k

t xz E x z−

− + = (3.1)

where z,t and z,x are the partial derivatives of the depth, z, with respect to the transverse coordinate,

x, (Fig. 3.6) and time, t, respectively. The velocity exponent, k, expresses the dependence of the

erosion rate on particle velocity, and can be obtained from fundamental erosion rate measurements

conducted using very shallow channels or holes [5]. The best fit velocity exponents, k, for 10 and

25 µm were 1.69 and 1.55 respectively, as shown in Fig. 3.7. Although the trajectories and impact

velocities of particles in ASJM and AJM are quite different, the ASJM k values (k =1.3) were fairly

close to those obtained in AJM (k =1.43) [5], probably because k is a relatively weak function of the

particle velocity, as shown in ref. [21]. A time constant, T, was defined as the time required to

propagate the flat surface at x = 0 over a characteristic length, L, such that Eq. (3.1) can be modified

to be non-dimensional and expressed as

( )* ** * * * 2 2, ,

1 0k

t xz E x z

− − + = (3.2)

where z* = z / L, x* = x / L and t* = t / T are the non-dimensional depth, channel width and time,

respectively. The time constant, T, essentially a measure of the erosion rate at the center of a very

shallow channel, was extrapolated from the measured center depth of the first pass channel.

Following the previous work of Ghobeity et al. [9] for abrasive air jets, the characteristic length, L,

was chosen to be equal to the orifice to surface standoff distance (i.e. do = 15 mm).

74

The dimensionless center depth of the channel after the first pass of the jet, z1*, is equal to the

dimensionless time, t1*, to reach that depth (i.e. z1

* = t1*) [22]. Hence, if the etch rate on the

centerline remains constant with depth, the dimensionless time for n passes is then

* *1nt nz= (3.3)

The non-dimensional erosive efficacy function, E*(x*), can be obtained by solving the following

equation [9],

( ) ( )* ** * * * 2 2

, ,1

k

t xE x z z= + (3.4)

with

( ) ( ) ( )*

* * * * **

*,

, ,0i i

t i

z x t z xz

t−

= (3.5)

( ) ( ) ( )*

* * * * * *1*

* *,1

, ,i i

x ii i

z x t z x tz

x x+

+

−=

− (3.6)

where xi* and zi

* are non-dimensional coordinates obtained along the experimental first-pass profile.

Equations (3.5) and (3.6) are the first order approximation to the time and space derivatives in Eq.

(3.4), respectively. To obtain the erosive efficacy, E*(x*), Eq. (3.4) was solved using one-sided first-

order approximations to these derivatives with a uniform spatial step size of 1.33 ×10-4

(2 µm).

This ensured that numerical errors due to the use of first-order approximations to the derivatives

were negligible [9]. A non-dimensional, normalized polynomial equation (least squares method,

75

MATLAB version 7.12.0, curve fitting tool box, Mathworks, Natick, MA, USA) was fitted to the

resulting E*(x*), and then used in Eq. (3.2) to solve the surface evolution equation.

3.3.3 Surface evolution modeling of micro-holes

The governing partial differential equation for predicting the hole profile in brittle materials was

adapted from the model of ref. [10] by replacing x in Eq. (3.2) with the radial coordinate, r, to give

( )* ** * * * 2 2, ,

1 0k

t rz E r z

− − + = (3.7)

where z*,t* and z*

,r* are the normalized partial derivatives of the normalized depth, z*, with respect to

the normalized radial coordinate, r*, (Fig. 3.6) and time, t*, respectively. The characteristic length,

L, for normalizing the radial coordinate and the profile depth was again selected to be equal to the

standoff distance of 15 mm. The characteristic time, T, is thus the time required to erode the target

at r = 0 to a depth of 15 mm, assuming a constant etch rate. E*(r*) is the normalized erosive efficacy

distribution seen by the exposed target surface and can be obtained using a procedure that is

analogous to that outlined for channels in Eqs. (3.4) - (3.6).

3.4 Results and discussion

3.4.1 Prediction of ASJ micro-channel profiles using the first-pass results

The first-pass profile of a channel machined at 0.5 mm/s traverse speed was used to determine

E*(x*) as described in Section 3.3.2 using a least-squares fit to a 9th order polynomial (R2 ≈ 0.99):

76

( ) 9 8 7 6 5 4 3 2 1* * * * * * * * * * *1 2 3 4 5 6 7 8 9 1 0E x a x a x a x a x a x a x a x a x a x a= + + + + + + + + + (3.8)

with

17 81 6

16 52 7

14 23 8

12 -14 9

10 -35 10

2.58 10 1.31 10

1.50 10 3.09 10

3.54 10 3.77 10

4.40 10 1.80 10

3.14 10 1.29 10

a aa aa aa aa a

= − × = ×

= × = − ×

= − × = ×

= × = − ×

= − × = − ×

Once E*(x*) was determined in this manner, Eq. (3.2) with k = 1.69 (Fig. 3.7) was solved

numerically with the initial condition of z*(x*, t* = 0) = 0, using the method of lines technique

implemented in Mathcad 14 (Parametric Technology Corp., Needham, MA, USA). In order to

obtain a converged and accurate numerical solution, 500 time and space steps were used.

Multi-pass channels were machined by scanning the jet repeatedly over the target substrate at 0.5

mm/s traverse speed. Figure 3.8 compares these multi-pass machined channel cross-sectional

profiles with the predictions of the solution of Eq. (3.2) using dimensional coordinates (i.e. x = x* do

and z = z* do). The surface evolution predictions were within 8% of the measured depth at any

distance x from the centerline for aspect ratios (depth/width) of up to 1.5.

77

-400

-375

-350

-325

-300

-275

-250

-225

-200

-175

-150

-125

-100

-75

-50

-25

00 20 40 60 80 100 120 140 160

Dep

th (µ

m)

Width (µm)

P1

P2

P12

P10

P8

P6

P4

P20

P18

P16

P14

Figure 3.8: Comparison of predicted (solid lines) and measured (symbols) channel cross-sectional profiles for aspect ratio <1.5. Half of the symmetric profile is shown. Experimental conditions: 1 g/min 10 µm Al2O3, traverse speed of 0.5 mm/s, number of nozzle passes shown above each curve.

Rather than using multiple passes, channel depth can also varied by scanning the jet at lower

traverse speeds to increase the particle dose delivered to the surface. If no other factors are

involved, the depth should be directly proportional to the dose; i.e. the erosion rate should be

constant. Figure 3.9(a) shows a series of single-pass channels machined at traverse speeds between

0.5 and 0.05 mm/s. Although there was a ten-fold increase in particle dose, the depth only increased

by a factor of 6 (Fig. 3.9(b)). This reduction in erosion rate was due to the increased slope of the

leading edge of the jet footprint; i.e. the slope given by tan-1(increment in channel depth for a given

78

pass/jet diameter) increased from approximately 8° to 41° as the traverse speed decreased from 0.5

to 0.05 mm/s. The increase in the leading edge slope reduced the local impact angle of particles

along the leading edge, α, by 40% (from 82° to 49°), and as a result, the erosion rate decreased

nonlinearly with traverse speed. Similar behavior was seen in ref. [5]. This decrease in the local

erosion rate with decreasing scan speed can be estimated using the measured angular dependence of

the erosion rate of Fig. 3.7, as was done in [5]. If the time constant, T, is multiplied by 1/sin (α)1.69,

the corrected erosion rate is obtained for different traverse speeds. Figure 3.10 illustrates that

correcting the erosion rate in this manner for 10 passes at 0.5 mm/s results in a similar profile to a

single-pass channel machined at a traverse speed of 0.05 mm/s. Although the traverse speed was

varied by a factor of 10, the difference between the side wall slopes was less than 12%. It is

hypothesized that using such corrections, the profiles of channels machined at any traverse speed

can be predicted by utilizing a shallow first pass profile obtained at a high scan speed.

-180

-160

-140

-120

-100

-80

-60

-40

-20

00 20 40 60 80 100 120 140 160 180

Dep

th (µ

m)

Width (µm)

0.05 mm/s 0.1 mm/s 0.2 mm/s

0.3 mm/s 0.4 mm/s 0.5 mm/s

0

20

40

60

80

100

120

140

00.10.20.30.40.50.6

Dep

th,C

d(µ

m)

Traverse speed,vs (mm/s) (a) (b)

Figure 3.9: (a) Comparison of first-pass channels machined at various traverse speeds, and (b) depth of single-pass channel versus traverse speed. Solid line is to guide the eye. Half of the symmetric profile is shown. Experimental conditions: 1 g/min 10 µm Al2O3.

79

-200-180-160-140-120-100-80-60-40-20

00 20 40 60 80 100 120 140 160

Dep

th (µ

m)

Width (µm)

1 Pass at 0.05 mm/s

10 Pass at 0.5 mm/s

Corrected 10 Pass at 0.5 mm/s

Figure 3.10: Comparison of measured single-pass profile at 0.05 mm/s, 10-pass channel and corrected 10 pass channel machined at 0.5 mm/s. Half of the symmetric profile shown. Experimental conditions: 1 g/min 10 µm Al2O3.

To test this hypothesis, the 0.5 mm/s first-pass profile was used to predict the profiles of high aspect

ratio multi-pass channels machined at 0.05 mm/s, implementing the leading edge slope correction

discussed above. Figure 3.11 indicates that the profile predictions are reasonably good up to an

aspect ratio close to 5, with a maximum difference between the measured and predicted center

depths of less than 7%.

Consistent with ref. [5], the number of passes did not significantly affect the width, Cw, of the

machined channels, which was approximately 2 times the jet diameter when machining at 0.5 mm/s

(Fig. 3.8) and 2.5 times the jet diameter when machining at 0.05 mm/s (Fig. 3.11).

80

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

00 20 40 60 80 100 120 140 160 180

Dep

th (µ

m)

Width (µm)

P1

P2

P4

P6

P8

P10

P12

P14

Figure 3.11: Comparison of predicted (solid lines) and measured channel profiles for aspect ratios >1. Half of the symmetric profile is shown. Experimental conditions: 1 g/min 10 µm Al2O3, traverse speeds of 0.05 mm/s. The non-dimensional erosive efficacy function, E*(x*), measured at 0.05 mm/s was modified to account for the reduced erosion caused by the large slope at the leading edge of the jet.

3.4.2 Prediction of ASJ micro-hole profiles

A series of holes were machined with exposure times from 30 to 180 s using 10 µm Al2O3 particles,

as shown in Fig. 3.12(a). The ratio of the jet diameter to the hole diameter was approximately 0.65.

As the depth of the machined hole increased, its diameter at the opening enlarged due to the

secondary erosion brought about by the slurry backflow from its bottom. Figure 3.12(b) shows that

the center depth, Hd, increased nonlinearly, in contrast to the linear dependence of depth with

particle dose (or exposure time) seen with channels at high scan speeds (Fig. 3.8). As discussed

81

below, this was attributable to the high degree of confinement of the return flow within a hole,

which in turn progressively increased the drag on the 10 µm incident particles, reducing their

impact velocity. This dependence of erosion rate on time prevented direct application of the first-

pass profile approach that was used to predict channel cross-sectional profiles; i.e. Eqs. (3.2) and

(3.7) assume a constant centerline erosion rate.

(a)

Hd = 4.93t

0

200

400

600

800

1000

0 30 60 90 120 150 180 210

Dep

th o

f hol

e,H

d(µ

m)

Exposure time, t (s) (b)

Figure 3.12: (a) Profile development and (b) depth of micro holes, at various exposure times. Experimental conditions: 0.23 g/min 10 µm Al2O3. Line represents linear erosion rate based on depth of 30 s hole.

Figure 3.13(a) illustrates that the relationship between hole depth and machining time was linear to

a larger depth with 25 µm Al2O3 particles compared to 10 µm particles (Fig. 3.12(b)), since the

effect of drag on these larger particles was smaller [23, 24]. Therefore, the hole profiles machined

with 25 µm particles were predicted using the erosive efficacy, E*(r*), derived from the best-fit to

30 s

60 s

90 s

120 s

150 s

180 s

82

the 60 s hole profile using the procedure outlined in Section 3.3.3. Equation (3.7) was solved

numerically using the initial condition of z*(r*, t* = 0) = 0, and k = 1.55. Figure 3.13(b) compares

the measured and predicted hole profiles of the solution of Eq. (3.7) using dimensional coordinates

(i.e. r = r* do and z = z* do). The center depth predictions were within 14% of the measured values,

for aspect ratios to 0.9 (400 µm). For larger aspect ratios, as implied by Fig. 3.13(a), the error in the

predicted profiles is expected to continually increase. An experimental correction factor based on

Figs. 3.12(a) and 3.13(a) could be used to account for decreased etch rate over exposure time,

however that would defeat the purpose of the proposed surface evolution modeling approach to be

independent of the properties of the machining apparatus and target material due to the use of first

pass for micro-channels and shallow holes for micro-holes. In order to account for decreased etch

rate over exposure time, more complex models are needed. Such a model could be developed with

the aid of CFD analysis of flow velocities and particle trajectories inside the hole profile, and is

presented in detail in Chapter 4.

83

Hd = 1.83t

0

200

400

600

800

1000

1200

0 60 120 180 240 300 360 420 480 540 600 660

Dep

th o

f hol

e,H

d(µ

m)

Expousre time, t (s) (a)

-700

-600

-500

-400

-300

-200

-100

00 50 100 150 200 250

Dep

th (µ

m)

Width (µm)

60 s120 s180 s240 s300 s

(b)

Figure 3.13: (a) Depth of machined holes versus exposure time and (b) Comparison of predicted (solid lines) and measured hole profiles. The 60 s profile was used to infer erosive efficacy. Half of the symmetric profile shown. Experimental conditions: 0.23 g/min 25 µm Al2O3. A 60 s micro-machined hole was used to fit E*(r*) = 3.03×10

15 r* 9-1.75×10

14 r* 8+2.98×10

12 r* 7

+8.04×108 r* 6-

3.88×108 r* 5+9.46×10

5 r* 4+1.94×10

4 r* 3 +1.52×10

1 r* 2- 9.16×10

-2 r*-7.33×10

-3, R2 ≈ 0.99.

84

3.5 Conclusions

The fundamental erosion rate of the borosilicate glass as a function of impact angle was measured

using a slurry of water mixed with a low concentration of 10 µm and 25 µm nominal diameter

aluminum oxide particles. This erosion rate-impact angle relationship was used in an existing

surface evolution model, originally developed for abrasive air jet micromachining, to predict the

development of cross-sectional profiles of micro-channels and holes machined in borosilicate glass

using abrasive slurry jet micromachining (ASJM). The center-line depth, side wall slope and shape

of the micro-channels were accurately predicted as a function of the machining time up to an aspect

ratio of 5 with a maximum error of 7%. The predicted cross-sectional profiles of micro-holes

machined for various lengths of time with for 25 µm particles were also in reasonable agreement

with a maximum error of 14% for aspect ratios close to 1. The development of profiles of holes

made with 10 µm particles could not be predicted because of the relatively large drag force on these

smaller impacting particles as they penetrated the highly confined flow within the holes. The results

demonstrated for the first time that the size and shape of features machined using ASJM can be

accurately predicted as a function of machining time using surface evolution models.

The low-pressure ASJM apparatus used to manufacture the channels and holes was based on an

open, stirred slurry tank feeding a slurry pump fitted with a pulsation damper. It was capable of

producing micro-channels of low waviness, with a depth and width variation along their length of

less than 3%, and a channel-to-channel variability of less than 5% in depth. The open tank

arrangement facilitated effective mixing of the slurry and continuous operation for relatively long

periods of time. Erosion of pump components was negligible with 10 µm aluminum oxide particles,

but was more significant with 25 µm particles which limited pump operation to approximately 120

h before valve components needed replacement.

85

3.6 References

[1] H.T. Liu, Waterjet technology for machining fine features pertaining to micro-machining, Journal of Manufacturing Processes 12 (2010) 8-18.

[2] H. Nouraei, A. Wodoslawsky, J.K. Spelt, M. Papini, Micro-machining using an Abrasive Slurry Jet , Poster, Wear of Materials, 18th International Conference, Philadelphia, USA, (April 3-7, 2011).



[5] H. Nouraei, A. Wodoslawsky, M. Papini, J.K. Spelt, Characteristics of abrasive slurry jet micro-machining: a comparison with abrasive air jet micro-machining, Journal of Materials Processing Technology 213 (2013) 1711-1724.

[6] K. Pang, T. Nguyen, J. Fan, J. Wang, Modeling of the micro-channelling process on glasses using an abrasive slurry jet, International Journal of Machine Tools and Manufacture 53 (2012) 118-126.

[7] J.H.M. ten Thije Boonkkamp, J.K.M. Jansen, An analytical solution for mechanical etching of glass by powder blasting, Journal of Engineering Mathematics 43 (2002) 385-399.

[8] P.J. Slikkerveer, F.H. in't Veld, Model for patterned erosion, Wear 233 (1999) 377-386.

[9] A. Ghobeity, T. Krajac, T. Burzynski, M. Papini, J.K. Spelt, Surface evolution models in abrasive jet micro-machining, Wear 264 (2008) 185-198.

[10] A. Ghobeity, H. Getu, M. Papini, J.K. Spelt, Surface evolution models for abrasive jet micro-machining of holes in glass and polymethylmethacrylate (PMMA), Journal of Micro-mechanics and Micro-engineering 17 (2007) 2175-2185.

[11] A. Ghobeity, D. Ciampini, M. Papini, An analytical model of the effect of particle size distribution on the surface profile evolution in abrasive jet micro-machining, Journal of Materials Processing Technology 209 (2009) 6067-6077.

[12] H. Getu, A. Ghobeity, J.K. Spelt, M. Papini, Abrasive jet micro-machining of polymethylmethacrylate, Wear 263 (2007) 1008-1015.

[13] H. Getu, A. Ghobeity, J.K. Spelt, M. Papini, Abrasive jet micro-machining of acrylic and polycarbonate polymers at oblique angles of attack, Wear 265 (2008) 888-901.

86

[14] D.A. Axinte, D.S. Srinivasu, J. Billingham, M. Cooper, Geometrical modeling of abrasive waterjet footprints: a study for 90° jet impact angle, CIRP Annals- Manufacturing Technology 59 (2010) 341-346.

[15] M.C. Kong, S. Anwar, J. Billingham, D.A. Axinte, Mathematical modeling of abrasive waterjet footprints for arbitrarily moving jets: Part I-single straight paths, International Journal of Machine Tools and Manufacture 53 (2012) 58-68.

[16] N.N. Dutta, V.G. Pangarkar, Critical impeller speed for solid suspension in multi-impeller three phase agitated contactors, The Canadian Journal of Chemical Engineering 73 (1995) 273-283.

[17] M.A. Kölpinar, M. Göğüs, Critical flow velocity in slurry transporting horizontal pipelines, Journal of Hydraulic Engineering 127-9 (2001) 763-771.

[18] H. Nouraei, K. Kowsari, M. Papini, J.K. Spelt, Prediction of machined surface evolution in abrasive slurry jet micro-machining, Wear of Materials, 19th International Conference, Portland, USA, (April 14-18, 2013).

[19] T.E. Wilantewicz, J.R. Varner, Vickers indentation behavior of several commercial glasses at high temperatures, Journal of Materials Science 43 (2008) 281-298.


[21] T. Burzynski, M. Papini, Measurement of the particle spatial and velocity distributions in micro-abrasive jets, Measurement Science and Technology 22, (2011) 025104 1-15.

[22] S. Ally, J.K. Spelt, M. Papini, Prediction of machined surface evolution in the abrasive jet micro-machining of metals, Wear 292-293 (2012) 89-99.

[23] H.T. Liu, Hole drilling with abrasive fluid jets, International Journal of Advanced Manufacturing Technology 32 (2007) 942-957.

[24] J. Humphrey, Fundamentals of fluid motion in erosion by solid particle impact. International Journal of Heat and Fluid Flow 11 (1990) 170-195.

87

Chapter 4: Combined Numerical-analytical Modeling

of Abrasive Slurry Jet Micro-machined Holes

4.1 Introduction

Abrasive slurry jet micro-machining (ASJM) can erode practically any material using a focused

pressurized jet of water to accelerate suspended abrasive particles such as garnet, silicon carbide

(SiC), tungsten oxide (WO3) and aluminum oxide (Al2O3) toward the target substrate. Material

removal occurs by mechanical erosion of impacting particles without altering the specimen material

properties. In ASJM, the geometrical control of micro-machined features can easily be controlled

through the operating parameters such as slurry jet flow rate (i.e. pressure), amount of particle

concentration, impact angle and machining traverse speed. During the past decade, it has been

shown that low-pressure ASJM is a promising technology that can be used in the manufacturing of

micro-electromechanical and micro-fluidic devices [1-3]. For the further development of ASJM

technology, it is essential to develop models capable of predicting the shape and size of micro-

machined features. Surface evolution models have been originally developed to predict the profile

of features fabricated by abrasive air jet micro-machining (AJM) in which the particles are carried

by air instead of water [4-7]. Nouraei et al. [3] compared the mechanics of the erosion process in

AJM and ASJM and concluded brittle erosion was the main mode of material removal in both

ASJM and AJM. However, it was determined that ASJM is a much more complicated process than

AJM in the sense that the particle trajectories are significantly influenced by the fluid flow

88

behaviour as the jet impinges the target. In another study, Nouraei et al. [8] investigated the ability

of an existing AJM model in predicting the profiles of ASJ machined holes and channels in

borosilicate glass. It was shown that a cross-sectional profile of a shallow channel can be used to

characterize the slurry jet erosion pattern for the surface evolution model and the developed model

accurately predicted the profiles of micro-channels having aspect ratios (depth/width) of up to 5

with a maximum error of 7%. In spite of this, the existing surface evolution model was incapable of

predicting the profile of holes characterized with the cross-sectional profile of a shallow hole

machined with 10 µm Al2O3 particles due to nonlinearity trend of depth as a function of machining

time. This was due to the progressively increased drag on the incident particles as the hole depth

increased which in turn reduces the impact velocities. As a result, Nouraei et al. [8] used larger

Al2O3 particles (25 µm nominal diameter) in machining of holes since the effect of drag on these

larger particles was smaller and the relationship between hole depth and machining time was linear

to a larger depth. The predicted profiles of holes were also in reasonable agreement with a

maximum error of 14% for aspect ratios close to 1.

In summary, the existing surface evolution model that utilizes the shallow profile approach was

incapable of accounting for changes of flow filed as function of machining time (i.e. depth).

Therefore, the objective of the present study was to characterize the changes in flow field and

particle trajectories of the impinging jet as function of machining time through the use of CFD

models and improve the accuracy of surface evolution model in predicting profiles of holes

independent of particle size.

89

4.2 Experiments

4.2.1 ASJM system

Micro-holes machining experiments with a high degree of repeatability were conducted using the

low-pressure ASJM system developed by Nouraei et al. [8]. The main components of the system as

illustrated in Fig. 4.1 (a) were an open-reservoir stirred slurry tank, a positive displacement slurry

pump (LCA/M9/11-DC, LEWA Inc., Leonberg, Germany) with pulsation damper (FG 44969/01-9,

Flowguard Ltd., Houston, TX, USA), a 840 µm thick sapphire orifice (KMT Waterjet, KS, USA),

and a computer controlled linear stage (KT-LSM100A, Zaber Technologies Inc., Vancouver, BC,

Canada) to adjust the target substrate relative to the orifice. Following the procedure described by

Nouraei et al. [8], the discharge coefficient (ratio of the actual mass flow rate at the orifice exit to

that of an ideal orifice) for 180 µm orifices used in this study was measured to be 0.68±0.05. Thus

the actual slurry jet diameter was approximately 150 µm. The evolution of the hole profiles was

extremely sensitive to minute deviations in the incident angle of the jet as shown by Kowsari et al.

[9]. Accordingly, the three-point level of Fig. 4.1(b) was used to connect the orifice perpendicular

to the target substrate to minimize misalignment up to 0.2°. During the experiments, the machining

time on target was controlled through a manual shutter that intercepts the impinging jet.

90

Slurry

Propeller

Pulsation damper

Specimen

Linear stage

DC motor

Slurry pump

Orifice setup

(a)

Exit tubeOrifice

Slurry flow

Three-point level

Specimen

r

z

(b) Figure 4.1: (a) Schematic of the ASJM system and (b) three-point level used to connect the orifice to specimen (not to scale).

4.2.2 Micro-hole machining tests

Micro-holes were machined on 50×50×3 mm plates of borosilicate glass (Borofloat®, Schott Inc.,

NY, USA; Young’s modulus of 63 GPa, Poisson’s ratio of 0.2, fracture toughness of 0.76 MPa

m1/2, and a Vickers hardness of 5.4 GPa), due to vast use of this material in small-scale devices such

as micro-fluidic platforms. The slurry flow rate was maintained at 1.7 mL/s at a pump pressure of 4

MPa in all experiments. The jet velocity was calculated to be 90 m/s (4 MPa pressure) using

Bernoulli's equation. The calculated Reynolds number (13,350) was above the transitional Reynolds

number of 10,000 for a free water jet, therefore the jet was considered as turbulent [10]. Aluminum

oxide (Al2O3) particles with 10 µm nominal diameter (Comco Inc., Burbank, CA, USA; Vickers

91

hardness 16 GPa) using an ASTM quartering technique [11] were mixed with water at 1 wt%

concentrations to make the slurry. The orifice to target standoff distance was set to 15 mm based on

the mathematical model presented by Li et al. [12] to ensure that the abrasive particles reached the

water velocity prior impacting the target. Based on the orifice geometry and flow characteristics,

this standoff was less than the theoretical breakup length of the jet (40 mm) as shown by Leu et al.

[13]. The cross-sectional profiles of the machined holes were obtained by first producing a negative

cast using Reprorubber (Flexbar Machine Corporation, NY, USA), captured via a microscope with

a field of view of 2000×1500 µm, and a digital software (ImageJ software-

http://rsb.info.nih.gov/ij/) as described by Kowsari et al. [9].

The depth of holes, Hd, were measured at the centerline, while the locations of the edges, used to

define the hole diameter, Hw, were defined as the points corresponding to a 10% decrease in the

slope measured using five consecutive digitized profile points, each 2 µm apart as described by

Nouraei et al. [8]. The repeatability of experiments was assessed by replicating some of the

machined holes three times. It was found that the variation in the measured dimensions of the

replicate features was always less than approximately 11%. Figure 4.2 shows a typical profile of

ASJ machined hole after 10 min of machining with a 150 µm slurry jet containing water and 1 wt%

Al2O3 at 15 mm standoff and 1.7 mL/s (4 MPa) flow rate.

92

Figure 4.2: Typical profile of ASJ machined hole in borosilicate glass after 10 min of machining.

4.3 Modeling

4.3.1 Surface evolution modeling of micro-holes

The governing partial differential equation for the profile evolution of an abrasive jet machined hole

was expressed by Ghobeity et al. [14] as

( )( )2 2, ,1 0

k

t rz E r z−

− + = (4.1)

where z,t and z,r are the partial derivatives of the depth, z, with respect to the time, t, and transverse

coordinate, r, (Fig. 4.1(b)). The velocity exponent, k, expresses the dependence of the erosion rate

on particle velocity, and can be obtained from fundamental erosion rate measurements. The best fit

velocity exponent, k, for 10 µm Al2O3 particles was obtained by Nouraei et al. [8] to be 1.69.

Equation (4.1) was modified to be non-dimensional by a time constant, T, defined as the machining

time required to advance the flat surface at r = 0 to a characteristic depth, L, assuming a constant

etch rate and expressed as

93

( )( )* ** * * * 2 2, ,

1 0k

t rz E r z

−− + = (4.2)

where z* = z/L, r* = r/L and t* = t/T are the normalized hole depth, hole diameter, and time,

respectively. The time constant, T, is thus a measure of the erosion rate at r = 0 for a relatively

shallow hole, which was extrapolated from the measured depth of a hole after 30 s machining time.

The characteristic length, L, was chosen to be equal to the orifice to surface standoff distance (i.e.

15 mm). The non-dimensional erosive efficacy function, E*(r*), can be calculated using

( ) ( )* ** * * * 2 2

, ,1

k

t rE r z z= + (4.3)

( ) ( ) ( )** * * * * * *,

, ,0i it iz z r t z r t = − (4.4)

( ) ( ) ( ) ( )** * * * * * * * *

1 1,, ,i i i ir i

z z r t z r t r r+ + = − − (4.5)

where ri* and zi

* are non-dimensional coordinates obtained along a shallow hole after 30 s

machining time. Equations (4.4) and (4.5) are the first order approximation to the time and space

derivatives in Eq. (4.3). The erosive efficacy, E*(r*), (Eq. (4.3)), was numerically solved using one-

sided first-order approximations to the time and space derivatives with a spatial step size of 2 µm to

ensure errors from the use of first-order approximations were insignificant [14]. A non-dimensional,

normalized polynomial equation (least squares method, MATLAB version 7.12.0, curve fitting tool

box, Mathworks, Natick, MA, USA) was fitted to the resulting E*(r*), and then used in Eq. (4.2) to

solve the surface evolution equation. A shallow hole after 30 s machining time was used to infer the

E*(r*) using a least-square fit to a 9th order polynomial (R2 ≈ 0.99):

94

( ) 9 8 7 6 5 4 3 2* * * * * * * * * * *1 2 3 4 5 6 7 8 9 1 0E r b r b r b r b r b r b r b r b r b r b= + + + + + + + + + (4.6)

with

17 81.87 10 0.95 101 616 51.09 10 2.24 102 7

14 22.57 10 2.73 103 812 -13.20 10 1.31 104 9

10 -32.27 10 0.94 105 10

b b

b b

b b

b b

b b

= − × = ×

= × = − ×

= − × = ×

= × = − ×

= − × = − ×

4.3.2 CFD modeling of micro-holes

In order to evaluate the evolution model, a series of holes were machined with machining times

from 30 to 120 s using 10 µm Al2O3 particles. However, as it was mentioned earlier, the surface

evolution model was incapable of predicting the profile of holes characterized with the cross-

sectional profile of a shallow hole machined (30 s machining time) due to nonlinearity trend of

depth as a function of machining time (Fig. 4.3). This was attributed to the high degree of

confinement of the return flow within a hole, which in turn progressively reduced the particle

impact velocity due to increase of drag on the incident particles. As a result, a series of 2D

axisymmetric CFD models of a slurry jet in air striking the profile of holes with machining time

from 30 to 120 s (i.e. digitized from experiments) were conducted using the commercial CFD

simulation software Ansys-Fluent 14.0 (ANSYS Inc., PA, USA) in order to obtain a depreciation

function that describes the reduction of the particle impact velocity at centerline with respect to

machining time.

95

Hd= -0.009t2 + 3.656tR² = 0.988

Hd = 4.367t

0

100

200

300

400

500

600

0 30 60 90 120 150

Dep

th o

f hol

e,H

d(µ

m)

Machining time, t (s)

Figure 4.3: Depth of micro-machined holes at various machining time. Error bars represent ±1 standard deviation for 3 measurements.

In the CFD models, the water was considered as a continuum by solving the Navier-Stokes

equations (incompressible, Newtonian), and the solid particles were tracked allowing for the

exchange of momentum and energy between the phases. The Eulerian approach and the k–ε

turbulence model were used for the water, while the Lagrangian approach was used for tracking the

particles. A second order differential scheme was used to reduce computational errors, and the

simulations were terminated when the residuals of all monitored flow parameters were less than

1×10−6

, usually within approximately 1×108 iterations. Due to the low concentration of particles (1

wt%) in the slurry (i.e. dilute flow), particle–particle interactions and the effect of particles on the

flow field were considered negligible. For drag calculations, Al2O3 particles were modeled as non-

spherical by using an average shape factor of 0.76 (ratio of surface area of a sphere having the

particle volume to the actual particle surface area), as measured by Dehnadfar et al. [15]. The

rebound of abrasive particles after their initial impact was modelled using a coefficient of restitution

of 0.3, which was selected based on the 0.2-0.5 range found by Slikkerveer et al. [16] for Al2O3

96

particles impacting borosilicate glass. No slip boundary condition was considered, thus the water

velocity was set equal to zero near the surface. The other bounding planes of the model domain

were modeled as free boundaries with pressure outlet condition. Nouraei et al. [3] showed that the

velocity of the abrasive particles in the jet was approximately equal to the water velocity in the jet

10 mm upstream of the target. Accordingly, the exit plane of the incident jet was placed 10 mm

above the target and the particles were uniformly spaced over the inlet at a velocity equal to the

water velocity (90 m/s). The number of mesh elements used in the models was approximately

between 4×107 (30 s hole) and 9×10

7 (120 s hole). The CFD models were validated with existing

data by comparing the jet velocity prior to impact and pressure distribution on a flat target under an

impacting jet. Figure 4.4 illustrates the contours of the incoming water jet volume fraction for a 30 s

machined hole as an example. Figures 4.5 and 4.6 show the pressure distribution and the particle

trajectories at the stagnation zone, respectively. Figure 4.6 shows that as the incoming particle at jet

centerline passes through the stagnation zone, the impact velocity was approximately 27 m/s, which

was 69% lower than the particle centerline velocity (90 m/s) far from the target.

The depreciation function, D*(t*), was obtained from a linear fit of the centerline particle impact

velocity as a function of the machining time, as shown in Fig. 4.7. As a result, Eq. (4.2) was

modified as

( ) ( )( )* ** * * * * * 2 2, ,

1 0k

t rz E r D t z

−− + = (4.7)

97

Volume fraction (water)

Inlet (150 µm diameter)

Upper boundary

Outlet

Target

Incoming slurry jet

Figure 4.4: Incoming jet volume fraction for a 30 s machined hole.

Pressure (Pa)

Stagnation zone

Figure 4.5: Pressure distribution for a 30 s machined hole.

Particle velocity (m/s) Particle trajectory

Figure 4.6: Particle trajectories during the jet impingement for 10 µm Al2O3 particles.

98

Vp = -0.123t + 29.532R² = 0.917

0

5

10

15

20

25

30

0 30 60 90 120 150

Cen

terli

ne p

artic

le im

pact

vel

ociit

y,

Vp

(m/s

)

Machining time (s)

Figure 4.7: Centerline particle impact velocity at various machining times.

Equation (4.7) with k = 1.69 and E*(r*), obtained from Eq. (4.6), was solved numerically with the

initial condition of z*(r*, t*= 0) = 0, using the method of lines technique implemented in Mathcad 14

(Parametric Technology Corp., Needham, MA, USA). In order to obtain a converged and accurate

numerical solution, 500 time and space steps were used. Figure 4.8 compares the measured and

predicted hole profiles of the solution of Eq. (4.7) using dimensional coordinates (i.e. r = r*L and z

= z*L). The center depth predictions were within 5% of the measured values. For larger holes (i.e.

deeper than 300 µm), the velocity of impacting particles reduces significantly, which in turn

changes the mode of material removal from dominant brittle erosion to ductile erosion and

consequently the error in the predicted profiles is expected to continually increase.

99

-350

-300

-250

-200

-150

-100

-50

00 50 100 150 200 250 300 350

Hol

e de

pth,

Hd

(µm

)

Hole diameter, Hw (µm)

30 s60 s90 s120 s

Figure 4.8: Comparison of predicted (solid lines) and measured hole profiles. Half of the symmetric profile shown.

4.4 Conclusions

The existing surface evolution model was modified to incorporate the nonlinearity effect of depth as

a function of machining time. A series of holes were machined with machining times from 30 to

120 s using 10 µm Al2O3 particles. The center depth predictions were within 5% of the measured

values.

The proposed numerical-analytical model can generally be applied for predicting the profile of

holes machined at different target materials, slurry jet flow rates (i.e. orifice sizes and pressures),

particle sizes and concentrations regardless of the machining time as long as the dominant mode of

material removal remains unaffected. In the case where the mode of material removal changes (e.g.

100

from brittle to ductile erosion due to the loss of kinetic energy of impacting particles as mentioned

in previous section), the depreciation function is no longer applicable and as a result the predictive

model is not effective.

The results presented in this study demonstrated for the first time that the CFD modeling of slurry

jet impinging the target can be used to compensate for the retardation of particle impact velocities

on the material removal as a function of the machining time for ASJ machined micro-holes.

4.5 References








[8] H. Nouraei, A. Kowsari, J.K. Spelt, M. Papini, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in glass, Wear (2014) 309: 65–73.

[9] K. Kowsari, H. Nouraei, D.F. James, J.K. Spelt, M. Papini, Abrasive Slurry Jet Micro-machining of Holes in Brittle and Ductile Materials, Journal of Materials Processing Technology (2014) 214(9): 1909-1920.

101

[10] P.E. Dimotakis, The mixing transition in turbulent flows, Journal of Fluid Mechanics (2000), 409: 69-98.


[12] H. Li, J. Wang, J. Fan, Analysis and modeling of particle velocities in micro-abrasive air jet, International Journal of Machine Tools and Manufacture (2009), 49: 850-858.

[13] M.C. Leu et al., Mathematical modeling and experimental verification of stationary water jet cleaning process, Journal of Manu. Sci. and Eng. (1998), 120: 571-579.

[14] A. Ghobeity, H. Getu, M. Papini, J.K. Spelt, Surface evolution models for abrasive jet micromachining of holes in glass and polymethylmethacrylate (PMMA), Journal of Micro-mechanics and Micro-engineering 17 (2007) 2175-2185.

[15] D. Dehnadfar, J. Friedman, M. Papini, Laser shadowgraphy measurements of abrasive particle spatial, size and velocity distributions through micro-masks used in abrasive jet micro-machining, Journal of Materials processing Technology 212 (2012) 137-149.


102

Chapter 5: Operating Parameters to Minimize Feature

Size in Abrasive Slurry Jet Micro-machining

5.1 Introduction

In low-pressure abrasive slurry jet micro-machining (ASJM), an aqueous slurry of abrasive

particles such as aluminum oxide (Al2O3) and tungsten oxide (WO3) is used to erode features in a

target workpiece. Because the jet is highly focused with a divergence of less than 1°, ASJM is well-

suited for the fabrication of features such as micro-holes and micro-channels.

During the past decade, most studies of ASJM have focused on the determination of material

removal mechanisms, the estimation of the material removal rate, and the prediction of the

machined feature profile. Nguyen et al. [1] and Wang et al. [2] investigated the mechanisms of

material removal during the machining of holes in glass. It was determined that ductile erosion was

the dominant mode of material removal and consequently no cracks were detected on the holes.

Matsumura et al. [3] studied the mechanisms of material removal during slurry-jet polishing of pre-

machined channels on glass. They showed that the stagnation zone of the slurry jet and the

transverse flow along the channel and consequently local impact angle and velocity of impinging

particles could be controlled using tapered masks in order to obtain a crack-free surface during the

polishing process. Wang et al. [4] showed that the etch rate during the machining of holes in glass

increased with slurry pressure, machining time, and particle concentration, and decreased with the

standoff distance between the orifice plate and the target. Pang et al. [5, 6] used dimensional

103

analysis and multi-variable regression techniques to successfully model the etch rate, opening width

and wall slope of micro-machined channels in glass, although the machined channels were very

wavy due to vibration of the equipment. Qi et al. [7] investigated the effect of pressure, abrasive

particle size and concentration, jet impact angle and nozzle traverse speed on the erosion rate,

surface quality and depth of micro-machined channels in quartz crystals. Good channel edge

definition and bottom surface quality without any waviness were achieved by using relatively small

particles and machining at shallow impact angles. Nouraei et al. [8] examined the effect of particle

velocity and concentration, jet impact angle and traverse speed on the depth, width and profile of

micro-machined channels and holes in glass. The mechanics of the erosion process in ASJM was

also compared with that in abrasive air jet micro-machining (AJM) where particle trajectories are

much less influenced by fluid flow. Brittle erosion was found to be the main material removal mode

in both ASJM and AJM, and a much sharper channel edge definition was obtained using ASJM.

Nouraei et al. [9] showed that the profiles of micro-channels and holes machined in borosilicate

glass could be predicted accurately using a surface evolution model based on the characterization of

the jet erosion pattern obtained from the cross-sectional profile of a shallow channel. Jafar et al.

[10] modeled the effects of particle kinetic energy and jet impact angle on the erosion rate and

roughness of channels machined in borosilicate glass. As with AJM, decreasing the normal

component of impact velocity by reducing the jet impact angle, decreased the erosion rate and

produced smoother channels.

Most recently, Kowsari et al. [11, 12], studied the effects of dilute concentrations of polyethylene

oxide (PEO, 50 to 400 wppm; i.e. weight parts per million) on the roughness, shape, and width of

channels and holes machined in brittle (borosilicate glass) and ductile materials (6061-T6 aluminum

alloy, 110 copper, 316 stainless steel). It was found that approximately 20% narrower features

104

could be machined when 50 wppm of 8-M (million molecular weight) PEO was added to the slurry.

The reduction in feature size was attributed mostly to the normal stresses generated in the fluid by

the polymer, which affected the abrasive particle trajectories and focused the erosion to a smaller

footprint. These papers demonstrated that the size of micro-machined features could be reduced by

influencing the trajectories of abrasive particles. However, the effect of ASJM operating parameters

on the trajectories of impacting particles, and consequently the shape and size of machined features,

remains relatively unexplored.

Humphrey [13] reported that the momentum equilibration number, λ, could be used to assess the

degree to which entrained particles follow fluid flow streamlines. He suggested that particles with λ

< 0.1 follow streamlines closely, whereas they do not if λ > 10. As a consequence, the eroded

surface underneath a jet footprint was formed primarily by impacting particles with λ > 0.1; i.e.

those that tended to follow their original trajectories without being deflected by the diverging flow

field in the footprint region.

In brittle erosion, deformation wear and fracture cause the removal of chips in the impact zone, and

the maximum erosion rate occurs at normal incidence. In ductile erosion, material is removed in the

fully-developed plastic zone under the impacting particle by cutting wear, and the maximum

erosion rate occurs at oblique impact angles less than 90°. These fundamental differences

necessitated complementary investigations of the effects of ASJM operating parameters on the

minimum size of features made with ASJM in brittle and ductile materials. The objective of the

present study was to do this for operating parameters such as jet traverse speed and orientation,

number of machining passes, particle density and diameter, orifice size, slurry temperature and

velocity. The results were explained in terms of differences in the impacting particle energies and

trajectories, as predicted using computational fluid dynamics models.

105

5.2 Experiments

5.2.1 ASJM setup

The experiments were conducted using the ASJM system developed by Nouraei et al. [9] (Fig.

5.1(a)) consisting of an open stirred slurry tank, a positive displacement slurry pump (LCA/M9/11-

DC, LEWA Inc., Leonberg, Germany) with pulsation damper (FG 44969/01-9, Flowguard Ltd.,

Houston, TX, USA), an 840 µm thick sapphire orifice (KMT Water jet, KS, USA; Fig. 5.1(b)), and

a computer controlled linear stage (KT- LSM100A, Zaber Technologies Inc., Vancouver, BC,

Canada) for the specimen. Following the procedure described by Nouraei et al. [9], the discharge

coefficients (ratio of the actual mass flow rate at the orifice exit to that of an ideal orifice) for the

50, 75, 100, and 180 µm orifices used in this study were measured to be 0.68±0.05. The effect of jet

temperature was investigated by heating the slurry tank and insulating the tubes between it and the

orifice. The targets were also heated as shown in Fig. 5.1(c) to prevent cooling of the jet as it

impacted the surface. Measurements of the jet temperature at a standoff distance of 15 mm gave

values that were essentially the same as the reservoir temperature. Figure 5.1(d) illustrates the

orientation of the slurry jet and sample motion at oblique impact angles.

106

Slurry tank

Propeller

Pulsation damper Pressure gauge

Orifice

Specimen

Linear stage

Stirring motor

Slurry pump

M

(a)

Slurry Flow

Sapphire orifice Exit tube

Heating elements

Linear stage

Specimen

(b) (c)

Orifice

Linear stage

Specimen

Tripod mount θ

do

Forward motion

(d)

Figure 5.1: Schematic of (a) the ASJM apparatus, (b) sapphire orifice, (c) heating elements and (d) jet orientation at various impact angles.

107


Micro-channels were machined on 50×50×3 mm thick plates of borosilicate glass (Borofloat®,

Schott Inc., NY, USA; Vickers hardness 5.4 GPa) and polymethylmethacrylate (PMMA) (Piedmont

Plastics Inc., ON, Canada; Vickers hardness 0.17 GPa). Borosilicate glass and PMMA, a

thermoplastic acrylic, are useful model materials for studies of brittle and ductile erosion, and are

typical of materials used in small-scale devices such as micro-fluidic platforms. Table 5.1

summarizes the ranges of the primary variables that were controlled in the experiments: slurry flow

rate, Q, slurry temperature, T, target traverse speed, vs, particle dose, D, jet impact angle, θ, orifice

diameter, dorifice, orifice to target standoff distance, do, particle diameter, dp, and particle density, ρp.

The standoff distance, do, was adjusted for the various orifice sizes based on the mathematical

model presented by Li et al. [14] to ensure that the abrasive particles reach the water velocity prior

impacting the target substrate, as described by Nouraei et al. [8]. The erosion rate was measured as

a function of impact angle using a typical set of operating conditions. Nouraei et al. [8] found that

this trend was insensitive to the exact values of these parameters provided that the amount of

material removed per pass of the jet was relatively small so that the inclination of the channel

bottom at the erosion front could be assumed to be negligibly small.

Table 5.2 shows the measured slurry flow rates and the corresponding jet velocities used in the

experiments. For the range of jet velocites used in this study (90 m/s- 127 m/s), the calculated

Reynolds numbers were above 10,000, therefore the free jet was considered to be turbulent [15].

Both angular Al2O3 (Comco Inc., Burbank, CA, USA; Vickers hardness 16 GPa) and WO3

(Inframat® Advanced MaterialsTM LLC, Manchester, CT, USA; Vickers hardness 9 GPa) particles,

as shown in Fig. 5.2, were used in the slurries (Table 5.1). The mixing tank particle concentration,

C, was adjusted (Tables 5.1 and 5.2) so that the various pressures and slurry flow rates at the

108

traverse speed of 0.5 mm/s provided a constant particle dose, D, (mass of particles striking the

channel in a pass per unit length) of: 34 mg/mm for 10 µm Al2O3, 20 µm Al2O3 and 20 µm WO3;

and 17 mg/mm for 3 µm Al2O3. A standard quartering technique [16] was used to ensure a

consistent sampling of the powder sizes when preparing the slurries.

Table 5.1: Ranges of operating parameters used for channel machining and measurements of erosion rate as a function of jet angle for glass and PMMA.

Range of operating parameters

Operating parameter Machining channels Measuring erosion rate Slurry flow rate, Q (mL/s) 0.2, 0.4, 0.5, 0.6, 1.7, 2.0, 2.3 1.7 Slurry temperature, T (°C) 15, 20, 35, 60, 75 15 Traverse speed, vs(mm/s) 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 0.5 Particle dose, D (mg/mm) 17, 34 34 Slurry jet impact angle, θ (°) 15, 30, 45, 60, 75, 90 15, 30, 45, 60, 75, 90 Orifice standoff distance, do(mm) 5, 8, 12, 15 15 Orifice diameter, dorifice (µm) 50, 75, 100, 180 180 Particle diameter, dp(µm) Al2O3: 3, 10, 20 , WO3: 20 10 (Al2O3) Particle density, ρp(kg/m3) 3900, 7160 3900

Table 5.2: Measured slurry flow rates and corresponding jet velocities.

Orifice diameter (µm) 180 100 75 50 Pressure, P (MPa) 8 6 4 6 4 6 6 Slurry flow rate, Q (mL/s) 2.3 2.0 1.7 0.6 0.5 0.4 0.2 Mixing tank particle concentration, C (wt%) 0.75 0.40 1.0 1.4 3.3 2.0 4.2 Slurry jet velocity, vjet (m/s) 127 110 90 110 90 110 110

109

(a) (b)

Figure 5.2: Scanning electron micrographs of 20 µm nominal diameter (a) Al2O3 and (b) WO3 particles.

The micro-channel profiles were obtained using an optical profilometer (ST400, Nanovea Inc., CA,

USA) taking measurements every 2 µm along a cross-section, each with a depth and lateral

resolution of 0.02 and 0.4 µm, respectively. The cross-sections were used to calculate the volume of

material removed and hence the erosion rate. The channel depth was measured at the centerline. As

in Nouraei et al. [9], the channel width was defined based on the channel edges being located where

a 10% decrease occurred in the absolute slope measured using five consecutive profile points.

Figure 5.3 shows the typical profile of micro-channels machined in glass and PMMA. The

maximum variation in the measured dimensions of identically reproduced channels was always less

than 10%. In each trial, one experiment was performed for each target materials (glass and PMMA)

and each measurement was repeated using three different channel cross-sections 1 mm apart. It was

found that the variation of channel depth and width along the channel length were less than 8%. The

surface roughness, Ra, was measured by scanning a 5 mm length of the channel centerline using the

profilometer with a cut-off length of 250 µm, sampling every 2 µm [17]. The particle size

distribution was quantified using a Leica microscope (Leica Microsystems, Buffalo Grove, IL,

110

USA; x25–x1000 magnification) and Clemex PE Vison 5.0 image analysis software (Clemex

Technologies Inc., Longueuil, QC, Canada).

(a) (b)

Figure 5.3: Scanning electron micrographs of the typical channels machined with ASJM in: (a) glass and (b) PMMA using 5 passes of the jet under identical experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

5.2.3 Erosion rate vs. impact angle

The specific erosion rate (mass of material removed per mass of erodent), Er, as a function of the

slurry jet impact angle, θ, can be used to assess the typical mechanism of material removal. Figure

5.4 shows the measured normalized erosion rate (specific erosion rate at a given angle divided by

that at 90°), Er*, of PMMA as a function of the slurry jet impact angle. For comparison, the

normalized erosion rate of borosilicate glass obtained in Nouraei et al. [9] is also shown (Fig.

5.4(a)). As mentioned previously, these measurements were made on very shallow channels in

order to approximate impact on a flat surface. Slikkerveer et al. [18] showed that the erosion

associated with brittle materials such as glass is controlled by the normal component of the impact

velocity. The material removal in ductile materials is controlled by cutting and ploughing

111

mechanisms, so that the tangential component of impact velocity is as important as the normal

component [19]. It is noted that the slurry jet impact angles were not necessarily representative of

the whole range of local particle impact angles due to stagnation zone and other flow effects.

Nevertheless, the trends of Fig. 5.4 reflect typical brittle and ductile erosion mechanisms.

0

0.2

0.4

0.6

0.8

1

1.2

0 15 30 45 60 75 90 105

Nor

mal

ized

ero

sion

rate

, E* r

Slurry jet impact angle,θ

Glass

00.20.40.60.8

11.21.41.61.8

22.22.4

0 15 30 45 60 75 90 105

Nor

mal

ized

ero

sion

rate

, E* r


PMMA

(a) (b) Figure 5.4: Normalized erosion rate as a function of slurry jet impact angle of (a) borosilicate glass [9], and (b) PMMA. Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, do = 15 mm. Solid lines were added to guide the eye.

5.2.4 CFD modeling

The selection of the operating parameters and their ranges was guided by predictions of particle

trajectories and impact velocities obtained from computational fluid dynamic (CFD) models

(ANSYS Fluent 14.0, ANSYS Inc., Cecil Township, PA, USA). Figure 5.5 illustrates the geometry

of the 3D computational domain of a slurry jet in air striking the channel profile at 90°. The jet

velocities used at the inlet and the channel cross-section used for constructing the domain were

obtained from experiments. The domain was meshed with approximately 5 µm quadrilateral

112

elements. Additional mesh refinement near the target wall was used to maintain the dimensionless

wall coordinate, y+, below 1. The Eulerian approach and the standard k–ε turbulence model were

used for the multi-phase air-water flow, while the particles were uniformly injected over the inlet at

a velocity equal to the water velocity (Table 5.2) and tracked using the discrete phase model

(DPM). A second order differential scheme was used to reduce computational errors, and the

simulations were terminated when the residuals of all monitored flow parameters were less than

10−3. The channel profile boundary was treated as a smooth no-slip wall.

Z X

Y

Upper boundary Side boundary

(outlet)

Symmetry plane Inlet

Channel profile

Target (wall)

Side boundary

Figure 5.5: Domains and boundary conditions of the CFD model for the 3D simulation of the particle trajectories within a channel.


5.3.1 Measurement of jet footprint

The particle momentum equilibration number, λ, was given by Humphrey [13] as

( )( )

2

p p jet

orifice

d v

18 d

ρλ

µ=

(5.1)

113

where ρp is the particle density, dp is the particle diameter, vjet is the jet velocity, µ is the dynamic

viscosity of water and dorifice is the orifice diameter. Therefore, the tendency of a particle to deviate

from the flow streamlines and continue on its original trajectory within the footprint increases with

increasing particle density, diameter and velocity, and decreasing dynamic viscosity and orifice

size. So increasing λ causes an increase in the local impact angle of particles, thereby affecting the

amount of erosion. These trends are illustrated in Fig. 5.6 during jet impingement of 10 and 20 µm

Al2O3 particles.

Jet boundary

Target

P1

α1 α2

L2 L1

λ2 > λ1

α2 > α 1 L1 > L2

Stagnation zone

Particle trajectory P2

Figure 5.6: CFD predictions of particle trajectories during jet impingement of 10 µm (P1) and 20 µm (P2) Al2O3 particles. Modeling conditions: P = 4 MPa (water velocity of 90 m/s), dorifice =180 µm (jet diameter of 150 µm) , C = 1 wt%, Q = 1.7 mL/s, θ = 90°, do = 15 mm.

A key parameter governing the minimum feature size was the jet footprint, defined as the zone on

the surface in which impinging particles had sufficient kinetic energy to cause damage to the target

substrate. The width of the jet footprint was measured using a relatively high traverse speed (10

114

mm/s) under various experimental conditions (Table 5.1) to ensure that the machined channel was

very shallow, thereby minimizing the influence of channel walls on the fluid flow field. Figure 5.7

shows an example of a 225 µm wide jet footprint on glass using a 180 µm orifice at slurry flow rate

of 1.7 mL/s. The footprint on PMMA was essentially the same under similar experimental

conditions, being only slightly larger (approximately 5%) than the footprint in glass, because

particles at the periphery of the footprint impacting at relatively shallow angles had sufficient

energy to damage PMMA (erosion maximum at shallow incidence) but not glass (erosion

maximum at perpendicular incidence).

Unblasted

Jet foot print

Single impact

225 µm

Figure 5.7: Scanning electron micrograph of the ASJ footprint on glass. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 10 mm/s, D = 1.7 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

5.3.2 Mechanism of channel formation in glass and PMMA

Figure 5.8 shows that single-pass micro-channels machined under identical conditions were wider

and deeper in PMMA than in glass. The profile of both channels were "U" shaped (flat bottoms and

115

steep sidewalls) since slurry jets have a relatively uniform distribution of both particle flux and

impact velocity, leading to a fairly uniform erosive power across the jet [8]. The ratio of the slurry

jet diameter to the channel width, defined as the ASJM resolution, was approximately 0.5,

indicating that additional erosion occurred at the periphery of the stagnation flow directly under the

jet, as illustrated in Fig. 5.9. The flow away from the zone of primary jet impact (termed the “return

flow” out of zone I) accelerates the rebounding particles after their initial impact and causes a

secondary impact on the channel sidewall (zone II). A related ‘second strike’ phenomenon was also

observed by Slikkerveer and in't Veld [20] for air-driven particles, although in that case particles

rebound from the sidewalls and subsequently impact the center of machined holes. Around the

channel opening in ASJM, as shown by Nguyen et al. [21], a small region with static pressure drop

forms that corresponds with the high velocity region of the return flow. This low-pressure region

intensifies as the machined channel deepens, thereby increasing the velocity of the return flow at

the channel opening and causing the rounding of channel edges and an additional damage in the

form of a frosting zone outside of the channel opening. Kowsari et al. [11, 22] demonstrated that if

the return flow is prevented from producing this additional erosion of the channel sidewalls, a more

V-shaped than U-shaped profile results, and the channel width is decreased.

116

-70

-60

-50

-40

-30

-20

-10

00 50 100 150 200 250 300 350

Dep

th (µ

m)

Width (µm)

GlassPMMA

Figure 5.8: Profiles of channels machined with ASJM in glass and PMMA under identical experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

Static pressure (Pa)

Jet boundary

Target

Return flow Frosting zone

Particle trajectory

Initial impact zone

Stagnation point

Secondary impact zone Stagnation zone

Figure 5.9: CFD predictions of initial (in zone I) and secondary particle impact (in zone II) during jet impingement of 10 µm Al2O3 particles. Modeling conditions: P = 4 MPa (water velocity of 90 m/s), dorifice =180 µm (jet diameter of 150 µm) , C = 1 wt%, Q = 1.7 mL/s, θ = 90° and do = 15 mm.

117

As shown in Fig. 5.8, the channel machined in PMMA was about 10 µm deeper and 25 µm wider

than that in glass, and the removed volume was 60% higher than in glass where the channel was 20

µm deep and 275 µm wide. This trend was opposite to the abrasive air jet machining (AJM) results

reported by Shafiei et al. [23] and Getu et al. [24], who both showed that glass had an erosion rate

of approximately 10 times greater than that of PMMA when eroded under identical conditions. This

apparent contradiction is explained by the large difference in the local impact angle of particles

incident to the surface in AJM and ASJM, as shown in Fig. 5.10. This effect was due to the

combined effects of the size of the stagnation zone and the magnitude of the particle momentum

equilibration number, λ (Eq. (5.1)). In AJM, at the 15 mm to 20 mm standoffs used by Shafiei et al.

[23] and Getu et al. [24], the air jet decelerated so that the air velocity became nearly zero very

close to the target surface [14]. Therefore, the stagnation zone in air was relatively small compared

with that in water. In addition, the viscosity of air in AJM was about 100 times less than that of

water in ASJM which resulted in a much larger λ for air-driven particles. Consequently, the

trajectories of particles in air were less affected by the changes of the flow field near the target

surface (Fig. 5.10(a)). In ASJM however, the local impact angles varied considerably across the jet

footprint, being nearly 90° in the central section, but becoming increasingly shallow at larger

distances from the jet centerline where the secondary flows moved parallel to the substrate surface

(Fig. 5.10(b)). As a result, there was a much larger difference between the global and local impact

angles of particles in ASJM than in AJM. Since the erosion rate of ductile materials is greater at

lower impact angles (Fig. 5.4), the overall material removal rate at the bottom of ASJM channels in

PMMA was larger than in glass (Fig. 5.8). Similarly, the slurry return flow and secondary particle

impact on the channel sidewalls was responsible for the 9% increase in the width of channels

machined using ASJM in PMMA (300 µm) compared with glass (275 µm) (Fig. 5.8). The slurry jet

118

streamlines and particle trajectories became increasingly parallel to the target surface away from the

stagnation point [25]. Therefore, after the initial impact, the rebounding particles struck the channel

sidewall with impact angles much less than 90°. Consequently, the erosion rate due to secondary

impacts on the channel sidewalls in ductile PMMA was greater than in brittle glass.

αAJM Target

Particle trajectory Air jet flow

θ=90°

αASJM

Particle trajectory Slurry jet flow

θ=90°

Target

(a) (b)

Figure 5.10: Increase of local impact angle of particles near jet centerline in (a) AJM [26] compared with (b) ASJM [10].

5.3.3 Effect of operating parameters on channel depth and width

As discussed above, the initial impact of particles in the jet footprint (zone I) affected the channel

depth, while the secondary impact of particles on the channel sidewalls (zone II) was responsible

for enlarging the width of machined channels (Fig. 5.9). In most cases, the operating parameters

were found to affect the machined channels through distinctive mechanisms, as listed below in their

order of presentation.

1. Particle size and density had a common dominant mechanism of changing the momentum of the

impinging particles and consequently affecting the kinetic energy and the local impact angles in

119

zones I and II. Particle velocity (varied by slurry pressure) also affected the kinetic energy but not

the local impact angles in zones I and II.

2. Slurry temperature influenced the drag force on the impinging particles, thereby affecting both

kinetic energy and local impact angles in zones I and II.

3. Scan speed controlled the local impact angle of the leading edge of the erosion front.

4. Jet angle affected the direction of the bulk flow relative to the channel and consequently the local

impact angle of impinging particles in both zones I and II.

5. Scan direction controlled whether the bulk flow preceded the footprint or followed it.

6. Orifice size related directly to the diameter of the footprint.

7. Sacrificial coatings affected mostly frosting and channel edge rounding.

120

5.3.3.1 CFD results

The CFD models were used to estimate the average kinetic energy and local impact angle of

impinging particles in zones I (bottom of channel under jet footprint) and II (channel sidewalls) for

the operating parameters of Tables 5.1 and 5.2, as shown in Table 5.3.

Table 5.3: CFD predictions of average kinetic energy and impact angle of particles in zones I and II for specified operating parameters holding everything else constant. With increases in the parameter (↑) indicates an increase, (↓) indicates a decrease and (-) indicates no change. Operating parameters Average particle kinetic energy (nJ) Average particle impact angle (°)

Zone I Zone II Zone I Zone II Particle density, ρp (kg/m3) (↑) (↑) (↑) (↓) 7160 26.2 19.3 78 27 3900 6.9 4.7 64 35 Particle diameter, dp (µm) (↑) (↑) (↑) (↓) 20 6.9 4.7 64 35 10 0.6 0.4 50 46 Slurry jet velocity, vjet (m/s) (↑) (↑) (-) (-) 127 (8 MPa) 1.5 1.2 50 46 90 (4 MPa) 0.6 0.4 50 46 Slurry temperature, T (°C) (↑) (↓) (↑) (↓) 75 3.3 0.18 62 37 15 0.6 0.4 50 46

The CFD results showed that increasing particle density, diameter and velocity tended to increase

the kinetic energy of impacting particles in both zones I and II, thereby increasing both the depth

and width of channels. In contrast, an increase in slurry jet temperature was predicted to increase

the average particle kinetic energy in zone I, but decrease it in zone II, thus creating the potentially

useful conditions for deepening a channel while decreasing its width. Increasing jet velocity did not

change the average impact angles in zones I and II, but increases in particle density, diameter and

slurry temperature caused an increase in the impact angle in zone I and a decrease in zone II as a

result of changes in λ (Eq. (5.1)). These effects are discussed further in the following sections.

121

5.3.3.2 Effect of particle density, diameter and velocity at θ = 90°

The effect of particle density on the size of the jet footprint and the dimensions of channels

machined in glass and PMMA was investigated with 20 µm nominal diameter Al2O3 (ρp = 3900

kg/m3) and WO3 (ρp = 7160 kg/m3). The widths of the footprints on glass and PMMA for Al2O3

particles, as measured using a single pass of the 150 µm-diameter slurry jet at θ = 90° and vs = 0.5

mm/s, were 200 µm and 223 µm, respectively. However, when WO3 particles were used, the

footprints were 18% smaller on glass and 14% smaller on PMMA. This was caused by the 84%

greater density of WO3 particles which resulted in a larger λ (Eq. (5.1)), indicating that the

trajectories of the WO3 particles were less affected by the lateral flow of the water near the target

surface, and consequently the footprint was narrower and the local impact angles of WO3 particles

were higher than those of Al2O3 particles.

Figure 5.11 shows that the greater density and kinetic energy of the WO3 particles caused channels

in glass and PMMA to be 60% and 65% deeper, respectively, than those machined using Al2O3

particles with 3 passes. This can be understood in terms of the impact velocities of the two particles

as estimated using the CFD model to account for particle deceleration through the stagnation zone.

The impact velocity of WO3 particles at the jet centerline was computed to be 49 m/s, which was

44% higher than that of Al2O3 particles (34 m/s). Since the cross-sectional area of the 20 µm

nominal diameter Al2O3 and WO3 particles was almost identical, so was the drag force, and so this

difference in impact velocities was due to the greater density of the WO3 particles. Therefore, the

deeper channels machined using WO3 particles were caused by an increase in the impact velocity

and erosive power.

122

It is also seen that the channels machined with 3 passes of Al2O3 were narrower than those

machined with 3 passes of WO3, which appears to contradict the observation that the WO3 footprint

was smaller. To clarify this, the width comparison was made using channels of equal depth by

machining with 5 passes of Al2O3. Figure 5.11 shows that the Al2O3 channels continued to be

narrower; i.e. 8% narrower (318 µm) in glass, and 10% narrower (372 µm) in PMMA. These small

differences were due to the greater kinetic energy of the WO3 particles striking the sidewalls after

being carried by the transverse flow spreading out from the jet footprint.

-400

-350

-300

-250

-200

-150

-100

-50

00 50 100 150 200 250 300 350 400

Dep

th ( µ

m)

Width (µm)

3 P3 P 5 P

, WO3

, Al2O3

, Al2O3

Glass

-500

-400

-300

-200

-100

00 100 200 300 400 500

Dep

th (µ

m)

Width (µm)

3 P3 P 5 P

, WO3

, Al2O3, Al2O3

PMMA

(a) (b)

Figure 5.11: Effect of particle density on channel profiles in: (a) glass and (b) PMMA using 3 and 5 passes (P) of the jet. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

The effect of particle diameter on the size of the jet footprint and channel dimensions was studied

using slurries containing 10 and 20 µm nominal diameter Al2O3 particles to machine channels in

glass and PMMA at θ = 90°. The larger particles had a larger λ (Eq. (5.1)), and as with particle

density, produced smaller footprints and hit the target with higher local impact angles; i.e. the

123

footprints with 20 µm particles were approximately 12% (200 µm footprint) and 6% (223 µm

footprint) smaller than with the 10 µm particles on glass and PMMA, respectively. It will be seen in

Section 5.3.3.5 that the opposite trend exists at θ = 30° so that larger particles produce narrower

channels.

Figure 5.12 shows that the effect of Al2O3 particle size on channel depth and width was analogous

to the effect of particle density; i.e. particles with a larger λ did not follow the streamlines as closely

and also had a greater kinetic energy, thereby producing deeper and wider channels. For example,

the 20 µm particles created channels that were 66% and 70% deeper than those of the 10 µm

particles, in glass and PMMA, respectively. This depth increase was mostly due to the greater

centerline particle impact velocity of the 20 µm particles; i.e. 34 m/s which was 65% greater than

that of the 10 µm particles.

For a given depth, the 10 µm particles produced channels that were 9% (290 µm wide) and 11%

(324 µm wide) narrower than those made with the 20 µm particles in glass and PMMA,

respectively. As with particles of differing density, those particles with greater kinetic energy

produced more sidewall erosion due to the transverse flow from the footprint at a 90° impact angle.

124

-400

-350

-300

-250

-200

-150

-100

-50

00 50 100 150 200 250 300 350 400

Dep

th (µ

m)

Width (µm)

3 P3 P5 P

, dp = 20 µm, dp = 10 µm, dp = 10 µm

Glass

-500

-400

-300

-200

-100

00 100 200 300 400 500

Dep

th (µ

m)

Width (µm)

3 P3 P 5 P

, dp = 20 µm, dp = 10 µm, dp = 10 µm

PMMA

(a) (b)

Figure 5.12: Effect of particle diameter on channel profiles in: (a) glass and (b) PMMA. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

Nouraei et al. [8] found that an increase in slurry jet pressure produced deeper and wider channels

because of the combined effects of increased particle dose and kinetic energy. In the present

experiments, the effect of jet velocity was isolated by using pressures of 4 and 8 MPa (jet velocities

of 90 m/s and 127 m/s) and adjusting the particle concentration (1 wt% and 0.75 wt%) to deliver the

same particle dose per pass. In order to compare the profiles of channels of equal depth, the scan

speed was then increased to 0.7 mm/s in the 8 MPa experiments (0.5 mm/s at 4 MPa).

The footprints for 10 µm Al2O3 particles at 8 MPa were approximately 6% (238 µm wide) and 9%

(257 µm wide) wider in glass and PMMA, respectively, than those at 4 MPa. This was puzzling at

first given that λ (Eq. (5.1)) was greater at 8 MPa and so the higher velocity jet should have

produced a more focused footprint. However, since kinetic energy is proportional to the square of

the particle velocity, a significant number of peripheral particles at 8 MPa (127 m/s jet velocity)

125

could erode the target whereas those at 4 MPa (90 m/s jet velocity) could not. Therefore, the

footprint became larger at the higher velocity. Figure 5.13 shows that the channels at 8 MPa in glass

and PMMA were, respectively, 36% and 43% wider than those machined at 4 MPa. As with the

denser and larger particles, this was caused by the increase in the particle impact velocity on the

channel sidewalls.

-100

-80

-60

-40

-20

00 100 200 300 400 500

Dep

th (µ

m)

Width (µm)

4 MPa, 1 P (0.5 mm/s)8 MPa, 1 P (0.7 mm/s)

Glass

-120

-100

-80

-60

-40

-20

00 100 200 300 400 500 600

Dep

th (µ

m)

Width (µm)

4 MPa, 1 P (0.5 mm/s)8 MPa, 1 P (0.7 mm/s)

PMMA

(a) (b)

Figure 5.13: Channel profiles machined in a single pass at 8 MPa and 4 MPa slurry pressures in: (a) glass and (b) PMMA. Experimental conditions: dorifice =180 µm, dp = 10 µm Al2O3, T = 15°C, θ = 90°, do = 15 mm. 8 MPa: C = 0.75 wt%, vs = 0.7 mm/s, D = 24 mg/mm, Q = 2.3 mL/s. 4 MPa: C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, Q = 1.7 mL/s.

5.3.3.3 Effect of slurry jet temperature

Increasing the temperature of the slurry jet from 15°C to 75°C caused a 67% reduction in the

dynamic viscosity (from 1.11 µPa⋅s to 0.37 µPa⋅s [27]), thereby increasing λ (Eq. (5.1)) and

consequently the local impact angle of particles in the footprint (zone I). This was similar to the

effect of increasing particle kinetic energy (Section 5.3.3.2). However, the 67% reduction in the

126

dynamic viscosity also caused the particles in the warmer flow to undergo less deceleration in the

stagnation zone prior to impact, and thus impacted at higher velocities [28]. Although the less

viscous fluid increased the initial particle impact velocities, the momentum transfer to the

rebounding particle was decreased, thereby reducing the secondary impact velocities on the channel

sidewalls, and hence the width. These effects are illustrated in Fig. 5.14 which shows that a channel

machined with a 75°C slurry was 43% deeper and 21% narrower than at 15°C.

The slurry temperature experiments were conducted only with glass since the hardness of PMMA in

water is known to decrease with increasing temperature [29]. Increasing the slurry temperature in

ASJM of ductile materials is expected to reduce both the channel width and depth, mainly due to

the increase of the local impact angle of impinging particles as proposed by Ma et al. [30].

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

0 15 30 45 60 75 90

Dep

th (µ

m)

Wid

th (µ

m)

Temperature (°C)

Width DepthGlass

Figure 5.14: Effect of slurry temperature on width and depth of 5 pass channel machined in glass. Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, θ = 90°, do = 15 mm.

127

5.3.3.4 Effect of scan speed

Figure 5.15 shows that reducing the scan speed from 0.5 to 0.05 mm/s caused a nonlinear increase

in the depth and channel volume during a single pass in both glass and PMMA. As explained by

Nouraei et al. [8], this nonlinear behavior in ASJM was due mostly to the increase of the angle, β,

of the leading edge of the jet footprint as the scan speed decreased, and its effect on the local impact

angle, α, of the incident particles (Fig. 5.16). A similar phenomenon was observed by Shipway et

al. [31] in abrasive water jet milling (AWJM) of titanium alloys, where the increase in the β due to

lower traverse speeds altered the mode of material removal from micro-indentation to micro-

cutting. For channels machined in glass (Fig. 5.15(a)), β = tan-1(channel depth / jet diameter)

increased from approximately 8° to 40° as the scan speed decreased from 0.5 to 0.05 mm/s, while in

PMMA (Fig. 5.15(b)), β increased from 11° to 72°.

128

0

50

100

150

200

250

300

0

75

150

225

300

375

0 0.1 0.2 0.3 0.4 0.5 0.6

Dep

th (µ

m)

Wid

th (µ

m)

Scan speed (mm/s)

Width DepthGlass

0

100

200

300

400

500

600

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4 0.5 0.6

Dep

th (µ

m)

Wid

th (µ

m)

Scan speed (mm/s)

Width DepthPMMA

(a) (b)

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6

Volu

me

rem

oved

×103

(µm

3 )

Scan speed (mm/s)

Glass

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6

Volu

me

rem

oved

×103

(µm

3 )

Scan speed (mm/s)

PMMA

(c) (d)

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 0.1 0.2 0.3 0.4 0.5 0.6

Aspe

ct ra

tio

Scan speed (mm/s)

Glass

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 0.1 0.2 0.3 0.4 0.5 0.6

Asp

ect r

atio

Scan speed (mm/s)

PMMA

(e) (f)

Figure 5.15: Effect of scan speed on depth, width, volume removed and aspect ratio (depth/width) during a single pass in: (a), (c), (e) glass, and (b), (d), (f) PMMA. Dashed lines show expected values if depth and volume were linearly proportional to the10 fold increase in dose from 0.5 to 0.05 mm/s (i.e. vs = 0.5 mm/s: D = 34 mg/mm, vs = 0.05 mm/s: D = 340 mg/mm). Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

129

α Particle

Traverse direction

Return flow

β

Figure 5.16: Scanning electron micrograph of the local front geometry of a channel in glass (side view). Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.2 mm/s, D = 85 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

As shown in Fig. 5.15(a), the width of channels in glass increased by 9%, mainly because of the

increase in the jet exposure time as the scan speed reduced from 0.5 to 0.05 mm/s. The small

increase of width was related to the weak dependency of the glass channel sidewall erosion rate on

the secondary impact of the rebounding particles, as discussed in Section 5.3.2. In contrast, the

width of channels in PMMA first increased by 15% in going from 0.5 mm/s to 0.2 mm/s, and then

decreased by 16% at 0.05 mm/s as shown in Fig. 5.15(b). The initial increase in the width with

slowing scan speed was consistent with the additional sidewall erosion caused by the additional

abrasive dose. The abrupt decrease in width from 0.2 to 0.05 mm/s (Fig. 5.15(b)) can be explained

by considering how the erosion of the slurry flow changed as the aspect ratio increased (Figs.

5.15(e) and (f)). Figure 5.17(a) illustrates that in high aspect-ratio channels (machined at low scan

speeds) the majority of the flow moves along the bottom of the channel, thereby decreasing the

130

relative amount of sidewall erosion compared with the low aspect-ratio situation in Fig. 5.17(b).

This is similar to the mechanism proposed by Fowler et al. [32] who investigated the role of jet

traverse speed on the rate of material removal in AWJM of titanium alloys. Therefore, the abrupt

decrease in width from 0.2 to 0.05 mm/s seen in Fig. 5.15(b) for PMMA was caused by the rapid

increase in the aspect ratio (Fig. 5.15(f)) and the corresponding reduction in the relative erosion of

the side-walls.

Incoming jet

Redirection of slurry flow along the bottom of channel

(x axis)

Leading edge

Return flow

x

z

Incoming jet

Return flow

Spread of slurry flow along the channel side walls

(y axis)

z

y

(a) (b)

Figure 5.17: Streamlines in ASJM of PMMA: (a) relatively slow scan speed (e.g. 0.05 mm/s) developing a high aspect-ratio (depth/width) channel, and (b) relatively fast scan speeds (e.g. 0.5 mm/s) developing a low aspect-ratio channel.

This effect of the aspect ratio achieved during a machining pass was further examined by

comparing two cases with equal abrasive dose; i.e. 5 passes at 0.5 mm/s and 50 passes at 5 mm/s.

Each pass of the latter produced an increment in channel profile having a much smaller aspect ratio

than did each pass at the slower scan speed. As expected from Fig. 5.15, in glass there was very

little effect of scan speed on width (Fig. 5.18(a)), while in PMMA (Fig. 5.18(b)) the width of the

machined channel was increased by 10% when the higher scan speed was used. These trends can be

131

explained by the differing flow fields present during the machining of shallow and relatively deep

channels. That is, the return slurry tends to flow along the length of a channel of sufficient depth

rather than radially and up the sidewalls, whereas the return flow spreads evenly in all directions in

shallow cases without relatively steep sidewalls that control the flow direction. This is similar to the

observations of Haghbin et al. [33] in AWJM. The effect of aspect ratio produced a larger initial

width in the 5 mm/s PMMA channel than that machined at 0.5 mm/s, beyond which flow

confinement remained constant; i.e. the flow was confined by the same aspect ratio except for the

initial machining pass.

-350

-300

-250

-200

-150

-100

-50

00 50 100 150 200 250 300 350

Dep

th (µ

m)

Width (µm)

5 P (0.5 mm/s)50 P (5 mm/s)

Glass

-400

-350

-300

-250

-200

-150

-100

-50

00 50 100 150 200 250 300 350 400

Dep

th (µ

m)

Width (µm)

5 P (0.5 mm/s)50 P (5 mm/s)

PMMA

(a) (b)

Figure 5.18: Channel profiles machined using a fixed abrasive dose delivered in two ways: 5 passes at 0.5 mm/s or 50 passes at 5 mm/s. (a) glass and (b) PMMA. Experimental conditions: dorifice =180 µm, C = 1 wt%, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm. vs = 0.5 mm/s: D = 34 mg/mm, vs = 5 mm/s: D = 3.4 mg/mm.

132

5.3.3.5 Effect of jet angle

Figure 5.19 shows the effect of jet angle (Fig. 5.1(d)) on the dimensions of channels machined in

glass and PMMA for a standoff distance do = 15 mm. These channels were machined in 5 forward

passes (Fig. 5.1(d)) at a scan speed of 0.5 mm/s giving a relatively small leading edge angle of less

than 11° per pass for both glass and PMMA. Figure 5.19(a) shows that the width and depth of

machined channels in glass decreased by 37% and 85%, respectively, as the jet angle was inclined

from 90° to 15°. These reductions were due to two effects: a) the decreased depth resulted mostly

from the reduced erosion in brittle materials with decreasing impact angle, and b) the reduction in

width was caused mainly by the decrease in the transverse spreading of the slurry flow at lower

impact angles, although changes in the local sidewall impact angle also played a role; i.e. slurry

flow was directed primarily along the channel as the jet angle decreased. For PMMA however, Fig.

5.19(b) shows that the width and depth were maximum at 45° and lowest at 15°, where the width

and depth were, respectively, 19% and 13% lower than at 90°. The observed trends on the width

and depth reflect the behaviour of the PMMA erosion rate as a function of the impact angle (Fig.

5.4(b)) in which the maximum material removal rate was reached at approximately 45°. The same

trend of decreasing width with decreasing jet angle was also observed when the particle density and

size were increased. It was found that the widths of channels machined with WO3 particles at a jet

incidence of θ = 30° reduced by 15% in glass (195 µm width, 160 µm depth) and 9% in PMMA

(335 µm width, 303 µm depth) compared with those machined using Al2O3 at the same depth and

jet angle (30°). For a given density but larger particles, the widths of channels machined using 20

µm diameter Al2O3 at a 30° jet incidence were 12% lower (212 µm width, 100 µm depth) in glass

and 7% lower (353 µm width, 243 µm depth) in PMMA compared to those of channels machined

133

with 10 µm Al2O3 at the same depth and jet angle. This trend was opposite to that presented in

Section 5.3.3.2 at θ = 90°, where larger particles produced wider channels.

0

30

60

90

120

150

180

0

50

100

150

200

250

300

350

0 15 30 45 60 75 90 105D

epth

(µm

)

Wid

th (µ

m)


Width DepthGlass

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

400

450

0 15 30 45 60 75 90 105

Dep

th (µ

m)

Wid

th (µ

m)


Width DepthPMMA

(a) (b)

Figure 5.19: Effect of slurry jet angle on depth and width of 5-pass channels in: (a) glass and (b) PMMA. Error bars represent the standard deviation for 3 measurements. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, do = 15 mm.

5.3.3.6 Effect of scan direction

The effect of jet orientation (forward and backward motion, Fig. 5.1(d)) in the multi-pass

machining of the channels of Fig. 5.19 was examined at a jet angle of 30°. Since the leading edge

angle was small (β < 5°), the local impact angle and the channel dimensions were the same in the

forward and backward directions. The machined channels at θ = 30° in glass, regardless of the

direction of motion, were smoother (Fig. 5.20) than those machined at θ = 90°. The average

roughnesses, Ra, of the bottom of the channel along the centerline were 57% (Ra = 0.4 µm) and 41%

(Ra = 0.54 µm) lower in backward and forward motion, respectively, compared to that of θ = 90°

(Ra = 0.92 µm). In the case of PMMA, the smoothing effect of backward motion was more evident,

134

with Ra being 67% and 81% smaller (Ra = 0.1 µm) than for forward motion at θ = 30° and θ = 90°,

respectively.

At jet impact angles lower than 90° in the backward orientation, the lateral slurry flow from the

footprint was directed along the channel length, thereby smoothing the channel surface in both glass

and PMMA as particles struck the channel surfaces at relatively small angles.

135

(a) (b)

(c) (d)

Figure 5.20: Scanning electron micrographs of the surface quality at the bottom of a 5-pass channel along centerline in: glass (a) backward (Ra = 0.4 µm), (b) forward (Ra = 0.54 µm) and PMMA (c) backward (Ra = 0.1 µm), (d) forward (Ra = 0.17 µm) as a function of jet orientation. Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 30°, do = 15 mm.

136

5.3.3.7 Effect of orifice size

One might expect that a decrease in the orifice diameter from 180 µm to 100 µm under identical

conditions would cause a 44% (100/180) decrease in the footprint and the channel width at a given

depth. However, for a slurry of 10 µm Al2O3 particles at 4 MPa with the 100 µm orifice, the

footprints in glass (157 µm wide) and PMMA (177 µm wide) were only 30% and 25% smaller,

respectively, than those with the 180 µm orifice. These larger than expected footprints could not be

explained by the increase in λ as the orifice diameter decreased.

To investigate this further, the particle size distributions passing through the two orifices were

measured and found to be significantly different; i.e. 180 µm orifice: average diameter 11.3 µm

(standard deviation 1.2, 500 counts), 100 µm orifice: average diameter 7.3 µm (standard deviation

1.4, 500 counts). Therefore, the 100 µm orifice filtered out larger particles, not by physical

blockage, but by a reduction in flow velocity which caused the larger particles to settle out of the

flow upstream of the orifice. The effect of the smaller particles from the 100 µm orifice was to

decrease λ, thereby increasing the footprint more than expected. This artifact of the present ASJM

system also changed abrasive concentration by filtering larger particles. The average concentration

of 5 60-second samples from the 100 µm orifice at 4 MPa was 0.58 wt% compared with 0.92 wt%

for the 180 µm orifice. These alterations of the average particle diameter and the particle

concentration resulted in a significant decrease of the erosive power of the jet and consequently the

need for additional passes to achieve a given depth with the smaller orifice.

In order to eliminate the effect of settling caused by the reduction in flow rate through smaller

orifices, 3 µm nominal diameter Al2O3 was used through 180, 100, 75 and 50 µm orifices. A

pressure of 6 MPa was used since these smaller particles could not erode glass appreciably at 4

137

MPa. The standoff distances and the particle concentrations were adjusted as shown in Tables 5.1

and 5.2 to maintain a constant jet velocity (110 m/s at 6 MPa) and particle dose (17 mg/mm). Figure

5.21 shows that in this case, the channel width decreased linearly with decreasing orifice size at

fixed depths of 20 µm in glass and 30 µm in PMMA. The maximum reductions in the channel

width were approximately 65% in glass and 62% in PMMA using the 50 µm orifice.

0

50

100

150

200

250

300

0 25 50 75 100 125 150 175 200

Wid

th (µ

m)

Orifice size (µm)

Glass

0

50

100

150

200

250

300

0 25 50 75 100 125 150 175 200

Wid

th (µ

m)

Orifice size (µm)

PMMA

(a) (b)

Figure 5.21: Channel width as a function of orifice size in (a) glass (11-pass, depth: 20 µm) and (b) PMMA (6-pass, depth: 30 µm). Experimental conditions: dp = 3 µm Al2O3, T = 15°C, θ = 90°, vs = 0.5 mm/s, D = 17 mg/mm; dorifice = 180 µm - Q = 2.0 mL/s , C = 0.4 wt%, do= 15 mm; dorifice = 100 µm - Q = 0.6 mL/s , C = 1.4 wt%, do=12 mm; dorifice = 75 µm - Q = 0.4 mL/s , C = 2.0 wt%, do=8 mm; dorifice = 50 µm - Q = 0.2 mL/s , C = 4.2 wt%, do = 5 mm. Error bars represent the standard deviation for 3 measurements. Solid lines added to guide the eye.

5.3.3.8 Effect of sacrificial coatings

As explained in Section 5.3.2, the low-pressure zone near the opening of a channel results in

rounded edges and effectively wider channels. As well, a frosted region of discrete particle impacts

borders the channels and could potentially create leakage in sealed micro-fluidic devices. Kowsari

138

et al. [12] examined the use of sacrificial layers of epoxy and glass sheets to minimize the diameter

and frosted region in micro-machined holes. It was shown that the sacrificial layers reduced the

diameter of the frosted zone and the opening hole diameter (increased the hole edge sharpness). A

similar approach was tested for channels by coating the glass target with a 1 mm thick sacrificial

layer of epoxy adhesive (J-B Weld, Sulphur Springs, Texas, USA). To match the depths of

channels, 9 passes were used with the coated glass while 5 passes were on the bare glass. After

machining, the coating was removed from the glass using a plastic scraper. Figure 5.22 shows that

the sacrificial layer eliminated the frosting zone, decreased the width, and reduced the rounding at

the glass edges of the channel.

139

-200

-150

-100

-50

00 50 100 150 200 250 300 350 400

Dep

th (µ

m)

Width (µm)

Without sacrificial layer

Epoxy coating

Glass

(a)

(b) (c)

Figure 5.22: (a) Channel profiles, (b) microscope image (top view) of 5-pass micro-channel machined in glass without sacrificial layer, and(c) with 1 mm thick epoxy coating (coating removed for photograph). Experimental conditions: dorifice =180 µm, C = 1 wt%, vs = 0.5 mm/s, D = 34 mg/mm, dp = 10 µm Al2O3, Q = 1.7 mL/s, T = 15°C, θ = 90°, do = 15 mm.

5.3.4 Summary of findings

Table 5.4 summarizes the percentage changes in channel width for a given depth as the ASJM

parameters were changed by the indicated amounts, i.e. those listed in the second column of Table

5.1. It is seen that channel width in glass was decreased by increasing the slurry temperature, and

decreasing the jet angle and orifice diameter. For PMMA, narrower channels resulted from

decreases in the scan speed, jet angle and orifice diameter.

140

For most of the operating parameters, the mechanism responsible for changes in the channel width

was a change in the kinetic energy of particles impacting the channel sidewall (zone II of Fig. 5.9).

Changes in the local impact angle were mainly responsible for the effects of scan speed and jet

angle, while the decreasing the jet orifice diameter decreased the channel width simply because of a

smaller jet footprint.

Table 5.4: Percentage change in channel width for the specified changes in the ASJM parameter for a given depth; (↑) indicates an increase, (↓) indicates a decrease.

Parameter Variation range Change in width (%) Primary reason for trend Glass PMMA Particle density, ρp (kg/m3) 3900-7160 +8 +10 Kinetic energy (↑) in zone II

Particle diameter, dp (µm) 10-20 +9 +11 Kinetic energy (↑) in zone II

Slurry jet velocity, vjet (m/s) 90-127 +36 +43 Kinetic energy (↑) in zone II

Slurry temperature, T (°C) 15-75 -21 N/A Kinetic energy (↓) in zone II Scan speed, vs (mm/s) 0.5-0.05 +9 -16 Change in local impact angle

Slurry jet impact angle, θ (°) 90-15 -37 -19 Change in local impact angle Orifice diameter, dorifice (µm) 180-50 -65 -62 Diameter of foot print (↓)

5.4 Conclusions

The effects of ASJM operating parameters such as jet traverse speed and orientation, number of

machining pass, particle density and diameter, orifice size, slurry temperature and velocity on the

minimum size of micro-channels machined with ASJ in borosilicate glass and

polymethylmethacrylate (PMMA) were investigated. The channels machined in PMMA were found

to be deeper with higher removed volumes than in glass under similar experimental conditions. It

was found that, although the ASJM operating parameters could be adjusted to affect the trajectory

of particles and thereby reduce the footprint (primary impact zone), this did not necessarily result in

narrower channels. This was because the channel width was governed by the additional erosion due

141

to the flow out of the footprint which caused the secondary impact of abrasive particles at impact

angles less than 90° on the channel sidewalls. This effect was substantial in the PMMA since the

material removal was controlled by cutting and ploughing mechanisms, but less important in glass

due to its greater erosion resistance at oblique incidence.

Channel depth in glass and PMMA increased with increasing particle kinetic energy, and

momentum equilibration number, λ; e.g. particle size, density, and impact velocity. However, due to

the additional erosion caused by the return flow on the channel side walls, increasing the particle

kinetic energy widened the machined channels. In contrast, narrower micro-channels for a given

depth could be machined by: (a) increasing the slurry temperature, (b) reducing the jet impingement

angle, and (c) machining at a slower scan speeds in PMMA, but not in glass. The use of smaller

orifices or sacrificial surface layers also significantly reduced the channel width and frosting in

glass.

The results of the study suggest that, in order to machine the narrowest channel at a given depth, the

orifice size should be minimized, the slurry temperature maximized, machining should be

conducted at oblique jet incidence and sacrificial layer should be used.

5.5 References



[3] T. Matsumura, T. Muramatsu, S. Fueki, Abrasive water jet machining of glass with stagnation effect, Journal of Manufacturing Technology 60 (2011) 355-358.

142



[6] K.L. Pang, T. Nguyen, J.M. Fan, J. Wang, Modeling of the micro-channeling process on glasses using an abrasive slurry jet, International Journal of Machine Tools and Manufacture 53 (2012) 118-126.

[7] H. Qi, J.M. Fan, J. Wang, An experimental study of the abrasive water jet micro-machining process for quartz crystals, Journal of Advanced Materials Research 565 (2012) 339-344.

[8] H. Nouraei, A. Wodoslawsky, M. Papini, J.K. Spelt, Characteristics of abrasive slurry jet micro-machining: a comparison with abrasive air jet micro-machining, Journal of Materials Processing Technology 213 (2013) 1711–1724.


[10] R.H.M. Jafar, H. Nouraei, M. Emamifar, M. Papini, J.K. Spelt, Erosion modelling in abrasive slurry jet micro-machining of brittle materials, Journal of Manufacturing Processes 17 (2015) 127-140.

[11] K. Kowsari, D.F. James, M. Papini, J.K. Spelt. The effects of dilute polymer solutions on the shape, roughness and width of abrasive slurry jet micro-machined channels, Wear 309 (2014) 112-119.

[12] K. Kowsari, H. Nouraei, D.F. James, J.K. Spelt, M. Papini, Abrasive Slurry Jet Micro-machining of Holes in Brittle and Ductile Materials, Journal of Materials Processing Technology 214 (2014) 1909-1920.



[15] P.E. Dimotakis, The mixing transition in turbulent flows, Journal of Fluid Mechanics 409 (2000) 69-98.


[17] R.H.M. Jafar, J.K. Spelt, M. Papini, Surface roughness and erosion rate of abrasive jet micro-machined channels: experiments and analytical model, Wear 303 (2013) 138-48.

143


[19] Y.M. Ali, J. Wang, Impact Abrasive Machining. In: Jackson MJ, Davim JP, editors. Machining with Abrasives, Springer, West Lafayette (2011) 385-422.


[21] V.B. Nguyen, Q.B. Nguyen, Z.G. Liu, S. Wan, S.Y.H. Lim, Y.W. Zhang, A combined numerical-experimental study on the effect of surface evolution on the water-sand multiphase flow characteristics and the material erosion behavior, Wear 319 (2014) 96-109.

[22] K. Kowsari, H. Nouraei, M. Papini, J.K. Spelt, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in alumina, ICOMM 2014-9th International Conference on Micro-manufacturing, Singapore (2014).


[24] H. Getu, A. Ghobeity, J.K. Spelt, M. Papini, Abrasive jet micromachining of polymethylmethacrylate, Wear 263 (2007) 1008-1015.

[25] J. Fan, C. Fan, J. Wang, Flow dynamic simulation of micro abrasive water jet, Solid State Phenomena 175 (2011) 171-176.


[27] J. Kestin, M. Sokolov, W.A. Wakeham, Viscosity of liquid water in the range -8°C to 150°C, Journal of Physical and Chemical Reference Data 7 (1978) 941-948.


[29] H. Devlin, P. Kaushik, The effect of water absorption on acrylic surface properties, Journal of Prosthodontics 14 (2005) 233-238.

[30] L. Ma, C. Huang, Y. Xie, J. Jiang, K.Y. Tufa, R. Hui, Modeling of erodent particle trajectories in slurry flow, Wear 334-335 (2015) 49-55.

[31] P.H. Shipway, G. Fowler, I.R. Pashby, Characteristics of the surface of a titanium alloy following milling with abrasive water jets, Wear 258 (2005) 123-132.

[32] G. Fowler, P.H. Shipway, I.R. Pashby, Abrasive water jet controlled depth milling of Ti-6Al-4V alloy: an investigation of the role of jet-workpiece traverse speed and abrasive grit

144

size on the characteristics of the milled material, Journal of Materials Processing Technology 161 (2005) 407-414.

[33] N. Haghbin, J.K. Spelt, M. Papini, Abrasive water jet micro-machining of channels in metals: Model to predict high aspect-ratio channel profiles for submerged and unsubmerged machining, Journal of Materials Processing Technology 222 (2015) 399-409.

145

Chapter 6: Calibrated CFD Erosion Modeling of

Abrasive Slurry Jet Micro-machining of Channels in

Ductile Materials

6.1 Introduction

6.1.1 Abrasive slurry jet micro-machining (ASJM)

Abrasive slurry jet micro-machining (ASJM) uses a jet of fine abrasive slurry to machine

controlled-depth features such as micro-channels in a wide range of ductile and brittle materials.

Similar to abrasive water (AWJM) and air (AJM) jet machining, material removal occurs by

mechanical erosion without altering the substrate material properties. The machining of micro-

channels has application in the fabrication of micro-fluidic and micro-electromechanical systems,

such as those in lab-on-chip and biomedical devices, heat sinks of electrical devices and capillary

electrophoresis chips. For example, Bhagat et al. [1] introduced a novel method to enhance particle

filtration based on their size by using shear-modulated inertial migration in high aspect ratio (depth

to width ratio) micro-channels. Chang et al. [2] investigated the use of a power law model for blood

flow mechanics in micro-channels for lab-on-chip applications. Thakre et al. [3] studied the heat

efficiency of micro-channels with liquid cooling in electronic devices.

Guijt et al. [4] and Schlautmann et al. [5] introduced powder blasting with air (AJM) as an

alternative method for the fabrication of micro-channels in capillary electrophoresis devices. ASJM

146

is recognized as a non-conventional and relatively inexpensive machining process for producing

micro-channels in such devices, as discussed by Kipling et al. [6]. The further development of

ASJM requires models capable of predicting the shape and size of micro-machined features without

the need to conduct extensive testing. For example, Taguchi and dimensional analysis methods

have been used by Pang et al. [7, 8] to predict the profiles of micro-machined channels; however,

these modeling techniques require a relatively large set of experimental trials.

6.1.2 Existing profile modeling in abrasive jet processes

Surface evolution models for predicting the evolving shape of features machined in brittle materials

using abrasive air jets in AJM, distinct from the presently utilized ASJM liquid slurry system, were

pioneered by Slikkerveer and in’t Veld [9], and ten Thije Boonkkamp and Jansen [10]. Ghobeity et

al. [11] introduced the use of a shallow "first-pass eroded profile" in these AJM models to

characterize the distribution of erosive potential (the ‘erosive efficacy’) provided to the surface by

the passing jet. This approach conveniently captured the erosion characteristics of the machining

apparatus and target material, which was initially glass. As a result, the methodology was adapted

to develop evolution models for the AJM of ductile targets, and has also been applied to channels

machined with AWJM and ASJM, although the fluid flow of the impinging jet, and thus the particle

trajectories and interactions with the target substrate differ significantly from those in air-based

AJM. For example, Getu et al. [12, 13] and Ally et al. [14] modified the earlier surface evolution

model for AJM of brittle materials to enable profile prediction in ductile materials such as

polymethylmethacrylate (PMMA) and metals (6061-T6 aluminum, Ti-6Al-4V titanium and 316L

stainless steel) at both normal and oblique jet angles, respectively. Axinte and coworkers [15, 16]

used a water-jet footprint (i.e. a shallow channel) in order to model the AWJ milling process in

147

brittle (SiC ceramic) and ductile (Ti-6Al-4V titanium alloy) materials. Haghbin et al. [17] used a

surface evolution model to predict the profile of high aspect-ratio (depth/width) channels in the

AWJ micro-machining of metals (316L stainless steel and 6061-T6 aluminum alloy) by

incorporating empirical coefficients to account for the changes in the flow field with increasing

depth. They successfully corrected the nonlinearity in the depth increase with abrasive dose and the

general shapes of the channels, but, for reasons discussed in Section 6.1.3, their model was

incapable of capturing the progressive widening of the channel openings as the depth increased.

Nouraei et al. [18] showed that, for ASJM, the widening of the channel opening was mainly due to

the additional erosion caused by the lateral flow outside of the jet footprint zone. Due to differences

in the erosion mechanisms and the shallow particle impact angles, this additional erosion was found

to be significant in channels machined in ductile materials, but not in brittle materials. This

widening of channels as they become deeper was not evident in AJM, because the much lower

viscosity of air compared with water eliminated erosion due to lateral flow. Therefore, the “first-

pass eroded profile” approach used in AJM profile modeling does not work for the ASJM of ductile

materials.

6.1.3 Motivation for a CFD approach

All of the previous studies described in Section 6.1.2 assumed that the distribution of erosive

efficacy within the footprint of the jet at any time could be estimated based on measurements of

shallow first-pass channel profiles. This approach is justified for air-particle jet systems, but when

water-particle slurries are used, lateral flow occurs outside the footprint, causing additional

progressive channel widening that cannot be captured by the first pass. For AWJM, Haghbin et al.

[17] suggested that this widening effect might properly be modeled using computational fluid

148

dynamic (CFD) models that incorporate the effects of flow fields and particle trajectories on the

erosion pattern in and around the footprint. They did not, however, implement this suggestion in

their AWJM work. As discussed below, the present study will adopt such an approach for ASJM.

Although a number of previous studies incorporated CFD models to predict erosion in slurry

erosion testers, they were limited to flat targets and neglected the effect of a deepening wear scar on

the slurry flow field. For example, Gnanavelu et al. [19, 20] used CFD simulations to characterize

the particle impact angles and velocities, and thus obtain the material wear map for a slurry jet

impinging on a plate that remained flat. Mansouri et al. [21] also used CFD results to relate particle

impact angles and velocities to measured erosion depths on a flat target in order to develop an

erosion equation. Moreover, these simulations were conducted at much lower Reynolds numbers

and the experimental systems were on a much larger scale than is typical of ASJM, as discussed by

Kowsari et al. [22].

In summary, the present study focused on the development of a new numerical-empirical profile

prediction model using CFD models to account for the effect of flow fields within the cavity of an

eroded feature in order to accurately predict the shape and size of micro-channels machined with

ASJM. To the knowledge of the author, this is the first study to consider the modeling of ASJM

features machined in ductile materials such as acrylic and metallic targets.

149

6.2 Experiments

6.2.1 ASJM setup and machining tests

The ASJM apparatus, developed by Nouraei et al. [23], with a sharp 180 µm diameter sapphire

orifice (length to diameter ratio of 1.67; contraction coefficient of 0.72; KMT Waterjet, KS, USA)

was used for machining micro-channels. The apparatus consisted of a stirred slurry tank, a positive

displacement slurry pump (LCA/M9/11-DC, LEWA Inc., Leonberg, Germany) with pulsation

damper (FG44969/01-9, Flowguard Ltd., Houston, TX, USA) and a linear stage system (KT-

LSM100A, Zaber Technologies Inc., Vancouver, BC, Canada).

Micro-channels were machined on 50×50×3 mm thick plates of polymethylmethacrylate (PMMA),

6061-T6 aluminum, 316L stainless steel and Ti–6Al–4V titanium alloys. The slurry was prepared

by mixing water at room temperature (T = 20°C) with a given wt% of 10 µm nominal diameter

Al2O3 abrasive particles (Comco Inc., Burbank, CA, USA; density 3900 kg/m3; Vickers hardness 16

GPa). In order to ensure a uniform particle size sampling, a standard quartering technique [24] was

used. The homogeneity of the slurry was ensured by continuously mixing it in the open slurry tank.

The centerline depth, width, volume of material removal, specific erosion rate and profiles of

micro-channels were obtained using an optical profilometer (ST400, Nanovea Inc., CA, USA), as

described in detail by Nouraei et al. [23]. Each measurement was repeated using three different

cross-sections 1 mm apart. It was established that the variation of centerline depth and width along

the channel length was less than 7%. The process repeatability of ASJM was evaluated by

replicating some of machined channels three times on separate days. It was found that the variation

in centerline depth and width of the replicate features were less than 11%.

150

Table 6.1 summarizes the properties of the test materials and Table 6.2 outlines the machining

conditions. The diameter of the slurry jet produced by the 180 µm diameter orifice for the range of

applied pressures (4-7 MPa) was measured to be 150 µm, as described by Nouraei et al. [18].

Table 6.1: Properties of the target materials.

Material Vickers hardness (GPa)

Density (kg/m³) Supplier

PMMA 0.17 1180 Piedmont Plastics Inc., ON, Canada 6061-T6 aluminum 1.10 2713 McMaster-Carr, Elmhurst, IL, USA 316L stainless steel 2.20 8027 McMaster-Carr, Elmhurst, IL, USA Ti–6Al–4V titanium 3.25 4430 McMaster-Carr, Elmhurst, IL, USA

Table 6.2: Process parameters used in channel machining, velocity exponent and erosion rate measurements.

Type of experiment Operating parameter Machining channels Velocity exponent Measuring erosion rate

Slurry pressure, P (MPa) 4 4 5 6 7 4 Jet flow rate, Q (mL/s) 1.7 1.7 1.8 2.0 2.2 1.7 Jet velocity, vjet (m/s) 90 90 100 110 118 90 Particle concentration, C (wt%) 1 1 0.94 0.85 0.77 1 Particle dose, D (mg/mm) 34 34 34 Scan speed, vs (mm/s) PMMA 0.5 0.5 0.5 AL6061-T6 0.2 0.5 0.5 316L SS 0.05 0.5 0.5 Ti–6Al–4V 0.07 0.5 0.5 Jet impact angle, θ (°) 90 90 15, 30, 45, 60, 75, 90 Orifice to target distance, do (mm) 20 20 20

6.3. Modeling

The profile prediction model required two main steps: a) obtaining an estimate of the initial spatial

distribution of the erosive efficacy, E(x), of the slurry jet (Fig. 6.1) using a CFD model of the slurry

151

flow in the cross-sectional profile of an actual shallow channel, including the effects of flow outside

of the footprint and profile, and b) predicting how the cross-sectional shape of machined channels

changes as they become deeper using the obtained erosive efficacy distribution, E(x), and a

numerical model.

6.3.1 CFD modeling

Due to the variation of the drag forces on the particles within the stagnation zone, the particle local

impact angles and velocities are not equal to the nominal slurry jet impact angle and velocity.

Suspended particles that move closer to the center of the jet impact the target surface with higher

impact angles and lower impact velocities compared to those moving further from the jet centerline,

as discussed by Jafar et al. [25]. Thus, a complete understanding of the distribution of the local

impact angles and impact velocities of particles in a slurry jet was required. The following three-

dimensional multi-phase CFD models of a slurry jet surrounded by air and striking a target were

developed using ANSYS-Fluent 15.0 (ANSYS Inc., Cecil Township, PA, USA) and then used to

predict channel profiles:

Model 1. A model with the jet at θ = 90° (perpendicular incidence) to a flat wall was developed for

the range of applied pressures (4, 5, 6 and 7 MPa) to determine the average local particle impact

velocity of particles. The flat wall accurately represented the typically flat bottom of shallow single-

pass ASJM channels. This model was used in Section 6.4.1 to determine the velocity exponent, n,

which relates the specific erosion rate of the target material (mass of material removed per mass of

erodent), Er, to the particle impact velocity.

152

Model 2. Models of the impingement of slurry jets on a flat wall at jet impact angles, θ, between

15° and 90° at 15° intervals were developed to estimate the average local particle impact angle, α,

in order to interpret the corresponding erosion experiments. These were used in Section 6.4.2 to

obtain the specific erosion rate as a function of the particle impact angle.

Model 3. Models of a slurry jet striking measured shallow (<35µm), first-pass channel profiles

created at θ = 90° incidence in the acrylic and metallic targets were developed and used to obtain

the erosive efficacy distribution, E(x), of the jet on the surface, both within and outside of the

eroded profile, as described in Section 6.4.4.

The first two models were developed to interpret fundamental erosion data for the specific target

material. The third model then used these property data to predict channel cross-sectional shapes

evolving from the initial shallow first-pass profile. The approach used in all three models neglected

the change in the impact angle created by the shallow (<15°) slope of the leading edge of the

machining kerf in the direction of scanning. In practice, such small leading-edge slopes are readily

achieved using sufficiently large scanning speeds to limit the depth increase per pass of the jet.

6.3.1.1 Domain, boundary conditions and assumptions used for the CFD models

Figure 6.1 illustrates the geometry and the boundary conditions of the 3D computational domain for

a slurry jet striking a flat target at θ = 45° (i.e. as an example of oblique jet incidence), and a

shallow channel profile at θ = 90°. The fluid entered the domain with a specified velocity over a

150 µm diameter plane and the particles were uniformly injected over the inlet plane at a velocity

equal to the fluid velocity. Nouraei et al. [26] showed that, for typical conditions in ASJM, the

153

particles reach the jet fluid velocity at about 10 mm from the orifice exit, prior to entering the

stagnation zone near the target where the particles are slowed and deflected before striking the

target (i.e. do = 20 mm, Table 6.2). Emamifar [27] modeled ASJM on a flat target and measured the

stagnation length to be less than 160 µm. Thus, in order to accurately capture the slurry flow

interactions with the target, the inlet was placed 250 µm away from the target in all CFD

simulations and the jet velocities used at the inlet were calculated using flow rate measurements

provided in Table 6.2.

The channel profile and flat target boundary were treated as a smooth, no-slip wall. The other

bounding planes of the domain were treated as free boundaries with a pressure outlet condition. A

grid sensitivity analysis revealed that the accuracy of the CFD simulations were approximately

independent of the mesh size when the interior domain was meshed with approximately 3 µm

hexahedral elements. The fluid flow was treated as steady, incompressible and Newtonian. As

suggested by Mansouri et al. [21], the volume of fluid (VOF) front tracking scheme and the shear-

stress transport (SST) k-ω turbulence model were used for the primary phase (water) and the

surrounding secondary phase (air). Simulations were terminated when the residuals of the

monitored flow parameters were less than 10-4, as recommended by Gnanavelu et al. [20].

Since the particle concentration was low (~1 wt%), particle-particle collisions and the effect of

particles on the flow field were considered insignificant. Therefore, the particle tracking was

performed after flow modeling as a post-processing step, as suggested by Zhang et al. [28]. Particle

trajectories were modeled using the discrete particle model (DPM) in which Lagrangian particle

tracking was conducted by considering the fluid forces acting on the solid particles. These forces

include the drag force, the pressure gradient force and the added mass force, as suggested by Zhang

et al. [28]. The particle shape factor (ratio of surface area of a sphere having the particle volume to

154

the actual particle surface area) was set at 0.76 for the 10 µm nominal diameter angular Al2O3

abrasives, as measured by Dehnadfar et al. [29]. For erosion modeling, the discrete random walk

(DRW) model was used to account for any possible changes in the particle trajectories caused by

flow turbulence. Since the coefficient of restitution for the four materials examined in this study

was unknown, the coefficient of restitution was selected by varying its value in CFD Model 3

between 0.2 to 0.5 with 0.05 increments. This range encompassed the value found by Slikkerveer

and in't Veld [9] for similarly sized Al2O3 particles impacting glass. Values less than 0.2 and higher

than 0.5 were also tested, but were found to significantly under-estimate or over-estimate the

channel sidewall erosion. A coefficient of restitution of 0.3 provided the best fit with the measured

channel sidewall erosion and consequently channel widening.

The effect of the squeeze film (a thin layer of liquid separating the approaching solid particles from

the target wall) was considered negligible, mainly because the relative Reynolds number of the

particles (calculated using the relative water/particle velocity, 300 ≤ Re ≤ 500) at the time of impact

was significantly higher than the critical range (17 ≤ Rec ≤ 32) reported by Clark [30], who

examined the influence of the squeeze film in slurry erosion.

155

Z X

Y

Outlet (pressure outlet)

150 µm Ø Inlet (velocity inlet)

Target (wall)

Outlet

Outlet

Outlet

θ

(a)

Z X

Y

Outlet (pressure outlet)

Symmetry plane

150 µm Ø Inlet (velocity inlet)

Channel profile

Target (wall)

Outlet Outlet

Symmetry plane

(b)

Figure 6.1: Domains and boundary conditions of the CFD models for the 3D simulation of the particle trajectories within: (a) a channel at θ = 90° incidence and (b) a flat target at oblique incidence (θ = 45°; half the channel modelled).

156

6.3.1.2 Calculation of the erosive efficacy distribution during ASJM

The specific erosion rate (mass of material removed per mass of erodent), Er, as a function of the

particle impact angle, α, and velocity, vP, were used to express the solid particle erosion, EP, in

brittle and ductile materials as suggested by Oka et al. [31, 32],

( )90nPrE Av° = (6.1)

( ) ( ) ( )90r rE g Eα α °= (6.2)

where Er(90°) and Er (α) are, respectively, the specific erosion rate at perpendicular incidence and at

an arbitrary angle, n is the velocity exponent which expresses the dependence of erosion on the

particle impact velocity, g(α) is the dependence of erosion on the particle impact angle, and A is

associated with the material properties of the abrasive erodent and target substrate, generally taken

as constant for a given system.

Empirical curve fits based on the experimentally measured erosion scars and the averaged value of

the local particle impact velocities and angles calculated from Models 1 and 2, respectively, were

used to obtain the average n, A and g(α) for the jet impinging on acrylic and metallic targets

(Sections 6.4.1 and 6.4.2). This information was then used in Model 3 to calculate the rate of

surface erosion (kg/m2s-1), Rerosion, using the following definition, as provided by ANSYS-Fluent

15.0 [33],

1

ParticlesNp r

erosionp cell

m ER

A=

= ∑

(6.3)

157

where ṁP is the abrasive particle mass flow rate and Acell is the area of a given computational cell on

the target wall. Figure 6.2 shows an example of jet impingement of 10 µm Al2O3 particles and the

resulting erosion pattern on the target surface of a shallow channel machined in PMMA. It is seen

that the erosion was mostly concentrated directly underneath the jet with evidence of erosion on the

sidewalls. As the jet scans in the z direction (Fig. 6.2), any point on a cross-section along the

channel length (e.g. point A in Fig. 6.2) is exposed to a total particle dose equivalent to the sum of

the doses along a line through that point and parallel to the traverse path; i.e. line A-A' in Fig. 6.2.

Therefore, the 3D erosion map created by scanning the jet could be represented in a 2D cross-

sectional plane by summing along multiple lines parallel to the centerline offset by a known

distance. In the present case, 32 lines with 5 µm offset distance were used across the 150 µm jet in

Model 3. The numerical results were normalized by dividing by the centerline value (at x = 0), and

then fitted with a polynomial function using the curve-fit toolbox of MATLAB 8.3.0 (Mathworks,

Natick, MA, USA), as discussed in Section 6.4.4.

158

Z X

Y

Particle velocity (m/s)

Inlet

Channel profile

Particle trajectory

(a)

Z X

Y

Erosion rate (kg/m2s-1)

Inlet

Erosion pattern

Channel profile

A E(xA)=∑ Rerosion (Line AA')

A'

Line AA'

(b)

Figure 6.2: CFD predictions of Model 3 for: (a) particle trajectories during jet impingement of 10 µm Al2O3 particles and (b) the resulting erosion pattern on the target surface of a shallow (35 µm deep) channel machined in PMMA. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 90°.

159

6.3.2 Micro-channel profile development

For a given point on the channel profile, P(xo, yo) in Fig. 6.3, it was assumed that the surface eroded

instantaneously in the direction of the local normal, as described by Slikkerveer and in’t Veld [9].

Referring to Fig. 6.3, the surface movement of the profile in a time dt can be expressed as

n ox x dx= + (6.4)

n oy y dy= + (6.5)

( ) ( )* sin .o cdx E x D dtβ= (6.6)

( ) ( )* cos .o cdy E x D dtβ= (6.7)

where E*(xo) is the non-dimensional normalized erosive efficacy distribution (i.e. the erosive

efficacy distribution at a given point was divided by that at x = 0), β is the angle between the local

normal to the surface and the perpendicular coordinate, y, Dc (µm) is an erosion constant that

converts the surface erosion rate to the corresponding shift in the target wall location, and t is the

etching time. The micro-channels were fabricated by scanning the slurry jet repeatedly over the

target surface at a given scan speed. Since the etch rate on the channel centerline remained constant

at all depths, as discussed in Section 6.4.3, the number of machined passes, Np, could be substituted

for the etching time, t, in Eqs. (6.6) and (6.7). The centerline depths of first-pass channels machined

in the four tested materials were used to obtain the constant, Dc. As discussed in more detail in

Section 6.4.5, these first-pass profiles were also used to calculate β, the angle between the local

160

normal to the surface and the y coordinate (Fig. 6.3) for any given point on the channel profile,

P(xo, yo), by fitting a polynomial function, f(x), and solving the following equations,

( )( )( )

12' 2

1sin1 of x

β−

=

+

(6.8)

( )( )( )

12' 2

1cos1 of x

β =

+

(6.9)

where f '(x) is the first derivative of the polynomial function, f(x), with respect to x.

Y

n

dx

dy

xo

yn

β

X

xn

yo

Channel profile β

P(xo, yo)

P(xn, yn)

Figure 6.3: Schematic of the propagation of a given point on an eroding two-dimensional channel profile.

The cross-sectional channel profiles at any given pass, Np, were then obtained numerically using

Eqs. (6.4)-(6.9) by inputting E*(xo), extracted from Model 3 using a code written using MATLAB

8.3.0.

161


6.4.1 Target erosion characterization: Velocity exponent at perpendicular incidence derived from specific erosion rate measurements and Model 1

To quantify the relationship between the ASJM specific erosion rate and particle impact velocity at

perpendicular incidence (θ = 90°), Er(90°), single-pass channels were machined at various jet

velocities, vjet (90-118 m/s corresponding to 4-7 MPa), in PMMA, AL6061-T6, 316L SS and Ti–

6Al–4V. The specific erosion rates were measured following the methodology used by Jafar et al.

[34], in which the volume of material removed and the specific erosion rates (mass of material

removed per mass of erodent) were measured along the channel centerline. Since the ASJM specific

erosion rates were measured at the centerline, the average local particle impact velocities and angles

were also computed along the jet diameter in the direction of motion (y-z plane, Section 6.3.1) using

Models 1 and 2. Depending on the jet pressure, the particle concentration in the mixing tank was

adjusted (Table 6.2) to ensure a constant particle dose (mass of particles striking the channel in a

pass per unit length) for all experiments. The ASJM channels were relatively shallow (i.e. aspect

ratio below 0.2) with relatively flat bottoms at the centerline, consistent with the flat wall

assumption used in Model 1 (Section 6.3.1) to compute the average impact velocity of particles. In

order to account for the range of particle impact velocities seen by the target surface as the jet

passes at the centerline, as shown in Fig. 6.4(a), the particle impact velocities for each applied

pressure were averaged along the y-z plane, parallel to the direction of motion. As illustrated in Fig.

6.4(b), particles near the jet axis travelled slower than those nearer the periphery. This can be

explained by examining the effect of fluid flow on the particle velocity components in the y and z

directions (Fig. 6.4(a)). The particles travelling close to the jet axis (i.e. stagnation point) are not

deflected by the fluid and travel in straight line trajectories. In this region, the drag force is more

effective in decelerating the suspended particles along the y direction compared to the jet periphery,

162

as discussed by Jafar et al. [25]. The particles that travel away from the jet axis experience

relatively less deceleration through the fluid in the y direction along with an acceleration in the z

direction due to the fluid accelerating away from the stagnation point, as described by Laitone [35].

This results in an overall increase in the magnitude of the vector sum of the y and z velocity

components, and consequently increases the particle impact velocity.

Table 6.3 summarizes the range of local particle impact velocities on the centerline for the specified

jet velocities at perpendicular incidence. The obtained specific erosion rates were then plotted as a

function of the average particle impact velocities and the velocity exponent, n, and the constant, A,

were determined by fitting the results to Eq. (6.1).

Figure 6.5 shows the specific erosion rates as function of the particle impact velocities and Table

6.4 summarizes the best fit values for these target materials. As expected, the specific erosion rate

increased with increasing particle kinetic energy on the target. The resulting velocity exponents

were in the range of 2-4, consistent with those reported by Feng and Ball [36] for solid particle

erosion of ductile materials obtained using various erodent particles.

163

Pressure (Pa)

Jet boundary

Particle trajectory

Stagnation point

Stagnation zone

Target

vjet = 90 m/s

34 m/s < vP < 57 m/s

P1 P2

vP1< vP2

Z Y

Stagnation point (a)

0

20

40

60

80

100

120

0 50 100 150 200 250 300

Par

ticle

vel

ocity

(m/s

)

Distance from the inlet (µm)

P P1 2

Target

(b)

Figure 6.4: (a) CFD predictions of Model 1 for 10 µm nominal diameter particle trajectories at normal jet impingement and (b) comparison of the particle impact velocities on the centerline (P1) and periphery of the jet (P2). Particles P1 and P2 illustrate change in impact angle and velocity with position in the jet. The ''o’s" indicate the particle impact velocity at the target. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 90°.

164

Table 6.3: CFD predictions (Model 1) of the range of local particle impact velocities over the jet footprint along the centerline for the specified jet velocity.

Particle impact velocity, vP (m/s) Slurry pressure, P (MPa) Jet velocity, vjet (m/s) Range Average

4 90 34-57 47 5 100 38-66 52 6 110 42-73 57 7 118 46-80 63

80 90 100 110 120 130 140 150

0.0

0.2

0.4

0.6

0.8

1.0

1.2

40 45 50 55 60 65 70 75

Jet velocity,vjet (m/s)

Spe

cific

ero

sion

rate

, Er(m

g/g)

Particle velocity,vP (m/s)

PMMA Al6061-T6316L SS Ti-6Al-4V

Figure 6.5: Specific erosion rate as a function of particle impact velocity for PMMA, Al6061-T6, 316L SS and Ti-6Al-4V. Error bars represent the standard deviation for 3 cross-sectional profile measurements 1 mm apart on a given channel. Solid lines represent the best-fit of erosion data to Eq. (6.1). Experimental conditions: D = 1 mg/mm, vs = 0.5 mm/s.

Table 6.4: Best-fit constants (Eq. (6.1)) for the impact velocity dependence of erosion.

Material A ((mg/g)×(m/s)-n

) n PMMA 1×10-9 3.3 AL6061-T6 2×10-6 3.05 316L SS 2×10-5 2.35 Ti–6Al–4V 3×10-5 2.07

165

6.4.2 Target erosion characterization: Erosion constants for oblique impact derived from specific erosion rate measurements and CFD Model 2

The specific erosion rate for each of the test materials as a function of the particle impact angle,

Er(α), was measured at the centerline by machining single-pass channels at a pressure of 4 MPa (vjet =

90 m/s) and at jet impact angles, θ, from 90° to 15° in the y-z plane. These measurements were made

on shallow channels (i.e. aspect ratio below 0.1) in order to approximate impact on a flat surface

(Model 2 in Section 6.3.1). Similar to Section 6.4.1, to take into account the range of local particle

impact angles seen by the target surface, illustrated in Fig. 6.6, the particle impact angles were

averaged along the centerline y-z plane for each jet impact angle. Table 6.5 summarizes the range of

local particle impact angles for the specified jet impact angles. For each material, the measured

specific erosion rates at a given angle were normalized, Er*, to their values at θ = 90°, and the results

were then plotted as function of average particle impact angle, as illustrated in Fig. 6.7. The trends of

Fig. 6.7 indicated a typical ductile erosion behavior in which the maximum erosion occurred between

20° and 30°. Following the work of Haghbin et al. [17], the semi-empirical relation proposed by Oka

et al. [32] was used to characterize the dependence of erosion on the particle impact angle, g(α),

( ) ( ) ( )( ) 21sin 1 HV 1-sinnng α α α= + (6.10)

where n1 and n2 are constants, HV is the Vickers hardness of the specimen before machining (Table

6.1) and α is the average particle impact angle for the specified jet impact angle, θ. The n1

and n2 constants (Table 6.6) were obtained by fitting the normalized erosion data using the

nonlinear least squares method of MATLAB 8.3.0 to Eq. (6.10). The results presented in Table 6.4

indicate that the mass loss and volumetric erosion rates of the three metals were noticeably lower

than those in PMMA.

166

Pressure (Pa) Jet boundary

Target

Particle trajectory

Stagnation zone

α2 < α1

P1

27° < α < 45°

θ = 45°

α1 P2 α2

Z Y

Figure 6.6: CFD predictions of Model 2 for 10 µm nominal diameter particle trajectories at oblique jet impingement. Particles P1 and P2 illustrate variation in local impact angle across footprint. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 45°.

Table 6.5: CFD predictions (Model 2) of the local particle impact angles along the centerline for the specified jet impact angle.

Particle impact angle, α (°)

Jet impact angle, θ (°) Range Average 15 7-15 10 30 16-30 23 45 27-45 35 60 42-64 50 75 57-83 70 90 58-90 74

167

0 10 20 30 40 50 60 70 80 90 100

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80

Jet impact angle, θ (deg)

Nor

mal

ized

ero

sion

rate

, E* r

Particle impact angle, α (deg)

PMMA Al6061-T6316L SS Ti-6Al-4V

Figure 6.7: Normalized erosion rate along the centerline as a function of average particle impact angle of PMMA, Al6061-T6, 316L SS and Ti-6Al-4V. Error bars represent the standard deviation for 3 cross-sectional profile measurements 1 mm apart on a given channel. Solid lines represent the best-fit of erosion data to Eq. (6.10). Experimental conditions: P = 4 MPa (vjet = 90 m/s), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s, vs = 0.5 mm/s.

Table 6.6: Best-fit constants (Eq. (6.10)) for the impact angle dependence of the specific erosion rates.

Material Vickers hardness

(GPa) n1 n2

Measured erosion rate at θ = 90° (P = 4 MPa, vjet = 90 m/s)

(mg/g) (mm3/g)×103

PMMA 0.17 2.36 29.5 0.28 237 AL6061-T6 1.10 1.54 3.88 0.20 74 316L SS 2.20 1.26 1.92 0.13 17 Ti–6Al–4V 3.25 1.08 1.17 0.09 22

6.4.3 Comparison of channel shapes in acrylic and metallic targets

Figure 6.8 shows the cross-sectional profiles of shallow single-pass channels machined in the test

materials, PMMA, AL6061-T6, 316L SS and Ti–6Al–4V, at θ = 90° and P = 4 MPa (vjet = 90 m/s).

Since the resistance of the test materials to solid particle erosion differed (Fig. 6.5 and Fig. 6.7), the

scan speeds were adjusted (Table 6.2) to ensure that the depths of the machined channels were

168

approximately equal. Figure 6.8 demonstrates that the ASJM channel profiles were all "U"-shaped

having steep sidewalls and flat bottoms. Nouraei et al. [18] attributed this general profile shape in

brittle and ductile materials such as glass and PMMA, respectively, to the uniform erosive efficacy

distribution of ASJM across the jet footprint. The machined channels were approximately 2 times

wider than the jet diameter (150 µm), due to the additional erosion caused by secondary impacts of

particles carried by the slurry return flow along the channel sidewalls, as explained by Nouraei et al.

[18]. The channel machined in PMMA was the widest, 19% (307 µm) wider than that of the

narrowest channel in Ti–6Al–4V (258 µm), mainly because the erosion rate is highest in PMMA

and lowest in Ti–6Al–4V at shallow incidence (Fig. 6.7). This indicates that the particles at the

periphery of the jet and those carried by the slurry return flow are more likely to erode PMMA

compared to metallic targets, thus making the machined channel in PMMA the widest.

-66

-55

-44

-33

-22

-11

00 66 132 198 264 330

Dep

th (µ

m)

Width (µm)

PMMAAL6061-T6316L SSTi-6Al-4V

Figure 6.8: Comparison of the profiles of shallow, single-pass channels in PMMA, AL6061-T6, 316L SS and Ti–6Al–4V. Experimental conditions: P = 4 MPa (vjet = 90 m/s), dorifice =180 µm, C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s. Scan speeds adjusted to give approximately equal depths.

169

Multi-pass channels were machined by repeatedly scanning the jet over the target under identical

conditions (Table 6.2). Figure 6.9(a) shows that increasing the number of machining passes on the

channels noticeably increased their widths. The multi-pass channels machined in PMMA had the

highest degree of width increase per pass (about 9 µm) and Ti–6Al–4V had the highest resistance

against channel widening with approximately 2 µm increase in width per pass. As with Fig. 6.8, this

variation in channel widening was due to the differences in the erosion rates at shallow incidence in

these materials.

200

250

300

350

400

0 2 4 6 8 10 12

Cha

nnel

wid

th (µ

m)

Number of pass, NP


0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12

Cha

nnel

dep

th (µ

m)

Number of pass, NP


(a) (b)

Figure 6.9: (a) Width and (b) depth of micro-channels at a function of number of machined passes in PMMA, AL6061-T6, 316L SS and Ti–6Al–4V. Error bars represent the standard deviation for 3 cross-sectional profile measurements 1 mm apart on a given channel. Solid lines added to guide the eye. Experimental conditions: P = 4 MPa (vjet = 90 m/s), dorifice =180 µm, C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s.

Figure 6.9(b) shows that the depths of the channels increased linearly with increasing number of

passes; i.e. the depth was directly proportional to the particle dose incident to the target surface.

This linear trend of channel depth can be explained by comparing the thickness of the stagnation

zone, which directly influences the particle local impact velocities and angles in shallow and deep

170

channels. Figures 6.10(a) and (b) show that the difference between the stagnation zone thicknesses

(defined as the distance between the location having a gage pressure of 0.5 MPa and the stagnation

point on the target) in both a shallow channel (NP =1, 35 µm depth) and a deep channel (NP =10,

342 µm depth) was about 155 µm, a difference of less than 2%, despite the 10-fold increase in the

channel aspect ratio. As a result, Fig. 6.10(c) demonstrates that the particle impact velocities at the

jet centerline were virtually identical for the shallow and deep channels (difference <4%). This was

due to the much larger cross-sectional profiles of ASJM channels compared to the jet diameter,

which in return allows the size of stagnation zone to remain constant with increasing depth.

Therefore, the erosion rate at the bottom of multi-pass ASJM channels remained constant.

171

Inlet

Stagnation point

Channel Profile

Jet boundary

Stagnation length

(a)

Inlet

Channel Profile

Jet boundary

Stagnation point Stagnation length

(b)

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Par

ticle

vel

ocity

(m/s

)

Distance from the inlet (µm)

= 30= 300

CDCD

µmµm

Target Target

(c)

Figure 6.10: Comparison of (a) the size of stagnation zone in shallow (NP =1, 35 µm depth) and (b) deep (NP =10, 342 µm depth) machined channels in PMMA and (c) the 10 µm nominal diameter particle velocities on jet centerline. The ''x" indicates the particle impact velocity along the centerline. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), Q = 1.7 mL/s and θ = 90°.

172

6.4.4 Characterization of jet erosion pattern: Erosive efficacy distribution

As discussed in Section 6.4.3, the erosion at the bottom of multi-pass channels remained constant in

each machining pass. Therefore, the present modeling approach generalized the erosive efficacy

distribution for multi-pass channels at any depth based on that of the first-pass profile in each target

material (i.e. that obtained by first modeling the flow fields within these shallow channels using

CFD Model 3). The simulation predicted a 3D erosion map of the channel surface similar to that

shown in Fig. 6.2, as explained in Section 6.3.1.2, which was transformed into a 2D version in

which the erosion at each point on the cross-section represents the total erosion seen by that point as

the jet passed over it. Figure 6.11 presents the resulting 2D erosion maps for all the target materials.

These erosive efficacy distributions were normalized by dividing by the centerline value at x = 0,

and the normalized erosive efficacy distributions, E*(x), were fitted (least-squares method) with a

9th order polynomial (R2 ≈ 0.99):

( )* 9 8 7 6 5 4 3 29 8 7 6 5 4 3 2 1 0E x a x a x a x a x a x a x a x a x a x a= + + + + + + + + + (6.11)

Figure 6.11 shows E*(x) as function of the distance from the centerline, and Table 6.7 summarizes

the best fit values for the four target materials. Figure 6.11(a) compares the erosive efficacy

distributions on PMMA derived using previously developed first-pass approach such as in Ghobeity

et al. [11] (Section 6.1.2), to that obtained using the present CFD approach (Model 3). It can be

seen that the finite erosion tending to widen the channel, caused by the lateral flow near the channel

opening at approximately 150 µm away from jet centerline (i.e. half width of first-pass channel in

PMMA), was predicted using the CFD approach (E*(150) > 0), but not the first-pass approach

(E*(150) = 0). This highlights the need to use the more fundamental CFD methodology in the

modeling process for ASJM of ductile materials. As a result, the previous first-pass profile

173

approach was incapable of predicting the progressive widening of the channel opening as number of

machined passes increases, as discussed by Haghbin et al. [17]. Only the present CFD-based

approach captured the finite erosion at the edges of the channel (e.g. Fig. 6.11(a)).

174

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 25 50 75 100 125 150 175 200 225

Nor

mal

ized

ero

sive

effi

cacy

, E

* (x)

Distance from jet centerline (µm)

CFD model 3First-pass approach PMMA

Sidewall erosion near channel

opening

0

0.2

0.4

0.6

0.8

1

1.2

0 25 50 75 100 125 150 175

Nor

mal

ized

ero

sive

effi

cacy

, E

* (x)


AL6061-T6

(a) (b)

0

0.2

0.4

0.6

0.8

1

1.2

0 25 50 75 100 125 150

Nor

mal

ized

ero

sive

effi

cacy

, E

* (x)


316L SS

0

0.2

0.4

0.6

0.8

1

1.2

0 25 50 75 100 125 150

Nor

mal

ized

ero

sive

effi

cacy

, E

* (x)


Ti-6Al-4V

(c) (d)

Figure 6.11: Normalized erosive efficacy distribution of slurry jet (symbols) across channel width in (a) PMMA (o –first pass approach; ×-CFD approach), (b) AL6061-T6 (CFD approach), (c) 316L SS (CFD approach) and (d) Ti–6Al–4V (CFD approach). Half of the symmetric erosion data is shown. Solid lines represent the best-fit of data to 9th order polynomial. Modeling conditions: P = 4 MPa (vjet = 90 m/s), dorifice = 180 µm (jet diameter of 150 µm), C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s and θ = 90°.

175

Table 6.7: Best fit coefficients of erosion data to 9th order polynomial fit.

Coefficients of 9th order polynomial fit (R2 ≈ 0.99) Material PMMA AL6061-T6 316L SS Ti–6Al–4V

a9 7.78×10-18

1.90×10-17

3.13×10-17

8.13×10-17

a8 -5.13×10

-15 -1.23×10

-14 -1.91×10

-14 -4.64×10

-14

a7 1.43×10-12

3.32×10-12

4.90×10-12

1.11×10-11

a6 -2.17×10

-10 -4.90×10

-10 -6.84×10

-10 -1.45×10

-9

a5 1.96×10-8 4.24×10

-8 5.59×10

-8 1.09×10

-7

a4 -1.07×10-6 -2.16×10

-6 -2.70×10

-6 -4.91×10

-6

a3 3.33×10-5 6.13×10

-5 7.24×10

-5 1.23×10

-4

a2 -5.28×10-4 -8.60×10

-4 -9.70×10

-4 -1.54×10

-3

a1 3.32×10-3 4.52×10

-3 4.77×10

-3 7.15×10

-3

a0 1.01 0.99 0.97 1.00

6.4.5 Profile modeling of multi-pass micro-channels in ASJM of ductile materials

The computed erosive efficacy distributions, E*(x), in Section 6.4.4 (Eq. (6.11), Table 6.7) were

used in combination with Eqs. (6.4)-(6.7) to predict the multi-pass channel cross-sectional profile

resulting from any given number of machined passes, Np. As mentioned in Section 6.3.2, the

etching time, t, in Eqs. (6.6) and (6.7) was replaced using Np and the centerline depths of first-pass

channels (Section 6.4.3, Fig. 6.8) were used for the constant, Dc. Since the erosion at the bottom of

multi-pass channels remained constant (Section 6.4.3) and the profiles of multi-pass machined

channels were self-similar (i.e. "U"-shaped), as described Nouraei et al. [23], the angle β in Eqs.

(6.6) and (6.7) was calculated by fitting the first-pass channel profiles to a 9th order polynomial

function, f(x), and solving Eqs. (6.8) and (6.9). Table 6.8 summarizes the best fit values of the

function, f(x), for the first-pass channel profiles machined in the four target materials.

176

Figure 6.12 compares the multi-pass machined channel cross-sectional profiles with the predictions

and shows the depth predictions were within 5% of the measured value at any distance x from the

centerline for aspect ratios of approximately 1. The results in Fig. 6.12 also indicate that the

sidewall slope and channel widening were accurately estimated with a maximum difference

between the measured and predicted profile of less than 4%.

Table 6.8: Best fit coefficients of the first-pass channel profiles to 9th order polynomial fit.

Coefficients of 9th order polynomial fit (R2 ≈ 0.99)

PMMA AL6061-T6 316L SS Ti–6Al–4V b9 (µm)-9

-1.45×10-16

-1.43×10-16

3.54×10-16

2.51×10-15

b8 (µm)-8 9.36 ×10

-14 1.28×10

-13 -2.91×10

-13 -1.40×10

-12

b7 (µm)-7 -2.52×10-11

-4.51×10-11

9.29×10-11

3.28×10-10

b6 (µm)-6 3.65×10

-9 8.18×10

-9 -1.53×10

-8 -4.13×10

-8

b5 (µm)-5 -3.07×10-7 -8.38×10

-7 1.42×10

-6 3.02×10

-6

b4 (µm)-4 1.52×10-5 4.91×10

-5 -7.54×10

-5 -1.28×10

-4

b3 (µm)-3 -4.13×10-4 -1.60×10

-3 2.20×10

-3 3.02×10

-3

b2 (µm)-2 5.90×10-3 2.44×10

-2 -3.12×10

-2 -3.32×10

-2

b1 (µm)-1 -3.09×10-2 -1.41×10

-1 1.62×10

-1 1.03×10

-1

b0 (µm) -33.98 -30.45 -27.04 -29.43

177

-440

-400

-360

-320

-280

-240

-200

-160

-120

-80

-40

00 40 80 120 160 200 240

Dep

th (µ

m)

Width (µm)

Pass 2Pass 4Pass 6Pass 8Pass 10

PMMA

-440

-400

-360

-320

-280

-240

-200

-160

-120

-80

-40

00 40 80 120 160 200 240

Dep

th (µ

m)

Width (µm)


AL6061-T6

(a) (b)

-440

-400

-360

-320

-280

-240

-200

-160

-120

-80

-40

00 40 80 120 160 200 240

Dep

th (µ

m)

Width (µm)


316L SS

-440

-400

-360

-320

-280

-240

-200

-160

-120

-80

-40

00 40 80 120 160 200 240

Dep

th (µ

m)

Width (µm)


Ti-6Al-4V

(c) (d)

Figure 6.12: Comparison of predicted (solid lines) and measured (symbols) channel cross-sectional profiles in (a) PMMA, (b) AL6061-T6, (c) 316L SS and (d) Ti–6Al–4V for aspect ratios of up to

178

approximately 1. Half of each symmetric profile is shown. Experimental conditions: P = 4 MPa (vjet = 90 m/s), dorifice =180 µm, C = 1 wt% (D = 1 mg/mm), Q = 1.7 mL/s.

6.5 Conclusions

A novel numerical-empirical model was used to predict the profiles of micro-channels machined

with ASJM in PMMA, 6061-T6 aluminum alloy, 316L stainless steel and Ti–6Al–4V titanium

alloy. Three-dimensional multi-phase CFD models of a slurry jet in air striking the shallow first-

pass micro-channels were developed to account for the effects of flow field on the particle

trajectories, and obtain accurate relationships between target material erosion and the impact

velocity and angle. The specific erosion rates of acrylic and metallic targets were measured as a

function of jet angle using a 10 µm nominal diameter aluminum oxide slurry. CFD models of

particle trajectories were then used to replace the jet angle with the actual average impact angles

over the jet footprint in these data. The erosion rate-impact angle relations were then used in CFD

models to obtain the erosive efficacy distribution of the slurry jet, and predict the erosion for deeper

profiles. The model was verified by comparison with experiments which showed that the machined

channels widened as the depth increased due to the secondary erosion by particles impacting the

channel sidewalls. The widening effect was found to be substantial in the PMMA, but less

important in Ti–6Al–4V titanium alloy due to its greater erosion resistance. The depth, sidewall

slope and channel widening of the multi-pass micro-channels were accurately predicted using the

novel numerical-empirical approach up to an aspect ratio of approximately 1 with a maximum error

of less than 5%.

179

6.6 References

[1] A.A.S. Bhagat, S.S. Kuntaegowdanahalli, I. Papautsky, Enhanced particle filtration in straight micro-channels using shear-modulated inertial migration, Journal of Physics of Fluids 20 (2008) 101702 1-4.

[2] W. Chang, D. Trebotich, L.P. Lee, D. Liepmann, Blood flow in simple micro-channels. 1st International IEEE-EMBS Special Topic Conference on Micro-technologies in Medicine and Biology, Lyon, France, (2000) 1-5.

[3] S.D. Thakre, V.B. Swami, P.D. Malwe, Cooling systems of electronics devices using micro-channel heat sink, International Journal of Thermal Technologies 4 (2014) 58-60.

[4] R.M. Guijt, E. Baltussen, G. Van der Steen, R. Schasfoort, S. Schlautmann, H.A.H Billiet, J. Frank, G.W.K. Van Dedem, A. Van den Berg, New approaches for fabrication of micro-fluidic capillary electrophoresis devices with on-chip conductivity detection, Electrophoresis 22 (2001) 235-241.

[5] S. Schlautmann, H. Wensink, R. Schasfoort, M. Elwenspoek, A. Berg, Powder-blasting technology as an alternative tool for micro-fabrication of capillary electrophoresis chips with integrated conductivity sensors, Journal of Micro-mechanics and Micro-engineering 11 (2001) 386-389.

[6] G.D. Kipling, S.J. Haswell, N.J. Brown, A Considered Approach to Lab-on-a-Chip Fabrication, In: Castillo-León, J., Svendsen, W.E. (Eds.), Lab-on-a-Chip Devices and Micro-Total Analysis Systems-A Practical Guide, Springer, Cham, (2015) 53-81.








180


[15] D. A. Axinte, D. S. Srinvasu, J. Billingham, M. Cooper, Geometrical modelling of abrasive waterjet footprints: A study for 90º jet impact angle, CIRP Annals-Manufacturing Technology 59 (2010) 341-346.

[16] Kong, M.C., Anwar, S., Billingham, J., Axinte, D.A., Mathematical modeling of abrasive water jet footprints for arbitrarily moving jets: Part I-single straight paths, International Journal of Machine Tools and Manufacture 53 (2012) 58-68.

[17] N. Haghbin, J.K. Spelt, M. Papini, Abrasive waterjet micro-machining of channels in metals: comparison between machining in air and submerged in water, International Journal of Machine Tools and Manufacture 88 (2015) 108-117.

[18] H. Nouraei, K. Kowsari, M. Papini, J.K. Spelt, Operating Parameters to Minimize Feature Size in Abrasive Slurry Jet Micro-machining, Journal of Precision Engineering (2015) (submitted).

[19] A. Gnanavelu, N. Kapur, A. Neville, J.F. Flores, An integrated methodology for predicting material wear rates due to erosion, Wear 267 (2009) 1935–1944.

[20] A. Gnanavelu, N. Kapur, A. Neville, J.F. Flores, N. Ghorbani, A numerical investigation of a geometry independent integrated method to predict erosion rates in slurry erosion, Wear 271 (2011) 712-719.

[21] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332-333 (2015) 1090–1097.

[22] K. Kowsari, M.R. Sookhaklari, H. Nouraei, M. Papini, J.K. Spelt, Hybrid erosive jet micro-milling of sintered ceramic wafers with and without copper-filled through-holes. Journal of Material Processing Technology (2015) (submitted).

[23] H. Nouraei, A. Kowsari, J.K. Spelt, M. Papini, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in glass, Wear 309 (2014) 65–73.




181


[28] Y. Zhang, B.S. McLaury, S.A. Shirazi, Improvements of particle near-wall velocity and erosion predictions using a commercial CFD code, Journal of Fluids Engineering 131 (2009) 031303 1-9.


[30] H. McI. Clark, The influence of the squeeze film in slurry erosion, Wear 256 (2004) 918-926.

[31] Y.I. Oka, H. Ohnogi, T. Hosokawa, M. Matsumura, The impact angle dependence of erosion damage caused by solid particle impact, Wear 203-204 (1997) 573-579.

[32] Y.I. Oka, K. Okamura, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact Part 1: effects of impact parameters on a predictive equation, Wear 209 (2005) 90-101.

[33] ANSYS Fluent 15.0 (2015): Theory guide. ANSYS, Inc.

[34] R.H.M. Jafar, J.K. Spelt, M. Papini, Numerical simulation of surface roughness and erosion rate of abrasive jet micro-machined channels, Wear 303 (2013) 302-312.

[35] J. A. Laitone, Aerodynamic effects in the erosion process, Wear 56 (1976) 239-246.

[36] Z. Feng, A. Ball, The erosion of four materials using seven erodents-towards an understanding, Wear 233-235(1999) 674-684.

182

Chapter 7: Conclusions and Future Work

7.1 Conclusions

Given below is a summary of the principal findings of the presented work:

(i) Comparison of ASJM with AJM

The differences in the shapes and erosion rates of features machined with ASJM and

AJM could be attributed directly to the differences in the fluid flow and particle impact

conditions since it was found that the crushing strength of the abrasive Al2O3 particles

was not affected by water.

The depth of both holes and channels machined using the ASJM system were found

to be linearly proportional to the dose of abrasive delivered, with the exception of single

pass channels machined at lower traverse speeds, where differences in the slope of the

leading machined edge led to a nonlinear relationship resulting from a decrease in the

local impact angle. This effect is rarely evident in AJM due to the much greater radius of

the blast zone impinging on masked or unmasked channels.

The resolution (ratio of orifice diameter to feature width; i.e. channel width or hole

diameter) of the holes and channels produced using ASJM without a mask was found to

be approximately 0.5, which remained constant as the depth of these features was

increased by repeated passes of the slurry jet. This important observation supports the

183

potential of unmasked ASJM as a direct-write machining tool in contrast to AJM that

typically requires the use of masks to achieve adequate feature definition.

Examination of individual particle impact sites indicated that the borosilicate glass

experienced both brittle and ductile erosion in the range of ASJM operating conditions

utilized in the present study. However, brittle erosion was found to lead to most of the

bulk material removal, with ductile erosion playing mainly a role in reducing the

roughness and waviness of the channels. A typically brittle erosive response

characterized by an increasing normalized erosion rate with increasing impact angle was

found for both ASJM and AJM.

(ii) Surface evolution models of channels and holes machined with ASJM in glass

The center-line depth, sidewall slope, and shape of the micro-channels machined

with ASJM in glass were accurately predicted as a function of the machining time. The

predicted cross-sectional profiles of micro-holes machined for various lengths of time

with 25 µm particles were also in reasonable agreement with experimental

measurements; however, the development of hole profiles made with 10 µm particles

could not be predicted because of the relatively large drag force on these smaller

impacting particles as they penetrated the highly confined flow within the holes.

(iii) Combined numerical-analytical modeling of abrasive slurry jet micro-machining of

holes

The proposed numerical-analytical model could be used for predicting the cross-

sectional profiles of holes machined in various target materials, over a range of slurry jet

flow rates (i.e. orifice sizes and pressures), particle sizes and concentrations regardless

184

of the machining time as long as the dominant mode of material removal remained the

same. The model became inaccurate when the mode of material removal changed from

brittle to ductile erosion as the kinetic energy of impacting particles decreased with

increasing hole depth. It was found that CFD modeling of the slurry jet impingement

could be used to quantify this deceleration and its effect on the erosion in micro-holes

machined with ASJM.

(iv) Operating Parameters to Minimize Feature Size with ASJM

It was found that, although the ASJM operating parameters could be adjusted to

affect the trajectory of particles and thereby reduce the jet footprint, this did not

necessarily result in narrower channels. This was due to the additional erosion of the

flow out of the footprint which caused the secondary impact of abrasive particles at

impact angles less than 90° on the channel sidewalls. This effect was substantial in

ductile materials such as PMMA, since erosion was controlled by cutting and ploughing

mechanisms, but less important in brittle materials such as glass due to its greater

erosion resistance at oblique incidence.

Channel depth in glass and PMMA increased with increasing particle kinetic energy,

and momentum equilibration number, λ; e.g. particle size, density, and impact velocity.

However, due to the additional erosion caused by the return flow on the channel

sidewalls, increasing the particle kinetic energy widened the machined channels. In

contrast, narrower micro-channels for a given depth could be machined by: (a)

increasing the slurry temperature, (b) reducing the jet impingement angle, and (c)

machining at a slower scan speeds in PMMA, but not in glass. The use of smaller

185

orifices or sacrificial surface layers also significantly reduced the channel width and

frosting.

In order to machine the narrowest channel at a given depth, the orifice size should be

minimized, the slurry temperature maximized, machining should be conducted at

oblique jet incidence and a sacrificial layer should be used.

(v) Combined Numerical and Empirical Modeling of Abrasive Slurry Jet Micro-

machining of Channels in Ductile Materials

The channel widening effect was found to be substantial in PMMA, but less

important in Ti–6Al–4V titanium alloy due to its greater erosion resistance.

The depth, sidewall slope, and channel widening of multi-pass micro-channels were

accurately predicted up to an aspect ratio of approximately 1 with a maximum error

of less than 5%.

7.2 Directions for Future Work

The following topics may prove to be fruitful areas for future research:

(i) An investigation of the effect of ASJM process parameters on minimum surface roughness

of machined features with ASJM.

(ii) The design and development of a new ASJM orifice to overcome the shortcomings of the

existing orifice such as particle sedimentation and clogging of the orifice, and extend the

machining time.

186

Thesis References

Chapter 1

[1] C. Iliescu, B. Chen, F.E.H. Tay, G. Xu, J. Miao, Characterization of deep wet etching of glass, Proc. of SPIE Vol. 6037 (2003) 60370A-2.

[2] X. Cheng, A. Wang, K. Nakamoto, K. Yamazaki, A study on the micro tooling for micro/nano milling, International Journal of Advanced Manufacturing Technology 53 (2011) 523-533.


[4] C. T. Yang, S.S. Ho, B.H. Yan, Micro-hole machining of borosilicate glass through electro mechanical discharge machining, Key Engineering Materials 196 (2001) 149- 166.

[5] H. Ogura, Y. Yoshida, Hole drilling of glass substrates with a CO2 laser, Japanese Journal of Applied Physics 42 (2003) 2881–2886.

[6] K. Pang, T. Nguyen, J. Fan , J. Wang, Machining of micro-channels on brittle glass using an abrasive slurry jet, Key Engieering Materials 443 (2010) 639-644.

[7] G. Kucukturk, C. Cogun, A new method for machining electrically nonconductive work piece using electric discharge machining technique, International Journal of Machining Science and Technology 14 (2010) 189-207.

[8] A. Abgrall, A-M Gu'e, Lab-on-chip technologies: making a micro-fluidic network and coupling it into a complete micro system-a review, Journal of Micro-mechanics and Micro-engineering 1 (2007) 15-49.

[9] E. Blloy, S. Thurre, E. Walchiers, A. Sayah, M.A.M. Gijs, The introduction of powder blasting for sensor and micro system applications, Sensors and Actuators 84 (2000) 330-337.

[10] D.S. Park, M.W. Cho, H. Lee, W.S. Cho, Micro-grooving of glass using micro-abrasive jet machining, Journal of Materials Processing Technology 146 (2004) 234-240.

[11] S. Schlautmann, H. Wensink, R. Schasfoort, M. Elwenspoek, A. Vandenberg, Powder-blasting technology as an alternative tool for micro fabrication of capillary electrophoresis chips with

187

integrated conductivity sensor, Journal of Micro-mechanics and Micro-engineering 11 (2001) 386-389.

[12] R. M. Guijt, E. Baltussen, G. Van Der Steen, R.B.M. Schasfoort, S. Schlautmann, H.A.H. Billet, F. Frank, G.W.K. van Dedem, A. Van Den Berg, New approaches for fabrication of micro-fluidic capillary electrophoresis devices with on-chip conductivity detection, Electrophoresis 22 (2001) 235–241.

[13] L. Zhang, T. Kuriyagawa, Y. Yasutomi, J. Zhao, Investigation into micro abrasive intermittent jet machining, International Journal of Machine Tools and Manufacture 45 (2005) 873–879.

[14] H. Wensink, S. Schlautmann, M. H. Goedbloed, M. C. Elwenspoek, Fine tuning the roughness of powder blasted surfaces, Journal of Micro-mechanics and Micro-engineering 12 (2002) 616-620.

[15] H. T. Liu, Water jet technology for machining fine features pertaining to micro-machining, Journal of Manufacturing Processes 12 (2010) 8-18.


[17] J. Wang, T. Nguyen, K. L. Pang, Mechanisms of micro-hole formation on glasses by an abrasive slurry jet, Journal of Applied Physics 105 (2009) 044906.

[18] R.K. Miller, Water jet Cutting: Technology and Industrial Applications. Lilburn,GA: The Fairmont Press, Inc. (1991).

[19] D.S. Miller, Micro-machining with abrasive water jets, J. of Materials Processing Technology 149 (2004) 37-42.

[20] T. Nguyen, K. Pang, J. Wang, A preliminary study of the erosion process in micro-machining of glasses with a low pressure slurry jet, Key Engineering Materials 389-390 (2009) 378-380.

[21] C. Burnham, Abrasive water jets come of age, Machine Design, (1990) 93-97.

[22] J. Zeng, T.J. Kim, An erosion model for abrasive water jet milling of polycrystalline ceramics, Wear 199 (1996) 275–282.

[23] M. Hashish, A model for abrasive water jet (AWJ) machining, Journal of Engineering Materials and Technology 111 (1989) 154–162.

[24] S. Paul, A.M. Hoogstrate, C.A. van Luttervelt, H.J.J Kals, Analytical modelling of the total depth of cut in the abrasive water jet machining of polycrystalline brittle material, Journal of Material Processing Technology 73 (1998) 206-212.

[25] A.A.E. Domiaty, M.A. Shabara, A.A. Abdel-Rahman, A.K. Al-sabeeh, On the modelling of abrasive water jet cutting, International Journal of Advanced Manufacturing Technology 12 (1996) 255-265.

188

[26] A. Alberdi, A. Rivero, L.N. Lopez de Lacalle, I. Etxeberria, A. Suarez, Effect of process parameter on the kerf geometry in abrasive water jet milling, International Journal of Advanced Manufacturing Technology 51 (2010) 467-480.

[27] S. Paul, A.M. Hoogstrate, C.A. van Luttervelt, H.J. Kals, An experimental investigation of rectangular pocket milling with abrasive water jet, Journal of Material Processing Technology 73 (1998) 179-188.

[28] K. Maniadaki, T. Kestis, N. Bilalis, A. Antoniadis, A finite element-based model for pure water jet process simulation, International Journal of Advanced Manufacturing Technology 31 (2007) 933–940.

[29] D. A. Axinte, D. S. Srinvasu, J. Billingham, M. Cooper, Geometrical modelling of abrasive water jet footprints: A study for 90º jet impact angle, CIRP Annals-Manufacturing Technology 59 (2010) 341-346.

[30] H. Nouraei, A. Wodoslawsky, M. Papini, J.K. Spelt, Characteristics of abrasive slurry jet micro-machining: A comparison with abrasive air jet micro-machining, Journal of Materials Processing Technology 213 (2013) 1711-1724.


Chapter 2

[1] C.Y. Huang, C.H. Kuo, W.T. Hsiao, K.C. Huang, S.F. Tseng, C.P. Chou, Glass biochip fabrication by laser micromachining and glass-molding process, Journal of Materials Processing Technology 212 (2011) 633-639.


[3] X. Cheng, Z. Wang, K. Nakamoto, K. Yamazaki, A study on the micro tooling for micro/nano milling, The International Journal of Advanced Manufacturing Technology 53 (2011) 523-533.

[4] G. Kucukturk, C. Cogun, A new method for machining electrically nonconductive work piece using electric discharge machining technique, Machining Science and Technology: An International Journal 14 (2010) 189-207.

[5] H. Ogura, Y. Yoshida, Hole drilling of glass substrates with a CO2 laser, Japanese Journal of Applied Physics 42 (2003) 2881-2886.

[6] E. Belloy, S. Thurre, E. Walckiers, A. Sayah, M. Gijs, The introduction of powder blasting for sensor and micro-system applications, Sensors and Actuators A: Physical 84 (2000) 330-337.

189

[7] S. Schlautmann, H. Wensink, R. Schasfoort, M. Elwenspoek, A. Berg, Powder-blasting technology as an alternative tool for micro-fabrication of capillary electrophoresis chips with integrated conductivity sensors, Journal of Micromechanics and Micro-engineering 11 (2001) 386-389.

[8] R.M. Guijt, E. Baltussen, G. Van der Steen, R. Schasfoort, S. Schlautmann, H.A.H. Billiet, J. Frank, G.W.K. Van Dedem, A. Van den Berg, New approaches for fabrication of micro-fluidic capillary electrophoresis devices with on-chip conductivity detection, Electrophoresis 22 (2001) 235-241.

[9] L. Zhang, T. Kuriyagawa, Y. Yasutomi, J. Zhao Investigation into micro abrasive intermittent jet machining, International Journal of Machine Tools and Manufacture 45 (2005) 873-879.

[10] H. Wensink, S. Schlautmann, M.H. Goedbloed, M.C. Elwenspoek, Fine tuning the roughness of powder blasted surfaces, Journal of Micro-mechanics and Micro-engineering 12 (2002) 616-620.

[11] H.T. Liu, Water jet technology for machining fine features pertaining to micro-machining, Journal of Manufacturing Processes 12 (2010) 8-18.







[18] K. Pang, T. Nguyen, J. Fan, J. Wang, Modeling of the micro-channeling process on glasses using an abrasive slurry jet, International Journal of Machine Tools and Manufacture 53 (2012) 118-126.

[19] M. Hashish, Optimization factors in abrasive-water jet machining, Journal of Engineering for Industry 113 (1991) 29-37.

[20] H. Nouraei, A. Wodoslawsky, J.K. Spelt, M. Papini, Micro-machining using an Abrasive Slurry Jet, Wear of Materials, 18th International Conference, Philadelphia, USA, Poster, 2011.

190


[22] S. Nahvi, P. Shipway, D. McCartney, Effects of particle crushing in abrasion testing of steels with ash from biomass-fired power plants, Wear 267 (2009) 34-42.

[23] Z. Feng, A. Ball, The erosion of four materials using seven erodents: towards an understanding, Wear 233 (1999) 674-684.

[24] N.J. Van der Laag, L.J.M.G. Dortmans, G. de With, Influence of relative humidity on mechanical properties of Alumina, PZT, Ziconia, Key Engineering Materials, Euro Ceramics VII (2002) 751-754.

[25] A. Ghobeity, T. Krajac, T. Burzynski, M. Papini, J.K. Spelt, Surface evolution models in abrasive jet micromachining, Wear 264 (2008) 185-198.


[27] D. Dehnadfar, J. Friedman, M. Papini, Laser shadowgraphy measurements of abrasive particle spatial, size and velocity distributions through micro-masks used in abrasive jet micro-machining, Journal of Materials Processing Technology 212 (2011) 137-149.

[28] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and non-spherical particles, Powder Technology 58 (1989) 63-70.

[29] H. Wadell, Volume, shape, and roundness of quartz particles, Journal of Geology 43 (1935) 250-280.

[30] M.C. Leu, P. Meng, E.S. Geskin, L. Tismeneskiy, Mathematical modeling and experimental verification of stationary water jet cleaning process, Journal of Manufacturing Science and Engineering 120 (1998) 571-579.

[31] N. Rajaratnam, S. Rizvi, P. Steffler, P. Smy, An experimental study of very high velocity circular water jets in air, Journal of Hydraulic Research 32 (1994) 461-470.

[32] N. Rajaratnam, C. Albers, Water distribution in very high velocity water jets in air, Journal of Hydraulic Engineering 124 (1998) 647-650.

[33] N. Rajaratnam, Turbulent Jets, Elsevier Scientific Publishing Company, Amsterdam, 1976.



191

[36] S. Ashforth-Frost, K. Jambunathan, Effect of nozzle geometry and semi-confinement on the potential core of a turbulent axisymmetric free jet, International Communications in Heat Mass Transfer 23 (1996) 155-162.

[37] A. Guha, R.M. Barron, R. Balachandar, Numerical simulation of high-speed turbulent water jets in air, Journal of Hydraulic Research 48 (2010) 119-124.

[38] Y.M. Ali, J. Wang, Impact Abrasive Machining. In: M.J. Jackson, J.P. Davim (Eds.), Machining with Abrasives, Springer, West Lafayette (2011) 385-422.


[40] G. Sheldon, I. Finnie, On the ductile behavior of nominally brittle materials during erosive cutting, Journal of Engineering for Industry 88 (1966) 387-392.

[41] H. Wensink, M.C. Elwenspoek, A closer look at the ductile-brittle transition in solid particle erosion, Wear 253 (2002) 1035-1043.

[42] T. Mineta, T. Takada, E. Makino, T. Kawashima, T. Shibata, 2009. A wet abrasive blasting process for smooth micromachining of glass by ductile-mode removal, Journal of Micro-mechanics and Micro-engineering 19 (2009) 015031 1-9.

[43] T. Matsumura, T. Muramatsu, S. Fueki, Abrasive water jet machining of glass with stagnation effect, CIRP Annals-Manufacturing Technology 60 (2011) 355-358.

[44] A. Ghobeity, D. Ciampini, M. Papini, An analytical model of the effect of particle size distribution on the surface profile evolution in abrasive jet micromachining, Journal of Materials Processing Technology 209 (2009) 6067-6077.

[45] A. Ghobeity, H. Getu, M. Papini, J.K. Spelt, Surface evolution models for abrasive jet micromachining of holes in glass and polymethylmethacrylate (PMMA), Journal of Micromechanics and Micro-engineering 17 (2007) 2175-2185.

[46] J.M. Fan, C.M. Fan, J. Wang, Flow dynamic simulation of micro abrasive water jet, Solid State Phenomena 175 (2011) 171-176.


[48] H. Uuemǒis, I. Kleis, A critical analysis of erosion problems which have been little studied, Wear 31 (1975) 359-371.

[49] T. Burzynski, M. Papini, Measurement of the particle spatial and velocity distributions in micro-abrasive jets, Measurement Science and Technology 22 (2011) 025104 1-15.

192


[51] J.M. Fan, C.M. Fan, J. Wang, Modeling the material removal rate in micro abrasive water jet machining of glasses, Advanced Materials Research 135 (2010) 370-375.

[52] G. Fowler, P.H. Shipway, I.R. Pashby, Abrasive water-jet controlled depth milling of Ti6A14V alloy-an investigation of the role of jet-workpiece traverse speed and abrasive grit size on the characteristics of the milled material, Journal of Materials Processing Technology 161 (2005) 407-414.

Chapter 3

[1] H.T. Liu, Waterjet technology for machining fine features pertaining to micro-machining, Journal of Manufacturing Processes 12 (2010) 8-18.

[2] H. Nouraei, A. Wodoslawsky, J.K. Spelt, M. Papini, Micro-machining using an Abrasive Slurry Jet , Poster, Wear of Materials, 18th International Conference, Philadelphia, USA, (April 3-7, 2011).




[6] K. Pang, T. Nguyen, J. Fan, J. Wang, Modeling of the micro-channelling process on glasses using an abrasive slurry jet, International Journal of Machine Tools and Manufacture 53 (2012) 118-126.




[10] A. Ghobeity, H. Getu, M. Papini, J.K. Spelt, Surface evolution models for abrasive jet micro-machining of holes in glass and polymethylmethacrylate (PMMA), Journal of Micro-mechanics and Micro-engineering 17 (2007) 2175-2185.

193




[14] D.A. Axinte, D.S. Srinivasu, J. Billingham, M. Cooper, Geometrical modeling of abrasive waterjet footprints: a study for 90° jet impact angle, CIRP Annals- Manufacturing Technology 59 (2010) 341-346.

[15] M.C. Kong, S. Anwar, J. Billingham, D.A. Axinte, Mathematical modeling of abrasive waterjet footprints for arbitrarily moving jets: Part I-single straight paths, International Journal of Machine Tools and Manufacture 53 (2012) 58-68.

[16] N.N. Dutta, V.G. Pangarkar, Critical impeller speed for solid suspension in multi-impeller three phase agitated contactors, The Canadian Journal of Chemical Engineering 73 (1995) 273-283.

[17] M.A. Kölpinar, M. Göğüs, Critical flow velocity in slurry transporting horizontal pipelines, Journal of Hydraulic Engineering 127-9 (2001) 763-771.

[18] H. Nouraei, K. Kowsari, M. Papini, J.K. Spelt, Prediction of machined surface evolution in abrasive slurry jet micro-machining, Wear of Materials, 19th International Conference, Portland, USA, (April 14-18, 2013).

[19] T.E. Wilantewicz, J.R. Varner, Vickers indentation behavior of several commercial glasses at high temperatures, Journal of Materials Science 43 (2008) 281-298.


[21] T. Burzynski, M. Papini, Measurement of the particle spatial and velocity distributions in micro-abrasive jets, Measurement Science and Technology 22, (2011) 025104 1-15.


[23] H.T. Liu, Hole drilling with abrasive fluid jets, International Journal of Advanced Manufacturing Technology 32 (2007) 942-957.

[24] J. Humphrey, Fundamentals of fluid motion in erosion by solid particle impact. International Journal of Heat and Fluid Flow 11 (1990) 170-195.

194

Chapter 4








[8] H. Nouraei, A. Kowsari, J.K. Spelt, M. Papini, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in glass, Wear (2014) 309: 65–73.

[9] K. Kowsari, H. Nouraei, D.F. James, J.K. Spelt, M. Papini, Abrasive Slurry Jet Micro-machining of Holes in Brittle and Ductile Materials, Journal of Materials Processing Technology (2014) 214(9): 1909-1920.

[10] P.E. Dimotakis, The mixing transition in turbulent flows, Journal of Fluid Mechanics (2000), 409: 69-98.


[12] H. Li, J. Wang, J. Fan, Analysis and modeling of particle velocities in micro-abrasive air jet, International Journal of Machine Tools and Manufacture (2009), 49: 850-858.

[13] M.C. Leu et al., Mathematical modeling and experimental verification of stationary water jet cleaning process, Journal of Manu. Sci. and Eng. (1998), 120: 571-579.

[14] A. Ghobeity, H. Getu, M. Papini, J.K. Spelt, Surface evolution models for abrasive jet micromachining of holes in glass and polymethylmethacrylate (PMMA), Journal of Micro-mechanics and Micro-engineering 17 (2007) 2175-2185.

195



Chapter 5



[3] T. Matsumura, T. Muramatsu, S. Fueki, Abrasive water jet machining of glass with stagnation effect, Journal of Manufacturing Technology 60 (2011) 355-358.




[7] H. Qi, J.M. Fan, J. Wang, An experimental study of the abrasive water jet micro-machining process for quartz crystals, Journal of Advanced Materials Research 565 (2012) 339-344.




[11] K. Kowsari, D.F. James, M. Papini, J.K. Spelt. The effects of dilute polymer solutions on the shape, roughness and width of abrasive slurry jet micro-machined channels, Wear 309 (2014) 112-119.

196

[12] K. Kowsari, H. Nouraei, D.F. James, J.K. Spelt, M. Papini, Abrasive Slurry Jet Micro-machining of Holes in Brittle and Ductile Materials, Journal of Materials Processing Technology 214 (2014) 1909-1920.



[15] P.E. Dimotakis, The mixing transition in turbulent flows, Journal of Fluid Mechanics 409 (2000) 69-98.


[17] R.H.M. Jafar, J.K. Spelt, M. Papini, Surface roughness and erosion rate of abrasive jet micro-machined channels: experiments and analytical model, Wear 303 (2013) 138-48.


[19] Y.M. Ali, J. Wang, Impact Abrasive Machining. In: Jackson MJ, Davim JP, editors. Machining with Abrasives, Springer, West Lafayette (2011) 385-422.


[21] V.B. Nguyen, Q.B. Nguyen, Z.G. Liu, S. Wan, S.Y.H. Lim, Y.W. Zhang, A combined numerical-experimental study on the effect of surface evolution on the water-sand multiphase flow characteristics and the material erosion behavior, Wear 319 (2014) 96-109.

[22] K. Kowsari, H. Nouraei, M. Papini, J.K. Spelt, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in alumina, ICOMM 2014-9th International Conference on Micro-manufacturing, Singapore (2014).


[24] H. Getu, A. Ghobeity, J.K. Spelt, M. Papini, Abrasive jet micromachining of polymethylmethacrylate, Wear 263 (2007) 1008-1015.

[25] J. Fan, C. Fan, J. Wang, Flow dynamic simulation of micro abrasive water jet, Solid State Phenomena 175 (2011) 171-176.


197

[27] J. Kestin, M. Sokolov, W.A. Wakeham, Viscosity of liquid water in the range -8°C to 150°C, Journal of Physical and Chemical Reference Data 7 (1978) 941-948.


[29] H. Devlin, P. Kaushik, The effect of water absorption on acrylic surface properties, Journal of Prosthodontics 14 (2005) 233-238.

[30] L. Ma, C. Huang, Y. Xie, J. Jiang, K.Y. Tufa, R. Hui, Modeling of erodent particle trajectories in slurry flow, Wear 334-335 (2015) 49-55.

[31] P.H. Shipway, G. Fowler, I.R. Pashby, Characteristics of the surface of a titanium alloy following milling with abrasive water jets, Wear 258 (2005) 123-132.

[32] G. Fowler, P.H. Shipway, I.R. Pashby, Abrasive water jet controlled depth milling of Ti-6Al-4V alloy: an investigation of the role of jet-workpiece traverse speed and abrasive grit size on the characteristics of the milled material, Journal of Materials Processing Technology 161 (2005) 407-414.

[33] N. Haghbin, J.K. Spelt, M. Papini, Abrasive water jet micro-machining of channels in metals: Model to predict high aspect-ratio channel profiles for submerged and unsubmerged machining, Journal of Materials Processing Technology 222 (2015) 399-409.

Chapter 6

[1] A.A.S. Bhagat, S.S. Kuntaegowdanahalli, I. Papautsky, Enhanced particle filtration in straight micro-channels using shear-modulated inertial migration, Journal of Physics of Fluids 20 (2008) 101702 1-4.

[2] W. Chang, D. Trebotich, L.P. Lee, D. Liepmann, Blood flow in simple micro-channels. 1st International IEEE-EMBS Special Topic Conference on Micro-technologies in Medicine and Biology, Lyon, France, (2000) 1-5.

[3] S.D. Thakre, V.B. Swami, P.D. Malwe, Cooling systems of electronics devices using micro-channel heat sink, International Journal of Thermal Technologies 4 (2014) 58-60.

[4] R.M. Guijt, E. Baltussen, G. Van der Steen, R. Schasfoort, S. Schlautmann, H.A.H Billiet, J. Frank, G.W.K. Van Dedem, A. Van den Berg, New approaches for fabrication of micro-fluidic capillary electrophoresis devices with on-chip conductivity detection, Electrophoresis 22 (2001) 235-241.

[5] S. Schlautmann, H. Wensink, R. Schasfoort, M. Elwenspoek, A. Berg, Powder-blasting technology as an alternative tool for micro-fabrication of capillary electrophoresis chips with integrated conductivity sensors, Journal of Micro-mechanics and Micro-engineering 11 (2001) 386-389.

198

[6] G.D. Kipling, S.J. Haswell, N.J. Brown, A Considered Approach to Lab-on-a-Chip Fabrication, In: Castillo-León, J., Svendsen, W.E. (Eds.), Lab-on-a-Chip Devices and Micro-Total Analysis Systems-A Practical Guide, Springer, Cham, (2015) 53-81.









[15] D. A. Axinte, D. S. Srinvasu, J. Billingham, M. Cooper, Geometrical modelling of abrasive waterjet footprints: A study for 90º jet impact angle, CIRP Annals-Manufacturing Technology 59 (2010) 341-346.

[16] Kong, M.C., Anwar, S., Billingham, J., Axinte, D.A., Mathematical modeling of abrasive water jet footprints for arbitrarily moving jets: Part I-single straight paths, International Journal of Machine Tools and Manufacture 53 (2012) 58-68.

[17] N. Haghbin, J.K. Spelt, M. Papini, Abrasive waterjet micro-machining of channels in metals: comparison between machining in air and submerged in water, International Journal of Machine Tools and Manufacture 88 (2015) 108-117.

[18] H. Nouraei, K. Kowsari, M. Papini, J.K. Spelt, Operating Parameters to Minimize Feature Size in Abrasive Slurry Jet Micro-machining, Journal of Precision Engineering (2015) (submitted).

[19] A. Gnanavelu, N. Kapur, A. Neville, J.F. Flores, An integrated methodology for predicting material wear rates due to erosion, Wear 267 (2009) 1935–1944.

199

[20] A. Gnanavelu, N. Kapur, A. Neville, J.F. Flores, N. Ghorbani, A numerical investigation of a geometry independent integrated method to predict erosion rates in slurry erosion, Wear 271 (2011) 712-719.

[21] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332-333 (2015) 1090–1097.

[22] K. Kowsari, M.R. Sookhaklari, H. Nouraei, M. Papini, J.K. Spelt, Hybrid erosive jet micro-milling of sintered ceramic wafers with and without copper-filled through-holes. Journal of Material Processing Technology (2015) (submitted).

[23] H. Nouraei, A. Kowsari, J.K. Spelt, M. Papini, Surface evolution models for abrasive slurry jet micro-machining of channels and holes in glass, Wear 309 (2014) 65–73.





[28] Y. Zhang, B.S. McLaury, S.A. Shirazi, Improvements of particle near-wall velocity and erosion predictions using a commercial CFD code, Journal of Fluids Engineering 131 (2009) 031303 1-9.


[30] H. McI. Clark, The influence of the squeeze film in slurry erosion, Wear 256 (2004) 918-926.

[31] Y.I. Oka, H. Ohnogi, T. Hosokawa, M. Matsumura, The impact angle dependence of erosion damage caused by solid particle impact, Wear 203-204 (1997) 573-579.

[32] Y.I. Oka, K. Okamura, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact Part 1: effects of impact parameters on a predictive equation, Wear 209 (2005) 90-101.

[33] ANSYS Fluent 15.0 (2015): Theory guide. ANSYS, Inc.

[34] R.H.M. Jafar, J.K. Spelt, M. Papini, Numerical simulation of surface roughness and erosion rate of abrasive jet micro-machined channels, Wear 303 (2013) 302-312.

200

[35] J. A. Laitone, Aerodynamic effects in the erosion process, Wear 56 (1976) 239-246.

[36] Z. Feng, A. Ball, The erosion of four materials using seven erodents-towards an understanding, Wear 233-235(1999) 674-684.

Documents

The Development of Surface Profile Models in Abrasive Slurry Jet … · 2016. 7. 19. · the jet in slurry jet (Emamifar [35]; Guha et al. [37]) and air jet (Dehnadfar et al. [27])