Abrasive Slurry Jet Micro-Machining of Talc Filled

Polypropylene - Planar Area, Transitional Slope and

Curved Edges Machining

by

Neda Tamannaee

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Neda Tamannaee 2015

ii

Abrasive Slurry Jet Micro-Machining of Talc Filled Polypropylene-

Planar Area, Transitional Slope and Curved Edges Machining

Neda Tamannaee

Master of Applied Science

Graduate department of Mechanical and Industrial Engineering

University of Toronto

2015

Abstract

The abrasive slurry-jet erosion of a talc-filled TPO (60% PP, 25% EP rubber and 15% talc) was

measured as a function of the impact angle and the talc filler content. A ductile erosion response

was observed, showing a maximum erosion rate at 45°. A superposition model was then

developed to predict the cross-sectional shapes of small-scale flat-bottomed pockets and curved

edges machined in TPO using abrasive slurry-jet micro-machining (ASJM). The model was

based on the spatial distribution of the erosion across the jet footprint measured during a shallow

“first pass” channel at a specific angle. The model predictions of planar depth and waviness were

in close agreement with experimental measurements. The measured dependence of the erosion

rate on the impact angle was used to develop novel machining configurations to increase the

slope of bounding sidewalls. A model was then developed to predict these slopes.

iii

Acknowledgments

I would like to express my deepest appreciation to my supervisors, Dr. Jan K. Spelt and Dr.

Marcello Papini; without their guidance and persistence help this thesis would not have been

possible.

I would like acknowledge the support of Natural Sciences and Engineering Research Council of

Canada, Canada Research Chairs, POLYCON Industries, and MAGNA International Inc.

Grateful acknowledgement must be paid to my beloved husband, Mehran, for his special support

and understanding through my study period. This job would not be accomplished unless through

his passion-infusing advice.

I would like to thank my parents; if it was not for their endless love and consideration for twenty

five years, I would not be standing anywhere near this.

Moreover, I would like to thank my fellow researchers for the great work space we had together

during my study period; Dr. Kamyar Hashemnia, Hooman Nouraei, Amir Nourani, Saeed Akbari

and Kavin Kowsari.

This thesis is dedicated to my future children.

iv

Table of Contents

Contents

Acknowledgments.......................................................................................................................... iii

Table of Contents ........................................................................................................................... iv

List of Tables ................................................................................................................................. vi

List of Figures ............................................................................................................................... vii

Chapter 1 Introduction .....................................................................................................................1

1.1 Overview ..............................................................................................................................1

1.2 Motivation ............................................................................................................................5

1.3 Thesis Outline and Objectives .............................................................................................5

Chapter 2 Experimental Analysis on Talc-Filled Polypropylene for Erosion Characterization,

Planar Area and Curved Edge Machining ...................................................................................7

2.1 Overview ..............................................................................................................................7

2.2 Experimental Apparatus.......................................................................................................7

2.3 Abrasive Slurries ..................................................................................................................8

2.4 Target Material.....................................................................................................................9

2.5 Erosion Characterization ......................................................................................................9

2.6 Roughness Measurement ...................................................................................................14

2.7 Effect of Filler Concentration ............................................................................................14

2.8 Planar Area Machining ......................................................................................................15

2.9 Curved Edge Machining ....................................................................................................16

Chapter 3 Erosive Efficacy Superposition Modeling and Nozzle Path Plan Algorithm for

Machining Edges and Planar Areas ..........................................................................................17

v

3.1 Overview ............................................................................................................................17

3.2 Erosive Efficacy Function..................................................................................................17

3.3 Superposition Model for Machining Planar Area ..............................................................19

3.4 Superposition Model for Machining a Curved Edge .........................................................24

Chapter 4 Experimental Results and Superposition Model Verification for Machining Planar

Area and Curved Edges .............................................................................................................26

4.1 Overview ............................................................................................................................26

4.2 Erosion Characterization ....................................................................................................26

4.2.1 Effect of Angle of Attack .......................................................................................26

4.2.2 Roughness Measurements ......................................................................................29

4.3 Planar Area Machining ......................................................................................................30

4.4 Curved Edge Machining ....................................................................................................41

4.5 Control of Side-Wall Slope ................................................................................................45

Chapter 5 Conclusion .....................................................................................................................50

5.1 Summary ............................................................................................................................50

5.2 Contributions......................................................................................................................51

References ......................................................................................................................................52

vi

List of Tables

Table 1 ASJM experimental conditions ........................................................................................ 12

Table 2 Predicted and measured depth and waviness. ................................................................. 39

Table 3 Predicted and measured depth and waviness for machined planar areas with smoothing

passes. ................................................................................................................................... 40

Table 4-Machining parameters for edge (c) in Fig. 4-9. δ =100 μm. ΔXi =200 μm. ..................... 43

vii

List of Figures

Figure 2-1 ASJM Apparatus Set up (not to scale) (Kowsari 2013) ................................................ 8

Figure 2-2 Talc-filled polypropylene images: (a) SEM, arrows indicate talc particles, and (b)

EDX with light areas being Si. ............................................................................................... 9

Figure 2-3 Schematic of stages (not to scale). .............................................................................. 11

Figure 2-4 (a) Asymmetrical configuration used to measure angular dependence of erosion rate,

(b) Forward inclination for roughness measurements and planar machining (α=45°). ........ 13

Figure 3-1 Schematic of approach to machine flat, planar areas using parallel shallow channels

(not to scale). Nozzle offsets, δi, were assigned to produce a surface having a waviness less

than a prescribed limit ........................................................................................................... 20

Figure 3-2 Superposition model for cross-sectional profiles resulting from 2 , 3 and 4 passes of a

nozzle with a pitch of 150 μm and constant scan speed of 0.7 mm/s, nozzle configuration

α=45° forward inclination (Fig. 2-4 (b)). The profile of channel 1 represents the shallow

first-pass profile used to determine the erosive efficacy function for the ASJM system. .... 22

Figure 3-3 (a) Schematic of procedure used to machine rounded edges. ∆𝑋𝑖 is nozzle step-over

prior to machining each level with depth ΔYi. (b) Illustration of arrangement of individual

machined channels with pitch δ used to remove layer 1. Planar area of uniform depth begins

after a development distance equal to the width of a single channel. ................................... 25

Figure 4-1 Dependence of specific erosion rate of talc-filled polypropylene on impact angle.

Error bars indicate ±1 standard deviation for 3 cross-sectional measurements on a single

channel 30 mm in length. ...................................................................................................... 27

viii

Figure 4-2 Normalized erosion rate as a function of impact angle for TPO with 15 wt% talc.

Dashed line represents the best fit to the data based on Eq. (2). Error bars indicate ±1

standard deviation for 3 cross-sectional measurements on a single channel 30 mm in length.

............................................................................................................................................... 29

Figure 4-3 Centerline average roughness as a function of impact angle for shallow channels

machined in TPO (15 wt% talc). Error bars indicate ±1 standard deviation for 3

measurements. ....................................................................................................................... 30

Figure 4-4 Schematic of the local front geometry during ASJM of a channel at a relatively low

scan speed (not to scale) showing local impact angle θ. At sufficiently high scan speed β≈0.

............................................................................................................................................... 32

Figure 4-5 Channel centerline depth as a function of particle dose and scan speed. Error bars

indicate ±1 standard deviation for 3 cross-sectional measurements on a single 30 mm long

channel. The straight line gives the predicted dependence of erosion on dose. ................... 33

Figure 4-6 Predicted dependence of local front angle (β, Fig. 10) on scan speed and abrasive

dose. ...................................................................................................................................... 34

Figure 4-7 Measured (data points) and model predictions (dashed lines) for machining of planar

areas using one (upper curves) and two sets of passes. 15 wt% talc-filled TPO, nozzle

pitch=200 μm, scan speed=0.35 mm/s, α=45° forward inclination (Fig. 2-4 (b)). Note that

the scales of depth and width are different. Experiment #1 in Table 2. ............................... 37

Figure 4-8 Measured (data points) and model predictions (dashed lines) for machining of planar

areas using one (upper curves) to four sets of passes. 15 wt% talc-filled TPO, nozzle

pitch=100 μm, scan speed=0.70 mm/s, α=45° forward inclination (Fig. 2-4(b)). Note that

the scales of depth and width are different. Experiment #2 in Table 2. ............................... 38

ix

Figure 4-9 Comparison of measured (data points) and predicted (dashed lines) curved edge

profiles in 15% talc-filled TPO. Positions of the initial sharp edges are indicated by the

vertical solid lines. Desired curves were defined by: 1 780 00019a

.X.Y ( ) , 1 8

0 0002b

.X.Y ( ) ,

1 820 00021c

.X.Y ( ) and 1 82

0 00056d

.X.Y ( ) . .......................................................................... 42

Figure 4-10 Model predictions of edge shape for nozzle step-overs (ΔXi) of 200, 300 and 400

μm. Nozzle pitch δ =100 μm. Desired shape was that of case (c) in Fig. 4-9. ..................... 44

Figure 4-11 Schematic of forward machining with a compound inclination- of the nozzle. ψ is

the tilt angle about the Y axis in the XZ plane, and α is the angle in the YZ plane. The

objective was to steepen the indicated bounding sidewall. The outlines of subsequent nozzle

passes to machine an adjacent planar area are illustrated by the dashed curves on the right

edge of the target. .................................................................................................................. 46

Figure 4-12 Excessively wavy surface profiles measured for two levels of planar area with α=45°

asymmetrical nozzle inclination of Fig. 2-4(a). Nozzle passes began at the left edge and

shifted to the right with a 100 μm pitch. Scan speed of 0.7 mm/s. Width and depth have

different scales. ..................................................................................................................... 47

Figure 4-13 Measured sidewall slope vs. feature depth machined using: (a) A single multi-pass

channel machined with compound inclination α=45°, ψ=45° (Fig. 4-11). (b) Planar area

machined with the compound inclination α=45°, ψ=45° (Fig. 4-11). (c) Planar area

machined with the inclined forward orientation α=45° (Fig. 2-4(b)). Experimental

conditions for (b) and (c): Nozzle pitch: 100 μm, scan speed: 0.7 mm/s. Error bars indicate

1 standard deviation for 3 cross-sectional measurements. .................................................. 49

1

Chapter 1

Introduction

1.1 Overview

Abrasive slurry jet micromachining (ASJM) is a relatively new machining technique that

employs a narrow jet of abrasive slurry to create small features in a variety of materials such as

glass, metals and polymers. The jet diameter is often small enough to produce high-resolution

features without the use of erosion-resistant masks typically used with abrasive air jet micro-

machining (AJM). Surfaces machined by slurry jet do not suffer from heat-affected zones and are

much smoother that those usually produce by high-pressure abrasive water jets.

A number of investigators have utilized ASJM to micro-machine features in a variety of

materials. For example, Miller (2004) developed a novel ASJM apparatus that used pre-mixed

20 wt% aqueous abrasive slurry operating at 70 MPa to produce fine cuts in metals. Pang et al.

(2012) used another ASJM system operating at 8-14 MPa to investigate the machining of micro-

channels in glass as a function of process parameters, and their experimental results show that

increases slurry pressure, particle size, and particle concentration all increase the channel depth

as well as overall material removal. They also noticed a significant secondary material removal

caused by returning flow.

Nouraei et al. (2013) found that micro-channels and holes machined in borosilicate glass using a

relatively low-pressure (1-7 MPa) ASJM were smoother than those machined with masked AJM,

and were of a comparable size. Kowsari et al. (2014) found that the changes in the liquid

extensional properties resulting from the addition of a high-molecular-weight polymer to the

2

slurry mix could produce narrower machined features in borosilicate glass for a given diameter

of slurry jet.

Nouraei et al. (2014) predicted the shape of micro-channels machined in borosilicate glass with

ASJM using an adaptation of the model developed by Ghobeity et al. (2008) for the abrasive air

jet micro-machining of glass. The brittle nature of the erosion made it possible to consider only

the component of the incident particle velocity that was normal to the evolving glass surface.

Micromachining of polymers has been of a great recent interest due to its growing application in

the fabrication of microfluidics devices. Although the ASJM of polymers has not previous been

studied, a number of investigators have utilized abrasive air jets to micro-machine features in

polymers. For example, Getu et al. (2007) and (2008) investigated the micro-machining of

Polymethylmethaacrylate using AJM, and developed a model to predict the evolution of the

cross-sectional shape and depth of masked micro-channels as a function of the dose of abrasive

delivered to the surface at a given kinetic energy. The model was more complex than that

previously developed for the AJM of brittle materials since polymer erosion is a function of both

the normal and tangential components of particle velocity, whereas the erosion of glass depends

largely on the normal component. This required the measurement of the erosion rate of the

target polymer as a function of the jet inclination angle.

Getu et al. (2008) used liquid nitrogen (LN2) in a cryogenic abrasive jet micro-machining

(CAJM) setup in order to increase the machinability of polydimethylsiloxane (PDMS),

acrylonitrile butadiene styrene (ABS) and polytetrafluoroethylene (PTFE). According to the

reported results, the use of LN2 cooling resulted in brittle erosion in the samples, showing a

higher erosion rate at higher impact angles, as well as reduction in particle embedding and the

incubation period.

3

In the continuation of Getu’s work, Gradeen et al. (2012) and (2014) employed a novel CAJM

system to investigate the PDMS erosion over a wide range of temperature (-178 - 17°C). They

determined that a lowering of the temperature to -178°C, below the transition temperature≃-

120°C resulted in a shift toward a more brittle erosion behavior.

In the production of micro-devices, it is often required to manufacture complex parts, which is

often made feasible by machining primary features such as channels, holes, recessed planar areas

and transitional slopes. Hence, it is essential to have a methodology that allows the prediction of

the machining path required to produce a desired feature shape.

Ghobeity et al. (2008) developed a computational model to predict the surface evolution of

recessed planar areas, and transitional slopes between such areas, machined in glass using AJM.

Since the energy distributions across the nozzle were found to be non-uniform in a single pass,

multiple passes were arranged in a way that the summation of their energy distributions provided

a uniform energy flux to the surface resulting in a machined planar area. An erosion resistant

mask was used to create relatively steep side walls bounding the recessed pockets having flat

bottoms.

Billingham et al. (2013) used overlapping channel footprints created by high pressure abrasive

waterjet in order to machine planar pockets in Ti6Al4V. Their model was based on the calibration

and validation of a predictive mathematical model for the machining a single trench footprint,

delivering a reasonable prediction of the final profile shape of the machined pocket. Despite the

relatively good results obtained in previous studies, no approaches have yet been introduced

that allow control over the side wall slope as surface waviness resulting from multiple machining

passes.

4

Comparisons between neat polymers and their composites have been also an important portion of

studies related to composite materials. The manner in which the addition of fillers and fibers

affects the properties is generally directly related to how the properties of additives compare to

those of the neat matrix.

Sole and Ball (1996) surveyed the effect of mineral filler percentage on the wear resistance of

filled polypropylene conducting dry abrasion tests on a Rockwell belt modified sanding machine.

For Talc, it was shown that wear rate of filled composite was higher than of neat polymer, and

there were also an increase in wear rate with higher wt% of talc.

In previous work, the effect of filler percentage on the erosion rate of Polypropylene composites

has been explored, and unlike the investigations on fiber reinforced composites (Barkoula 2002,

Arjula 2008, Suresh 2009) erosion behavior changes in terms of angular dependency (the

probable change in the angle which corresponds to the highest erosion rate, and a shift in the

erosion behavior toward a more brittle manner) have not been explored.

The present work first investigated the angular dependence of the erosion of a talc-filled

thermoplastic olefin (TPO) consisting of polypropylene and rubber. Such composites are being

widely used to manufacture injection-molded interior and exterior automotive parts. A model

was then developed to predict the shape, waviness and inclination of recessed pockets machined

using ASJM. The model was demonstrated to be capable of providing nozzle path instructions to

machine complex features of desired geometry. Approaches to control the slope of bounding

sidewalls without using masks were also developed and tested. The model was also employed to

predict paths necessary to trim sharp edges to a desired radius.

5

1.2 Motivation

ASJM has great potential as a versatile, low-cost method to micro-machine a very wide variety

of materials. To machine complex components, it is essential to have methodologies to predict

the abrasive jet machining path required to produce a desired feature shape. The goal of the

present research was to develop such models for the ASJM of planar areas and transitional slopes

in a common polymeric material. The knowledge gained is applicable to other ductile materials

and the development of ASJM models for the production of other feature shapes.

1.3 Thesis Outline and Objectives

Chapter 2 provides the details on abrasive slurry jet machining apparatus as well as complete

information on experimental procedures. Measurement methods employed through the data

acquisition and analysis are also introduced.

Chapter 3 explains the basis of the erosive efficacy superposition model in detail, and describes

the terms and methods utilized within its development. Moreover, theoretical limitations of

superposition model are discussed, and the employment methods for machining edges and planar

areas are proposed through the nozzle path planning algorithm.

The first part of Chapter 4 delivers the experimental results on the erosion rate angular

dependence of Talc filled polypropylene, effect of talc percentage on the erosion rate and effect

of angle on channel centerline roughness along with comprehensive discussions. The second part

of this chapter evaluates the applicability of erosive efficacy superposition model in predicting

the depth and waviness of flat bottom recesses as well as the curved edges, all machined through

the prescribed nozzle path plan resulted from algorithm. The third part of this chapter introduces

6

the novel nozzle configuration proposed for machining planar areas with enhanced and

controlled bounding sidewalls.

7

Chapter 2

Experimental Analysis on Talc-Filled Polypropylene for Erosion

Characterization, Planar Area and Curved Edge Machining

2

2.1 Overview

In this chapter, the ASJM apparatus utilized for experimental analysis is introduced, and

preliminary information on target material is summarized. In addition, experimental approaches

are explained in detail, along with associated measurement techniques.

2.2 Experimental Apparatus

The ASJM set up used to conduct the experiments in this study had been previously developed

by Nouraei et al. (2013) and Kowsari et al. (2014). The set up utilizes an abrasive slurry pump

and pulsation damper connected to an open reservoir tank (Figure 2-1). It consisted of an open,

stirred slurry tank feeding a diaphragm pump connected to a pulsation damper. Current

experiments were conducted using a pressure of 4 MPa and a flow rate of 1.61 ± 0.1% mL/s

through a 180 μm sapphire water jet orifice (KMT Water jet, KS, USA) which produced a jet

diameter of 140 μm.

8

Figure 2-1 ASJM Apparatus Set up (not to scale) (Kowsari 2013)

2.3 Abrasive Slurries

Aqueous slurries with the concentrations of 1 wt% Al2O3 were prepared using abrasive particles

with nominal diameter of 10 μm (Comco Inc., CA, USA). The 18 L reservoir tank was

continuously stirred using an 8 cm diameter propeller rotated at 100 rpm to prevent particle

sedimentation. The slurry concentration in the jet was verified by collecting the discharge for a

period of time, passing it through filter paper, and then drying and weighing the retained

abrasive. Consistent with similar measurements reported in (Kowsari 2014), the abrasive

concentration in the jet was 90% of that in the reservoir tank due to particle settling in the tubes

and fittings leading to the orifice. This degree of settling was constant over the duration of the

present machining experiments.

9

2.4 Target Material

The TPO used in the experiments consisted of approximately 60 wt% polypropylene, 25 wt%

ethylene propylene rubber, and 15 wt% talc having an average size of 5 μm. Scanning electron

micrographs (SEM) and energy dispersive x-ray analysis (EDX) confirmed that the talc particles

were approximately uniformly distributed within the TPO matrix (Figure 2-2). The hardness of

samples were experimentally measured to be Hv=0.25 GPa using BUEHLER micro hardness

tester.

Figure 2-2 Talc-filled polypropylene images: (a) SEM, arrows indicate talc particles, and (b)

EDX with light areas being Si.

2.5 Erosion Characterization

Oka et al. (1997) investigated many factors affecting the solid particle erosion of various

materials, and concluded that the target hardness and particle incidence angle were the most

10

important. The erosion rate, E, at any angle of attack, α, can be non-dimensioned using the

erosion rate at normal incidence.

90( ) ( )E g E (1)

where g(α) is a function that expresses the angular dependency of the erosion rate . Oka (2005)

found that g(α) can be expressed in a semi-empirical form as

1 2( ) (sin( )) (1 (1 sin( )))n n

vg H (2)

where the first term represents the contribution due to repeated plastic deformation, dependent on

the impact energy transferred normal to the surface, while the second term expresses the cutting

action, dependent on the energy transferred parallel to the surface. The constants n1 and n2 are

found experimentally and depend on the particle hardness and other impact conditions, and Hv

(GPa) is the initial target hardness. The incorporation of Hv makes Eqs. (1) and (2) applicable to

a wide range of materials at any impact angle.

Equations (1) and (2) have been used in the modeling of the cross-sectional profiles of channels

machined using AJM in PMMA (Getu 2007) and metals (Ally 2012). Although the use of water

as the accelerating medium in ASJM creates uncertainty in the local particle impact angle since

small particles tend to follow the streamlines of the impinging jet, Nouraei et al. (2014) found

that a similar model could be used to predict the shapes of channels machined with ASJM in

brittle targets such as glass. Therefore, it was of interest to determine whether Eqs. (1) and (2)

could capture the angular dependency of the erosion rate measured using ASJM on a ductile

material such as talc-filled polypropylene.

11

Channels were machined in 50×50×3 mm plates of the TPO by mounting them on a computer-

controlled x-y stage that could provide scan speeds up to 7 mm/s. The stage was mounted on

hinges that allowed rotation about two orthogonal axes as shown in Fig. 2-3. The hinges were

then connected to manually-controlled vertical and horizontal stages, making it possible to adjust

the initial position of sample relative to nozzle.

Linear Stages

Hinges

Figure 2-3 Schematic of stages (not to scale).

12

The angular dependency of the erosion rate of the talc-filled TPO was measured using 30 mm

long shallow, asymmetrical channels as illustrated in Fig. 2-4 (θ = 30, 45, 60, 75, 90°). The scan

speed was 0.3 mm/s at a standoff distance of 20 mm (distance between the nozzle orifice and the

original target plane along the jet centerline). The slopes of the channel walls were kept

sufficiently small to permit the approximation that the local particle angle of attack was equal to

the inclination angle of the nozzle. The validity of this assumption was aided by the negligible

divergence of the free slurry jet.

Table 1 ASJM experimental conditions

Process Parameter

Slurry pressure 4 MPa

Abrasive concentration 1 wt%

Slurry Flow Rate 1.61 ml.s-1

Talc concentration 3 and 15 wt%

Standoff distance 20 mm

Nozzle inclination 30, 45, 60, 75, 90°

Scan speed 0.2,.., 3 mm.s-1

Jet diameter 140 μm

13

The results were reported in terms of a gravimetric dimensionless erosion rate; i.e. the mass of

target material removed per unit mass of abrasive delivered. The mass of material removed was

derived from the target scan speed, the target density (0.98 g/cm3), and the channel cross-

sectional area, measured using an optical profilometer having depth resolution of 0.1 μm (ST400,

Nanovea Inc., CA, USA) with a lateral measurement step of 5 μm. The mass of abrasive

delivered was calculated from the slurry flow rate, particle concentration, and particle density.

All profile measurements were repeated three times at three different cross sections along the

machined channels (30 mm in lengths) to confirm the accuracy of reported result. All profile

measurements were repeated at three different cross-sections 5 mm apart along the machined

channels. Associated standard deviations based on these measurements were calculated and

presented in Section 4.

Scan Direction

α=90°

d= 20mm Asymmetrical

Channel Orifice Scan Direction

α

(a)

Orifice

α

d= 20mm

(b)

Figure 2-4 (a) Asymmetrical configuration used to measure angular dependence of erosion rate,

(b) Forward inclination for roughness measurements and planar machining (α=45°).

14

The repeatability of the process was assessed by machining three channels for a given angle of

attack without turning off the pump. The average channel depth for nozzle angles α = 30, 45, 60,

75, 90° varied by less than 6% for a given angle, which was similar to the variability reported by

Nouraei et al. (2014) using the same ASJM system.

2.6 Roughness Measurement

The effect of impact angle on the channel centerline roughness was measured using forward

nozzle inclinations of α = 30, 45, 60, 75 and 90° (Fig. 2-4(b)). The optical profilometer was

scanned over a 10 mm length of each channel using a 1 μm sampling interval, and the roughness

was calculated according to the ISO 4288 (1996) with a 0.25 mm cut-off length (low-pass

wavelength filter). The measurements were repeated over each separate the three 10 mm

sections comprising the 30 mm long channel. Associated standard deviations based on these

measurements were calculated and presented in Section 4.

2.7 Effect of Filler Concentration

The effect of talc concentration on the erosion rate of TPO was measured using samples

containing 15 and 3 wt% talc. Channels were created in both samples using 1 wt% Al2O3 slurry

at 4 MPa and a scan speed of 0.3 mm/s.

15

2.8 Planar Area Machining

The machine path model presented in Section 3 is based on the hypothesis that flat surfaces can

be achieved if a uniform erosive flux is established over the machined area by superimposing

linear parallel passes with specified nozzle offsets. The erosion produced in a single pass of the

nozzle is characterized by the “erosive efficacy”, which is the transverse distribution of the

erosive energy in the jet footprint on the target surface. This distribution is due to the combined

effects of the distributions of the particle velocity, mass flux and local impact angle over the jet

footprint. Previous work has indicated that it can be measured for the AJM of brittle and ductile

targets, and for the ASJM of brittle targets from a shallow, “first-pass” profile machined in the

target (Getu 2007, Ghobeity 2008, Nouraei 2014). In the present work, the erosive efficacy was

acquired by machining shallow passes in TPO samples using 1 wt% Al2O3 slurries at 4 MPa. The

measured profiles of the machined shallow passes were then used in Eq. (4) below to determine

the erosive efficacy function, as described in Section 3.

To test the machining path model, single and multi-level planar areas were machined in 50×50×3

mm plates of the TPO using overlapping adjacent passes. Experiments were conducted using 1

wt% Al2O3 slurries at 4 MPa, with scan speeds varying from 0.2 to 0.7 mm/s. The cross-sectional

profiles of the resulting planar areas were measured using the optical profilometer and compared

with the model predictions. The amplitude and dominant frequency of the planar area waviness

were obtained using MATLAB R2011.

16

2.9 Curved Edge Machining

A modified version of the superposition model was also utilized to determine the nozzle path

required to create a curved edge. This model was tested by machining sharp 90° edges to a

specified curvature using the multi-level planar machining algorithm presented in Section 3.

These experiments were also performed using 1 wt% Al2O3 slurry at 4 MPa.

17

Chapter 3

Erosive Efficacy Superposition Modeling and Nozzle Path Plan

Algorithm for Machining Edges and Planar Areas

3.1 Overview

This chapter explains the methods based on which the erosive efficacy superposition model is

developed. The application of this model in delivering the required nozzle path plan for

machining planar area and curved edge with desired conditions is introduced by defining new

process parameters prescribed with values resulted from the model.

3.2 Erosive Efficacy Function

Ghobeity et al. (2007),(2008) and Getu et al. (2007) determined the erosive efficacy of AJM

nozzles eroding brittle and ductile materials by measuring the cross-sectional profiles of shallow

channels under the machining conditions of interest. Nouraei et al. (2014) showed that the same

approach could be used in the ASJM of glass substrates, in spite of the large differences in

particle trajectories within the footprints of impacting air jets and slurry jets.

The erosive efficacy function is defined as

,t

2

,

( )( 1 (z ) ) ( )x

zQ x

g

(3)

18

where g(α) is defined by Eq. (2), and ,tz and ,xz are the partial derivatives of the cross-sectional

profile ( )z x with respect to position and time. In the present case of very shallow channels, xz

was negligible, the local impact angle, θ, was equal to the global nozzle angle, α. Therefore, the

distribution of the erosion rate, z,t (x), across the channel produced by a shallow pass of the jet

footprint at any nozzle angle, α, could be obtained as:

,( )( )

( )

tzQ x

g (4)

Equation (4) can be rewritten in non-dimensional form by defining characteristic length (L) and

time (T). In this manner, non-dimensioned erosive efficacy can be obtained as:

*

*

,* *( )

( )( )

tz

Q xg

(5)

where

* xx

L , * z

zL

* tt

T (6)

The characteristic length was chosen to be L=h (stand-off distance), and T is the time required to

reach a depth L.

The coordinate points of the first-pass profile were used to calculate coordinate partial

derivatives as in Eq. (7), and the resulting array was fit to obtain the erosive efficacy function for

a single straight shallow pass of the nozzle.

*

** *

*,z ( )

t

dzx

dt (7)

19

As long as the channel was sufficiently shallow, the magnitude of the erosive efficacy at any

point on a channel cross-section was linearly proportional to the centerline depth of that channel,

and hence to the dose of abrasive delivered to the surface, or, equivalently, to the inverse of the

nozzle scan speed.

3.3 Superposition Model for Machining Planar Area

As discussed in the preceding section, a flat planar area can be produced if a uniform erosive

efficacy can be delivered to the target surface. The present superposition algorithm calculates the

required nozzle offsets and the number of parallel traverses necessary to obtain the desired depth,

width, and residual waviness of the planar area (Fig. 3-1), using as the primary input the erosive

efficacy determined from the profile of a shallow, single-pass reference channel.

20

Figure 3-1 Schematic of approach to machine flat, planar areas using parallel shallow channels

(not to scale). Nozzle offsets, δi, were assigned to produce a surface having a waviness less than

a prescribed limit

21

The nozzle path algorithm summed the erosive efficacies received by each surface point for a

single set of nozzle passes over the planar area. Two variables were available to adjust the

erosive efficacy received by a given point: (i) the nozzle speed was linearly related to the dose

and hence the magnitude of the erosive efficacy delivered to each point on the surface during that

pass, and (ii) the nozzle offset controlled the amount of superposition from one pass to the next.

To initiate the optimization procedure having the maximum waviness as the constraint, a few

preliminary experiments along with related runs of the model were conducted to deliver a

reasonable initial guess for nozzle speed and offset to produce the desired planar area (Section 4

and Table 2). As will be discussed in Section 4, there was a lower limit on the scan speed too

avoid making a channel that was too deep in a single pass. In very deep channels, the slurry flow

field could be quite different from that in a shallow channel, leading to an altered erosive

efficacy distribution. The tentative nozzle pass sequence was then evaluated for its waviness

using a fast Fourier transform of the resultant erosive efficacy distribution to determine the

amplitude of the dominant frequency. If this exceeded the specified flatness of the surface, the

tentative offset, δ0, and the scan speed, V0, were adjusted simultaneously as

δ = (δ0)*K (9)

Vi = (V0)/K (10)

where K was initially 0.9, and was then decreased by 10% for each waviness correction loop

needed thereafter. By altering the scan speed and nozzle offset using the same factor, K, the total

machining time and overall dose delivered to the surface would remain constant and the feature

depth would be unchanged. For example, if the nozzle offset was halved (K=0.5), twice the

number of passes would be required to machine a given area, and thus the scan speed had to be

doubled to keep the machining time and overall dose constant.

22

Once the machining algorithm for the smooth planar area was established, it could be repeated

any number of times to create pockets of arbitrary depth.

-15

-12

-9

-6

-3

0

0 150 300 450 600 750

Dep

th(μ

m)

Width (μm)

Channel 1

Channel 2

Channel 3

Channel 4

Superposition of Channels 1 and 2

Superposition of Channels 1,2 and 3

Superposition of Channels1,2,3 and 4

Figure 3-2 Superposition model for cross-sectional profiles resulting from 2 , 3 and 4 passes of a

nozzle with a pitch of 150 μm and constant scan speed of 0.7 mm/s, nozzle configuration α=45°

forward inclination (Fig. 2-4 (b)). The profile of channel 1 represents the shallow first-pass

profile used to determine the erosive efficacy function for the ASJM system.

23

Figure 3-2 illustrates that each point on the surface was exposed to the summation of the erosive

efficacies from the all passes that overlapped that point. Therefore, the flat portion of the planar

area began a distance from the left-most edge (Fig. 3-2) equal to the width of the erosive efficacy

distribution (i.e. the width of the shallow, first-pass channel produced by the jet; 380 μm).

Beyond this point, all portions of the planar area would be exposed to the same total erosive

efficacy as the nozzle was scanned over the surface in overlapping passes. The width of the

erosive efficacy distribution could thus be viewed as the distance over which the bounding

sidewall of the planar area developed and merged with the flat bottom.

A key difference between the present ASJM model and that developed by Ghobeity et al. (2008)

for AJM, was the requirement to avoid excessive secondary erosion created by slurry flow

beyond the primary footprint of the impinging jet. Secondary erosion became significant when

the surface topography altered the footprint erosion pattern characteristic of the shallow first-

pass. This could occur, for example, when the footprint overlapped a relatively steep slope,

thereby deflecting the jet and creating unpredictable erosion patterns. It is also noted that the jet

divergence in ASJM was much smaller than in AJM, thereby permitting the machining of

features with much higher resolution. For example, Nouraei et al. (2013) measured a slurry jet

divergence angle of about 0.015° for a 254 μm orifice at 2 MPa, while it was approximately 10°

in a 760 μm air jet nozzle (Ghobeity 2008).

24

3.4 Superposition Model for Machining a Curved Edge

Figure 3-3 illustrates the procedure used to machine curved edges of a desired radius when

starting from a sharp edge. The material to be removed was discretized into a number of layers,

each with a thicknesses ΔYi and an adjusted starting point ΔXi prescribed to be less than or equal

to the development distance (i.e. the width of the erosive efficacy function, as described Section

3.3). The algorithm to machine each of these layers beginning at the end of the step-over ΔXi was

then identical to that for planar areas (Section 3.3).

The step-over distances, ΔXi, and the planar area depths for each layer, ΔYi, of Fig. 3-3 were

selected using the machining model to provide an acceptable agreement between the predicted

curved-edge profile and the desired profile. Choosing smaller values of ΔXi and ΔYi corresponded

to shorter segments of the developing slope (left side of profile illustrated in Fig. 3-2) being

matched to the desired edge profile over the distance ΔXi, and therefore could produce a better

fit.

25

X1

ΔX2

ΔX3

ΔX4

ΔY1

ΔY2

ΔY3

ΔY4

ΔX5

Edge of

Initial Pass

Initial Edge

Desired

Curve

(a)

δ δ δ δ δ

X1

Individual Channels

Resultant

Surface

Development Distance

ΔY1

Planar Removal (b)

Figure 3-3 (a) Schematic of procedure used to machine rounded edges. ∆𝑋𝑖 is nozzle step-over

prior to machining each level with depth ΔYi. (b) Illustration of arrangement of individual

machined channels with pitch δ used to remove layer 1. Planar area of uniform depth begins after

a development distance equal to the width of a single channel.

26

Chapter 4

Experimental Results and Superposition Model Verification for

Machining Planar Area and Curved Edges

4.1 Overview

In the first section of this chapter (Section 4.2), experimental results on erosion behavior and

surface roughness are summarized. Followed by Sections 4.3 and 4.4, the applicability of erosive

efficacy superposition model in delivering the required nozzle path plan for machining planar

area and curved edge at desired conditions are evaluated by comparing the experimental results

and model predictions. Section 4.5 introduces the novel machining configuration employed in

planar area machining for side wall slope enhancement; experimental results on side wall slopes

are also compared and analyzed in this section.

4.2 Erosion Characterization

4.2.1 Effect of Angle of Attack

Figure 4-1 shows that the maximum specific gravimetric erosion rate occurred at 45, and was

approximately twice the erosion rate at 90, indicating that a ductile erosion mechanism was

dominant. The higher weight percentage of talc increased the erosion rate by over four times at

45°, but did not change the overall shape of the angular dependence.

Talc is composed of Si2O52-

sheets that are weakly bonded together, leading to a hardness (1

Mohs, approximately 0.06 GPa) (Mallock 1926)) which is much less than that of the

27

polypropylene matrix (Hv=0.25 GPa); therefore, the talc particles essentially act as voids, leading

to the much higher erosion rate. This is consistent with the analysis of the EDX images (Fig. 2-2)

that showed that talc comprised approximately 22% of the surface area of the 15 wt% talc

samples. The present results are consistent with the trend Sole et al. (1996) reported where the

increase in the abrasive wear of talc-filled polypropylene increased as the amount of filler

increased. Similarly, Chu et al. (2000) found that the addition of 20 wt% talc particles to

polypropylene more than doubled the scratch depth, attributing this to talc/resin debonding and

delamination within the talc particles.

0

0.04

0.08

0.12

0.16

0 15 30 45 60 75 90

Sp

ecific

Ero

sio

n R

ate

(m

g/g

)

Impact Angle (deg)

15 wt% talc

3 wt% talc

Figure 4-1 Dependence of specific erosion rate of talc-filled polypropylene on impact angle.

Error bars indicate ±1 standard deviation for 3 cross-sectional measurements on a single channel

30 mm in length.

28

The presence of the talc caused the specific erosion rates in Fig. 4-1 to be much higher than those

reported by Tilly (1969) for the erosion of unfilled polypropylene by 60 μm quartz particles at

104 m/s; e.g. 0.016 mg/g. This paper also described ductile erosion behavior and incubation

periods with significant weight gains due to particle embedment at angles greater than 55°. In

contrast, an EDX analysis of the present channels did not reveal any alumina, perhaps because

these particles (10 μm Al2O3) were much smaller than those used by Tilly (1969). Moreover, the

particle impact velocity in the present ASJM setup was much smaller than that used by Tilly

(1969); i.e. it was estimated to be 41 m/s for the present conditions (Nouraei 2013).

Figure 4-2 shows the normalized erosion rate (erosion rate at a given angle divided by that at

90), together with a best-fit to the g(α) expression in Eq. (2) for the 15 wt% data of Fig. 4-1.

The best fit was found using MATLAB R2011 curve-fit tool based on Eq. (2) with the value of

Hv=0.25 GPa as measured using a micro-hardness tester.

29

0

0.5

1

1.5

2

0 15 30 45 60 75 90

No

rma

lize

d E

rosio

n R

ate

g(

)

Impact Angle (deg)

R2 = 0.99

Figure 4-2 Normalized erosion rate as a function of impact angle for TPO with 15 wt% talc.

Dashed line represents the best fit to the data based on Eq. (2). Error bars indicate ±1 standard

deviation for 3 cross-sectional measurements on a single channel 30 mm in length.

4.2.2 Roughness Measurements

Figure 4-3 shows that the highest centerline average roughness (Ra) on shallow channels

occurred at 45°, which was also the angle for the maximum specific erosion rate of Fig. 4-1. For

the AJM of channels in borosilicate glass, Jafar et al. (2013) found that both the centerline

roughness and the erosion rate increased with the incident particle kinetic energy associated with

the normal component of the impact velocity, since this governed material removal by fracture. It

is interesting to note that for ductile materials such as TPO where both cutting and repeated

plastic deformation lead to material removal both the erosion rate and roughness were found to

30

depend on the relative amounts of normal and tangential velocity components, with both

exhibiting a maximum at 45°.

0

0.3

0.6

0.9

1.2

0 15 30 45 60 75 90

Ro

ughn

ess (

mm

)

Impact Angle (deg)

Figure 4-3 Centerline average roughness as a function of impact angle for shallow channels

machined in TPO (15 wt% talc). Error bars indicate ±1 standard deviation for 3 measurements.

4.3 Planar Area Machining

The present ASJM path model assumed that the nozzle scan speed was linearly proportional to

the abrasive dose delivered to the target and hence the erosion rate. However, as mentioned

previously, this assumption implied a sufficiently shallow channel, where the sidewalls and the

channel front were small enough so that the local impact angle was equal to the global nozzle

angle. Figure 4-4 illustrates that if the scan speed was too small the erosion rate of the local front

31

would be increased as the local impact angle approached 45. In this case, the angle of the front

of the channel as it was being machined is given by

1tan ( )D

W (11)

where D is channel depth and W is the width of the jet. This behavior is illustrated in Fig. 4-5,

where the centerline erosion rate is seen to diverge from its predicted linear dependence on dose

(or scan speed) when the scan speed fell below approximately 0.3 mm/s. As shown in Fig. 4-6, at

lower abrasive doses (higher scan speeds, shallower channels), the local front angle, β,

approached 0°, maintaining the local impact angle, θ, equal to the global nozzle angle, α (Fig. 4-

4). To ensure that the erosion rate was linearly proportional to the dose and scan speed, the

machining parameters were selected to keep the overall depth of each machined planar level (i.e.

the depth produced by a set of adjacent passes) less than 15 μm, leading to a local front slope (β,

Fig. 4-4) smaller than about 6°.

32

Jet width Scan Direction

Nozzle

D β

W

θ

Figure 4-4 Schematic of the local front geometry during ASJM of a channel at a relatively low

scan speed (not to scale) showing local impact angle θ. At sufficiently high scan speed β≈0.

33

y = 0.096x

0

15

30

45

60

0 50 100 150 200 250 300 350

Ch

anne

l D

epth

(m

m)

Particle Dose (mg/mm2)

Experimental Data

Predicted Linear Pattern

Scan Speed (mm/s)

0.7 0.5 0.3 0.2 0.1

Figure 4-5 Channel centerline depth as a function of particle dose and scan speed. Error bars

indicate ±1 standard deviation for 3 cross-sectional measurements on a single 30 mm long

channel. The straight line gives the predicted dependence of erosion on dose.

34

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Local F

ron

t A

ngle

(deg)

Scan Speed (mm/s)

Particle Dose (mg/mm2)

336 167 121 93 76 64 55

Figure 4-6 Predicted dependence of local front angle (β, Fig. 10) on scan speed and abrasive

dose.

In order to test the ASJM nozzle path model, planar areas were machined to various depths using

two different combinations of nozzle pitch and speed, both with a nozzle forward inclination of

45°, as shown in Fig. 2-4(b). The width of the erosive efficacy distribution was 380 μm. As

described in Section 3.3, this was also the distance from the edge of the first machining pass

required to establish the flat bottom of the planar area.

35

Figure 4-7 shows the measured and predicted planar area cross-sections for a nozzle pitch of 200

μm and a scan speed 0.35 mm/s, with one set of 8 passes creating the shallower level and a

repeated set of 8 passes doubling the average depth to about 25 μm. It is seen that there was

good agreement between the model predictions and the measured surface profiles with an

average error in the predicted depth of about 4% (Table 2, experiment #1). In this case, two

overlapping traverses were within the development distance (380 μm, equal to the width of the

erosive efficacy distribution) required to establish the uniform depth of 25 μm from the edge of

the planar area. The average slope of the walls on either side of the planar area was about 12° at

the depth of 60 μm.

The predictions of waviness in experiment #1 had an error of 46% after the first set of passes and

32% after the second set. The reason for these waviness over-predictions was believed to be the

inability of the model to account for the erosion of peaks bounding each channel due to the

spreading of the incident jet beyond its primary footprint. Such secondary erosion occurred as

the flow impacted the peaks at small local impact angles and therefore had a relatively large

effect on ductile materials. This explanation is consistent with the observation in experiment #2

(Fig. 4-8 and Table 2) that decreasing the pitch between the passes from 200 μm to 100 μm,

while doubling the scan speed to keep the dose the same, decreased the measured waviness.

Moreover, in this case and the model under-predicted the waviness since peak erosion due to

secondary erosion was less prevalent.

Figure 4-8 also illustrates that the depth of the final planar area could be increased in a

predictable manner by simply repeating the sets of nozzle passes, with each pass removing about

12 μm. Once again, the predictions of the average depth were in very good agreement with the

measurements.

36

The waviness predictions for experiment #2 (Table 2) were reasonable, but underestimated the

measured values by 63% at the first level to 12% at the fourth level. It is believed that the

relatively large differences in waviness seen in the shallower levels was due mainly to the model

assumption of an initially flat TPO surface, whereas the waviness of the as-received talc-filled

TPO was actually 1.3 μm. This is consistent with the progressive reduction in the difference

between the model and the measurements as the levels became deeper (Table 2).

It is noted that the average slope of the sidewall in experiment #2 (Fig. 4-8) increased with the

depth of the planar area, starting from 3° at 14.4 μm, and reaching a maximum of 12° at a depth

of 60 μm.

37

-40

-30

-20

-10

0

0 400 800 1200 1600 2000D

ep

th (

mm

)

Width (mm)

Figure 4-7 Measured (data points) and model predictions (dashed lines) for machining of planar

areas using one (upper curves) and two sets of passes. 15 wt% talc-filled TPO, nozzle pitch=200

μm, scan speed=0.35 mm/s, α=45° forward inclination (Fig. 2-4 (b)). Note that the scales of

depth and width are different. Experiment #1 in Table 2.

38

-75

-60

-45

-30

-15

0

0 400 800 1200 1600 2000D

ep

th (

mm

)

Width (mm)

Figure 4-8 Measured (data points) and model predictions (dashed lines) for machining of planar

areas using one (upper curves) to four sets of passes. 15 wt% talc-filled TPO, nozzle pitch=100

μm, scan speed=0.70 mm/s, α=45° forward inclination (Fig. 2-4(b)). Note that the scales of depth

and width are different. Experiment #2 in Table 2.

39

Table 2 Predicted and measured depth and waviness. Error is defined as predicted measured

messured

d dE

d

Machining Conditions Average Planar Depth (μm) Waviness (μm)

Level Scan Speed

(mm/s)

Nozzle pitch

(μm) Model Experiment Error Model Experiment Error

Experiment #1

1 0.35 200 12.4 12.9 -3% 3.8 2.6 46%

2 0.35 200 24.9 26.1 -4% 6.9 5.2 32%

Experiment #2

1 0.7 100 14.2 14.4 -2% 0.5 1.4 -63%

2 0.7 100 28.4 29.7 -4% 1.1 1.6 -31%

3 0.7 100 42.5 44.2 -4% 1.6 1.9 -15%

4 0.7 100 56.8 59.3 -4% 2.1 2.4 -12%

The waviness measured on each of the levels of both experiments #1 and #2 (Table 2) continued

to grow due to the superposition of the shallow channels in each set of passes. This could be

minimized by shifting each set of passes so that they did not directly overlie the previous set.

Table 3 illustrates a smoothing method that decreased this waviness and prevented it from

growing. In this case, levels 3 and 6 were machined as high-speed (5 mm/s) leveling sets of

passes, removing only 1-2 μm and being offset from the previous passes by 50 μm. Depth

predictions were in a close agreement with experimental result, showing a maximum error of

4%, as in Table 2. The waviness predictions were in reasonable agreement with the experimental

results as the depth increased, and the measured waviness remained approximately constant at

about 2 μm, not growing with depth as it did in Table 2. Therefore, high-speed smoothing passes,

40

offset from the preceding deeper sets of passes, could be used to decrease waviness and prevent

it from growing as the number of levels increased.

Table 3 Predicted and measured depth and waviness for machined planar areas with smoothing

passes. Error defined as predicted measured

messured

d dE

d

Machining Conditions Average Planar

Depth (μm)

Waviness (μm)

Level

Scan

Speed

(mm/s)

Nozzle

pitch (μm)

Nozzle

shift (μm) Model Expt Error Model Expt Error

1 0.7 100 N/A 14.3 14.5 -2% 0.5 1.4 -63%

2 0.7 100 N/A 28.6 29.1 -4% 1.1 1.7 -35%

3 5 100 50 30.1 31.1 -3% 0.7 1.4 -57%

4 0.7 100 -50 43.4 44.2 -2% 1.6 1.9 -15%

5 0.7 100 N/A 57.5 58.7 -2% 2.1 2.3 -12%

6 5 100 50 58.5 59.6 -2% 1.7 1.9 -10%

41

4.4 Curved Edge Machining

Two comparisons are of interest in curved-edge machining: (i) the actual profile of the machined

edge compared with the model predictions, and (ii) the model edge profile compared with the

desired curved edge. The former tests the ability of the model to reflect the actual erosion

produced by the jet, while the second illustrates the accuracy with which the model can replicate

an arbitrary, smooth curved edge. Figure 4-9 compares the predicted edge shapes with the

measured profiles for four desired edge geometries defined by the relation Xq

Y p.( ) , where p

and q are given in Fig.4-9. The layers removed to create the edges were machined using the

nozzle path machining model described in Section 3.4. In general, the agreement was very good,

with only a small under-prediction (about 8%) of the erosion near the vertical edge (toward the

right side of the machined edges in Fig. 4-9). It is believed that this additional erosion resulted

from deflection of the unbounded slurry jet toward the free edge where it rapidly eroded edge

material at a small local impact angle. The small hook seen in the machined edges of (a) and (b)

in Fig. 4-9 was due to small errors in the positioning of the first passes of the nozzle. This could

have been eliminated by simply continuing to the right with another set of passes.

42

-360

-300

-240

-180

-120

-60

0

0 300 600 900 1200 1500 1800D

ep

th (μ

m)

Width (μm)

(a) Exp

(b) Exp

(c) Exp

(d) exp

(a) Model

(b) Model

(d) Model

(c) Model

(a)

(b)

(d)

(c)

Exp

Exp

Exp

Exp

Figure 4-9 Comparison of measured (data points) and predicted (dashed lines) curved edge

profiles in 15% talc-filled TPO. Positions of the initial sharp edges are indicated by the vertical

solid lines. Desired curves were defined by: 1 780 00019a

.X.Y ( ) , 1 8

0 0002b

.X.Y ( ) ,

1 820 00021c

.X.Y ( ) and 1 82

0 00056d

.X.Y ( ) .

As an example, Table 4 gives the nozzle path parameters used in the model to machine edge (c)

through seven levels of planar machining, each with a nozzle step-over of ΔXi=200 μm (Fig. 3-

3). After each step-over, the level was machined using the path plan of the superposition model

43

for planar areas (Section 3.3), with the levels 4-7 on the steepest past of the curved edge having

more than one sublevel (set of passes).

Table 4-Machining parameters for edge (c) in Fig. 4-9. δ =100 μm. ΔXi =200 μm. Scan speed

adjusted to give desired dose in a given sublevel.

Level X start

(μm)

ΔYi

(μm)

Scan speed

(mm/s)

Number of

sublevels

1 0 4.2 2.4 1

2 200 7.93 1.3 1

3 400 13.1 0.79 1

4 600 17 1.19 2

5 800 20.8 0.97 2

6 1000 32.3 0.94 3

7 1200 47.1 0.86 4

As described in Section 3.3, for each machining level (Fig. 3-3) trial values of the nozzle step-

over ΔXi and the subsequent depth of the planar area ΔYi were input to the model to choose pairs

that gave an adequate fit to the desired edge profile. Figure 4-10 illustrates the effect on the

predicted edge shape of using ΔXi=300 and 400 μm instead of 200 μm for edge (c) in Fig. 4-9.

Although the larger nozzle step-overs would decrease the machining time, the resulting edge

would become increasingly jagged.

44

-150

-120

-90

-60

-30

0

0 200 400 600 800 1000 1200 1400D

ep

th (μ

m)

Width (μm)

200

300

400

Desired Curve (c)

ΔXi =200 μm

ΔXi =300 μm

ΔXi =400 μm

Figure 4-10 Model predictions of edge shape for nozzle step-overs (ΔXi) of 200, 300 and 400

μm. Nozzle pitch δ =100 μm. Desired shape was that of case (c) in Fig. 4-9.

45

4.5 Control of Side-Wall Slope

The inclined forward nozzle configuration of Fig. 2-4(b) produced sidewalls with relatively

shallow slopes of up to 12 at 60 μm depth (Figs. 4-7 and 4-8), which increased to 33 at a planar

depth of 188 μm (cross-section not shown). These slopes were defined largely by the slope of the

single-pass channel and the depth of the planar area.

It was of interest to investigate whether this slope could be increased and controlled for a given

planar area depth. An initial set of experiments to machine steeper sidewalls was performed

using the nozzle orientation of Fig. 2-4(a). Although repeated passes over the same channel in

this orientation produced a slope of 82 at a depth of 224 μm, it proved to be impossible to

continue to scan with this nozzle configuration to machine an adjacent smooth planar area. The

problem is illustrated in Fig. 4-12, which shows a planar area ending in a relatively steep right

sidewall. In this case, the passes progressed from left to right, and it was seen that as the abrasive

jet flowed across the ridges of the preceding passes, the slurry was diverted into these channels

and the waviness was accentuated.

46

x

z

Nozzle Direction

Target Material

α

ψ

y

Figure 4-11 Schematic of forward machining with a compound inclination- of the nozzle. ψ is

the tilt angle about the Y axis in the XZ plane, and α is the angle in the YZ plane. The objective

was to steepen the indicated bounding sidewall. The outlines of subsequent nozzle passes to

machine an adjacent planar area are illustrated by the dashed curves on the right edge of the

target.

47

-40

-30

-20

-10

0

0 300 600 900 1200 1500 1800D

epth

(m

m)

Width (mm)

Nozzle Direction

Figure 4-12 Excessively wavy surface profiles measured for two levels of planar area with α=45°

asymmetrical nozzle inclination of Fig. 2-4(a). Nozzle passes began at the left edge and shifted

to the right with a 100 μm pitch. Scan speed of 0.7 mm/s. Width and depth have different scales.

The nozzle orientation of Fig. 4-11 had a compound inclination which reduced the tendency of

the slurry to be diverted into the preceding channel while maintaining the higher erosion rates

seen at α=45. Figure 4-13 compares the sidewall slopes that were produced using multiple

passes with this orientation and the 45 inclined forward nozzle orientation of Fig. 2-4(b) (used

for Figs. 4-7 and 4-8). Case (a) is for a single channel machined using multiple passes with the

compound inclination, while case (b) is for planar areas of increasing depth made with the

compound inclination. Case (c) shows the sidewall slopes of planar areas of different depth

machined using the forward inclination with α=45 (Fig. 2-4(b); used in Figs. 4-7 and 4-8).

Comparing the planar area cases (b) and (c) in Fig. 4-13, it is evident that the compound

inclination (Fig. 4-11) increased the sidewall slope by about 50% at a depth of 190 μm. Although

48

the present machining models cannot predict these sidewall slopes, the linear trends seen in

Fig.4-13 make it possible in principle to predict the sidewall slope at an arbitrary depth using

only a single measurement of depth and slope for a given target and ASJM system. Case (a) in

Fig. 4-13 shows that repeated passes over a single channel using the compound nozzle

inclination produced slightly steeper sidewalls than those machined adjacent to planar areas (case

(b)).

49

y = 0.3xR² = 0.99

y = 0.27xR² = 0.99

y = 0.2xR² = 0.99

0

15

30

45

60

75

0 50 100 150 200 250

Sid

ew

all

Angle

(deg)

Feature Depth (μm)

(a)

(b)

(c)

Figure 4-13 Measured sidewall slope vs. feature depth machined using: (a) A single multi-pass

channel machined with compound inclination α=45°, ψ=45° (Fig. 4-11). (b) Planar area

machined with the compound inclination α=45°, ψ=45° (Fig. 4-11). (c) Planar area machined

with the inclined forward orientation α=45° (Fig. 2-4(b)). Experimental conditions for (b) and

(c): Nozzle pitch: 100 μm, scan speed: 0.7 mm/s. Error bars indicate 1 standard deviation for 3

cross-sectional measurements.

50

Chapter 5

Conclusions

5.1 Summary

An abrasive slurry jet micro-machining system (ASJM) was used to measure the angular

dependence of the erosion rate of 15 wt% talc-filled thermoplastic olefin (TPO). A typical

ductile erosion response was observed with the maximum erosion rate at 45° angle of incidence.

Reducing the talc concentration to 3 wt% caused a four-fold decrease in the erosion rate.

A model was developed to predict the depth and waviness of planar areas machined in the TPO

using repeated passes of the ASJM nozzle. Comparisons with machined areas showed that depth

and waviness could be predicted with an accuracy of 96%. It was demonstrated that the tendency

of waviness to grow with the number of machining passes could be circumvented by the

introduction of shallow smoothing passes.

The slopes of the sidewalls bounding the planar areas showed a linear dependence on the depth

of the area. A compound nozzle inclination (45° relative to both the target plane and the axis of

the machining pass) provided the steepest sidewalls while maintaining low values of planar area

waviness.

A second model was developed to predict the nozzle path and scan speed to machine curved

edges of arbitrary shape. The predicted and measured edge profiles had a maximum depth error

of about 7%, and it was shown that the smoothness of the machined edge could be controlled by

adjusting the spacing between the nozzle passes and the depth of each cut.

51

5.2 Contributions

The thesis presented a novel nozzle path model to machine planar areas of specified waviness in

ductile materials. The model is applicable to a wide variety of materials and needs only a few

preliminary experiments to capture the erosion behavior of the material and the erosive efficacy

distribution of the abrasive system. The research also investigated the machining of the sidewalls

bounding planar areas, and developed an approach to the creation of slopes having a desired

steepness. Finally, the thesis presented novel measurements of the dependence of the erosion rate

of a talc-filled thermoplastic polyolefin on the particle impact angle and the amount of talc filler.

52

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