Abrasive jet micromachining of acrylic and polycarbonate polymers at oblique angles of attack

Available online at www.sciencedirect.com

Wear 265 (2008) 888–901

Abrasive jet micromachining of acrylic and polycarbonate polymers at oblique angles of attack H. Getu a , A. Ghobeity b , J.K. Spelt b,a , M. Papini a,b,∗ a b

Department of Mechanical and Industrial Engineering, Ryerson University, Canada Department of Mechanical and Industrial Engineering, University of Toronto, Canada

Received 18 July 2007; received in revised form 3 January 2008; accepted 8 January 2008 Available online 4 March 2008

Abstract Masked and unmasked micro-channels were machined in polymethylmethacrylate (PMMA) using an abrasive jet of 25 ␮m Al2 O3 particles at a variety of impact angles. The erosion rate was found to depend on the jet scanning direction when the nozzle was inclined with respect to the target surface at 55◦ . This effect was explained in terms of the relative number of particles embedded in the target surface when scanning in the forwards, as opposed to backwards, directions. A simple, fast and relatively accurate analytical technique was introduced to predict the profiles of masked and unmasked micro-channels machined at oblique impact angles, and masked micro-holes machined at normal impact. Comparison of the predicted and measured profiles of micro-channels and micro-holes machined in PMMA showed good agreement in both shape and depth. Masked holes at normal incidence were also micromachined in LUCITETM (an acrylic) and LEXANTM (a polycarbonate), and revealed a similar shape to that found for PMMA (flat bottom and very steep side walls), implying that the present analytical technique may also be used for the prediction of the profile of abrasive jet micromachined features in a variety of polymers. © 2008 Elsevier B.V. All rights reserved. Keywords: Abrasive jet micromachining; Powder jet blasting; Polymers; Erosion modeling; PMMA

1. Introduction In abrasive jet micromachining (AJM), a jet of small particles is directed through an erosion resistant mask opening in order to machine features for use in micro-fluidic, micro-electromechanical systems (MEMS) and opto-electronic components [1,2]. The AJM of brittle materials such as glass and ceramics [3,4] has received most of the attention in the literature. One reason for the emphasis on glass and ceramics, is that traditional micro-fabrication technologies have been adopted from the electronics industry. However, these materials and their associated traditional fabrication methods (e.g. wet chemical etching) are very expensive [3,5]. A further limitation is that silicon-based materials can restrict applications in the biomedical field because of the lack of optical clarity in channel walls and poor biocompatibility [5].

∗ Corresponding author at: Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, Canada M5B 2K3. Tel.: +1 416 979 5000x7655; fax: +1 416 979 5265. E-mail address: [email protected] (M. Papini).

0043-1648/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2008.01.013

Polymeric materials, on the other hand, offer a wide range of desirable physical and chemical properties, are of relatively low cost and have good processibility for mass production [2–5]. This motivated the present study of the erosion mechanisms associated with the AJM of features such as channels and holes in several acrylic polymers. AJM involves the controlled erosion of target material by the impact of a jet of solid particles, and can thus benefit from the vast literature on solid particle erosion phenomena. Solid particle erosion has been classified into two major types of behaviour: brittle and ductile [6,7]. Brittle erosion is characterized by a peak in erosion rate at normal incidence, while ductile erosion has a peak erosion rate at an oblique impact angle. This reflects a difference in the fundamental erosion mechanisms. In brittle erosion processes, deformation wear and fracture are the main causes of material removal, while ductile erosion processes exhibit cutting wear. In polymeric materials, a more ductile response is generally observed in thermoplastics than in thermosets [8]. Polymethylmethacrylate (PMMA), an acrylic thermoplastic, responds in a ductile manner under the conditions typical of AJM processes, with the highest erosion rate observed when the particle jet is inclined 25◦ to the target surface [9]. In

H. Getu et al. / Wear 265 (2008) 888–901

the micromachining of PMMA, it is thus desirable to work at an oblique impact angle to increase the material removal rate. Although there is a large body of literature on solid particle erosion mechanisms in polymers and the influence of process conditions, e.g. Refs. [8,10–13], very little work exists on the application of AJM to polymeric materials. For example, the influence of the jet orientation relative to the traverse direction on the resulting material removal rate, at oblique impact angles, has not been investigated for AJM applications, although some related work has been done in this area for abrasive water jet machining (AWJM) [14,15]. Moreover, the possibility of maximizing the micromachining speed of polymeric materials by blasting at an inclined angle has not yet been investigated. The present authors have previously investigated fundamental erosion mechanisms in PMMA, and developed a profile evolution model suitable for the AJM of masked and unmasked micro-channels in PMMA, micromachined with the target normal to the incoming particle jet [9]. This present work extends the model to the cases of micro-holes machined at normal incidence and micro-channels machined at oblique angles of attack. In addition, the influence of the abrasive jet traverse orientation on the material removal rate is also investigated.

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measured using a Phase Doppler Particle Analyser [18]. The Vickers hardness was measured by indenting the PMMA sample with a diamond indenter. The elastic recovery in the direction of the diagonals is generally negligible in polymers of this type, and thus was not considered [19,20]. 2.2. Unmasked channels at oblique impact angle Unmasked micro-channels were machined in PMMA (type ACRYLITE® FF, CYRO Industries, Rockaway, NJ, USA) using the micro-blaster system with a target-to-nozzle standoff distance of 20 mm along the nozzle centerline. In most of the experiments, a round nozzle with 760 ␮m inner diameter was held stationary at θ * = 55 nominal impact angles, with respect to a line along the moving surface in the scanning direction (Fig. 2a and b). The target sample was mounted to a computer controlled linear stage (0.5 ␮m accuracy), which moved at a 0.25 mm/s constant traverse speed. The powder mass flow rate

2. Experiments 2.1. Experimental setup All experiments were conducted using a commercial microblaster (MB 1005 Microblaster, Comco Inc., Burbank, CA, USA), into which a mixing device [16] was incorporated to prevent particle bed compaction (Fig. 1). Dry air at 200 kPa entered the micro-blaster, where it was mixed with aluminium oxide powder of 25 ␮m nominal diameter hardness 20 GPa [17]. The average velocity of the particles across the jet for a round nozzle with 760 ␮m inner diameter was 100–110 m/s [16], as

Fig. 1. Schematic of the experimental apparatus.

Fig. 2. Schematic of the oblique micromachining process with the nozzle oriented at a standoff distance, h, along the nozzle centerline, and at a nominal angle of incidence of θ * , with respect to the surface for: (a) backward scanning; (b) forwards scanning.

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was held constant at 2.83 g/min (S.D. 0.12 g/min). For follow up experiments performed at other nominal impact angles in the range of θ * = 25–75◦ (see Section 4.4.2), a 0.5 mm/s scan speed and a 2.5 g/min mass flow rate was used. All other experimental conditions remained the same. Machining was carried out on samples having dimensions of 100 mm × 20 mm × 1.5 mm thick. The samples were divided into four sectors, each with a different channel depth corresponding to 1, 3, 5 and 7 nozzle passes. Micromachining was performed using three scanning orientations relative to the moving target: backward (Fig. 2a), forward (Fig. 2b), and a combination of both (i.e. backward and forward on alternate passes). A profilometer (Form Talysurf Intra, Taylor Hobson, Leicester, UK) was used to obtain the cross-sectional profiles. 2.3. Masked channels at oblique impact angle (θ * = 55◦ ) All blasting conditions were the same as those used for unmasked channels with the exception that a 0.3 mm × 3.8 mm rectangular cross-section nozzle was used with a 0.5 mm/s target scanning speed, and multiple pass machining was performed using alternating forward and backward scans at θ * = 55◦ angle of incidence with respect to the target. The powder mass flow rate was 5.21 g/min (S.D. 0.11 g/min). The wider rectangular nozzle (oriented with the 3.8 mm dimension across the channel width) was used to produce a more uniform particle stream over the mask opening, and to reduce possible alignment inaccuracies. The mask consisted of two 1 mm thick tool steel plates with edges machined to 90◦ , and clamped 250 ␮m apart on the 1.5 mm thick PMMA target. The channels were cross-sectioned using a low speed circular saw (BUEHLER® IsOMeT® , Chicago, IL, USA) and photographs of the channel profiles were obtained using scanning electron microscopy (SEM). Coordinates of the profiles were then obtained using digital image analysis software (ImageJ software, http://rsb.info.nih.gov/ij/). 2.4. Masked holes at normal impact angle (θ * = 90◦ ) AJM of holes at oblique incidence is not practical due to mask undercutting, and therefore the target was placed normal to the incident jet (θ * = 90◦ ). All other process conditions were as given in Section 2.3, except that a 0.25 mm/s target scan speed (θ * = 90◦ ) was used. The mask consisted of a 1 mm thick tool steel plate into which round 800 ± 60 ␮m diameter holes were drilled, approximately 15 mm apart. The mask was taped onto the 100 mm × 20 mm × 1.5 mm PMMA sample and mounted on the computer controlled linear stage. After machining, the samples were sectioned approximately 1 mm away from the hole, and the sectioned edges of the samples were polished using a 1200 grit silicon carbide abrasive paper (LECO Corporation, St. Joseph, MI, USA) to obtain clear edges through which the masked profile could be photographed. The profiles were photographed using an optical microscope coupled to a 5 mega-pixel digital camera and profile coordinates were obtained using digital image analysis software.

3. Modeling of abrasive jet micromachining of acrylic polymers 3.1. Surface evolution model for AJM of acrylic polymers at normal incidence An analytical surface evolution model, valid for materials which erode in a brittle manner, where the instantaneous surface slope is related to the local erosion rate through the normal component of the particle velocity vector, was developed by ten Thije Boonkkamp and Jansen [21] and Slikkerveer and in’t. Veld [22]. In this model, the particle velocity and mass flux vectors were assumed to be normal to the original target plane (z-direction), and the development of a two-dimensional channel (Fig. 3) by an abrasive jet was expressed as [21] z,t =

C −k/2 V (x)k φ(x)(1 + z2,x ) ρs

(1)

where z,t and z,x are the partial derivatives of the depth z with respect to the transverse coordinate x, and time, t, respectively, ρs the density of the target material (kg/m3 ), φ(x) the particle mass flux (kg m−2 s−1 ), V(x) the particle velocity distribution, and C and k are the experimentally determined erosion rate constants related to particle and target characteristics. In previous work by the present authors, Eq. (1) was modified so that it could be used with ductile materials having an erosion rate that is an arbitrary function of the impact angle and velocity [9], when the nozzle is held normal to the target surface. The modified, non-dimensional surface evolution differential equation for ductile materials, which includes the impact angle dependency of erosion rate, can be written as [9]     ∗ ∗ ∗ k ∗ ∗ ∗2 z,t ∗ = [V (x )] φ (x ) 1 + z,x∗ g(α) (2) where z* = z/L, x* = x/L and t* = t/T are the non-dimensional depth, channel width and time, respectively. A time constant, T, was defined as the time required to propagate the surface at x = 0 over a characteristic length, L, such that T = Lρs /C[V(0)]k φ(0)] [21]. The characteristic length for unmasked channels was taken to be the standoff distance, h. The characteristic length for unmasked channels was taken to be the mask width, w. V* (x* ) and φ* (x* ) are the normalized, non-dimensional particle velocity and mass flux distributions, respectively, obtained by dividing the values of velocity and mass flux by their values at x = 0 (chan-

Fig. 3. Coordinates for channel cross-sectional profiles. α is the angle made by the component of the velocity vector in the z-direction with the tangent to the channel surface in the x–z plane.

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nel centerline). They represent the distributions across the nozzle in a plane containing the nozzle axis, which is assumed to be normal to the target. g(α) is the semi-empirical function developed by Oka et al. [17,23,24] for a wide variety of metals, polymers and ceramics that describes the impact angle dependence of the erosion rate: g(α) = (sin α)n1 [1 + Hv (1 − sin α)]n2

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The angle between the tangent to the channel surface in the x–z plane and the z component of the incident velocity vector, α (Fig. 3), is given by ⎡ ⎞⎤ ⎛ π 1 ⎠⎦ α = ⎣ − arc cos ⎝  (4) 2 2 ∗ 1+z ,x∗

(3)

The constants n1 and n2 are determined experimentally and depend on the particle hardness and other impact conditions, while Hv is the initial target hardness in GPa, as reported by Oka et al. [23,24]. The first term of Eq. (3) is related to the impact energy associated with the particle velocity component normal to the surface, and represents the effect of repeated plastic deformation and fracture. The second term is related to the impact energy associated with the particle velocity component parallel to the surface, and represents the particle cutting action. Fig. 4a and b shows scanning electron micrographs of micromachined PMMA samples, taken originally as stereo pairs to reveal greater depth information using MeXTM software (Alicona Imaging GmbH). It can be seen that cutting is dominant at shallow impact angles, producing a rougher surface (Fig. 4a), while at high impact angles plastic deformation and fracture are dominant (Fig. 4b).

The erosion rate as a function of the local impact angle can then be expressed as [24] E(α) = g(α)E90 where E90 is erosion rate at normal incidence. 3.2. Surface evolution model for AJM of acrylic polymers at an oblique impact angle Eq. (2) is applicable to modeling of the evolution of a ductile surface micromachined with the particle jet at normal incidence to the target surface, in which case V(x) and φ(x) are the distributions across the nozzle in a plane containing its axis [9,25]. However, the erosion rate of ductile materials is generally greatest at an oblique impact angle [7,9]. When scanning at an oblique angle, the distributions of velocity, V, and particle mass flux, φ, incident on the target surface are different from those at 90◦ . Even if these distributions for V and φ are known at normal incidence, it is difficult to determine these quantities for use in Eq. (2) for the case of an oblique nominal impact angle since velocity and particle mass flux are a function of both time and position, which change instantaneously as the jet passes over a given location. In the present work, a simple technique based on a fit of the first-pass experimental profile was used to overcome this difficulty. After a channel was micromachined by scanning one pass, the shallow profile was used to characterize the erosive energy due to incident flux and velocity components in the z-direction, which was then used as an input to predict the profile and depth of successive passes (deeper channels). In other words, by fitting a curve to the experimental cross-sectional data of the first pass, it was possible to obtain a function that simulates both velocity and particle mass flux distributions in the z-direction at the particular nominal impact angle, and which includes the effect of particles ricocheting from the mask edge (if present). The particular form of the curve fit is unimportant; any curve fit of the first-pass profile which gives a sufficiently close fit to the experimental first-pass profile can be used. As a result, Eq. (2), can be rewritten as     z∗,t∗ =

Fig. 4. 3D stereo scanning electron microscopy image of channel surface machined in PMMA at nominal impact angle, θ * of: (a) 25◦ and (b) 90◦ . Experimental conditions: 25 ␮m Al2 O3 particles, 760 ␮m round nozzle, pressure = 200 kPa, scan speed = 0.5 mm/s, h = 20 mm.

(5)

γ ∗ (x∗ )

1 + z∗,x∗ 2

g(α)

(6)

where γ*(x*) is a non-dimensional, normalized polynomial function obtained from the fit of the first-pass profile, which describes the effects of both the velocity and particle mass flux distributions. The function was normalized by dividing it by its value at x = 0 (channel midpoint). The use of the first-pass profile to fit γ*(x*) is possible because, for such a shallow and flat pro2 file, z∗,x∗ = 0, and the angle between the tangent to the surface

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in the x–z plane and the z-direction velocity component, α = π/2 so that g(α) = 1 (Fig. 3). 4. Results and discussion 4.1. Unmasked channels micromachined at an oblique impact angle (θ * = 55◦ ) Eq. (6) was solved numerically using an initial condition of z* (x* , 0) = 0, by substituting a non-dimensional, normalized 6th degree polynomial fit (method of least squares) of the first-pass profile for γ*(x*) using Mathcad 11 (Mathsoft Engineering & Education Inc., Cambridge, MA, USA). Mathcad 11 uses the numerical method of lines (NMOL) for solving partial differential equations. The numerical errors are proportional to the time step and are of the fourth degree regarding the space step. The non-dimensional space step was 2 × 10−3 and the nondimensional time step 2.5 × 10−5 . This ensured the convergence and accuracy of the numerical solution. The numerical error was smaller than the experimental errors that might have occurred due to particle mass flux variations during the experiment, and the accuracy of the instruments. The best fit of the first-pass profile obtained under the conditions outlined in Section 2.2 at θ * = 55◦ gave the following functions for backward, forward and back-and-forth target scan orientations (Eqs. (7)–(9), respectively). The R2 value in each case was >0.99. It should be noted that for the back-and-forth case, the best fit was obtained by fitting to the average profile of the first and second passes γ ∗ (x∗) = 49200x∗6 − 52980x∗5 + 22060x∗4 − 4325x∗3 +359.5x∗2 − 1.4x∗ − 1

(7)

Fig. 5. Experimental (open symbols) and model predicted (solid lines) profiles of unmasked channels machined in PMMA at θ * = 55◦ for: (a) backward scanning, (b) forward and backward scanning and (c) forward scanning. Only the right hand side of a symmetric channel is shown. Experimental conditions: 25 ␮m Al2 O3 , 760 ␮m round nozzle, scan speed = 0.25 mm/s, pressure = 200 kPa, h = 20 mm.

(8)

in profile shape and size, particularly for channels less than 1 mm deep. For example, the predicted center depth after 7 passes was within 9% of the measured result. Fig. 5b shows that the error in the predicted center depth increased progressively reaching 25% for the 7th pass, in the case of channels micromachined by moving the target in the back-and-forth direction (i.e. a 3.5 cycles of a forward scan followed by a backward scan). The error in the predicted center depth for the forward machining orientation was at 28% (Fig. 5c). At θ * = 55◦ the center depth after 7 passes for the backward micromachining case was found to be 902 ␮m (Fig. 5a), while machining at θ * = 90◦ under identical conditions gave only a 426 ␮m center depth [9]. It is thus clear that the etch rate is significantly increased when machining at oblique incidence, as expected. It was apparent that the center depth in both the forward and back-and-forth scanning orientations was less than that in the backward orientation at θ * = 55◦ incidence. The average difference in the center depth increment per pass between forward and backward scans was 26.3 ␮m after 7 passes (Fig. 5a and c). Section 4.4 discusses the possible causes of center depth differences depending on the scanning orientation of the nozzle during micromachining.

γ ∗ (x∗) = 94610x∗6 − 89780x∗5 + 33210x∗4 − 5860x∗3 +450.5x∗2 − 3x∗ − 1 γ ∗ (x∗) = 47520x∗6 − 51140x∗5 + 21210x∗4 − 4125x∗3 +336.6x∗2 + 0.4x∗ − 1

(9)

The parameters n1 and n2 in Eq. (3) were found in previous work to be 1.27 and 15.5, respectively [9], and the Vickers hardness, Hv , for the PMMA was measured to be 0.25 GPa using a micro-hardness tester [9]. This is in close agreement with values reported by other researchers. For example, Oka et al. [23] reported a value of 0.23 GPa for PMMA. As mentioned in Section 1, the PMMA eroded in a ductile manner showing a maximum erosion rate at a nominal impact angle of 25◦ [9]. Fig. 5 shows a comparison of the experimental and predicted (Eq. (6)) profiles of unmasked channels micromachined at a nominal angle of incidence θ * = 55◦ in the forward, backward and back-and-forth scanning orientations. In the backward scanning orientation (Fig. 2a), Figure 5a shows generally good agreement between the model and the experimental results both

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Fig. 6. Experimental (symbols) and model predicted (solid lines) profiles of masked micro-channels machined in PMMA at θ * = 55◦ . Only half of a symmetric profile is shown. Experimental conditions: 25 ␮m Al2 O3 , 0.3 mm × 3.8 mm rectangular nozzle, pressure = 200 kPa, scan speed = 0.5 mm/s, h = 20 mm, mask opening width = 300 ␮m.

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The initial conditions were z* (x* , 0) = 0 and the boundary conditions were z* (−0.5, t* ) = z*(0.5, t* ) = 0, while n1 , n2 and Hv were as described in Section 4.1. The order of the polynomial was higher than that used for unmasked channels (Eqs. (7)–(9)) because of the need to fit the profile created by mask edge scattering superimposed on that due to the nozzle flux. The model predicted the masked channel center depth with 8% accuracy up to an aspect ratio of approximately 2. The channel shape was simulated well in all cases. As the channel depth grew, the channel widened by approximately 40 ␮m on both sides. This was due to the mask edge scattering effect; i.e. particles rebounding from one side of the mask edge to erode the opposite side of the channel. As was found previously for micro-channels machined in glass, the mask-edge undercutting can be reduced by the use of a thicker mask [25]. As can be seen in Fig. 7, the impact angle dependency of ductile material erosion resulted in PMMA channels with very steep sidewalls, when compared to those machined in glass [9,25]. This property might be advantageously utilized in the fabrication of components in which a steep sidewall is desirable.

4.2. Masked channels at oblique impact angle (θ * = 55◦ )

4.3. Masked holes

Fig. 6 compares the measured channel profiles, micromachined back-and-forth, with those predicted by the model of Eq. (6). The method of least squares was used to obtain the following best fit to the experimental first-pass profile (R2 = 0.999):

The prediction of the masked hole cross-sectional profiles was made using Eq. (6) with the hole radius, r, substituted for the coordinate x, giving z∗,t ∗ =

γ ∗ (x∗) = −122.32x∗14 − 363.53x∗13 + 845.06x∗12 +815.18x∗11 − 1574x∗10 − 700.72x∗9 + 1297x∗8 +287.75x∗7 − 519.05x∗6 − 56.70x∗5 + 88.83x∗4 +4.38x∗3 − 0.82x∗2 + 0.02x∗ − 1



(10)

γ ∗ (r ∗ )



1+z

∗2 ,r∗



 g(α)

(11)

where r* = r/d, with r the radial distance and d the characteristic length taken as the mask diameter. For γ * (r* ), the following polynomial provided the best fit of the first-pass experimental

Fig. 7. Typical shape of a masked micro-channel in PMMA (left) and glass (right) machined with θ * = 90◦ [9].

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Fig. 8. Experimental (symbols) and model predicted (solid lines) profiles of masked micro-holes machined in PMMA at θ * = 90◦ . Experimental conditions: 25 ␮m Al2 O3 particles, 0.3 mm × 3.8 mm rectangular cross-section nozzle, pressure = 200 kPa, scan speed = 0.25 mm/s, h = 20 mm, mask opening diameter = 800 ± 60 ␮m.

profile: γ ∗ (r∗) = 23r ∗9 − 177.67r ∗8 − 21.66r ∗7 + 57.51r ∗6 +7.04r ∗5 + 12.28r ∗4 − 0.91r ∗3 − 0.61r ∗2 +0.04r ∗ − 1

(12)

The initial conditions were z* (r* , 0) = 0 and boundary conditions were z* (−0.5, t* ) = z* (0.5, t* ) = 0, while n1 , n2 and Hv were as described in Section 4.1. Fig. 8 shows that the model predicts the center depth up to 0.8 mm with less than 10% error, and that the etch rate decreases as the hole grows deeper (Table 1). Heating effects leading to target material property changes can be excluded as a possible reason for this, because the nozzle was scanned over the target, exposing a given cross-section to the abrasive jet for only a short period of time. Previous investigations have shown that there is insignificant heating occurring under such experimental conditions [9]. In the work of Ref. [9], the authors continuously Table 1 Hole center depths of holes machined at normal incidence (i.e. θ * = 90◦ ) in PMMA

After 1 pass After 3 passes After 5 passes After 7 passes After 9 passes After 11 passes After 13 passes

Hole depth (␮m)

Average center depth increment per pass (␮m)

79 230 362 530 632 742 885

79 77 73 76 70 68 68

Experimental conditions: 25 ␮m Al2 O3 particles, 0.3 mm × 3.8 mm rectangular cross-section nozzle, pressure = 200 kPa, scan speed = 0.25 mm/s, standoff distance = 20 mm, mask opening diameter = 800 ± 60 ␮m.

recorded the output of an embedded thermocouple as the overlying 900 ␮m of PMMA was progressively eroded by an abrasive jet for 120 s until the thermocouple was exposed and destroyed. Very thin thermocouple wires (80 ␮m diameter, K type) were used to reduce conduction losses and the thermocouple bead was embedded in a 1 mm diameter hole using acrylic cement to enhance thermal contact. Extrapolating the recorded temperature versus the remaining thickness of PMMA overlying the thermocouple, led to the conclusion that the surface temperature did not rise more than approximately 13 ◦ C. There was no abrupt temperature increase observed as the erosion front approached the thermocouple, even when the remaining PMMA layer was approaching zero thickness. Furthermore, there was no evidence of surface darkening due to localized heating as was reported by Rao et al. [26]. This lack of significant heating is due to the very small mass flux, calculated to be 8.45 kg m−2 s−1 at the center of the jet where it was maximum. Using the analysis of Ref. [27], the corresponding impact zone frequency was calculated as 141 s−1 , which is lower than the calculated minimum frequency needed for the thermal mechanisms to be significant (213 s−1 ). This further reinforces the hypothesis that heating effects were insignificant in the present experiments. A more likely reason for the decreasing erosion rate as the hole becomes deeper is particle embedding, which will be discussed in Section 4.5. Masked holes were also machined in another acrylic polymer (LUCITETM ) and in a polycarbonate (LEXANTM ). The similarity in profile development evident in Fig. 9 suggests that the present modeling technique might be suited to the prediction of the evolving surface profiles in a variety of polymers. This hypothesis is the subject of future work. 4.4. The effect of abrasive jet scan orientation 4.4.1. At θ * = 55◦ nominal impact angle As indicated in Section 4.1, when machining at θ * = 55◦ there was a center depth difference between the forward and backward direction micromachined channels. Table 2 presents a comparison, for the forward versus backward scanning directions, of the mass, Mp , of incident particles needed to be launched per unit length of channel (along the scanning direction) to machine a unit depth (at the center) unmasked channel. Mp allows for changes in channel center depth to be directly compared for data obtained at different scan speeds and mass flow rates, and is calculated by dividing the particle mass flow rate by the product of the scan speed and the measured per pass center depth. Table 2 shows that, for unmasked channels under the given process conditions at θ * = 55◦ , 1.765 ␮g of Al2 O3 powder per ␮m of scanning length is required to machine a 1 ␮m deep channel using a forward scan, whereas, when using a backward scan, only 1.366 ␮g of Al2 O3 powder is required. A two-tailed t-test showed that there was a statistically significant (95% confidence) difference between these values for the forward versus backward directions. This of course, also implies that the difference in depth between the micro-channels micromachined in the forward and backward orientation (30 ␮m) was also statistically significant. This scan direction effect appears not to

Table 2 Comparison of the mass of particles needed to machine a 1 ␮m long unmasked channel to a depth of 1 ␮m in PMMA using the forward (FW) and backward (BW) scanning directions, at different impact angles Trial

Machining direction

Center depth increment per pass (␮m)

Mass of particles required to machine a 1 ␮m deep, 1 ␮m long channel, Mp (␮g)

Average (␮g)

S.D. (␮g)

Difference between average for BW and FW directions (␮g)

Difference statistically significant?

25

1 2 3 1 2 3

FW FW FW BW BW BW

29.6 29.4 31.1 33.4 28.1 29.6

2.819 2.837 2.678 2.500 2.964 2.819

2.778

0.087

0.017

No

2.761

0.237

1 2 3 1 2 3

FW FW FW BW BW BW

69.5 68.7 68.8 72.9 72.8 70.5

1.200 1.214 1.212 1.145 1.146 1.184

1.209

0.007

0.051

Yes

1.158

0.022

1 2 3 1 2 3

FW FW FW BW BW BW

93.0 121.8 110.0 133.0 144.1 138.0

2.030 1.548 1.716 1.420 1.311 1.368

1.765

0.245

0.398

Yes

1.366

0.054

1 2 3 1 2 3

FW FW FW BW BW BW

62.0 60.0 60.2 58.9 60.7 57.4

1.345 1.390 1.386 1.416 1.374 1.454

1.374

0.025

0.041

No

1.415

0.040

1 2 3 1 2 3

FW FW FW BW BW BW

43.6 42.4 40.8 41.5 38.4 39.3

1.914 1.966 2.045 2.010 2.175 2.121

1.975

0.066

0.013

No

2.102

0.084

45

55

65

75

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Nominal impact angle, θ* (◦ )

Experimental conditions: 25 ␮m Al2 O3 particles, 760 ␮m round nozzle, pressure = 200 kPa, standoff distance = 20 mm. For θ * = 55◦ : abrasive mass flow rate = 2.83 g/min, 0.25 mm/s. All other angles: abrasive mass flow rate = 2.50 g/min flow rate and scan speed = 0.5 mm/s. 95% confidence used for statistical significance test.

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Fig. 10. Leading edge of profile created by micromachining a channel at θ * = 55◦ in PMMA using the (a) forward and (b) backward directions. Arrows show direction of nozzle movement relative to target. Experimental conditions: 25 ␮m Al2 O3 particles, 0.3 mm × 3.8 mm rectangular nozzle, scan speed = 0.5 mm/s, pressure = 200 kPa, h = 20 mm.

Fig. 9. Experimental profiles of machined masked micro-holes machined at θ * = 90◦ in acrylic polymers: (a) PMMA, (b) LUCITETM and a polycarbonate (c) LEXANTM . Experimental conditions: 25 ␮m Al2 O3 particles, 0.3 mm × 3.8 mm rectangular nozzle, pressure = 200 kPa, scan speed = 0.25 mm/s, h = 20 mm.

have been previously reported in the literature on abrasive jet micromachining, but as discussed previously, it was a consistent observation in the present experiments. In related work, Fowler et al. [15] found that abrasive water jet machining of a titanium alloy (Ti6Al4V) in the forward orientation resulted in high levels of particle embedding due to the rapid change in momentum of the particles. This was believed to be due to the acute angle of the kerf face formed by the shallow impact angle of the leading edge of the water jet. The effect that this may have had on the erosion rate was not discussed. The possibility that the shape of the leading edge of the scanning jet may influence the amount of particle embedding, and thus the relative etching rate, was considered in the present case. To investigate this, the leading edges of channels micromachined only in the forward and only in the backward scanning orientations (Fig. 2a and b) were obtained by suddenly stopping the

flow of particles through the nozzle while scanning. However, in contrast to the results obtained by Fowler et al. [15] using AWJM, the shape of the leading edges formed using AJM were found to be very similar in the forward and backward orientations (Fig. 10). It was thus concluded that the shape of the leading edge was not responsible for the differences seen when machining forward versus backward. In order to determine whether the forward and backward scanning orientations indeed caused different amounts of particle embedding, scanning electron microscopy was used with energy dispersive X-ray spectroscopy (EDS) to map the locations and amounts of Al2 O3 particles remaining in the channels after machining. A channel machined in the forward orientation was sectioned along the centerline and placed alongside half of a symmetric micro-channel machined in the backward orientation as shown in Fig. 11a. The upper half of Fig. 11a shows the channel machined in the forward orientation and the lower half shows the channel machined in the backward orientation. As seen in the EDS results of Fig. 11b, at all locations (I)–(IV), the channel machined in the forward orientation at 55◦ always showed many more embedded particles, consistent with the observations reported in [15] for AWJM. Note that due to size limitations of the EDS chamber, it was not possible to evaluate all samples simultaneously, and it is only possible to compare the relative amounts of embedded particles within a single photograph in Fig. 11 (forward versus backward at a particular location), and not from photograph to photograph. It was thus not possible, for example, to deduce which of locations (I)–(IV) had more embedded particles. 4.4.2. Other oblique nominal impact angles A two-tail t-test showed that the difference in the mean values (three trials) of the mass of particles needed to micromachine a 1 ␮m deep, 1 ␮m long micro-channel in the forward and backward directions at various nominal impact angles was not statistically significant at 95% confidence level in all cases, except for θ * = 45◦ and θ * = 55◦ (Table 2). Even though a statistically significant difference was seen at θ * = 45◦ , it should be noted that the average center depth difference after two passes

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Fig. 11. (a) Locations I–IV along unmasked channels machined in PMMA used in EDS mapping. Point A is a located immediately next to the leading edge. (b) EDS mapping of channel surface when machining at θ * = 55◦ in the forward (FW) and backward (BW) scanning directions. White dots are sites of embedded Al2 O3 particles. Experimental conditions: 25 ␮m particles, 760 ␮m diameter round nozzle, pressure = 200 kPa, scan speed = 0.25 mm/s, h = 20 mm.

obtained using a 0.5 mm/s target scan speed and 2.5 g/min mass flow rate (all other conditions remaining as in Section 2.2) was only approximately 3 ␮m. SEM and EDS were again used to map the locations and amounts of Al2 O3 particles using the procedures described in Section 4.4.1. In contrast to the θ * = 55◦ case (Fig. 11), Fig. 12 shows that, for θ * = 35◦ , 45◦ , 65◦ and 75◦ , there was little difference in particle embedding between the two scanning orientations. This further supports the notion that embedded particles are responsible for the differences in material removal seen for the θ * = 55◦ case. As before, note that the relative amounts of embedded particles can only be compared within a single photograph (forward versus backward at a particular θ * ), and that it is not possible to deduce which θ * resulted in more embedded particles. Finally, it is also interesting to note that the nominal incident angle at which the erosion rate (mass removed per mass of powder used) was maximum, θ * = 25◦ [9], did not yield the deepest channels. For example, Table 2 shows that less incident particle mass was required at θ * = 55◦ than at θ * = 25◦ to machine a 1 ␮m deep (at the center) by 1 ␮m long unmasked channel. This can be explained in terms of the flux distribution and the definition of the erosion rate. When θ * = 25◦ , the abrasive jet is spread over a wider surface area than at 55◦ , resulting in a lower center

depth increment per pass. However, consistent with the trend of erosion rate variation with angle, after four passes with a 1 mm/s scan speed (conditions as in Section 2.2), the unmasked channel machined at θ * = 25◦ showed a slightly higher overall material removal than that at 55◦ ; i.e. the entire channel cross-sectional area was 2.10 mm2 for the 25◦ impact angle case, and 2.09 mm2 for 55◦ . 4.4.3. The influence of abrasive jet scan orientation on particle embedding The largest difference between channel dimensions using the forward versus backward orientations was found to be at 55◦ , which is similar to the trend reported by Fowler et al. [15], who found that the most significant differences between the two modes of machining were at intermediate angles, 45–75◦ , when using abrasive water jet machining to machine a titanium alloy (Ti6Al4V). It has been reported that particle embedding is greater at higher impact angles than at shallower impact angles [27,28]. For example, Walley and Field [27] reported more embedding of smaller particles (50 ␮m) at high impingement angles during the erosion of polyethylene by sand having a nominal size range of 300–600 ␮m. They were not certain whether these smaller par-

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Fig. 12. EDS mapping of unmasked channel surface when machining PMMA in the forward (FW) and backward (BW) scanning directions at (a) θ * = 35◦ (b) θ * = 45◦ (c) θ * = 65◦ and (d) θ * = 75◦ . White dots are sites of embedded Al2 O3 particles. Experimental conditions: 25 ␮m Al2 O3 particles, 760 ␮m round nozzle, pressure = 200 kPa, scan speed = 0.25 mm/s, h = 20 mm.

ticles were their original size or whether they were broken on impact or by subsequent impacts. This suggests that a possible reason for the greater amount of particle embedding in the forward orientation is the higher local impact angle of the trailing edge when compared to the trailing edge of the backward orientation, as illustrated in Fig. 13. In other words, for the forward scanning orientation the last portion of the jet impacts at a higher local angle, θ, and thus leaves behind more embedded particles than the backward orientation, which has a lower local impact angle on the trailing edge. It is hypothesized that the greater particle embedding seen in the forward orientation caused the lower

material removal rate compared with the backward orientation by partially shielding the PMMA from the jet in the subsequent nozzle pass. The scan direction effect on material removal can be explained further in terms of the net incident particle embedding energy flux. Assuming that the portion of the energy flux due to the velocity component perpendicular to the surface tends to embed particles, while the portion of the energy flux due to the velocity component parallel to the surface tends to remove particles, the normalized (i.e. divided by the total energy flux at the center of the stream) net energy flux that causes particle embedding at any given point along the normalized erosion scar centerline, y* = y/h can be written as net embedding energy flux (y∗ ) = φ∗ (y∗ )[V ∗ (y∗ )]2 [sin2 θ(y∗ ) − cos2 θ(y∗ )]

(13)

where φ* (y* ) and V* (y* ) are the normalized (to the center stream values) values of particle flux and velocity arriving to a given y* along the channel centerline, and θ is the local impact angle at a given normalized coordinate y* (Fig. 13). As an example, Fig. 14 shows a plot of the net embedding energy flux along the scar centerline, for a 760 ␮m inner diameter nozzle having a focus coefficient of β = 15 [25], inclined at a θ * = 55◦ nominal impact angle. The values for the normalized particle mass flux and velocity distributions were approximated for these conditions as y∗ sin θ ∗ (14) V ∗ (y∗ ) = 1 − 4.9187 1 − y∗ cos θ ∗ φ∗ (y∗ ) = − Fig. 13. Leading and trailing edge angles for the forward scanning direction.

2 1 −(β2 /(1−y∗ cos θ ∗ )2 )(y∗ sin2 θ ∗ ) e (1 − y∗ cos θ ∗ )2

(15)

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itive net embedding. In the reverse scan orientation, the surface first sees positive embedding, then negative embedding. However, at this impact angle, little effect of scan direction is expected as the net embedding energy flux is small. This is consistent with the experimental observations of Section 4.4.2. At θ * = 55◦ , the net embedding energy flux is positive and much greater than that at 45◦ . The asymmetry about the center of the stream is also high, implying that the effect of scan direction is pronounced. The forward direction (left to right on Fig. 14) has a higher net embedding energy flux at the trailing edge than the backward scan (right to left on Fig. 14), and therefore leaves more embedded particles. This is consistent with the EDS observations (Fig. 11). These particles that are embedded after the passage of the trailing edge shield the target from erosion during successive passes, and are responsible for the lower material removal seen in the forward versus backward scanning direction at θ * = 55◦ . 4.5. The effect of particle embedding on material removal rate in masked PMMA holes Fig. 14. Normalized net embedding energy flux (Eq. (13)) distributions on the centerline of the erosion scar as nozzle scans in the forward direction at different nominal impact angles.

 θ(y∗ ) =

π − a cos 2



sin θ ∗

 y∗2 − 2y∗ cos θ ∗ + 1

 (16)

based on previously derived values under similar conditions [25]. The spread in local impact angle can be obtained using Eq. (16) and Fig. 14, which shows the energy flux distribution along the non-dimensional centerline (y* ). For example, the approximate angle of the leading edge for nominal angles of 25◦ and 75◦ are 19◦ and 68◦ , respectively, while the corresponding trailing angles are 33◦ and 82◦ . Three different characteristics are seen in Fig. 14. At shallow impact angles: At θ * = 25◦ , the tangential energy flux responsible for particle removal is dominant, and the net embedding energy flux is negative. It is therefore expected that there would be fewer embedded particles regardless of scan direction. Furthermore, the distribution of the net embedding energy flux is symmetric about the nozzle axis, indicating that there is no difference between the net embedding at the leading and trailing edges of the blast zone. Consequently, it is immaterial which edge passes over the surface last depending on the scan direction. Hence, as observed in Section 4.4.2, there was no dependence of material removal on scanning direction at 25◦ . At high impact angles: At θ * = 75◦ , the net embedding energy flux is relatively large and symmetric about the center of the stream (Fig. 14). Therefore, more particle embedding is expected, but since the net embedding energy flux is symmetric about the center, no difference in material removal with scan direction should be seen. This is confirmed by the statistical significance test described in Section 4.4.2. At intermediate impact angles: Fig. 14 shows that the net embedding energy flux is asymmetric about the center of the stream at θ * = 45◦ . In the forward scan orientation (left to right on Fig. 14), the surface first sees negative net embedding, then pos-

Table 1 shows that the rate of erosion decreased as the masked holes in PMMA became deeper. To investigate whether embedded particles were responsible for the decrease in the erosion rate in deepening masked holes, two experiments were performed to separate particle embedding effects from possible geometric effects such as differences in the local impact angle caused by a changing profile shape and differences in the number of particles scattered from the mask edge reaching the bottom of the hole. In the first experiment, two 1.5 mm thick PMMA sheets were clamped together and a 1548 ␮m deep masked hole was micromachined into them. When the upper sheet was removed, a 48 ␮m deep hole remained in the lower one, presumably with a relatively large amount of powder embedded in the bottom. This sheet (with 48 ␮m deep hole) was masked and microma-

Fig. 15. EDS mapping of surface at the bottom of the micro-hole machined in PMMA for the first experiment described in Section 4.5. White dots are sites of embedded Al2 O3 particles. Experimental conditions: 25 ␮m Al2 O3 particles, 0.3 mm × 3.8 mm rectangular nozzle, pressure = 200 kPa, scan speed = 0.25 mm/s, h = 20 mm.

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chined at 0.25 mm/s using the blasting conditions of Section 2.4, and the depth increment after the additional pass was 62 ␮m. In the second experiment, a virgin PMMA sample was machined under the same experimental conditions, and the depth increment was measured after the first pass was 100 ␮m. After the second pass, the depth increment was 90 ␮m. Since the depth increment per pass in the first experiment on a previously blasted hole (48 ␮m) was much smaller than that in the second experiment, this demonstrates that reduction in the material removal rate is caused by embedded particles. In order to verify the presence of embedded particles, the hole of the first experiment was observed using scanning electron microscopy and EDS to confirm the presence of embedded Al2 O3 particles (Fig. 15). It is noted that the edge of the hole partially obstructed the X-ray detector, which was situated at an angle. 5. Conclusions A normalized, non-dimensional polynomial function, obtained from the fit to measured channel profile of the first pass, was used to simulate the velocity and particle mass flux distributions arriving at a PMMA surface when blasted at an oblique impact angle. Using this function, a previously derived analytical model for AJM of polymeric materials [9], was used to predict profiles of masked and unmasked micro-channels developed by successive passes in PMMA at an oblique impact angle. The same procedure was used to predict profiles of masked holes micromachined in PMMA at normal impact angle. In all cases, the model predicted the shape of the machined features well, and in most cases the model also predicted the depth of the features properly. The advantage of using the first-pass profile to obtain the erosive energy distribution lies in its ability to simulate in a single measurement the combined effects of the velocity and mass flux distributions at any impact angle with any nozzle and any target material. At shallow impact angles, there was no difference in net particle embedding caused by the scanning direction of the abrasive jet, and thus no difference in the etch rate with scan direction. At high impact angles, although more particle embedding occurred, it was independent of the abrasive jet scan direction, and thus no differences in etch rate with scan direction was seen. At intermediate angles, however, the scan direction did affect the net amount of particle embedding. EDS mapping of the forward and backward micromachined channels showed that there was more particle embedding in case of the forward machining than backward, which decreased the material removal rate at θ * = 55◦ nominal angle of incidence. This was explained in terms of differences in the energy flux distribution at the leading and trailing edges of the blast pattern which affected net particle embedding and hence the resistance of the material to erosion in subsequent passes. Acknowledgments The authors acknowledge the Natural Sciences and Engineering Research Council (NSERC) of Canada for financial support.

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