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Journal of Manufacturing Processes 12 (2010) 9298

Contents lists available at ScienceDirect

Journal of Manufacturing Processes

journal homepage: www.elsevier.com/locate/manpro

Technical paper

Understanding the effects of the system parameters of an ultrasonic cutting fluidapplication system for micro-machining

Max Rukosuyev, Chan Seo Goo, Martin B.G. Jun Department of Mechanical Engineering, University of Victoria, Victoria, Canada

a r t i c l e i n f o

Article history:

Received 22 September 2009Accepted 5 June 2010

Available online 7 July 2010

a b s t r a c t

Tool wear in micro-milling poses a serious limitation to increased production rate, and atomized cutting

fluids have been shown to be quite effective in increasing tool life in micro-milling operations. Anew compact cutting fluid application system has been designed and developed based on ultrasonic

atomization. In order to understand the effects of the system input parameters on system performance,two performance measures have been defined in terms of spray characteristics and experiments have

been performed to evaluate the system according to the defined performance measures. Based on theexperimental results, the system parameters can be adjusted to obtain the desired spray characteristics,

and areas of improvement on the design have been identified.Crown Copyright 2010 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.

All rights reserved.

1. Introduction

Micro-machining, in particular, micro-milling and micro-dri-lling, is becoming increasingly a viable and potentially preferable

process for machining mechanical components with micro-scalefeatures and high relative accuracy for a wide range of engineer-ing materials. However, the limitations of micro-tooling technolo-gies (large edge radii and poor geometry control) and the resultingploughing mechanism with the minimum chip thickness effect [1]lead to increasedlevels of tool wear andtool failure. Thus, tool wearposes a serious limitation to the increase of production rates andthe production repeatability. Application of cuttingfluidsis knownto benefit the machining operation through promoting longevityin tool life [2], and atomized cutting fluids have been shown to bequite effective in micro-milling operations [1]. However, there arestill limitedefforts in effective system design anddevelopment andlimited understanding of the design parameters for improved sys-tem performance.

Friedrich [3] developed a 22m diameter milling tool and usedliquid nitrogen for cooling the workpiece to the near-brittle statesuch that the specific cutting energy can be obtained and appro-priate feeds can be achieved at a low cutting speed. Yan et al. [4]looked at the surface roughness of single crystal silicon underdifferent coolant conditions (dry, kerosene, and water) in ultra-precision cutting using a diamond tool to study ductile mode ma-chining of singlecrystal silicon. However, it is likelythat traditionalmacro-machining process cuttingfluid systems such as flood, high-pressure coolant application, and liquidnitrogen-based cooling

Corresponding author. Tel.: +1 250 853 3179; fax: +1 250 721 6051.E-mail address: [email protected] (M.B.G. Jun).

are not viable approaches in micro-machining. The impact force ofthe cutting fluids may be greater than cutting forces that are onlyon the order of a few Newtons [5], resulting in tool deflection oreven damage. Also, reduced levels of surface tension and viscos-

ity and very small particle sizes will likely be required to pene-trate into the small cutting zone through the boundary layer of airaround the tool periphery, formed due to high rotational speeds(50500 K rpm). Furthermore, due to increased ploughing inmicro-machining, there is increased friction at the toolworkpieceinterface, and consequently, a good lubricating property of the cut-ting fluid is essential and important for extended tool life.

An alternative method for cutting fluid application that hasproved to be attractive in micro-machining is the atomization-based method, where atomized droplets can access the cuttingzone, absorb heat while acting as a lubricant, and remove heatfrom the cutting zone through evaporation [6]. Spray cooling hasbeen found to be very effective in cooling of electronic circuits(>100 W/cm2) [7]. Extensive research has also been done to un-

derstand the effect of spray characteristics on the interaction be-tween atomized droplets and the contact surface [8]. It has beenfound that cooling capacity and droplet impingement are influ-enced by spray characteristics (droplet size, distribution, and ve-locity), which are also affected by atomization parameters andcutting fluid properties [7,8]. The thin film due to impingementof the droplets can also provide good lubrication on the surface.Fluid properties such as surface tension and viscosity also havebeen found to be strongly related to heat transport and lubrica-tion in conventional machining [9]. Recently, the use of atomizeddroplets for cutting fluid application in micro-milling was provento be quite effective in terms of prolonging tool life, cooling, andimproving surface finish [1]. However, the developed system wasa proof-of-concept system; the atomized fluid delivery system had

1526-6125/$ see front matter Crown Copyright 2010 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers. All rights reserved.doi:10.1016/j.jmapro.2010.06.002
http://dx.doi.org/10.1016/j.jmapro.2010.06.002http://www.elsevier.com/locate/manprohttp://www.elsevier.com/locate/manpromailto:[email protected]://dx.doi.org/10.1016/j.jmapro.2010.06.002http://dx.doi.org/10.1016/j.jmapro.2010.06.002mailto:[email protected]://www.elsevier.com/locate/manprohttp://www.elsevier.com/locate/manprohttp://dx.doi.org/10.1016/j.jmapro.2010.06.002

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M. Rukosuyev et al. / Journal of Manufacturing Processes 12 (2010) 9298 93

limited controllability and poor focusing capability, and it wasrather bulky. Thus, further improvements in the design are re-quired. Also, the effects of the system parameters on its perfor-mance have not been studied for optimized system performance.

In this paper, new designs for an atomization-based cuttingfluid system are proposed. First, to aid in understanding of the de-sign parameters and issues, atomized particle dynamics and theperformance of atomized cutting fluids given in [1] are summa-

rized. The system design is then presented followed by an exper-imental setup for understanding the effect of the system inputparameters on the spray characteristics. Then, experimental re-sults are presented along with discussions on areas of improve-ment on the design, followed by some conclusions.

2. Performance of atomized cutting fluids

2.1. Atomized particle dynamics

The atomization method by ultrasonic vibration creates a quasi-monodispersespraywith easy control of theflow rate. This methodcan be made compact since no high-pressure pump is required[10,11]. Therefore, the atomization method based on the ultrasonicvibration is used here to develop the new cutting fluid application

system.The parameters that influence the impingement dynamics of

the atomization process are the droplet diameter (do) and velocity(wo) of the incident drop, the liquid dynamic viscosity (), theliquid density (), and the liquid surface tension () [12]. Theconditions of the receiving surface such as the film thickness ( h)for wet surfaces also play a major role in controlling the outcomeof a dropwall collision. The following non-dimensional numbersbased on the normal component of velocity, wo, are the mostrelevant [13];

We = w2o do

, Re = wodo

,

Oh

=

do, hnd

=

h

do

(1)

where We is the Weber number, Re is the Reynolds number, Ohis the Ohnesorge number, and hnd is the non-dimensional filmthickness number.

There are four impingement regimes identified in the spraysurface or sprayfilm interaction phenomenon. The first regime isthe stick regime, which occurs when an impinging drop adheresto the wall or film surface in nearly a spherical form. This oftenhappens when the impact energy is extremely low, and the sur-face temperature is below the pure adhesion temperature (Tpr).The transition criteria for the stick regime is We < 5 [13]. Therebounding regime occurs when the impinging drop bounces offthe wall or film. The air layer trapped between the drop and thesurface causes low energy loss resulting in bouncing. The transi-tion criterion for the rebounding regime is 5 < We < 10 [14]. The

third regime, spreading, is similar to the sticking regime but oc-curs when We > 10. Finally, the fourth regime is where splashingor further atomization occurs and droplets break into many sec-ondarydroplets. Non-dimensional groupshave been defined to de-termine the transition criterion for splashing [1517]. Forexample,if the value of the non-dimensional group (Km) given in Eq. (2) isless than the critical value (Kmc = 57.7),the droplets remain in thespreading regime [15],

Km =(do)

34 w

54

o

1214= (Oh 25 We) 58 . (2)

2.2. Effectiveness of atomized cutting fluids

From the experimental evaluation of the atomization-basedcutting fluid application system conducted by Jun et al. [1], the

Fig. 1. A schematic design of the atomization-based cutting fluid application

system developed in [1].

following requirements can be summarized for effective cuttingfluid application in micro-machining considering the size-scale ofthe tool, a difficult-to-penetrate small cutting zone, and increasedploughing and rubbing: (1) the disturbance force due to thedelivery of the cutting fluid to the cutting zone must be at least

an order of magnitude less than the cutting forces, (2) the cuttingfluid must possess a good wettability to be able to penetrate intothe cutting zone and lubricating property to minimize the effectsof excessive ploughing/rubbing in micro-machining, and (3) thevelocity of the droplets and the carrying air must be appropriateto effectively spread and wet the surface and simultaneously flushaway chips from the cutting zone since micro-scale chips tend tostick to the cutting zone.

The schematic of the system designed to meet the aforemen-tioned requirements is shown in Fig. 1. The atomized droplets arecarried at appropriately low velocity to avoid condensation of thedroplets within the tube that serve as a delivery channel for thedroplets. Thus, a low velocity supply is needed as shown in Fig. 1.Once the droplets are out of the tube and ready to be delivered tothe cutting zone, they are accelerated by the high velocity air jetcarried through a pipe located at the center ofthe tube.Jun et al. [1]conducted analytical analysis based on the droplet impingementdynamics [12,15] to ensure that the velocity of the air jet and thedroplets is high enough to flush away the chips and low enough towet the cutting zone instead of splashing.

A prototypeof the experimentalsetup forthe conceptual designgiven in Fig. 1 was devised by Jun et al. [1], and micro-millingexperiments were conducted to evaluate the performance of theprototype system. The experimental results by Jun et al. showeda more than five-fold improvement in tool life when atomizedcutting fluids were used as opposed to dry cutting. Compared toflood cooling, the atomized fluids performed much better as well.Due to clustering of the chips, tool chipping and chip depositionon the machined surface occurred in flood cooling, whereas

atomized fluids were able to cool, lubricate, and flush away chips.Temperature measurements during micro-milling showed thata significant decrease in temperature (even less than the roomtemperature) was observed with the atomized cutting fluids dueto evaporative cooling.

In their experiments, Jun et al. [1] proved the concept and effec-tiveness of the atomization based cutting fluid application. How-ever, because it was a prototype, the particle delivery system hadlimited controllability with poor focusing characteristics, it wasbulky with a footprint of 200 mm by 400 mm, and thus, it couldhardly be used in commercial applications. Therefore, new com-pact designs resulting in better controllability and focusing char-acteristics are needed. Also, design parameters and issues of thecutting fluid application system based on ultrasonic atomizationneed to be identified and their effects need to be investigated

such that optimum design with compact size and improved per-formance can be achieved.

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94 M. Rukosuyev et al. / Journal of Manufacturing Processes 12 (2010) 9298

Fig. 2. Preliminary system design.

Fig. 3. Photograph of an atomization-based cutting fluid delivery system with

droplets carried by a fan.

3. System design

A new compact system design for the atomization-based cut-ting fluid application is displayed in Fig. 2. The cutting fluid reser-voir maintains the fluid level within the atomizing chamber. Ascutting fluid is atomized into fine droplets within the atomizingchamber, low velocity air flow generated by a fan draws themthrough the flexible delivery tube. At the end of the tube is a noz-zle with a high velocity air jet at the center out of a small diameterpipe. When the droplets are carried to the nozzle, they are drawntowards the high velocity air jet, which then focuses the dropletsintoa narrowbeam to a certain diameter andacceleratesthem. The

nozzle is interchangeable so that the spray pattern can be alteredusing different nozzle geometries.

A photograph of thesystem setup is shown in Fig. 3. The systemhas a footprint of 12.0 mm by 19.0 mm with a 50.0 mm diameteratomizing chamber and a 60.0 mm diameter fan. The size of thesystem is an order of magnitude smaller than the prototype builtby Jun et al. [1]. The atomized droplets are carried through thetube of 25.4 mm diameter, and the air jet pipe has an innerdiameter of 1.6 mm. The ultrasonic atomizer is a 22.0mm diameterpiezo transducer at 1 MHz. For droplets generated by ultrasonicatomization, the droplet size generally depends on the frequencyof ultrasonic vibration and fluid properties. The fluid properties ofwater and typically used cutting fluid (5% Castrol 6519) are shownin Table 1 as an example [1].

According to the particle impingement dynamics analysis, adroplet velocity of less than 10.5 and 7.6 m/s ensures the rebound

Table 1

Fluid properties.

Properties Water 5% Castrol 6519

Surface tension (mN/m) 72 42

Viscosity (g/ms) 0.89 1.0752

Density (kg/m3) 1000 1000

Droplet diameter (m) 6.5 7.3

Fig. 4. An example of spray characteristics.

condition forwater and5% Castrol respectively,within the deliverytube. Thus, the rebound condition can always be achieved for bothfluids with a droplet velocity of less than 7.0 m/s. With the use andcontrol ofthe fan,thiscan beeasilyachieved. With the use ofthe air

jet located at the center of the nozzle, the droplets can be appliedto the cutting zone at a controlled velocity high enough to flushaway the chips and low enough to effectively wet the cutting zone.Since both velocities of the droplets within the delivery tubeand atthe nozzle will influence the spray characteristics, it is importantto examine how these velocities affect the spray applied to thecutting zone. Also, the optimum conditions for the fan and theair jet need to be determined. In addition, since the system canbe interchanged with nozzle tips of different geometry, it is alsoimportant to investigate the effects of different nozzle geometrieson the spray and system performance.

4. Design of experiments and setup

In this section, the experimental setup and design of experi-ments to evaluate the system presented in the previous section arediscussed. First, performance measures for the system are identi-fied. Experiments arethen designed to investigate theeffectof noz-zle geometry on the system performance measures. Experimentsare also prepared to study the effects of the system input parame-ters on the performance measures of the system. The input param-eters are the velocity of the air that carries the droplets or mist tothenozzle (referred to as mist velocity (Vm) hereafter) and the ve-locity of the air that accelerates the droplets at the nozzle (referredto as spray velocity (Vs) hereafter). Since the spray characteristicsare of interest and are likely to be independent of fluid type, water

is used as the working fluid.

4.1. Performance measures

Because of the small cutting zone in micro-milling, it is desiredto have a narrow and focused spray for effective penetration intothe cutting zone. Thus, it is important to determine the effectsof the system input parameters and nozzle designs on the spraycharacteristics. An example of the spray characteristics is shownin Fig. 4. The focus height of the spray is the spray diameter at thefocal point, and the focus length is the distance from the air jetpipe to the focal point. The focus length is also important becauseit will determine the position of the nozzle tip with respect to thecutting zone for effective wetting of the cutting fluids. Therefore,

two system performancemeasures considered for the experimentsare spray focus length and focus height.

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Fig. 5. Four different nozzle geometries studied.

Table 2

Nozzle geometries and experimental conditions.

Nozzle geometry Experimental

conditions

(a) Lh = 10.16 mm, n = 6(b) Lh = 10.16 mm, n = 0 Vm = 1.0 and 3.0 m/s(c) Lh = +10.16 mm, n = 6

Vs = 12.0 and 18.0 m/s(d) Lh = +10.16 mm, n = 0

4.2. Experiments to study geometry effects

Four different nozzle geometries are considered to study the ef-fects of the nozzle geometry on the spray characteristics. The noz-zlegeometries areshown in Fig.5. Twoaspects of the nozzledesignare investigated, which are the location of the high speed air jetoutlet with respect to the nozzle tip (Lh, with a positive sign rep-resenting the start of the jet outlet outside of the nozzle, i.e., thehigh speed air jet pipe sticks out of the nozzle) and the slope ofthe nozzle inside (n), as shown in Fig. 5. For each nozzle design,experiments are conducted at different mist and spray velocities

(Vm = 1.0 and 3.0 m/s, Vs = 12.0 and 18.0 m/s) to examine thespray. The four different geometries and the mist and spray veloc-ities for the experiments are listed in Table 2. The photographs ofthe spray out of the nozzle are taken using a Nikon D80 camera.The average values of the mist and spray velocities are measuredusing Extech Mini Thermo-Anemometer 45118, and they are allmeasured at 5 mm from the end of the nozzle (from the nozzlefor Fig. 5(a) and (b) and from the air jet pipe for Fig. 5(c) and (d)).

4.3. Experiments to study velocity effects

Experiments are conducted to investigate the velocity effects.Table 3 shows the values of the input parameters used for the ex-periments. For each combination of the mist and spray velocities, a

photograph of the spray is taken to observe the spray characteris-tics. The focus length and height are measured and calculated fromthe photograph. Note that the mist velocity values are chosen suchthat the rebound condition is maintained for the mist within thedelivery tube. Likewise, the spray velocities are selected to ensurethe spread condition when applied to a flat surface. For water, therebound condition, i.e., We < 10, is satisfied forvelocities less than10.5 m/s. The spread condition occurs for velocities greater than10.5 m/s, i.e., We > 10, and less than 45.2 m/s, i.e., Km < 57.7.

5. Experimental results and analysis

5.1. Effects of nozzle geometry

Foreach nozzlegiven in Fig.5, photographs aretaken at four dif-ferent experimental conditions given in Table 2. The photographs

Table 3

Experimental conditions for experiments to study velocity effects.

Experiments to

study effects of

Experimental conditions

Vm (m/s) Vs (m/s)

Mist velocity 0.5, 1.0, 1.5, . . . , 3.0,

3.5, and 4.0

11.0 and 21.0

Spray velocity 1.0 and 3.0 11.0, 13.0, . . . , 19.0, and 21.0

Table 4

Focus lengths and heights.

Focus length & focus height (mm)

Vm = 1.0 m/s Vm = 3.0 m/sVs = 12 m/s Vs = 18 m/s Vs = 12 m/s Vs = 18 m/s

(a) 16.6 & 4.1 13.6 & 3.5 37.1 & 8.2 31.6 & 6.2

(b) 16.6 & 4.4 13.5 & 3.6 38.4 & 10.5 34.7 & 8.5

(c) 16.0 & 4.5 9.5 & 3.6 34.5 & 10.7 34.7 & 7.1

(d) 14.9 & 4.3 12.2 & 3.5 45.2 & 11.8 38.1 & 10.3

of the spray are as shown in Fig. 6. The focus length and height are

measured and calculated from the photographs and they are listedin Table 4. The effects of nozzle geometry can be clearly seen fromthe photographs in Fig. 6 and from the measured focus lengths andheights in Table 4. It shows that the location of the air jet pipe hasa significant effect on the spray. Better focusing results when thepipe is within the nozzle, i.e., Lh = 10.16 mm, especially whenthe mist velocity is high. When Vm = 3 m/s and Lh = +10.16 mm,it is even difficult to pinpoint where the focal point is. For the focuslength, though the focus length seems to be slighter longer whenLh = 10.16 mm especially at lower mist velocities, it seems tobe more dependent on the mist velocity. For all nozzle geometries,the spray slows down and diverges farther down the stream af-ter focusing due to entrainment of the surrounding air into the jet.Hence, droplets down the stream are most likely less capable of

effectively wetting the cutting zone and simultaneously flushingaway the chips. This indicates that the position of the nozzle withrespect to the cutting zone is likely very critical for the systemscutting performance.

The slope of the nozzle inside seems to have a slightly favorableeffecton thesprayfocusingthough it hasa stronger influencewhen

the mist velocity is high. The small effect may be due to a smallslope angle difference (+6). A larger value of the slope angle maybe desired, but a too large value may lead to an increased diameterof thedelivery tube or disturbed fluid flow. Though theslope angle

clearly has a positive effect on the spray focusing, further study isrequired to determine the optimum value of the slope angle.

The results in Fig. 6 and Table 4 also show that the focusingis much better when the mist velocity ( Vm) is at 1.0 m/s than at

3.0 m/s. This is likely because of the decreased pressure differencebetween the air jet and the mist stream and the decreased time

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Fig. 6. Photograph of the spray at different nozzle geometries: (a) Lh = 10.16 mm, n = 6, (b) Lh = 10.16 mm, n = 0, (c) Lh = +10.16 mm, n = 6, and(d) Lh = +10.16 mm, n = 0.

Fig. 7. Photographs of the spray at mist velocities of 0.5, 1.5, 2.5, and 3.5 m/s and spray velocities of 11.0 and 21.0 m/s.

period for the droplets to be drawn into the air jet. Both thefocus length and height are also increased with the increase ofthe mist velocity. An increase in the spray velocity (V

s) seems to

have a positive effect on the spray focusing but its effects are notas significant as the mist velocity. Nevertheless, from Fig. 6 andTable 4, it is clear that the mist and spray velocities have a stronginfluence on the spray characteristics, so their effects need to becarefully examined. Thus, a more detailed study of the effects ofthe mist and spray velocities is presented in the next section.

5.2. Effects of mist and spray velocities

In order to study the effect of the mist velocity ( Vm), experi-ments are conducted using the nozzle with the geometry given inFig. 5(a) at the mist and spray velocities given in Table 3. The noz-zle with the geometry given in Fig. 5(a) is selected because it per-forms better than the other nozzle designs. The photographs of the

spray at some of the mist velocities are shown in Fig. 7. The focuslengths and heights are plotted against the mist velocity as shownin Fig. 8. As themistvelocity is increased, both the focus length andheight increase. Thus, since more focusing, i.e., lower values of fo-cus height, is desired, the mist velocity has clearly a negative effecton the spray focusing. However, when the mist velocity is less than1.5 m/s, the increase in focus height is quite small. It is only whenthe mist velocity is increased greater than 2.0 m/s that the focusheight increases with the mist velocity. Note that the increase inthe mass flow rate of the droplets can be observed in Fig. 7 as themist velocity is increased. Foreffective wettingof the cutting fluids,an increase in the mass flow rate is likely desirable as well as theminimized focus height. Thus, the mist velocity of 1.5 m/s seemsto be appropriate because though an increase of mass flow rate isobserved, the focus height remained pretty much the same when

the mist velocity is increased from 0.5 to 1.5 m/s. Higher values ofthe mist velocity than 1.5 m/s may not be appropriate because the

Fig. 8. Focus length and height at different mist velocities.

focus height is substantially increased. However, further study is

required to determine the effect of the mist velocity on the actualcutting performance.

The effect of the mist and spray velocities on the focus lengthhas a similar pattern as theeffect on the focus height.However, theeffect of the mist velocity on thefocus length is much more signifi-cant than on the focus height.As the mist velocity is increased from0.5 to 3.5 m/s, the focus length changes from around 14 to as highas 42 mm.This indicates that thefocus length for a givencombina-tion of the mist and spray velocities must be determined to set thenozzle position for optimized cutting performance of the system.

The spray velocity does not seem to influence the focus heightand length much when the mist velocity is less than 1.5 m/s asshown in Fig. 8. However, when the mist velocity is higher than1.5 m/s, an increase in the spray velocity decreases both the focus

length and height. Thus, at high mist velocity values, it is desirableto increase the spray velocity to maintain a low value of the focus

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Fig. 9. Photographs of the spray at spray velocities of 11, 15, 19, and 21 m/s and mist velocities of 1.0 and 3.0 m/s.

Fig. 10. Focus length and height at different spray velocities.

height. In order to obtain the effects of the spray velocity moreclearly, additional experiments are performed varying the sprayvelocity at two different mist velocities (Vm = 1.0 and 3.0 m/s)as shown in Table 3, and the results are displayed in Figs. 9 and

10. As shown, the focus height and length do not change much asthe spray velocity is increased when themist velocity is low (Vm =1.0 m/s). However, when the mist velocity is high, increasing the

spray velocity decreases both the focus height and length. Thisindicates that as long as the mist velocity is low enough, theposition of the nozzle with respect to the cutting zone does notneed to be altered at different spray velocities. When the mistvelocity is high, it is better to increase the spray velocity to havea more focused spray.

5.3. Discussion on system design issues

The experimental results given above show that the system caneffectively focus the spray to a beam diameter as small as 3.8 mm.Since the cutting zone in micro-milling is typically much smallerthan this, a nozzle design that can focus the spray smaller than1.0 mm is desired. However, if the nozzle diameter is decreased

too small in order to focus the spray to a smaller beam diame-ter, pressure builds up within the atomizing chamber because ofthe too small exit. In that case, it has been observed that dropletscondense near the fan and some droplets even exit the atomizingchamber through the fan if pressure inside the chamber is suffi-ciently high. Also, although the system size has been reduced sig-nificantly from the first prototype, the use of the fanstill causes thesystem to be bigger than desired. Thus, a new system design thataddresses these shortfalls is desired and under development.

6. Conclusions

A new compact cutting fluid application system based on ultra-sonic atomization has been designed and developed. The system

was evaluated in terms of its focusing capability of the generatedspray. The effects of different nozzle geometries and system input

parameters (mist and spray velocities) on spray focusing have beenexamined. Areas of improvement for the design have been identi-fied. The following conclusions can be drawn from this work.

The position of the nozzle with respect to the cutting zone islikely very critical for the systems cooling and lubricating per-formance since the spray focuses at a specific point and thendiverges.

It is preferable to have the high speed air jet pipe within thenozzle and a converging slope for the nozzle for better focusingof the spray.

The mist velocity has a negative effect and the spray velocitya positive effect on the spray focusing, but further study is re-quiredto determine their effectson actualcutting performance.

Acknowledgement

The authors would like to gratefully acknowledge the financialsupport of the Discovery program of the National Science andEngineering Research Council (NSERC) of Canada.

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