a correlation for predicting the abrasive water jet cutting

of 11 Research Article

A correlation for predicting the abrasive water jetcutting depth for natural stones

Author:Irfan C. Engin'

Affiliation:'Department of MiningEngineering, Afyon KocatepeUniversity, Afyonkarahisar,Turkey

Correspondence to:Irfan Engin

Email:[email protected]

Postal address:Department of MiningEngineering, Afyon KocatepeUniversity, ANS campus,03200 Afyonkarahisar, Turkey

Dates:Received: 25 May 2011Accepted: 20 Apr. 2012Published: 17 Sept. 2012

How to cite this article:Engin IC. A correlation forpredicting the abrasivewater jet cutting depthfor natural stones. S Afr JSei. 2012;108(9/10), Art.#692, 11 pages, http://dx.doi.org/10.4102/sajs.V108Í9/10.692

©2012. The Authors.Licensee: AOSISOpenJournais. This workis licensed under theCreative CommonsAttribution License.

! The abrasive water jet (AWJ) cutting method has been used widely for the cutting andi processing of materials because of its cool, damage-free, and precise cutting technique.

Nowadays, the use of AWJ cutting in the natural stone industry is increasing. However,the effectiveness of AWJ cutting of natural stones is dependent on the rock properties andmachine operating parameters. In this study, injection-type AWJ cutting was applied to 42different types of natural stones to investigate the effects of rock properties and operating

I parameters on the cutting depth. Shore hardness, Böhme surface abrasion resistance and thedensity of the rocks were the most significant rock properties affecfing the cutting depth.

\ The working pump pressure and traverse velocity were the most significant operatingparameters affecting cutting, as has been shown previously. The relationships betweenthe rock properties or operating parameters and the cutting depth were evaluated using

: multiple linear and nonlinear regression analyses, and estimation models were developed.Some of the models included only rock properties under fixed operating conditions, and

I others included both rock properties and operating parameters to predict cutting depth.The models allow for the preselection of particular operating parameters for the cuttingof specific rocks types. The prediction of cutting depth is a valuable tool for the controlled

j surface machining of rock materials.

IntroductionThe history of water jets extends back to the discovery of the erosional effect of water streamsin nature. Water power has been used in cutting and removal applications for many years.As mentioned by Summers', the first attempts to use water jets for cutting were carried outin Galifornia, USA, in 1852 to abrade gold-bearing rock. The method was adapted first for themining of steeply dipping coal seams and later for hydrauUc coal mining, in which it has beenappUed around the world. By increasing the pressure, the water becomes powerful enough to usefor cutting rocks. In 1970, the water jet method began to be used in industry to machine materialsin non-traditional machining operations.

High-pressure water jets are classified into two main types: pure water jets and abrasive water jets(AWJ). The basic difference between these two types is the addition of an abrasive medium in AWJto increase the cutting ability of fhe water jet. Water jet cutting sti.idies were focused first on coalcutting in the mining industry, and then researchers started to investigate the use of continuousand discontinuous water jets in the cutting of rocks. Some of these studies investigated theparameters affecting the rock-cutting process. Brook and Summers^ studied rock penetration bywater jets; Nikonov and Goldin- studied rock and coal penetration by continuous water jets; andChermensky" focused on rock breakage rafher than rock cutting by pulsed water jets, which wasan improved use of water jets. Hagan' investigated the cuttability of rocks using high-pressurewater jets and reported that water pressure had the greatest impact on the level of surface damageto the rock, although traverse speed was found to also alter the magnitvide of the surface damage.The addition of an abrasive agent made the water jets more powerful. The use of abrasive-containing water jets for the drilling, cutting and excavating of rocks has been investigated bya number of researchers. Laund et al.*- investigated the relationships between the linear ti-aversespeed and the depth of cuts and quaUty of cut surfaces in rock cutting by AWJ. Xiaohong et al.'performed experimental studies on rock cutting using colUmated AWJ. Various cutting modelsusing water jet and AWJ cutting mechanisms have been developed.''''-"''"'! '"'"''!^!«' Zeng and Kim"developed a model for the cutting of brittle materials. Babu et al.'' stiidied water jet cutting ofblack granite and suggested a fuzzy-based approach for process parameter selection. Brandt etal." made a technical and economical evaluation of water jet cutting applications. To increase thepower and cutting efficiency of water jets, Siores et al.'', Chen et al."* and Lemma et al." stiidieddifferent cutting techniques such as nozzle oscillation. Hashish et al. " and Susuzlu et al. ' studiedthe effects of increasing the pressure of water jets to ultra-high levels, while others ' ' - ' ' yinvestigated improving the quality of the cut surfaces. There have been other studies in addition

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to those menfioned above that have invesfigated water jetand AWJ cutting and processing appUcafions.

More recently, water jets and AWJ have been used in rock-cutting appUcafions for slotting or precision cutting purposes.Ferris and HalF** invesfigated water jet cutting and diamondwire sawing pracfices in dimensional stone quarries. Theyreported that water jet cutfing can simpUfy and improveoverall operating efficiency and predictability. While waterjet slotting is applied in natural stone quarries to cut andremove in-situ blocks, AWJ cutfing is used for the shapingof decorative natural stone file parts. AWJ cutting is the onlycutting method which is able to cut any shape or free form, aswell as sharply angled contours and oblique angles.

This study invesfigated the effect of the rock properfies andoperafing parameters on the cutting depth of injecfion-typeAWJ. The AWJ cutting depth of rocks was also esfimatedusing mulfiple linear and nonlinear regression analyses.AWJ cutting was applied to 42 different rock types. Thegeomechanical properties of the rock samples studied were:density, water absorpfion, hardness, abrasion resistance,uniaxial compressive strength and tensile strength. Thecutfing parameters tested were: the nozzle traverse speed,pump pressure and abrasive flow rate.

Although many studies have been conducted on AWJcutting, the target materials used were mostly metals,ceramics and glass. Stone type materials have very differentcharacterisfics and resistance to cutting by AWJ. The density,porosity, elasticity, and strength of rocks differ from those ofmetals, ceramics and glass. Use of the AWJ cutting systemin the natural stone industry is increasing globally.^' SomeAWJ cutfing machines were initially purchased for metalcutting, but later became used for cutting decorafive stoneproducts because of fhe excessive demand for these productsin Turkey. The results of this study will contribute to theeffectiveness of the cutting of natural stones using injection-type AWJ.

Materials and methodsDifferenf types of Turkish natural stones were cut byinjecfion-type AWJ under different operating conditions toinvestigate the effects of the rock material and the operafingparameters on cutting depth. A high traverse rate of thenozzle was selected for all cutting applicafions, so that thejet could reach orüy to a definite depth of the rock samplesand not penetrate the length of the rock. The depth valueindicates the resistance of the rock material to cutfing.Rocks with different mineralogical, physical and mechanicalcharacterisfics were chosen expressly to observe the effects ofthese properfies on cutting depth. The effects of the operatingparameters on cutting depth were invesfigated by cuttingthe rock samples using different pump pressures, nozzletraverse velocities and abrasive fiow rates. The relafionshipsamong the structural properfies of the rock samples, theoperating parameters, and the AWJ cutting depth wereanalysed statisfically.

Sample preparation and testing

Rock samples were collected from natural stone quarries or,in limited situafions, from natural stone processing plants.Table 1 provides the sample number, trade name, lithologiedescription and pétrographie rock type of all 42 samples.

Rock specimens were cut and treated prior to the laboratorytests and AWJ cutfing. Test specimens were prepared fromrock samples that were free of fractures and alteration zones.Laboratory test specimens were prepared according to themethods suggested by the Internafional Society for RockMechanics, prepared by Ulusay and Hudson^" as a book. Cutsamples were shaped as rectangular prisms with 50-mm,100-mm, and, if necessary, 200-mm and 300-mm thicknesses.In prelinünary AWJ cutting attempts in this study, using theplanned operafing condifions, it was observed that water jetscould pass through the specimen of some weaker naturalstone samples and spUt it. Therefore samples of 200-mm and300-mm thicknesses were prepared for these natural stones(e.g. Kufeki Stone) in order to measure the cutting depthunder the same operafing condifions.

Laboratory tests were used to determine the mineralogical,physical and mechanical properfies of the samples. Apparentdensities, water absorption at atmospheric pressure, and openporosity properfies of the rock samples were determined.The Shore scleroscope (C type) hardness test was used todetermine the rebound hardness of the rock specimens. Theabrasion resistance of the samples was determined accordingto the Böhme surface abrasion test. The modulus of elasficityof the samples was calculated using strain measurementstaken by a linear variable differenfial transformer sensor.Stress measurements were performed with the uniaxialcompressive strength test. The tensile strength of eachsample (cylindrically shaped with a diameter of 41 mm and astandard thickness) was determined by the Brazilian tensUestrength test. Tests were performed in accordance withthe methods of testing recommended by the InternationalSociety for Rock Mechanics. The results of these tests aregiven in Table 1.

Abrasive water jet cutting applications

As mentioned by Kûlekçi'', an AWJ cutting system consistsof five main parts, (1) a high-pressure pump (usually theintensifier type) that provides high-pressure water, (2)a cutfing head that produces the abrasive water jet, (3) anabrasive delivery system that carries abrasive grits to thecutting head, (4) a computer-controlled unit that controls themofion of the cutting head and (5) a catcher that absorbs theremaining jet energy after cutting. The AWJ cutting operationis shown schemaficaUy in Figure 1.

In this stvidy, AWJ cutfing was appUed by the injecfion-typehigh-pressure AWJ cutfing machine. All of the samples werecut by the same AWJ cutting machine, which had an orificeof 0.35 mm, a focusing tube of diameter 1.1 mm and length80 mm, a working pressure of 90 MPa - 360 MPa, an



Samplenumber

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

n28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

trade name

Mitas Pear

Blanco Ibiza

Ayhan Black

Amasya Beige

Sivrihisar Beige

Eskisehir Supren

Milas Leilac

Afyon White

Afyon Violet

Aksehir Black

Romance Beige

Kaman Pearl

Ayazini Tuf

Bilecik Beige

Crema TEM

usak Green

Rosso Laguna

Usak White

MarmaraDolomite

Akhisar Onyx

Denizli Travertine

Yellow Travertine

Kufeki Stone

Finike Limestone

Rosso Levanto

Amaretto

Rosa Tea

Noche Travertine

Daisy Beige

Bottocino Royal

Rosalia Pink

AfyonAndésite

Yesilirmak Diabase

Akdeniz Green

Beypazari Granite

Aydiner Ligth

Black Magic

ispir Pink

Aydiner Moonlight

Kufeki Stone 2

Emirdag Travertine

Beytepe Marn

Lithologiegroup

Real marble

Real marble

Real marble

Limestone

Limestone

Real marble

Real marble

Real marble

Real marble

Real marble

Limestone

Calcsilicaticmarble

Other(Sandstone)

Limestone

Limestone

Real marble

Real marble

Real marble

Dolomiticmarble

Onyx

Travertine

Travertine

Other(Sandstone)

Limestone

Limestone

Limestone

Limestone

Travertine

Limestone

Limestone

Limestone

Other(Andésite)

Diabase

Diabase

Granite

Granite

Granite

Granite

Granite

Other (Tuff)

Travertine

Other (Marn)

Apparentdensity

(g/cm=)

2.724

2.712

2.741

2.682

2.698

2.721

2.725

2.707

2.717

2.708

2.640

2.767

1.510

2.693

2.660

2.722

2.751

2.709

2.828

2.716

2.408

2.540

1.950

2.377

2.690

2.510

2.670

2.530

2.690

2.690

2.680

2.119

2.880

2.929

2.660

2.607

2.673

2.590

2.604

1.760

2.560

2.116

Waterabsorption(%)

0.023

0.065

0.166

0.072

0.172

0.110

0.085

0.071

0.084

0.109

0.464

0.161

17.350

0.133

0.330

0.091

0.075

0.059

0.186

0.078

2.001

1.020

11.780

3.011

0.700

2.060

0.460

1.460

0.480

0.140

0.180

4.900

0.120

0.339

0.468

0.486

0.059

0.617

0.276

14.560

0.810

1.430

Openporosity(%)

0.062

0.176

0.454

0.194

0.462

0.299

0.231

0.191

0.229

0.295

1.224

0.446

26.000

0.359

0.860

0.248

0.208

0.161

0.527

0.211

4.820

2.590

22.910

7.156

1.860

5.150

1.230

3.620

1.290

0.360

0.490

10.380

0.120

0.994

1.244

1.267

0.157

1.597

0.719

24.340

2.070

12.610

Böhmeabrasionresistance(cmV50 cm')

11.01

15.88

12.84

7.16

6.38

14.36

13.26

14.73

16.00

14.67

9.50

5.76

28.56

9.16

5.00

14.79

12.17

14.77

19.28

10.41

17.72

21.15

26.22

22.10

11.33

11.83

6.93

21.33

7.20

11.07

7.72

24.67

3.05

6.88

5.02

3.15

4.43

5.35

3.84

27.67

11.27

24.54

Uniaxialcompressivestrength(MPa)

100.4

64.9

113.7

140.9

130.3

95.0

89.1

79.7

81.2

85.4

118.0

60.5

13.6

130.9

86.9

98.0

81.3

76.2

157.9

70.2

35.5

49.6

15.3

97.8

94.5

78.4

110.3

71.1

126.8

61.4

123.8

70.4

256.4

133.9

75.3

79.9

129.6

158.7

109.6

13.8

65.8

18.3

Modulus ofelasticity(GPa)

33.4

11.9

23.3

35.4

23.0

16.7

17.2

14.2

18.6

12.1

16.4

6.1

2.6

14.4

27.5

12.4

10.9

10.1

13.8

11.1

5.7

8.6

3.2

12.7

19.7

14.8

26.1

19.5

16.6

16.9

29.3

15.8

62.2

22.4

19.8

21.5

36.4

45.9

26.8

2.9

18.7

4.8

Shorescleroscopehardness

52.9

49.5

47.5

66.2

58.5

53.0

54.0

44.2

44.5

51.3

56.7

53.1

14.6

60.2

62.5

48.1

55.0

42.0

50.4

53.9

42.5

49.2

18.7

35.8

54.7

57.8

51.0

49.2

64.0

59.0

61.3

23.2

110.2

101.2

97.6

86.5

105.8

108.3

102.7

15.2

52.3

19.2

Braziliantensilestrength(MPa)

7.0

6.6

8.4

8.1

10.0

9.5

8.5

5.9

6.1

8.2

8.1

6.5

1.1

10.7

8.5

8.7

10.1

6.3

7.2

5.9

2.6

7.6

2.0

5.5

8.5

5.8

8.1

6.3

10.1

5.7

6.2

4.2

26.9

11.0

10.7

5.0

5.5

10.4

9.3

1.6

6.0

4.1

Cuttingdepth(mm)t

25.2

25.2

26.8

24.8

25.0

27.6

25.4

27.8

28.3

28.1

29.2

22.7

177.6

20.3

26.4

28.9

26.8

27.6

35.9

30.0

30.4

34.6

106.6

45.5

26.6

26.8

22.7

31.2

22.3

29.1

24.5

82.1

6.7

8.8

11.8

11.2

9.2

8.6

11.4

136

33.5

103.8

t, cutting depth was determined at a nozzle traverse velocity of 800 mm/min, a pump pressure of 360 MPa, a stand-off distance of 5 mm and an abrasive flow rate of 450 g/min

intensifier-type high-pressure pump (37 kW) and abrasiveproperties of an 80 mesh Indian garnet. The same abrasiveproduct was used in all cuttings. Azmir and Ahsan""- statedthat 90% of all AWJ machining is performed using garnetbecause of the unrivalled advantages of this mineral. In thisstudy, a commercial garnet mineral called almandine wasused as the abrasive medium.

Measuring the cutting depthMeasuring the cutting depth within the kerf, or groove in thesample, after cutting was not possible because the kerf was toonarrow (1 mm - 1.5 mm). To measure the AWJ cutting depthof the rock samples, the test samples were first split through

the cutting kerf, and then the cutting surfaces were imagedby a scanner. The cut-surface images were transferred to acomputer. The depth attained by the jet was observed as acurve in the cutting direction, and the mean cutting depth fora sample was calculated by scaling the background using animage processing program called Paint Shop Pro^ (Figure 2).At least three test samples were prepared, cut, and measuredin this way for each rock type. The reported values of the AWJcutting depths are the overall mean cutting-depth values foreach type of rock. Cutting depth is also a good measure of theresistance of a natural stone to AWJ cutting, although it is notthe same as the specific cutting energy related to the removeddebris while cutting.



The cuttabiUty of rocks using AWJ is also affected bymachine operating parameters such as the operating waterpressure, nozzle traverse speed, abrasive flow rate andstand-off distance. AWJ cutting appUcations were performedimder different operating conditions, and the effects ofthese operating parameters on the cuttabiUty of rock wereinvestigated. Operating parameters such as pump pressure(P ), traverse velocity (VJ, abrasive flow rate (A/), water flowrate (MJ, stand-off distance (x) and cutting depth {h) areillustrated in Figure 1. Values of selected cutting parametersare given in Table 2. The pump pressure, abrasive now rateand nozzle traverse velocity values were arranged so as to beable to hold the jet at a particular depth in the natural stonesamples. In cutting appUcations, two parameters were heldconstant and the other was changed to investigate the effectsof the individual parameters on the cutting depth.

X , 1

- ^

j /X ' \

Rock samples

h

1

M , abrasive fiow rate; M ^ water flow rate; P , pump pressure; V„, nozzle traverse velocity;X, stand-off distance; h, cutting depth.

FIGURE 1: Graphical representation of the abrasive water jet cutting process,showing the operating parameters and the cutting depth.

Effects of rock properties andoperating parameters on cuttingdepthThe depth of the cut in a rock is affected by the properties ofthe rock and by the operating parameters. To investigate therelationships between the rock properties and cutting depth,all operating parameters were held constant. The nozzletraverse velocity was 800 mm/min, the pump pressure was360 MPa, the stand-off distance was 5 mm and the abrasiveflow rate was 450 g/min. The cutting depths of 42 differentrock types were compared.

The relationships between the operating parameters andcutting depth were investigated by cutting nine rock typesunder different operating conditions (Table 2). These

TABLE 2: Operating parameters and their values used in the determination ofthe cutting depth of roci<s.

Operatingconditions

Pump pressure(MPa)

Nozzle traversevelocity (mm/min)

Abrasive flow rate(g/min)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

350

360

360

360

360

360

360

360

360

360

360

90

120

180

230

300

120

180

230

250

320

320

350

800

400

600

800

1000

1500

2000

800

800

800

800

800

800

800

800

800

400

600

800

500

700

1200

1500

450

225

225

225

225

225

225

112

140

169

197

225

225

225

225

225

65

65

164

98

65

131

164

FIGURE 2: Measurement of cutting depth using a scaled image from an image processing program.


Page S of 11 Research Article

nine rocks (Amasya Beige, Sivrihisar Beige, Afyon White,Usak Green, Usak White, Akhisar Onyx, Finike Limestone,Beypazari Granite and Amaretto) represent the main rockgroups that were investigated. The operating parameterstested were: the pump pressure, nozzle traverse velocity,stand-off distance and abrasive flow rate. The relationshipsbetween the cutting depth and some physical and mechanicalproperties of the rocks are given in Figure 3.

At first attempts, all operating parameters were heldconstant, and all the natural stone samples were subject toAWJ cutting (grooving) applications. Then, the relationshipsbetween some rock properties (such as density, porosity.Shore scleroscope hardness, Böhme surface abrasion loss,uniaxial compressive strength, modulus of elasticity andtensile strength) and cutting depth were investigated.Although all rock properties affect the AWJ cutting of rocks,some properties were observed to have a greater influenceand were controlling factors in cutting applications. Thehardness, density, porosity and abrasion resistance of naturalstones had the strongest relationships with cutting depth.The cutting depth increased exponentially with an increasein the Böhme surface abrasion loss value, and decreased

exponentially with an increase in the hardness of the samples.Uniaxial compressive strength, modulus of elasticity, andtensile strength of the rock also correlated with the cuttingdepth, but these correlations were respectively low (0.60 < R^< 0.65; data not shown). AWJ cutting is based mainly on theerosion effect of abrasive particles in the jet during cutting.In this situation, microstructure of the natiiral stone samplesis considered as more important, and hardness, density andabrasion resistance properties of the samples are supposed togive important information about the microstructure of thesamples.

The relationships between the cutting depth and traversevelocity of the nozzle, pump pressure and abrasive flowrate are given for some rocks in Figure 4. Cutting depthdecreased with an increase in the traverse velocity of thenozzle. The rate of decrease in the cutting depth differedbetween rocks. Sample 35 is Beypazari Granite, which is oneof the strongest rocks investigated in the study, and Sample24 is Finike Limestone, one of the weakest rocks used in thisstudy. The inverse relationship between traverse velocityand cutting depth is more dramatic for the Finike Limestonethan for Beypazari Granite. Rock strength can be interpreted

E¿.c

dep

tut

ting

u

(uii

.c

dep

tL

ittin

g

u

200 ^ -.

180 -

160 -

140 -

120 -

100 -

80 -

60 -

40 -

20 -

0 -

1.0

200 -, v =

180 -

160 -

140 -

120 -

100 -

80 -

60 .-

40 -

20 -

0 -

R-

0.0

a. 3A + 328.07

= 0.88

X. •

^ \

>K *\ ^

' I I I

1.5 20 2.5 3.0

Apparent density (g/cm')

8 . 9 9 e - -c

= 0.78

•

?••• •1 1 (

10.0 20.0 30.0

Böhme surface abrasion (cmV50cm')

FIGURE 3: Relationship between cutting depth and (a) apparent density, (b) open po

E¿

dep

ttItt

ing

1

u

"§•_E

dept

l-Itt

ing

u

osity,

200 -

180 -

160 -

140 -

120 -

100 -

80 -

60 -

40 -

V =

R-

20 -y^

0

0.0

200 -| v =

180 -

160 -

140 -

120 -

100 -

80 -

60 -

40 -

20 ..

Q

R-

0.0

5.04.V +

= 0.90

6928r '

= 0.95

•

\

\

1—

20.0

b19.13

• y ^ •

t 1 1

10.0 20.0 30.0

Open porosity (Vo)

41 d

V\

' -^—Ns^^—1 i 1 1 1

40.0 60.0 80.0 100.0 120.0

Shore hardness

(c) Böhme surface abrasion and (d) Shore hardness of natural stones.



by different rock characteristics or their combinations, suchas density, hardness, abrasion resistance and compressivestrength, according to the specified usage area. For example,when a natural stone tue is intended to be used on the fioor ofa crowded place, it has to show high hardness and abrasionresistance. In such situations, the tile does not need to havehigh uniaxial compressive strength, but strength in termsof hardness and abrasion resistance. For example, FinikeLimestone has a high compressive strength but wears easilywhen laid on a floor. As a floor covering, Finike Limestonecan be classified as a weak rock. In AWJ cutting applications,hardness, abrasion resistance and density together constitutethe strength of a material because this cutting method is amicromachining and erosion-based material removingprocess. When an adequate traverse velocity is selected for agiven material, there will not be any excessive loading on thecut material by the AWJ. This situation can be experienceddramatically when the abrasive grit feeding is turned offduring the cutting application - the cut material is brokenin a few seconds because the erosive potential of the waterdrops is not enough to cut the material, and the velocity of thejets turns to velocity pressure (according to the Bernoulliequation), which exceeds the uniaxial compressive strengthof the cut material. When the rock strength is low, the cuttingdepth decreases by a greater power than that of an increasein the nozzle's traverse velocity. The same relationship existsbetween the cutting depth and the pump pressure and, to alesser extent, between the cutting depth and the abrasive fiowrate. Weak rocks are more sensitive to changes in operatingparameters than are strong rocks (see for example Figure 3).In Figure 3, Sample 24 (Finike Limestone) has a density of2.377 g/cm'', an abrasion loss of 22.1 cmV50 cm- and a Shorehardness of 35.8; whereas Sample 35 (Beypazari Granite) hasa density of 2.660 g/cm^ an abrasion loss of 5.02 cmV50 cm^and a Shore hardness of 97.6. The slope of the linearregression trend line of pump pressure versus cutting depthfor Finike Limestone is 0.11 whereas the slope for BeypazariGranite is 0.03. The slope values for the other natural stoneslie within these values according to their density, hardnessand abrasion resistance combinations. Weak natural stoneswith a low density, low hardness and high abrasion loss wiUhave high linear regression trend line slopes and vice versafor strong natural stones. Similar relationships are seen for allthe natural stones for the other operating conditions.

It was observed in the study of the relationships betweencutting depth and rock properties or operating parametersthat some parameters affect the cutting depth more thanothers do. Pump pressure, traverse velocity, abrasiveflow rate. Shore scleroscope hardness, apparent densityand Böhme abrasion resistance are the most influentialparameters determining the cutting depths.

Nozzle stand-off distance also affects cutting depth. A 5-mmstand-off distance was determined to be the optimum value.A stand-off distance shorter than 5 mm increases the cuttingdepth but may also cause damage to the nozzle and the rocksample because of back pressure or obstruction. The effectof the stand-off distance of the nozzle on the cutting depth

60 1

E 50

"Jó 40 -D.U^ 3 0

3 20 -(J

• Amasya beige

« Sivrihisar beige

+

1 *

—1 1

A Afyon white

Usak green

+

É

• Usak white

• Akhisar onyx

- f

%

•f Finike Limestone

— Amaretto

• f

A

I p 1

250 750 1250 1750

Traverse velocity of nozzle (mm/min)

2250

mm

)d

epth

tuc3u

10 -,

30 -

20 -

1 0 •

0 ..

• Amasya beige . Afyon white • Usak white

•i Sivrihisar beige Usak green •Akh isar onyx

•« 1

•

Finike Limestone

— Amaretto

(

É

-

100 150 200

Abrasive fiow rate (g/min)250

• Amasya beige ,. Afyon white • Usak white Finii<e Limestone

H Sivrihisar beige Usak green * Akhisar onyx —Amaretto

-p 30

Q. 20u

•obo

B 10 .

50 150 250Pump pressure (MPa)

350

FIGURE 4: Relationship between cutting depth and (a) traverse velocity of thenozzle, (b) abrasive flow rate and (c) pump pressure in abrasive water jet (AWJ)cutting of natural stones.

is shown for Finike Limestone in Figure 5. Cutting depthincreased exponentiaUy with a decrease in stand-off distance.Although the surfaces of the natural stone samples were fiatand smooth, the risk of back pressure or obstruction limitsthe stand-off distance to at least 5 mm.

Statistical analysisBecause the cutting depth of rocks is affected by manyfactors, it cannot be analysed using simple regressionmodels. Therefore, the analysis must be carried out by usingmultiple regression methods. These methods can be dividedinto two types: linear and nonlinear. In this study, multiplelinear and nonlinear regression models were used toanalyse the AWJ cutting depth of rock samples. The cuttingdepth was considered the dependent variable, and theoperating parameters and rock properties were consideredto be independent variables. The regression analyses wereperformed using a computing package called Statgraphics.^

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In the first model [Eqn 1], the operating parameters wereheld constant for all 42 samples (as given in Table 1) and onlythe effects of the rock properfies were invesfigated in detail.In the second model [Eqn 2], the same rock properfies wereanalysed by the nonlinear regression method.

h = 311.8-103.9x£)__- 0.351

and

0.093xUCS-[Eqnl]

where h is the cutting depth (mm), D is the apparent density(g/cm^), H^ is the Shore scleroscope hardness, R is theBöhme abrasion resistance (cmV50 cm^), UCS is the uniaxialcompressive strength (MPa), E^ is the modulus of elasficity(GPa) and Sj is the BraziUan tensile strength (MPa).

In the third model [Eqn 3], the effects on cutfing depth ofShore scleroscope hardness, Böhme abrasion resistance andapparent density were invesfigated. These rock properfieswere chosen based on the experimental results (Eigure 3).In the fourth model [Eqn 4], the same rock properties wereanalysed by the nonlinear regression method. In the thirdand fourth models, the operafing parameters were heldconstant.

h = 283.5+0.402xÄ^- 0.273xH- 91.95xD^, R'- = 0.91 [Eqn 3]

fj 0.876 1.017 / Ä- - 0 .99 [Eqn 4]

In the fifth model [Eqn 5], the pump pressure (P ; MPa),nozzle traverse velocity (V_ ; mm/s) and abrasive flow rate(M ; g/min) were used as operafing parameters, and fileShore scleroscope hardness, apparent density and Böhmeabrasion resistance were used as rock properties.

P5.35x 0.790 ^ j : ^ 0.890 ^ £ ) 1 [Eqn 5]

In the sixth model [Eqn 6], the pump pressure, nozzle traversevelocity, and abrasive flow rate were used as operafingparameters, and the Shore scleroscope hardness was the onlyrock property used. Calculafion of the AWJ cutting depthis simpler in this model because of the use of only one rockproperty. The fifth and sixth models take into considerafionthe cutting depths of different rocks at constant operatingparameters (listed in Table 1) and for the nine selectednatural stones under different operafing condifions (Usted inTable 2).

The models were validated by determining the regressioncoefficient, plotting the observed cutting depth versus the

estimated cutting depth (Figure 6), and the E-test. In Figure4, the points are scattered uniformly about the diagonal line,suggesting that the models are good.

Pump pressure, nozzle traverse velocity and rock hardnessshow nonlinear relationships with cutfing depth. Therelafionship between rock hardness and cutfing depth canbe defined by a power funcfion. Cutting depth decreasedexponenfially with an increase in Shore hardness, as canbe seen in Eigure 3. The same inverse relafionships exist fornozzle traverse velocity versus cutting depth and pressureversus cutting depth. Therefore, the determinafion coefficientsof the nonlinear models are higher than those of the linearmodels. Both the stafisfical models and the experimentalresults show that the microstrucfijre of the rocks is moreimportant than the macrostructure, in terms of AWJ cutting.

The correlafion coefficients (R^) of the models are higherthan 0.91. These values are acceptable but do not necessarüyverify that the models are valid. To test the significance ofthe regressions, analysis of variance was employed. In thistest a 95% level of confidence was selected. If the computedF-value is greater than the tabulated F-value, the nullhypothesis is rejected. The nuU hypothesis holds that there isa real relationship between the dependent and independentvariables. Because the computed F-values are greater thanthe tabulated i^-values for the models, the niiU hypothesisis rejected. Therefore the models are valid. The statisficalresults of the models are given in Table 3.

Results and discussionRock cutfing using AWJ is affected by the rock properties andoperating parameters. This study used both experimentalresults and several regression models to understand theimportance of these factors. The validity of the models wasestabUshed using stafisfical tests. The models can thereforebe used to predict AWJ cutting depth and to select operatingparameters for a given rock type and thickness.

Natural stone samples used in this study included real marble,limestone, calcsilicafic marble, sandstone, dolomific marble,onyx, fi-averfine, andésite, diabase, granite, tuff and marn, allof which have different physical and mechanical properfies.Within each lithologie group, some of the properties maybe similar amongst rock types, whilst others may differ. Forexample, densifies of the real marble samples such as AfyonWhite, Milas Pearl, Aksehir Black and Usak Green are similarto each other, but hardness, abrasion resistance, compressivestrength and other physical and mechanical properfies differamong samples. For this reason, more than one natural stonetype was selected from each Uthologic group.

In the first part of the study, the operating parameters wereheld constant to invesfigate the effects of the rock properfieson cutting depth. Density, porosity. Shore scleroscopehardness, Böhme surface abrasion loss, uniaxial compressivestrength, modulus of elasficity and tensile strength of thenatural stone samples were determined and correlated



with cutting depth. Correlations between cutting depthand some rock properties, such as imiaxial compressivestrength, modulus of elasficity and tensile strength, were low(0.60 < R^< 0.65; data not shown). Results of the mechanicalstrength tests hivesfigating the structure of the relativelylarge samples indicated that mechanical strength had only asmall effect on AWJ cutfing because the AWJ cutting processis a micromachining process. The highest AWJ cutting depthvalues were observed in the cutting of 'other' groups ofnatural stones, especially the tuffs, and then the travertines,real marbles, limestones, calcsilicatic marble and granites;the diabases exhibited the lowest cutting depths. Althoughthe real marbles have a higher density than the limestones,the cutting depths of the real marbles were lower thanthose of the limestones. This result is because limestoneshave a higher hardness and abrasion resistance than realmarbles. The main structure of the real marbles is formedby recrystallised calcite minerals, but the limestones used inthis study were formed by calcareous fossil remains, whichis why the hardness and abrasion resistance of the limestonesare higher than that of the real marbles. Diabase naturalstone samples (Yesilirmak Diabase and Akdeniz Green) hadthe highest density and hardness and very high abrasion

resistance; therefore the lowest cutting depths were observedfor diabases because of their high resistance to cutting.

In the second part of the study, Amasya Beige, SivrihisarBeige, Afyon White, Usak Green, Usak White, Akhisar Onyx,Finike Limestone, Beypazari Granite and Amaretto naturalstones were selected to invesfigate the effect of the operatingparameters on cutting depth. AWJ cutting depth decreasedexponentially with an increase in nozzle traverse velocity,increased exponentially with an increase in pump pressureand increased logarithmically with an increase in abrasiveflow rate. These relationships were evident for all the naturalstone types, but the cutting depth at any operating condifionwas different for the different natural stone types. AWJcutting depth can be increased by increasing pump pressureand abrasive now rate and decreasing traverse velocity.However, increases in the pump pressure and abrasiveflow rate are limited, because of the capacity of the pumpsand the risk of obstruction at excessive abrasive flow rates.When pump pressure and abrasive flow rate are insufficient,controlling the traverse velocity can control the cuttingdepth, if a high cutting depth is required.

TABLE 3: Results of the statistical analysis of the multiple and nonlinear regression models used in the prediction of cutting depth.

Model Independent Coefficient Standard error Standard error of F-ratio Tabulated F-ratio Determination Adjusted determinationcoefficient

Independentvariable

C

D.

UCS

£,,

c

D_

UCS

£„,

c

R^

C

C

F

D,

C

P^

Ai

H

Coefficient

311.8

-103.9

-0.351

0.162

0.093

-0.365

1.108

1956.7

0.194

0.862

1.639

0.035

0.005

-0.212

283.5

-91.95

-0.273

0.402

1449.7

0.195

0.876

1.017

8.967

1.369

0.754

0.415

0.920

0.103

1.098

21.034

1.382

0.754

0.434

1.394

Standard error

28.440

9.195

0.134

0.476

0.082

0.277

0.700

862.3

0.077

0.120

0.294

0.074

0.073

0.082

27.470

8.253

0.123

0.490

642.8

0.078

0.099

0.163

4.947

0.073

0.034

0.023

0.058

0.038

0.099

13.214

0.092

0.043

0.028

0.022

Standard error ofestimate9.764

-

-

-

-

-

3.866

-

-

-

-

-

-

10.300

-

-

-

4.109

-

-

.-

2.839

-

-

-

-

-

-

3.570

-

-

-

Determinationcoefficient

Eqnl 80.4 2.38 93.2

Eqn 2 984.7 2.29 98,9 98.8

Eqn 3

Eqn 4

Eqn 5

142.2 2.86

1523.8 2.63

2656.3 2.01

91.8

98.7

97.9

91.2

98.6

97.8

Eqn 6 2335.5 2.22 96.7 96.6

C, const;S, Brazili

änt; D^, apparent density (g/cm=); « , Shore scieroscope hardness; R^, Böhme abrasion resistance (cmV50 cm'); UCS, uniaxiai compressive strength (MPa); E^, modulus of elasticity (GPa);ian tensile strength (MPa); P , pump pressure (MPa); V^, nozzle traverse velocity (mm/s); AÍ, abrasive flow rate (g/min).

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2 3 4 5Nozzle stand off distance (cm)

FIGURE 5: Relationship between the cutting depth and the nozzle stand-offdistance for Finil<e Limestone (at constant pump pressure, nozzle traversevelocity and abrasive flow rate).

20 40 60 80 100 120 140 160 180

Observed cutting depth (mm)

FIGURE 6: Observed cutting depth versus predicted cutting depth for [Eqn 6].

The most significant parameters affecting the cuttabiUty ofnatural stones are the Shore scleroscope hardness, apparentdensity, Böhme abrasion resistance, pump pressure, nozzletraverse velocity and abrasive flow rate. In the constitutionof the models, weighting of the parameters in the estimationof cutting depth was determined by the iteration via theStatgraphics software. In the first four models, constantoperating parameters were selected, and the effects of therock properties on the AWJ cutting depth were investigatedfor 42 different types of natural stones. [Eqn 5] representsall significant rock properties and operating parameters andgives the best results. [Eqn 6] simplifies fhe prediction of thecutting depth and the effects of the operating parametersin practice but includes only one rock property - the Shorehardness value - although the other required parameters canbe easily calculated.

In this study, the Shore hardness, Böhme surface abrasionresistance and density of the rocks were the most significantrock properties affecting the cutting depth. When the abrasivematerial hits the surface of the target material, the mass of the

chip removed from the surface is related to the momentumof the abrasive grits. According to the conservation ofmomentum principle, a fragment is more difficult to remove,using AWJ, from a rock surface with a higher density.

The working pressure contiols the velocity of the waterjet leaving the orifice and also directiy affects the velocityand momentum of the abrasive grits within the jet. Thetraverse velocity of the nozzle and the abrasive flow ratedetermine the number of abrasive particles hitting the rocksurface per unit time and area and have a significant effecton the cutting. The number of abrasive particles hitting thesurface can be controlled by changing the traverse velocity.When the abrasive flow rate is too high, the focusing tubemay be obstiucted. Therefore, the working pump pressureand traverse velocity are the most significant operatingparameters in AWJ cutiing. In statistical analysis, the pumppressure, tiaverse velocity and abrasive flow rate wereselected as operating parameters, and the hardness and densitywere selected as rock properties in [Eqn 5] and [Eqn 6], becauseof their high correlation with the cutting depth. The cuttingdepth of a natiiral stone that has not been directly studied canbe calculated using the given statistical models.

Figure 7 shows the cut surfaces of some of the naturalstones. Figures 7a, 7b and 7c show Milas Leilac, SivrihisarBeige and Ispir Pink, respectively (cut at a nozzle traversevelocity of 800 mm/min, a pump pressure of 360 MPa anda abrasive flow rate of 450 g/min). Although they werecut at constant operating parameters they have differentAWJ cutting depths. These differences are caused by theirdifferent characteristics, especially hardness, density andabrasion resistance, which constitute their resistance toAWJ cutting. The microroughness of all the cut surfacesis almost the same (as can be seen in Figure 7), but thewaviness of the surfaces differs. Microroughness of thesurface is created by the abrasive grits used in AWJ, butwaviness of the surface is related to the movement anddrifts of the jets related to the difficulty of the AWJ cuttingof a natural stone. Figures 7d, 7e and 7f show the effectsof an operating parameter - nozzle traverse velocity - onthe AWJ cutting depth. Akhisar Onyx was cut at a nozzletraverse velocity of 600 mm/min (Figure 7d), at 800 mm/min (Figure 7e) and at 1500 mm/min (Figure 7f), whilstother parameters were held constant. AWJ cutting depthcan therefore be controlled by nozzle traverse velocity.

ConclusionsThe parameters affecting AWJ cutting depth of some naturalstones were investigated. These parameters included bothrock properties and machine operating parameters. Differentnatural stone types have different AWJ cutting depthsunder the same cutting conditions because of the differentresistances of the rocks to AWJ cutting. For instance, whenconstant operating parameters were selected, the cuttingdepth was only 8.6 mm for Ispir Pink granite but 177.6 mm forAyazini Tuff. The resisfance to AWJ cutting of natiiral stones


of 11 ^ H ] Research Article

FIGURE 7: Scanned images of the cutting surfaces of some natural stones: (a) Milas Leilac, (b) Sivrihisar Beige and (c) Ispir Pink (cut at a nozzle traverse velocity of 800mm/min, a pump pressure of 360 MPa and an abrasive flow rate of 450 g/min) and Onyxcut at a nozzle traverse velocity of (d) 500 mm/min, (e) 800 mm/min and (f) 1500mm/min (at a pump pressure of 360 MPa and an abrasive flow rate of 225 g/min).

is mainly related to the density and hardness according tothe results of this study. The traverse velocity of the nozzle isthe key operating parameter for controlling the cutting depthof the rocks. The traverse velocity can range from 1 mm/minto 3000 mm/min or more. No other operating parameter canhave such a wide range. For instance, the pump pressure canbe changed from 90 MPa to 450 MPa, and the abrasive flowrate must be between 60 g/min and 450 g/min. However,changing the pump pressure frequently can damage thepump system, and the abrasive flow rate has an upper limitbecause of the abrasive receiving capacity of the cutting head.

AcknowledgementsThis research was fvmded by TUBITAK (The Scientific &Technological Research Council of Turkey). I am grateful toCT Cutting Technologies and Machinery, and TOLKA WaterJet and Decoration for their valuable cooperation duringfieldwork.

Competing interest

I declare that I have no financial or personal relationshipswhich may have inappropriately influenced me in writingthis paper.

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