Hindawi Publishing CorporationAdvances in Mechanical EngineeringVolume 2009, Article ID 175817, 8 pagesdoi:10.1155/2009/175817

Research Article

Investigation on Stone Machining Performance UsingForce and Specific Energy

S. Turchetta,1 W. Polini,1 and I. S. Buyuksagis2

1 Dipartimento di Ingegneria Industriale, Universita degli Studi di Cassino, via G. di Biasio 43, 03043 Cassino, Italy2 Department of Marble Technology, Afyon Kocatepe University, Afyon 03100, Turkey

Correspondence should be addressed to S. Turchetta, turchetta@unicas.it

Received 18 June 2009; Accepted 26 October 2009

Recommended by Duc Pham

Cutting force and energy are often used as parameters for monitoring the stone cutting process. Empirical models are required toguide the selection of the cutting conditions. This paper shows a simple empirical model to predict the variation of the cuttingenergy. It puts into relationship the cutting force and the cutting energy with the idealized chip thickness. It has been testedon six different kinds of stone. The models can be used to guide the selection of cutting conditions. The chip generation andremoval process has been quantified with the intention of assisting both the toolmaker and the stonemason in optimizing the toolcomposition and cutting process parameters, respectively.

Copyright © 2009 S. Turchetta et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Stone cutting by means of diamond tools has a wide fieldof application in stone industry. With the growing useof natural stones as a construction material, there is anincreasing demand on optimizing the various processingparameters to improve productivity and reduce costs. Inorder to attain the economically best cutting conditions,the ideal balance between tool life and cutting rate has tobe achieved. The harder the stone to be cut, the strongerthe diamond type to be selected is a general rule, butthere are collateral factors, such as tool manufacturing,workpiece properties, cutting conditions, cooling efficiency,metal core design, and machine condition, which may affectthe performance and life of a saw blade.

An understanding of the prevailing mechanism ofabrasive-workpiece interactions during stone machining is anecessary step in order to efficiently use the cutting process.The understanding of the cutting phenomena leads tomodels that voice the relationship between cutting behaviourand control parameters. Stone removal is dominated by thekinematics of cutting. The kinematics of cutting is deter-mined by cutting speed and feed speed. Cutting behaviourcan be related explicitly to the cutting force. Cutting force

and energy are important parameters to better understandthe cutting process since they are directly related to toolwear, cutting temperatures, and surface integrity. In orderto achieve better control of a cutting process, a model isrequired to demonstrate the relationship between cuttingand control parameters.

Very few researches exist in literature on stone cutting.Jerro et al. showed a mathematical approach to defineand derive theoretical chipping geometries [1]. From theknowledge of the theoretical chipping geometries, chiparea and mean chip thickness relations were obtained. Therelationship between tangential cutting force and obtainedchip thickness is empirically investigated. Brach et al. studiedthe problem to convert dynamometer readings of specificcutting energy into power consumed [2]. Asche et al. showedthe empirical results of the influence of process parameterson tool wear [3]. Tonshoff et al. developed a model onstone cutting by disc-like diamond tools that is widely usedeven if it is not completely tested [4]. The model showsthe mechanical interaction of tool and workpiece as causedby the elastic and plastic workpiece deformation of thecutting grits, the friction between stone and diamonds, stoneand matrix, and swarf and matrix. Konstanty presenteda theoretical model of natural stone sawing by means of

2 Advances in Mechanical Engineering

diamond impregnated tools for both circular and framesawing [5]. These models seem not to have been tested bymeans of experiments. Pai et al. collected and observed chipsamples under a scanning microscope and related them tothe specific grinding energy [6]. These investigations do nottry to give an organic comprehension of phenomena thathappen at the interface tool-workpiece during stone cutting.

The literature offers many works on grinding of ductileor brittle materials. Malkin proposed an interesting modelof the relationship between the grinding power and therate of plowed surface area generated by abrasive cuttinggrits that interact with the workpiece in ceramics [7]. Hedeepened the model by taking into account the influence ofthe rounding at the tip of the triangular-shaped grit on thespecific grinding energy [8]. The work on metal grindingshows many approaches to model grinding force [9]. Theyare based on empirical [10] or physical considerations[11].

In a previous work, the authors have modelled theprocess of stone contouring by electroplated diamond mills[12], an empirical model of the relationship between thecutting force and energy and the relevant cutting parameters,such as the depth of cut and the feed rate, for the stone knownas Coreno Perlato Royal. The cutting force and energy havebeen modelled as a function of equivalent chip thickness andmaterial removal rate (MRR) by simple and general powerfunction. In [13], Buyuksagis studied the effect of cuttingmode on the sawability of granites using segmented circulardiamond sawblade.

The present work demonstrated that the same modelsare valid for five further kinds of stone. The machiningconditions that are most interesting from an industrial pointof view have been investigated. The models have been testedfor different values of the process parameters.

In the following, the design of the experimental set-upis shown together with the experimental work. Then, themodels developed for cutting force versus equivalent chipthickness and for specific cutting energy versus equivalentchip thickness or material removal rate are presented. Then,they have been tested for different process conditions.

2. Design of Experimental Set-Up

Experiments were undertaken on a Brembana MachineCNC machining centre. A diamond mill, commonly uses tocontour marble, was used, with a diameter of 20 mm, heightof 37.5 mm, diamond mesh no. 40/50, and concentrationof 0.18 crt/cm2. The cutting length is 50 mm. Five differenttypes of rocks (marble-limestone-travertine) which havesubstantial market demand were selected for the cuttingexperiments. All the samples used in the cutting tests wereapproximately 1.7–1.9 kg in weight, having a length of150 mm, and 150 mm × 30 mm section. Some mechanicalproperties of the tested rocks are given in Table 1, togetherwith their mineralogical compositions obtained from thinsections Table 2 [14]. The mechanical tests were performedaccording to related ISRM suggested methods [15] andtesting procedures of the used instruments.

Two feed speed values, three cutting speed values, andthree cutting depth values were taken into account foreach material; they were chosen in order to reproduce thecommonly used industrial range of process variables. Eachcut was replicated two times, yielding a total of 36 measuredforces. The experimental plan is shown in Table 3. The wholenumber of experimental tests was 180.

The cutting conditions were represented by the equiv-alent chip thickness heq. The experimental cuts were per-formed in a random sequence, in order to reduce the effectof any possible systematic error. The cutting forces F f n andF f have been measured by a Kistler piezoelectric platformdynamometer (Type 9257 BA).

3. Experimental Work

The cutting force has been measured by a dynamometerplaced under the workpiece during the marble cutting, asshown in Figure 1. A dynamometer may measure the com-ponents of the cutting force, which acts on the workpiece,along the feed rate direction and along the perpendicular tothe feed rate direction, F f and F f n, respectively. The resultantR of the F f and F f n components has been calculated as

R =√F2f + F2

f n. (1)

The resultant R forms an angle β with the component F f :

β = tan−1

(F f nF f

). (2)

The angle of contact between mill and workpiece is given by

θ = cos−1

(1− 2dp

d

). (3)

The tangential Fc and radial Ft components of the cuttingforce may be calculated by the resultant R (see Figure 2):

Fc = R sin δ,

Ft = R cos δ,(4)

where

δ = β − Z · θ. (5)

The Z parameter in (5) depends on the location of theapplication point of the resultant force R on the arc of contactAC between mill and workpiece. Thus,

Z = AB

AC. (6)

Before obtaining the components Ft and Fc by the measure-ments of F f and F f n values, some ways of estimating thevalue of Z must be found. If the depth of cut has a smallvalue, the tangential Fc and the radial Ft components of thecutting force roughly coincide (see Figure 2).

Advances in Mechanical Engineering 3

Table 1: Mechanical properties of tested rocks.

Rocktype

Materialtag

Uniaxialstrength[MPa]

Tensilestrength[MPa]

Bendingstrength[MPa]

Schmidthammerhardness

Shorescleros.index

Cercharabrasion

index

Density[g/cm3]

Porosity[%]

Meangrain

(calcite)size [mm]

Specificenergy

[J/mm3]

Usakgreen

U.G. 74.67 6.72 14.06 60 44 2 2.76 0.28 0.400 0.86

Afyonsugar

A.S. 54.29 4.70 15.39 52 34 2.5 2.75 0.20 0.500 1.05

Afyontravertine

A.T. 74.71 4.48 13.86 58 13.86 2.6 2.65 3.1 0.500 0.95

Sogutlimestone

S.B. 87.2 7.40 16.4 54.2 56.8 0.7 2.66 0.52 0.360 1.11

Bileciklimestone

B.B. 85.6 8.45 10.5 58.6 58.7 0.9 2.73 0.31 0.330 1.12

Table 2: Mineralogical properties of tested rocks.

Rock type Minerals Proportion (%) Summary of spectrographic description (texture, structure, and grainshape)

Usak green marbleCalcite >95

Microcrystalline, cataclastic deformation, very fine grainedEpidote 1

Quartz 1

Afyon sugar marble Calcite >95 Granoblastic and local polygonal texture, microcrystalline, very finegrained

Burdur limestone Calcite >95 Fractures filled by sparry calcite, recrystallion, fine grained

Sogut limestone Calcite >95 Foraminifera fragments, micritic texture, cryptocrystaline, pellets,sparry limestone

Afyon travertine Calcite >95 Microcrystalline, microfissur and cavity, fractures filled by sparrycalcite, fine grained

Table 3: Experimental plan.

Factors No. of levels Levels

Cutting depth[mm] 3 3-6-9

Feed speed [mm/min] 2 100-250

Cutting speed [rpm] 3 2000-4000-8000

Replications 2

Total cuts 36

Considering the model developed in [2], the tangentialFc and radial Ft cutting forces have been expressed by thefollowing models:

Ft = Kt · hυteq, (7)

Fc = Kc · hυceq, (8)

where Kt and Kc are the cutting force coefficients, υt and υcare constants, and heq is the equivalent chip thickness. Theequivalent chip thickness is equal to

heq =dp · vavt

. (9)

It is determined by depth of cut dp, the feed and thecutting speed, va and vt, respectively. These relationships

completely agree with those proposed by a CIRP cooperativeresearch program on grinding [10]. Based on (7) and (8), therelationship between cutting force and cutting conditions isnot linear but can be expressed by a single exponent.

The specific cutting power can be expressed as

Ec = Fc · vtva · dp · b

. (10)

The numerator is the time rate of power consumption,while the denominator is the time rate of stone volumeremoval. It tends to be constant for a given work material,mill specification, and undeformed chip thickness just asthe fracture stress tends to have a characteristic value fora given material and type of loading. It varies significantlywith chip thickness as well as with the condition of the millface due to dressing technique and grit wear. Specific energyis a convenient quantity to use in estimating cutting forces.Substituting (8) and (9) in (10), we obtain the followingresult:

Ec = Kcb· hυc−1

eq = Ke · hυeeq, (11)

where Ke = Kc/b and υe = υc − 1.We can conclude that by defining 4 parameters

(Kc,Kt, υc, υt), it is possible to model both the cutting forces(Fc,Ft) and the specific cutting energy (Ec) by means of (7),

4 Advances in Mechanical Engineering

Work piece

Dynamometer

Va

(a)

dp

R

β

F f n

F f

Stone

Va

dMill

Vt

(b)

Figure 1: F f and F f n measurements by dynamometer.

R

F f n

Ftδ

F f

B

Fc

C

Zθ θ Va

Vt

Stone

A

(a)

F f n

Fc

R

F f

δ

Ft

(b)

Figure 2: Ft and Fc force components.

(8), and (11). Those equations are general; they are valid forthe five considered marbles.

4. Prediction of Cutting Force andSpecific Energy

ANOVA analysis underlined that feed rate, cutting speed,depth of cut, and marble significantly influence the forcecomponents Fc and Ft , even if the depth of cut seems to bethe most significant variable, as shown in Figures 3 and 4. Anincrease of both the depth of cut and the feed speed causes anincrease of both the force components. However, an increaseof cutting speed causes a decrease of the force components.The influence of the marble type has not a univocal trend,since the kinds of considered stone are different.

Regression analysis of the experimental data is carriedout to the constant values in (7), (8), and (11). All the regres-sions satisfy the hypotheses of normality and homogeneity ofthe residuals.

The radial cutting force Ft versus the increase of theequivalent chip thickness is reported in Figure 5 for thefive considered rocks. It increases with the increase of theequivalent chip thickness from 174 N of Afyon Travertine to180 N of Afyon Sugar, 201 N of Usak Green, 325 N of SogutLimestone, and 367 N of Bilecik Limestone.

The tangential cutting force Fc versus the increase ofthe equivalent chip thickness is shown in Figure 6 for thefive considered rocks. It increases with the increase of theequivalent chip thickness from 95 N of Usak Green 101 N ofAfyon Sugar, 108 N of Afyon Travertine to 165 N of SogutLimestone, and 181 N of Bilecik Limestone. The values of the

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0

50

100

150

200

250

300Fo

rce

(N)

100 250

va (mm/min)

FcFt

(a)

0

50

100

150

200

250

300

350

Forc

e(N

)

3 6 9

dp (mm)

FcFt

(b)

Figure 3: Main effect plot of Ft and Fc versus depth of cut and feed speed.

0

50

100

150

200

250

300

350

Forc

e(N

)

2000 4000 8000

Spindle speed (rpm)

FcFt

(a)

0

50

100

150

200

250

300

350

400Fo

rce

(N)

A.S. A.T. U.G. S.B. B.B.

Marble’s tag

FcFt

(b)

Figure 4: Main Effect Plot of Ft and Fc versus cutting speed and marble type.

tangential cutting force Fc are significantly smaller than thoseof the radial cutting force Ft .

The specific cutting energy Ec versus the increase ofthe equivalent chip thickness heq is shown in Figure 7 forthe five considered rocks. It decreases with the increase ofthe equivalent chip thickness from 930 J/m3 of Usak Greenstone to 1021 J/m3 of Afyon Sugar stone, 1048 J/m3 of AfyonTravertine, 1623 J/m3 of Sogut Limestone, and 1752 J/m3 ofBilecik Limestone.

Some tests have been used to evaluate the obtainedregression models (see Table 4). To analyse the adequacyof the models to the experimental data the test of Fisherhas been used. This test calculates the variance of the dataexplained by the regression model by means of the statisticalratio F∗: the higher is this ratio, the adequate is the modelto the data. The coefficient of determination R2 gives anidea of the existing quantitative correlation between the

dependent and the independent variables of the regressionmodel. Finally, the lack of fit test has allowed verifying thatthe distribution of the data may be approximate by a linearrelationship. It is a function of the distances between theregression equation and the sample means by the statisticalratio F∗ lof, that is, as higher is this ratio as far the data arefrom the regression line. Table 4 reports the results of thosetests. It can be seen that the obtained models present a goodresult in terms of adequacy, correlation, and linearity.

The five rocks have provided five different models ofthe radial cutting force Ft , the tangential cutting force Fc,and the specific cutting energy Ec. The terms of thoseequations look similar. Therefore, it is necessary to evaluateif the five identified equations of the radial cutting forceFt or the tangential cutting force Fc or the specific cuttingenergy Ec are significantly different by an analytical point ofview. The five regression straight lines have been compared

6 Advances in Mechanical Engineering

Table 4: Adequacy tests of the regression models to the data.

Test di fischer Coefficient of determination Lack of fit

F∗ F(0.99, 1, 34) R2 F∗lof F(0.99, 12, 22)

Fc

A.S. 438.84 7.44 0.928 1.72 3.12

A.T. 493.60 7.44 0.934 1.65 3.12

U.G. 847.19 7.44 0.961 2.70 3.12

S.B. 479.96 7.44 0.936 2.44 3.12

B.B. 641.08 7.44 0.948 2.26 3.12

Ft

A.S. 287.51 7.44 0.894 1.02 3.12

A.T. 196.08 7.44 0.848 1.04 3.12

U.G. 498.49 7.44 0.936 2.35 3.12

S.B. 378.82 7.44 0.920 1.91 3.12

B.B. 841.44 7.44 0.96 1.24 3.12

Ec

A.S. 151.73 7.44 0.816 1.72 3.12

A.T. 94.32 7.44 0.727 1.65 3.12

U.G. 214.81 7.44 0.863 2.70 3.12

S.B. 83.67 7.44 0.715 2.44 3.12

B.B. 421.55 7.44 0.923 1.24 3.12

Table 5: Comparison between each couple of regression curves.

Fc Ft EcF∗comparison F(0.99, 2, 68) F∗comparison F(0.99, 2, 68) F∗comparison F(0.99, 2, 68)

A.S.-A.T. 1.80 4.93 1.68 4.93 1.79 4.93

A.S.-U.G. 3.08 4.93 4.47 4.93 3.06 4.93

A.S.-S.B. 80 4.93 124.31 4.93 82.32 4.93

A.S.-B.B. 128.25 4.93 254.88 4.93 118.37 4.93

A.T.-U.G. 6.46 4.93 6.43 4.93 6.47 4.93

A.T.-S.B. 63.54 4.93 105.76 4.93 65.48 4.93

A.T.-B.B. 104.90 4.93 104.89 4.93 190.94 4.93

U.G.-S.B. 133 4.93 100.36 4.93 137.76 4.93

U.G.-B.B. 212.62 4.93 242.11 4.93 212.62 4.93

S.B.-B.B. 2.77 4.93 4.77 4.93 2.76 4.93

by means of statistical tools. In detail, the statistical testsuitable to compare regression curves has been used. It isbased on the consideration that if the regression lines arevery near, all the experimental data may be considered asbelonging to the same population. On the contrary, if theyare significantly different, there are different populations ofdata by which the samples are extracted. It uses a statisticalratio F∗ comparison: as this ratio is lower as the comparedregression equations are nearer. Following the rules of thistest, it has been discovered that the five equations seem tobe significantly different. In fact, the F∗ comparison ratio(109.58 for Ft , 59.74 for Fc, 70.24 for Ec) is higher than theestablished percentile of the Fisher probability distributionF(0.99, 8, 170) equal to 2.62. Further investigations havebeen involved to verify the eventual equality of the six couplesof regression straight lines. The previous described test hasbeen applied to each couple of curves and the results are

reported in Table 5. It can be noted that the equation relatedto the three materials Afyon Sugar stone, Usak Green stone,and Afyon Travertine look similar, even if the equationsrelated to Afyon Sugar stone and Usak Green stone seemdifferent, the value of the statistical F∗ comparison is near tothe admitted limits. The equations related to the two furthermaterials Sogut Beige Limestone and Bilecik Limestone arethe same, but they are significantly different from the firstthree. This means that Sogut Beige Limestone and BilecikLimestone have cutting performances different from theother three materials. In fact, this is a result of origins andmineralogical properties differences of stones.

In a previous work [16], Buyuksagis uses specific energyas a commonly accepted measure of sawing efficiency, whenobtained under standardized conditions. He demonstratedthat specific energy of the same seven marbles dependsstrongly on three marble’s properties: the Cechar abrasion

Advances in Mechanical Engineering 7

0

100

200

300

400

500

600

700

800

900

1000

Ft

(N)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

heq (mm)

A.S.

A.T.

S.B.

U.G.

B.B.

Ft = 2951 · h0.5eq

Ft = 3980 · h0.56eq

Ft = 9321 · h0.6eq

Ft = 3678 · h0.52eq

Ft = 9701 · h0.59eq

Figure 5: Comparison of model and experimental data of Ft versusheq and marble’s kind.

0

100

200

300

400

500

600

Fc

(N)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

heq (mm)

A.S.

A.T.

S.B.

U.G.

B.B.

Fc = 3328 · h0.63eq

Fc = 5115 · h0.7eq

Fc = 8354 · h0.71eq

Fc = 3790 · h0.67eq

Fc = 8519 · h0.7eq

Figure 6: Comparison among model and experimental data of Fcversus heq and marble’s kind.

index, the Mohs’ hardness, and the uniaxial compressivestrength. This means the cutting efficiency may be evaluatedby means of these three marble’s properties.

When compared the specific energy values of a previoussawing study (Buyuksagis) and the milling test used in thisstudy, similar results have been obtained for same rocks inboth methods (see Figure 8). The reason of the differencebetween the specific energy values obtained for same stonesis due to using different specific removal rates (Q′w) in sawingand milling experiments. It can be stated that sawing and

0

500

1000

1500

2000

2500

3000

3500

Ec

(J/m

3)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

heq (mm)

A.S.

A.T.

S.B.

U.G.

B.B.

Ec = e18.5 · h−0.37eq

Ec = e19 · h−0.3eq

Ec = e19.4 · h−0.3eq

Ec = e18.7 · h−0.34eq

Ec = e19.6 · h−0.41eq

×106

Figure 7: Comparison among model and experimental data of Ecversus heq and marble’s kind.

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Mill

ing

(th

isst

udy

)

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15

Cutting (Buyuksagis)

y = 1.1972× 2.1761R2 = 0.7046

Figure 8: Comparison of Specific Energy in sawing and millingprocesses.

milling tests give similar results in terms of specific energyvalues for same rock groups (Figure 8).

5. Conclusions

This work shows that a simple and general model is ableto describe the relationship among the specific cuttingenergy and the process parameters to machine five differentstones by means of a diamond mill. The model is apower function between the specific cutting energy and theequivalent chip thickness. It has been developed to contour

8 Advances in Mechanical Engineering

Perlato Royal Coreno by a diamond mill. This work hasextended the model to contour by a diamond mill to fivefurther kinds of stones: Afyon Sugar stone, Usak Greenstone, Afyon Travertine, Sogut Beige Limestone, and BilecikLimestone.

This work represents a first step towards the increase ofthe knowledge on the stone machining processes in order tooptimise them.

Nomenclature

b: Width of cut [mm]d: Mill diameter [mm]dp: Depth of cut [mm]heq: Equivalent chip thickness [mm]vt: Cutting speed [m/min]va: Feed speed [m/min]Q′w: Specific removal rates [cm2/min]F f : Cutting force component along feed direction [N]F f n: Cutting force component along the perpendicular

to the feed direction [N]Ft : Radial cutting force [N]Fc: Tangential cutting force [N]R: Resultant of F f and F f n [N]β: Angle between R and F f [◦]δ: Angle between Ft and Fc [◦]θ: Angle of contact between mill and workpiece [◦]Ec: Specific cutting energy [J/m3]MRR: material removal rate [mm3/min].

Acknowledgments

Financial support to this work has been provided by MAP(Italian Ministry of the Production Activities) and MIUR(Italian Ministry of University and Research).

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