field andlaboratorystudiesonnaturalstonesleadingtoempirical performancepredictionofchainsawmachines

International Journal of Rock Mechanics & Mining Sciences 48 (2011) 269–282

Contents lists available at ScienceDirect

International Journal ofRock Mechanics & Mining Sciences

1365-16

doi:10.1

n Corr

E-m

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

Field and laboratory studies on natural stones leading to empiricalperformance prediction of chain saw machines

Hanifi Copur n, Cemal Balci, Deniz Tumac, Nuh Bilgin

Mining Engineering Department, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey

a r t i c l e i n f o

Article history:

Received 11 January 2010

Received in revised form

25 October 2010

Accepted 27 November 2010Available online 21 December 2010

Keywords:

Chain saw machines

Performance prediction

Chain saw penetration index

Linear cutting tests

Chisel tools

Sideways angle

Maximum tool forces

Optimum cutting geometry

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ijrmms.2010.11.011

esponding author. Tel.: +90 212 2856342; fax

ail address: [email protected] (H. Copur).

a b s t r a c t

Quarries using chain saw machines have been visited to collect natural stone samples and recording

performance and operational conditions of these chain saw machines. After defining the physical and

mechanical properties, the samples were tested with a linear cutting test rig using chisel type cutting tools

having different sideways angles to determine the cuttability of the stones; this included the maximum

tool forces and relationships between cutting performance of chisel tools and the mechanical properties

of the stones. Two empirical models for prediction of the areal net cutting rate of the chain saw machines

were developed, which is very important for decision makers at the feasibility stage of a quarrying

operation. One of the models is based on the chain saw penetration index, and uses the uniaxial

compressive strength of the stone, weight of the chain saw machine and useful cutting depth of the arm as

predictor parameters. The other model is based on the results of linear cutting experiments performed in

the unrelieved cutting mode with a standard chisel tool and uses specific energy as the predictor

parameter.

Experimental studies indicate that laboratory cutting performance and optimum cutting conditions

for chisel tools can be reliably predicted by using uniaxial compressive strength and Brazilian tensile

strength of the stone. Variation in maximum tool forces, which is very important and required by machine

manufacturers to design the tool, tool holder, and chain and evaluate machine vibrations, is found for

different sideways angles of the cutting tools. It is statistically proved that the model based on chain saw

penetration index and linear cutting experiments are valid and reliable for predicting the areal net cutting

rate of chain saw machines.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Chain saw machines are used for cutting vertical or horizontalslots for production of large blocks in low to medium abrasive andsoft to medium strength natural stones in both underground andsurface quarrying operations. Chain saw machines produce anexcellent working environment, produce less waste material anddust, eliminate collimation problems encountered with diamondwire cutting machines, reduce time and production losses to enter anew bench, and produce directly saleable blocks [1–3]. Theseenvironmental friendly machines cannot be used for cutting veryhard and abrasive stones and heavily fractured deposits. Anydevelopment provided for cutting harder and more abrasive stoneswould improve the competitive position of both machine manu-facturer and mining companies.

The cutting performance of a chain saw is mainly dependent ongeological and geotechnical features of the stone deposit, specifi-cations and design of the machine, and operational conditions.

ll rights reserved.

: +90 212 2856131.

Although the effect of some of these parameters on cuttingperformance has already been investigated, there is rather limitedliterature on predicting performance of chain saw machines.

Dalziel [4] investigated the effects of blunting of wedge type cuttingtools on performance of a model coal cutter. Mellor [5] analyzedkinematically the working principles and design parameters of con-tinuous belt type machines such as coal cutters, trenchers and chainsaw machines. Mancini et al. [6,7] simulated geostatistically the chaincutting using the spatial variability of the Knoop hardness of the stonesamples for prediction of chain pull force, which was verified by fieldmeasurements. Deketh et al. [8] investigated the cutting and tool wearrates of trenchers based on laboratory scraping tests and fieldmeasurements; they suggested a framework model (expert system)for prediction of cutting rates and tool wear rates. Mancini et al. [1] andCopur et al. [2] analyzed in-situ chain saw applications in terms ofcutting rates and tool wear rates. Primavori analyzed some of theoperational conditions of chain saw machines [3]. Copur et al. [9,10]analyzed the cutting characteristics of chain saw machines by full-scalelinear cutting experiments in unrelieved cutting mode using chiseltools with different sideways angles. Copur [11] investigated cuttingperformance of chain saw machines and suggested a deterministicperformance prediction and optimization model based on full-scale

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H. Copur et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 269–282270

linear cutting tests by simulating a full sequence of cutting tools withdifferent sideways angles and cutting patterns; the results of laboratoryexperimental studies and field investigations indicated that cuttingaction of chain saw machines could be successfully simulated by linearcutting experiments and the suggested deterministic model wasproved to be a useful and reliable tool for selection, design, andperformance prediction and optimization of chain saw machines.

Experimental studies relating laboratory cutting performance ofchisel (wedge and/or radial type) tools and stone/rock propertiesare usually limited to rock type and number of data, although manystudies have been performed for conical tools [12–15]. Dumbletonet al. [16] found a good relationship between ploughing (thrust)force of wedge type tools and compressive strength of 4 differentcoal samples for conditions parallel and perpendicular to beddingand cleat planes. Pomeroy and Foote [17] investigated the relation-ships between average maximum cutting force and mechanicalproperties of different coal samples; they found that impactstrength index and compressive strength were of little effect ontool force, while tensile strength obtained by an in-seam tester gavea better relationship. McFeat-Smith and Fowell [18,19] developed amodel for prediction of specific energy using cone indenter hard-ness and plasticity index obtained by the Shore scleroscopehardness tests for coal measure rocks. Fowell and Pycroft [20]found good correlations between specific energy and uniaxialcompressive strength and cone indenter hardness of different coalmeasure rocks. Demou et al. [21] found relationships betweenlaboratory cutting performance (normal force, cutting force, andspecific energy) and compressive strength of three different rocksamples. Fowell et al. [22] found a relationship between specificenergy and fracture toughness of different rock samples. Tiryakiand Dikmen [23] found a relationship between specific energy andtexture coefficient using six different sandstone samples. Yilmazet al. [24] found a relationship between cutting force and rockproperties (shear strength and uniaxial compressive strength) inaddition to some cutting conditions such as depth of cut and linespacing. Balci and Bilgin [25] correlated the specific energy anduniaxial compressive strength and Brazilian tensile strength ofdifferent rock samples, as well as specific energy values obtainedfrom small-scale and full-scale linear cutting tests. Tiryaki [26]found a relationship between specific energy and uniaxial com-pressive strength and cone indenter hardness for different rocks.

This study summarizes some of the results of a research projectsupported by the Scientific and Technological Research Council ofTurkey (TUBITAK) [27]. Block samples of different natural stonesobtained from quarries located in Turkey were first tested for definingsome of the basic physical and mechanical properties, and then cut on alinear cutting test rig using chisel type cutting tools with differentsideways angles at different cutting conditions. The linear cutting test isperformed to find out a stone’s cuttability and relationships betweencutting performances of chisel tools with different sideways angles andmechanical properties of the stone, and maximum tool forces, which isvery important and required by machine manufacturers to design tool,tool holder, and chain and evaluate machine vibrations. The results oflaboratory and field studies were used to develop empirical models forpredicting areal net cutting rates of chain saw machines. Two empiricalmodels are suggested and statistically verified. One of the models isbased on chain saw penetration index. The other model is based on theresults of linear cutting experiments performed in unrelieved cuttingmode with a standard chisel tool, which is simpler than full simulationof a sequence of tools.

2. Experimental studies

Different natural stone quarries were visited in Turkey formeasuring the field performance of different chain saw machines

and obtaining block samples with a minimum size of around30�30�30 cm3 to perform physical and mechanical propertytests and linear cutting tests. Some of the results of the experi-mental studies have already been presented in a previous study[11]. The maximum tool forces (which are used for the designing ofthe cutting tool, tool holder, and chain) along with determining therelationships between cutting performance of chisel tools withdifferent sideways angles and stone properties (including addi-tional stones), which have not been reported in the previous study,are presented in this paper.

2.1. Physical and mechanical property test equipment and procedures

Core samples were taken from the block samples after splittinginto two pieces for the determination of the physical and mechan-ical properties of six different stone samples. Uniaxial compressivestrength, Brazilian tensile strength, static elasticity modulus, andacoustic velocity tests were carried out using air dried NX coresamples based on suggestions of the International Society for RockMechanics (ISRM) [28]. Shore sclerescope tests were carried outusing a C-2 type equipment [28]. Schmidt hammer tests werecarried out with an L-9 type hammer by applying 10 impacts at apoint and averaging the last 5 readings, and repeating theprocedure at least 5 times and averaging the results [28]. Cercharabrasivity tests were performed based on the procedures describedby [29]. NCB cone indenter hardness tests were performed asdescribed in [30]. Porosity and grain size were defined based onpetrographical analysis of thin sections.

2.2. Linear cutting test equipment and procedures

The rig used for linear cutting experiments is a shaping machinefound in the laboratories of the Mining Engineering Department,Istanbul Technical University, which is similar to the one originallydeveloped in [18,19]. Detailed features of the linear cuttingmachine used in this study can be found elsewhere [9,31]. Detailsof experimental procedures and cutting mechanism can also befound elsewhere [11,32].

Three orthogonal force components (normal, cutting, and side-ways) acting on a tool and specific energy values are obtained fromlinear cutting tests to evaluate the efficiency of a cutting system fora certain stone/rock. Average tool forces are used for machinedesign and performance optimization. Maximum tool forces areimportant in terms of especially cutting tool–tool holder-chaindesign and machine vibrations. Specific energy is defined as theamount of energy required to excavate unit volume or mass ofstone, which is one of the most important factors in determiningthe efficiency of a cutting system and optimum cutting geometry,and estimating net cutting rates. Specific energy is estimated as[33,34]

SE¼ FC=Q ð1Þ

where SE is the specific energy in MJ/m3, FC is the average cuttingforce acting on the tool in kN, and Q is the yield defined as thevolume of stone obtained per unit length of cut in m3/km.

Net cutting rate, also called as instantaneous cutting rate, of amechanical miner can be estimated by [35]

NCR¼ kPcutting=SEopt ð2Þ

where NCR is the net cutting rate in m3/h, SEopt is the optimumspecific energy in kWh/m3 obtained from linear cutting experi-ments, Pcutting is the cutting power of the excavation machine in kW,and k is coefficient related to the transfer of cutting power to therock depending on the type of mechanical miner. It should be notedhere that NCR is the net cutting rate in operational time of themechanical miner, excluding stoppages (breakdowns).

H. Copur et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 269–282 271

2.3. Linear cutting test parameters

Linear cutting test program included five main independentvariables: natural stone type, sideways angle of the chisel cuttingtool, depth of cut, cutting mode (unrelieved and relieved cuttingmodes), and line spacing (for relieved cuts). The dependentvariables were tool forces (average and maximum normal andcutting forces), specific energy, optimum line spacing to depth ofcut ratio, breakout angle, and observations of breakage mechanism.The constant parameters throughout the testing program werecutting direction according to the sample stratification planes(same as at the sites visited), tool rake angle (�51), tool clearanceangle (51), cutting speed (�40 cm/s), and data acquisition rate(1000 Hz). Each test was replicated at least three times.

The linear cutting tests were performed on six different naturalstone samples: Beige Marble (micritic limestone), White Marble(recrystallized limestone), Travertine (B), Travertine (P), Overburden(P), and Isparta Beige Marble. Only one block was used in the tests foreach stone type and this helped to avoid a block confounding problem.Both of the travertine samples have some pores. The volumes of thepores in the Travertine (B) sample (16–18%) are higher than theTravertine (P) sample (7–8%). The White Marble sample has visiblegrains usually between 0.5 and 2.0 mm, while Beige Marble has agrain size smaller than 0.1 mm. Any stratification, foliation or beddingplane was not determined for the samples, except for Travertine (B).The cutting direction for Travertine (B) was kept as parallel to thebedding plane as in the field application of chain saw machine.Overburden (P) is a waste material (overburden) and found on thesame quarry with Travertine (P).

Experiments were carried out with specially shaped chisel toolsmade of tungsten carbide to be easily mounted in the tool holder.All the tools have the same width of 12.7 mm. However, their tipswere arranged to simulate the different sideways angles on acutting profile. Four different sideways angles of 01, 151, 301, and451 are tested in this study. Tip (included) angles of all the tools are901. Pointed and sharp tips are located at the symmetry axis of thetool to transfer the loads to the center of the load cell [11]. The 01tool is a standard chisel tool used for the prediction of roadheaderperformance.

Values of depth of cut were varied as 1–4 mm. However, slightlylower depth of cut values were used for cutting Beige Marble,

Table 1Summary of physical and mechanical properties of the stone samples (after [27,11] wit

Beige Marble Travertine (B) Travertine (P)

r (g/cm3) 2.6970.01 1.8470.14 2.4470.02

UCS (MPa) 83.7725.10 12.775.40 (?) 36.772.42

BTS (MPa) 8.5071.29 3.5470.99 (?) 6.7671.24

CAI 1.10 0.25 0.25

Esta (GPa) 17.1771.07 0.59370.49 (?) –

nsta 0.2070.03 0.1970.14 (?) –

P (m/s) 75537474 475771495 (?) –

S (m/s) 3346753 24587574 (?) –

Edyn (GPa) 82.873.7 44.4721.0 (?) –

ndyn 0.3870.02 0.3070.07 (?) –

SS 59.971.3 10.771.6 (?) 48.774.0

14.672.6 (//)

SH 70.071.6 24.872.3 (?) 53.978.7

46.373.1 (//)

CIHI 2.7270.26 1.1170.08 1.1970.16

(a)PO (%) – 16–18 7 to 8

(a)GS (mm) 50.1 o0.1 �0.1–1.0

r, density (natural unit weight); UCS, uniaxial compressive strength; BTS, Brazilian (indire

static Poisson’s ratio; P, P wave velocity; S, S wave velocity; Edyn, dynamic elasticity modu

L-9 type Schmidt hammer rebound hardness index; CIHI, cone indenter hardness index; P

loading applied parallel to bedding plane.

(a)¼ It is found out based on petrographical analysis of thin sections.

Overburden (P), and Isparta Beige Marble samples when cuttingwith the 01 tool in unrelieved cutting mode in order to reduce theforce requirement of the linear cutting rig; the exact cuttingperformance values for 1–3 mm depth of cut values were foundby curve fitting, when needed.

Line spacing values were varied as 2, 3, 5, 7, 9, 11, and 12 mmdepending on the sample, tool (sideways angle), depth of cut,observations on breakage pattern and the fact that optimum linespacing to depth of cut ratios (s/d) vary usually between 1 and 5 forchisel tools. Any relieved cutting tests could not be performed inIsparta Beige Marble sample due to the limited volume of samplethat was available during the tests.

Maximum tool force was found as a peak value along a cut lineand averaging at least 3 cut lines. Breakout angles were geome-trically estimated [34] based on unrelieved cutting tests with the 01tool using the known values of cut length, depth of cut, weight ofthe cut materials, and density of the samples.

2.4. Experimental results and discussions

Physical and mechanical properties of the natural stone samplesare summarized in Table 1. As seen in Table 1, the uniaxialcompressive strength of the samples varies between 12 and98 MPa, Brazilian tensile strength between 3.5 and 8.5 MPa andCerchar abrasivity index between 0.25 and 1.5, static elasticitymodulus between 0.6 and 17.2 GPa, static Poisson’s ratio between0.19 and 0.28, dynamic elasticity modulus between 44 and 94 GPa,and dynamic Poisson’s ratio between 0.30 and 0.38, showing a widerange of characteristics.

Average normal and cutting forces and specific energy obtainedfrom linear cutting tests performed by standard chisel tool (01sideways angle) in unrelieved cutting mode are summarized inFig. 1 for different natural stones tested and depths of cut. As seen,the average normal forces from the highest to the lowest areobtained as Isparta Beige Marble, Beige Marble, Overburden (P),White Marble, Travertine (P), and Travertine (B). The averagecutting force and specific energy values from the highest to thelowest are obtained as White Marble, Beige Marble, Isparta BeigeMarble, Overburden (P), Travertine (P), and Travertine (B), withsome discrepancy for depth of cut value lower than 1.5 mm.

h the addition of Isparta Beige Marble sample).

Overburden (P) White Marble Isparta Beige Marble

2.5170.07 2.7070.00 2.6970.01

43.0710.9 35.877.10 97.6712.69

4.5770.88 5.0370.93 8.2671.15

0.5 1.5 1.0

10.2471.76 12.2171.82 –

0.2270.03 0.2870.04 –

77897873 10,1277596 7525792

34987373 43807205 35877255

91.0719.7 143.0713.6 93.4711.0

0.3770.003 0.3870.004 0.3570.02

52.071.4 55.473.4 61.370.1

52.571.5 54.274.1 71.671.9

2.8870.97 1.3670.36 –

– – –

– 0.5–2.0 –

ct) tensile strength; CAI, Cerchar abrasivity index; Esta, static elasticity modulus; nsta,

lus; ndyn, dynamic Poisson’s ratio; SS, C-2 type Shore sclerescope hardness index; SH,

O, porosity; GS, grain size; (?), loading applied perpendicular to bedding plane; (//),

0

1

2

3

4

5

0

Ave

rage

Nor

mal

For

ce, F

N (k

N)

Isparta Beige MarbleBeige MarbleOverburden (P)White MarbleTravertine (P)Travertine (B)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

Ave

rage

Cut

ting

Forc

e, F

C (k

N)

White MarbleBeige MarbleIsparta Beige MarbleOverburden (P)Travertine (P)Travertine (B)

0

10

20

30

40

50

60

0

Spe

cific

Ene

rgy,

SE

(MJ

/ m3 ) White Marble

Beige MarbleIsparta Beige MarbleOverburden (P)Travertine (P)Travertine (B)

Depth of Cut, d (mm)1 2 3 4 5 1 2 3 4 5

Depth of Cut, d (mm)

1 2 3 4 5 6Depth of Cut, d (mm)

Fig. 1. Variation in average tool forces and specific energy for unrelieved cutting tests performed with standard chisel tool (01 sideways angle) at different depths of cut.


Since chain saw machines usually work in groove deepening(unrelieved cutting) mode, the maximum tool forces obtained fromunrelieved cutting tests can be used for design purposes. Unre-lieved cutting case is also considered to be the most conservativecase. Therefore, maximum tool forces are analyzed for unrelievedcutting mode in this study.

Maximum normal and cutting forces obtained from linearcutting tests performed by standard chisel tool (01 sideways angle)in unrelieved cutting mode are summarized in Fig. 2 for differentnatural stones tested and depths of cut. As seen in Fig. 2, themaximum normal forces follow similar trends as average normalforces (Fig. 1) in the same order; the order also follows the sametrend of uniaxial compressive strength of the samples from thehighest to the lowest. The maximum cutting forces follow similartrends as average cutting forces, although the order (rank) of thesamples changes, which can be expected in rock cutting mechanics.The effect of rock type on normal force (which is usually related tocompressive strength of the rock) and cutting force (which isusually related to tensile strength of the rock) can be different. Also,there are many parameters affecting cuttability of rocks and theeffects of some of these parameters, such as grain size, bondingforces between grains, and microfractures within the rock, arenot known.

Variation in maximum and average normal forces with side-ways angle is presented in Fig. 3 for unrelieved cutting testsperformed at different depths of cut. In this graph, the force valuesof the 01 tool are linearly reduced from 12.7 to 5 mm for tool width.As seen in Fig. 3, the sideways angle does not have much effect onaverage and maximum normal forces, with the exception ofmaximum normal force of Travertine (B) sample showing a slightdecrease with increase in sideways angle between 151 and 451.

Similar results are obtained for variation in average and maximumcutting forces, as seen in Fig. 4.

Variation in the ratio of maximum to average normal force withsideways angle is presented in Fig. 5 for unrelieved cutting testsperformed at different depths of cut. As seen in Fig. 5, the sidewaysangle does not have much effect on the ratio of maximum toaverage normal forces, although a general trend is seen as the ratioincreases slightly with increase in sideways angle. The ratio variesusually between 2 and 3.5 for homogeneous samples of BeigeMarble and White Marble and between 2.5 and 5 for the poroussamples of Travertine (P) and Travertine (B).

Similar results are obtained for variation in the ratio of max-imum to average cutting force, as seen in Fig. 6. The ratio variesusually between 2.5 and 5 for depths of cut of 2–4 mm, while itvaries from around 4 up to 10 for 1 mm of depth of cut, which islower for lower sideways angles. The ratios of maximum to averagecutting forces for 1 mm of depth of cut are higher than for thedeeper cuts. This might be due to dominant effect of grain size andinhomogeneities at very low depths of cut. Another reason mightbe the effect of sideways angle of chisel tools with sharp andpointed tips. Any literature value of maximum tool forces could notbe found for very low depths of cut for comparison of the results ofthis study.

Barker also found that in some cases the ratio of maximum toaverage tool forces was between 4.7 and 8.8 for a wedge type of toolfor depths of cut between 3 and 50 mm; ratios of maximum toaverage tool forces remained almost constant for all depths of cut[36]. Contrary to Barker’s findings, a general observation in thisstudy is that the ratio of maximum to average tool forces reduceswith increase in depth of cut, especially for lower sideways angles;this may mean that deeper cuts reduce machine vibrations, and

0

2

4

6

8

0

Max

imum

Nor

mal

For

ce, F

'N (k

N)

Isparta Beige MarbleBeige MarbleOverburden (P)White MarbleTravertine (P)Travertine (B)

0

2

4

6

8

Max

imum

Cut

ting

Forc

e, F

'C (k

N)

Beige MarbleWhite MarbleIsparta Beige MarbleTravertine (P)Overburden (P)Travertine (B)

Depth of Cut, d (mm)1 2 3 4 5

0 1 2 3 4 5Depth of Cut, d (mm)

Fig. 2. Variation in maximum tool forces for unrelieved cutting tests performed

with standard chisel tool (01 sideways angle) at different depths of cut.

Beige Marble

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0Sideways Angle (°)

Ave

rage

and

Max

imum

Nor

mal

For

ce, (

kN)

Maximum, d = 1mm

Average, d = 1mm

Maximum, d = 2mm

Average, d = 2mm

Maximum, d = 3mm

Average, d = 3mm

White Marble

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Ave

rage

and

Max

imum

Nor

mal

For

ce, (

kN) Maximum, d = 1mm

Average, d = 1mm

Maximum, d = 2mm

Average, d = 2mm

Maximum, d = 3mm

Average, d = 3mm

Maximum, d = 4mm

Average, d = 4mm

Travertine (P)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Ave

rage

and

Max

imum

Nor

mal

For

ce, (

kN) Maximum, d = 1mm

Average, d = 1mm

Maximum, d = 2mm

Average, d = 2mm

Maximum, d = 3mm

Average, d = 3mm

Maximum, d = 4mm

Average, d = 4mm

Travertine (B)

0.0

0.2

0.4

0.6

0.8

1.0

Ave

rage

and

Max

imum

Nor

mal

For

ce, (

kN)

Maximum, d = 2mm

Average, d = 2mm

Maximum, d = 3mm

Average, d = 3mm

15 30 45

0Sideways Angle (°)15 30 45



Fig. 3. Variation in maximum and average normal forces with sideways angle for

unrelieved cutting tests performed at different depths of cut for different natural

stones.


thus machine breakdowns. However, it should be noted that thedepths of cut in this study are usually lower than 3 mm, which isalso lower than the depths of cut values tested by Barker [36]. Verylow depths of cut values may be quite sensitive to textural andmicro-properties of the stone. Therefore, it can be considered thatthe ratio of maximum to average tool forces might remain constantfor a certain depth of cut value.

Variation in the ratio of average normal force to average cuttingforce with sideways angle is presented in Fig. 7 for unrelievedcutting tests performed at different depths of cut. As seen in Fig. 7,this ratio varies generally between 0.5 and 3.5, which is lower forthe lower strength samples. The ratio is also lower than 1.0 forTravertine (B) having the lowest strength and showing a breakage/failure mechanism of shear during linear cutting tests. The ratio ofaverage normal force to average cutting force can be considered tobe an indicator of wear shape of the tools; if it is close to 1.0,symmetrical wear and longer tool life may be expected.

Variation in specific energy and line spacing to depth of cut ratio(s/d) for relieved cutting tests are presented in Fig. 8 for differentnatural stones and sideways angle tools. Experimental studiesindicate that the optimum (s/d) ratios are close to each other for allsideways angle tools for a certain stone type. Breakout angles,optimum (s/d) ratios, and observations on breakage mechanisms ofstones are summarized in Table 2. As seen in Table 2, Travertine (B)sample has the lowest breakout angle of 371 and optimum (s/d)ratio of 1.0. Visual observations of the cut sample surfaces indicatethat shear stress/failure is dominant on the breakage mechanism ofTravertine (B) sample. Beige Marble sample has the highestbreakout angle of 661 and optimum (s/d) ratio of 3.0, and tensilefractures are dominant on its breakage. In addition, acute angle side(rake) of the 151 and 301 tools has usually a tendency to break in

shear mode. As expected in rock cutting mechanics, optimum (s/d)ratio increases with increase in breakout angle. This is alsoconsidered as being related to brittleness of stones as defined in

Beige Marble

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Ave

rage

and

Max

imum

Cut

ting

Forc

e, (k

N)

Maximum, d = 1mm

Average, d = 1mm

Maximum, d = 2mm

Average, d = 2mm

Maximum, d = 3mm

Average, d = 3mm

White Marble

0

1

2

3

4

5

Ave

rage

and

Max

imum

Cut

ting

Forc

e, (k

N) Maximum, d = 1mm

Average, d = 1mmMaximum, d = 2mmAverage, d = 2mmMaximum, d = 3mmAverage, d = 3mmMaximum, d = 4mmAverage, d = 4mm

Travertine (P)

0

1

2

3

4

5

6

Ave

rage

and

Max

imum

Cut

ting

Forc

e, (k

N) Maximum, d = 1mm

Average, d = 1mmMaximum, d = 2mmAverage, d = 2mmMaximum, d = 3mmAverage, d = 3mmMaximum, d = 4mmAverage, d = 4mm

Travertine (B)

0.00.20.40.60.81.01.21.41.6


Ave

rage

and

Max

imum

Cut

ting

Forc

e, (k

N)

Maximum, d = 2mmAverage, d = 2mmMaximum, d = 3mmAverage, d = 3mm

15 30 45




Fig. 4. Variation in maximum and average cutting forces with sideways angle for

unrelieved cutting tests performed at different depths of cut for different natural

stones.

Beige Marble

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5


Rat

io o

f Max

imum

toA

vera

ge N

orm

al F

orce

d = 1 mmd = 2 mmd = 3 mm

White Marble

0

1

2

3

4

Rat

io o

f Max

imum

toA

vera

ge N

orm

al F

orce

d = 1 mmd = 2 mmd = 3 mmd = 4 mm

Travertine (P)

0

1

2

3

4

5

Rat

io o

f Max

imum

toA

vera

ge N

orm

al F

orce

d = 1 mmd = 2 mmd = 3 mmd = 4 mm

Travertine (B)

0

1

2

3

4

5

6

Rat

io o

f Max

imum

toA

vera

ge N

orm

al F

orce

d = 2 mmd = 3 mmd = 4 mm

15 30 45


15 30 45


15 30 45


15 30 45

Fig. 5. Variation in ratio of maximum to average normal force with sideways angle

for unrelieved cutting tests performed at different depths of cut.


rock cutting mechanics, which links the brittleness to chip size(coarseness index of cut materials) [13]; if more brittle rocks arecut, the larger chips and greater optimum (s/d) ratios and breakoutangles are expected.

A good relationship for breakout angle is obtained with Braziliantensile strength as presented in Fig. 9. Breakout angle increaseswith increase in Brazilian tensile strength; this is in agreement with

Beige Marble

0

2

4

6

8

10

12

Rat

io o

f Max

imum

toA

vera

ge C

uttin

g Fo

rce d = 1 mm

d = 2 mmd = 3 mm

White Marble

0

2

4

6

8

10

12

Rat

io o

f Max

imum

toA

vera

ge C

uttin

g Fo

rce d = 1 mm

d = 2 mmd = 3 mmd = 4 mm

Travertine (P)

0

2

4

6

8

10

Rat

io o

f Max

imum

toA

vera

ge C

uttin

g Fo

rce

d = 2 mmd = 3 mmd = 4 mm

Travertine (B)

0.0

1.0

2.0

3.0

4.0

5.0


Rat

io o

f Max

imum

toA

vera

ge C

uttin

g Fo

rce

d = 2 mmd = 3 mmd = 4 mm

15 30 45


15 30 45


15 30 45


15 30 45

Fig. 6. Variation in ratio of maximum to average cutting force with sideways angle

for unrelieved cutting tests performed at different depths of cut.

Beige Marble

0

1

2

3

4

Rat

io o

f Ave

rage

Nor

mal

toA

vera

ge C

uttin

g Fo

rce

d = 1 mm

d = 2 mm

d = 3 mm

White Marble

0.0

0.5

1.0

1.5

2.0

Rat

io o

f Ave

rage

Nor

mal

toA

vera

ge C

uttin

g Fo

rce d = 1 mm

d = 2 mmd = 3 mmd = 4 mm

Travertine (P)

0.0

0.5

1.0

1.5

2.0

Rat

io o

f Ave

rage

Nor

mal

toA

vera

ge C

uttin

g Fo

rce

d = 1 mmd = 2 mmd = 3 mmd = 4 mm

Travertine (B)

0.0

0.2

0.4

0.6

0.8

1.0


Rat

io o

f Ave

rage

Nor

mal

toA

vera

ge C

uttin

g Fo

rce

d = 2 mmd = 3 mmd = 4 mm

15 30 45


15 30 45


15 30 45


15 30 45

Fig. 7. Variation in ratio of average normal force to average cutting force with

sideways angle for unrelieved cutting tests performed at different depths of cut.


the tensile fracture theory of Evans on rock cutting mechanics[37,38]. The relationship between breakout angle and optimum(s/d) ratio is presented in Fig. 10. Breakout angle can be predicted by

Fig. 9, and then, optimum (s/d) ratio can be predicted for naturalstones based on breakout angle by Fig. 10. Optimum (s/d) ratio is avery important parameter for optimizing the operational condi-tions (especially thrust and torque) and performance of mechanicalminers. For a certain value of line spacing, optimum depth of cut oroptimum operational parameters can be identified by usingoptimum (s/d) ratio.

0

10

20

30

40

50

60

0

Spe

cific

Ene

rgy,

SE

(MJ

/ m3 )

Sample = Beige MarbleTools = 15°, 30°, 45°; d = 1 mm, 2 mm, 3 mm

0

10

20

30

40

50

60

0

Spe

cific

Ene

rgy,

SE

(MJ

/ m3 )

Sample = White MarbleTools = 15°, 30°, 45°; d = 3 mm

0

10

20

30

40

0

Spe

cific

Ene

rgy,

SE

(MJ

/ m3 )

Sample = Travertine (P)Tools = 15°, 30°, 45°; d = 3 mm

0

10

20

30

40

Spe

cific

Ene

rgy,

SE

(MJ

/ m3 )

Sample = Travertine (B)Tool = 45°; d = 3 mm

Sample = Overburden (P)Tool = 45°; d = 3 mm

0

5

10

15

20

25

30

35

40

0

Spe

cific

Ene

rgy,

SE

(MJ/

m3 )

1 2 3 4 5 6 7 8 9 10Line Spacing to Depth of Cut Ratio, (s / d)

Line Spacing to Depth of Cut Ratio, (s / d)1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

Line Spacing to Depth of Cut Ratio, (s / d)1 2 3 4 5 6 7

Line Spacing to Depth of Cut Ratio, (s / d)

Line Spacing to Depth of Cut Ratio, (s / d)1 2 3 4 5 6 7

Fig. 8. Relationships between specific energy and line spacing to depth of cut ratio (s/d) for relieved cutting tests, all the stone samples and the tools with different sideways

angles (after [27,11] with addition of Overburden (P) sample).

Table 2Summary of breakout angles, optimum (s/d) ratios, and breakage mechanisms (after [27,11] with the addition of Overburden (P) sample).

Stone sample Breakout angle, y (deg.) Optimum (s/d) ratio Visual observations on breakage mechanism

Beige Marble 66 �3.0 Tensile fractures are dominant

White Marble 56 �2.3 Both tensile and shear failure observed

Travertine (B) 37 �1.0 Shear failure is dominant

Travertine (P) 57 �2.3 Both tensile and shear failure observed

Overburden (P) 44 �1.7 Both tensile and shear failure observed

s, line spacing; d, depth of cut.


A good relationship for normal force acting on a standard sharpchisel tool (01 tool) in unrelieved cutting mode is obtained with theratio of uniaxial compressive strength to Brazilian tensile strength

(UCS/BTS) as presented in Fig. 11. A highly correlated trend can beseen clearly as normal force acting on standard chisel tool, whichincreases with increase in (UCS/BTS) values. Prediction of average

R2 = 0.91

0

20

40

60

80

0

Bre

akou

t Ang

le, θ

(°)

2 4 6 8 10Brazilian Tensile Strength, BTS (MPa)

y = 17.0x0.65

Fig. 9. Relationship between breakout angle and Brazilian tensile strength.

y = 0.065x - 1.34R2 = 0.99

0

1

2

3

4

30

Opt

imum

(s /

d) R

atio

Breakout Angle, θ (°)40 50 60 70

Fig. 10. Relationship between breakout angle and optimum line spacing to depth of

cut ratio (s/d) for natural stones.

y = 0.039x1.987

R2 = 0.97y = 0.028x2.035

R2 = 0.99

y = 0.027x1.915

R2 = 0.99

0

1

2

3

4

5

6

0

Ave

rage

Nor

mal

For

ce, F

N (k

N)

d = 3 mm

d = 2 mm

d = 1 mm

4 8 12 16 20Ratio of (UCS/BTS)

Fig. 11. Relationships between average normal force and ratio of uniaxial com-

pressive strength to Brazilian tensile strength (UCS/BTS) for different depths of cut

and natural stones cut by standard chisel tool (01) in unrelieved cutting mode.

y = 4.816x0.769

R2 = 0.84

0

5

10

15

20

25

30

35

0Ratio of (UCS/BTS)

Opt

imum

Spe

cific

Ene

rgy,

(45°

tool

, d =

3 m

m)

SE

opt (

MJ/

m3 )

2 4 6 8 10 12

Fig. 12. Relationship between optimum specific energy obtained by 451 tool at

3 mm of depth of cut and ratio of uniaxial compressive strength to Brazilian tensile

strength (UCS/BTS).


normal force is very important for chain saw machines since theyare thrust limited machines [11]. It should be noted that all thestones tested have (UCS/BTS) ratios being less than 12. The ratio of(UCS/BTS) can be considered as a brittleness coefficient [39]. Paststudies indicated that this coefficient has a good relationship withcutting performance of tunnel boring machines using disc cutters[40,41].

Average cutting force acting on standard chisel tool (01 tool) inunrelieved cutting mode has also a good, but weaker than normalforce, relationship with the ratio of (UCS/BTS), while specific energydoes not have any certain relationship with any one of the

mechanical properties of the stones. More detailed study shouldbe performed to analyze the relationship between average cuttingforce and specific energy of chisel tools and physical and mechan-ical properties of natural stones.

Optimum specific energy values obtained by the 451 tool at3 mm of depth of cut for different natural stones have a goodrelationship with the ratio of (UCS/BTS), as presented in Fig. 12. Itshould be noted that additional linear cutting experiments atdifferent depths of cut in relieved cutting mode are required for awide range prediction of optimum specific energy.

The overall results of experimental studies indicate that cuttingperformance and optimum cutting conditions of chisel tools can bepredicted by using uniaxial compressive strength and Braziliantensile strength of natural stones. The relationships betweencutting performance of chisel tools and Schmidt hammer andbetween Shore scleroscope and cone indenter hardness indices areweaker compared to uniaxial compressive strength and Braziliantensile strength. The variation in maximum tool forces withsideways angle, which is very important for the designing of tool,tool holder and chain and has not been investigated up to now, isalso presented in this study. A first is also realized by relating theoptimum (s/d) ratio with a natural stone property, i.e. Braziliantensile strength. Additional parameters and stones, especiallytextural and micro-properties, should be further investigated infuture to improve the predictions of cutting performance ofchisel tools.

3. Field studies

Performances and operational conditions of chain sawmachines are recorded with a data acquisition system [27], whichincluded a power and ampere meter, optical tachometer for chainspeed, hydraulic pressure transducers for cart movement and chainrotation motors, portable computer for recording pressures, andstopwatch and tape measure for cart speed.

Field observations indicate that operators arrange the chainspeed, which is usually close to maximum, and then, the cartmovement speed is increased up to a safe limit. Operators arrangethe safe limit, defined by the manufacturer, based on the pressureand/or ampere readings on the control panel of the machine so thatthe machine operates at a safe maximum capacity.

The results of the field measurements are summarized in Table 3[27]. As seen, machine weights vary between 5.3 and 9 tons(without rails), which is a usual range for chain saw machines.Useful arm cutting depths vary between 2.60 and 6.50 m. The arealnet cutting rates based on long term records vary between 4.69 and

Table 3Summary of the field measurements [27].

Stone (deposit) name Beige Marblea Travertine (B)a Travertine (P)b Travertine (P) Overburden (P)b

Surface being cut Bottom Bottom Back Bottom Back

Machine weight (without rails) (tonnes) 5.5 5.5 9 5.3 9

Maximum arm reach (m) 3.4 3.4 7.4 3.4 7.4

Useful cutting depth of the arm (m) 2.60 3.20 6.20 3.20 4.50

Arm cutting angle (deg.) 78 75 75 75 52

Arm thickness (chain width) (mm) 42 42 38 42 38

Average areal net cutting rate (the authors’ measurements,

excluding sumping) (m2/h)

4.63 11.50 11.00 – 8.10

Average areal net cutting rate (operators’ long term records,

including sumping) (m2/h)

4.69 10.83c 11.00 5.70 –

Average cart motion speed (feed) (m2/h) 1.78 3.60 1.80 – 1.80

Average chain speed (linear) 1.15 m/s 1.00 m/s 0.72 m/h – 0.60 m/s

Effective depth of cut of a single tool (mm) 0.30 0.70 0.64 0.48 0.63

Water feeding 8–10 l/min 8–10 l/min Dry cut Dry cut Dry cut

Cutting tool type 4-edge chisel 4-edge chisel 8-edge chisel 4-edge chisel 8-edge chisel

Tool rake and back clearance angles (deg.) 0 and 8 0 and 8 �10 and 10 0 and 8 �10 and 10

Tool consumption rate (long term) (tool/m2) 0.250 0.129 0.448 0.166 –

Lubricator (grease) consumption (kg/m2) 0.50 0.50 0.20–0.25 – 0.20–0.25

Cart motion speed pressure (when cutting) (bar) 20.67 12.15 10–15 – 32.0

Cart motion speed pressure (not cutting, moving empty,

frictional) (bar)

3.28 3.30 – – 6.0

Chain rotation pressure (when cutting) (bar) 117.04 94.51 100–150 – 123.0

Chain rotation pressure (not cutting, d¼0 mm, friction

due to pretension) (bar)

21.89 25.14 – – 40.0

Ampere readings on control panel (A) 45 45 60 – 60

Total consumed power (kW) 18.90 19.30 22.86d – 22.60

Consumed power for only cutting (kW) 11.21d 11.58d 16.83d – 14.36d

a Same brand chain saw machines with same lacing design.b Same chain saw machine cutting two different stones at the same quarry.c It is average for only year 2003.d It is estimated based on deterministic simulation given in [11] after some simplifications and assumptions for some of the cutting modes.


11.00 m2/h. Effective depth of cut values vary between 0.30 and0.70 mm. Cutting tool consumption rates vary between 0.129 and0.448 tool/m2. Total power consumptions of the lighter machinesare around 19 kW, while it is around 23 kW for the heaviestmachine. These power consumption values include cutting thestone, cart movement, and friction between chain and arm guidedue to pretension of chain and frictional effect of normal force ofcutting tools acting perpendicular to arm guide.

4. Suggestion of empirical models for predicting areal netcutting rate

Predicting performance of mechanical miners is very importantfor feasibility and planning purposes. Instead of relying on only onemethod, using different approaches may improve the reliability ofpredictions and confidence of the decision makers.

Two empirical models for prediction of areal net cutting rates ofchain saw machines, which are simpler and cheaper compared todeterministic modeling, are developed and explained below. One ofthe models uses the stone, machine and operational parameters aspredictors, which are normalized as the chain saw penetrationindex. The other model is based on linear cutting tests performed inthe unrelieved mode with a standard chisel tool and uses specificenergy as the predictor.

Empirical models introduced in this study can be used forpredicting performance of mechanical miners if it is not necessaryto design chain saw machines and lacing of tools on chains, andoptimize machine performance. A deterministic model, which canbe used for designing chain saw machines and lacing of tools onchains, and optimizing machine performance, has already beenintroduced in a previous study [11].

4.1. Model based on chain saw penetration index

The parameters, which are considered to have the most importantimpact on areal net cutting rate of chain saw machines, are uniaxialcompressive strength of the stone, weight of the chain saw machine,and useful cutting depth of the arm. An index value is developed basedon these three parameters by normalizing them such as in [42–44].

It is known that the chain saw machines are thrust limitedmachines [11,27]. Therefore, the machine weight being directlyrelated to thrust capacity has an important effect on cuttingperformance and is considered to be directly proportional to arealnet cutting rate. Heavier machines are more stable than lighterones and may reduce vibration of machine elements, put morethrust (penetration) force onto tools, and thus, increase productionrates. Similarly, increase in the useful arm cutting depth mayimprove the cutting performance if enough machine weight andpower are provided. Also, it is known that the cutting rate decreaseswith increase in uniaxial compressive strength of natural stone; inother words, uniaxial compressive strength is inversely propor-tional to the areal net cutting rate. An index named as Chain SawPenetration Index (CSPI) is developed by normalizing the para-meters mentioned above to arrive at

CSPI¼WH

UCSð3Þ

where W is the weight of chain saw machine in tons, H is the usefulcutting depth of arm in meters, and UCS is the uniaxial compressivestrength of stone in MPa. If the weight of chain saw machine (W) isconsidered as force vector acting on the mass center of the machine,then, Eq. (3) results in unit of volume (m3).

Two additional data are added to the case history data given inTable 3 before correlating the case history data with chain sawpenetration index. The first additional data includes a chain saw

y = 5.18x + 3.68R2 = 0.97

0

2

4

6

8

10

12

14

0.0

Are

al N

et C

uttin

g R

ate,

AN

CR

(m2 /

h)

0.5 1.0 1.5 2.0

Chain Saw Penetration Index, CSPI

Fig. 13. Relationship between areal net cutting rate and chain saw penetration index.


machine with 5.5 tonnes of weight (without rails) cutting a travertine(Denizli Travertine) with 18.9 MPa of uniaxial compressive strengthwith 3.2 m of useful arm cutting depth [45]; its tool consumption ratewas 0.132 tools/m2. The second additional data includes a chain sawmachine with a weight of 7.6 tonnes (without rails) cutting IspartaBeige Marble with a 97.6 MPa of uniaxial compressive strength with a6.5 m of useful arm cutting depth [46]. It should also be noted that themachines given as additional data are both newly developed elec-trically driven chain saw machines, while all the machines given inTable 3 are electro-hydraulically driven.

By correlating the case history data (measured by the authors ofthis study, including the two additional data mentioned above)with chain saw penetration index using the least squares method, alinear relationship is obtained with a very high coefficient ofdetermination (R2) of 0.97, indicating a very strong relationshipas presented in Eq. (4) and Fig. 13:

ANCR¼ 5:18CSPIþ3:68 ð4Þ

4.2. Model based on linear cutting experiments

Estimation of areal net cutting rate (ANCR in m2/h) for chain sawmachines in this model is suggested as follows:

ANCR¼NCR

Tð5Þ

where NCR is the net cutting rate in m3/h given in Eq. (2) asNCR¼k(Pcutting/SEopt) and T is the arm thickness (chain width) inmeters.

Power consumed only for cutting the stone (Pcutting in kW) can beestimated by extracting, from the total power consumed (Ptotal), thepower consumption due to friction between chain and arm guideunder a certain pretension, including the effect of thrust force onchain rotation, and power consumption due to cart movement suchas explained in [11]. The field analyses and measurements indicatethat power consumed only for cutting the stone is around 60% ofthe total power for arm lengths of 3.4 m and 70% for arm lengths of7.4 m, as seen in Table 3. Power consumption only for cutting thestone can be taken to be 11.4 kW for the lighter machines or shortreach arms of 3.4 m and 15.6 kW for the heavier machine or longreach arm of 7.4 m, which are the averages of the field measure-ments. For the arm reaches between 3.4 and 7.4 m, a value could beassigned between 11.4 and 15.6 kW by linear extrapolation.

The field analyses and measurements also indicate that chainsaw machines operate mostly in an inefficient manner in terms ofrock cutting mechanics. In other words, the tools do not excavatethe stone under optimum cutting conditions, in fact quite theopposite; they operate in the groove deepening or unrelievedcutting mode. Therefore, instead of using a SEopt value in Eq. (2), the

specific energy (SE) value obtained for a certain effective depth ofcut in unrelieved cutting mode with a standard chisel tool can beused for ANCR estimations, although it is not optimum. It wasshown that SE obtained from full experimental simulation of asequence of tools on a chain saw machine at 0.3 mm of effectivedepth of cut was 1.3 times more than the SE obtained fromunrelieved cuts with standard chisel tool for Beige Marble[27,11]. The reason for the difference in SE values may be due tothe effect of the different sideways angles of the tools compared tothe 01 tool. It is assumed in this study that the coefficient of 1.3 isvalid for all the stones tested.

The coefficient of k is a coefficient related to the transfer ofcutting power to the stone depending on the type of mechanicalminer. Rostami et al. [35] gave k value of 0.45–0.55 for roadheaders,0.70–0.80 for continuous miners, and 0.85–0.90 for tunnel boringmachines. The value of k was estimated to be 0.3 for cutting BeigeMarble in groove deepening mode by a chain saw machine withmaximum arm reach of 3.4 m, although it was estimated to bearound 0.8 for cutting at optimum conditions [11]. The k value of0.3 is assumed in this study to be valid for chain saw machines,since operators usually run them in groove deepening mode.

These considerations require a revision of Eq. (5) as follows:

ANCR¼NCR

T¼

kðPcutting=SEoptÞ

T¼

0:3ðPcutting=1:3SEÞ

Tð6Þ

where SE is the specific energy obtained at predefined effectivedepth of cut value in kWh/m3 by unrelieved cuts with a standardchisel tool.

Specific energy (SE) is given as an exponential function ofeffective depth of cut (d) as follows:

SE¼ AeBd ð7Þ

where A and B are constants depending on stone type and found bycurve fitting of the results of linear cutting experiments and e is thebase of natural logarithms. The constant B is a negative number,indicating an inverse relationship between SE and d.

4.3. Predictions, validity, and discussions for the model based on chain

saw penetration index

Predictions of areal net cutting rate are presented in Table 4 for themodel based on chain saw penetration index together with measuredfield performance. In order to find reliability of the model or how wellthe model fits the data, F-test and student’s t-test statistics, which arebased on sum of squares of errors, are applied to the data. Analysisindicates that the prediction model presented in Eq. (4) as a simplelinear regression line is statistically meaningful with overwhelminglyvery high confidence level (more than 95%) and/or very low sig-nificance value (p-value less than 1%) in two-tail analysis. Also, a veryhigh coefficient of determination (R2) of 0.97 indicates a very strongrelationship between chain saw penetration index and areal netcutting rate. It is seen that the model developed based on chain sawpenetration index is statistically highly reliable for predictions of arealnet cutting rate of chain saw machines.

The parameters included in the chain saw penetration indexmight also be used for predicting the tool consumption rate. In thiscase, considering the effect of normalization parameters on the toolconsumption rate, Chain Saw Tool Consumption Index (CSTCI) canbe given as

CSTCI¼UCS

WHð8Þ

Considering the field data given in Table 3 and one additionaldata given in [45], the relationship between tool consumption rate(TCR) and chain saw tool consumption index (CSTCI) can beobtained for the chain saw machines with 3.4 m of arm reach

Table 4Summary of the areal net cutting rate predictions based on chain saw penetration index.

Stone name W (tonnes) H (m) UCS (MPa) CSPI Measured ANCR

(m2/h)

Predicted ANCR

(m2/h)

Beige Marble 5.5 2.6 83.7 0.171 4.63b 4.57

Travertine (B) 5.5 3.2 12.7 1.386 11.50b 10.86

Travertine (P)a 9.0 6.2 36.7 1.520 11.00b 11.56

Travertine (P)a 5.3 3.2 36.7 0.462 5.70b 6.07

Overburden (P) 9.0 4.5 43.0 0.942 8.10b 8.56

Denizli Travertine 5.5 3.2 18.9 0.932 9.00 c 8.51

Isparta Beige Marble 7.6 6.5 97.6 0.506 6.50d 6.30

W, weight of chain saw machine without rails; H, useful arm cutting depth; UCS, uniaxial compressive strength of stone; CSPI, chain saw penetration index; ANCR, areal net

cutting rate.

Note: The chain saw machines given in [45] and [46] are electrically driven, while the others electro-hydraulically driven.

a Same natural stone cut by different machines.b The measurements performed by the authors of this study given in Table 3.c It is obtained from Ref. [45].d It is obtained from Ref. [46].

y = 0.024x + 0.111R2 = 0.997

0

0.1

0.2

0.3

0.4

0.5

0

Tool

Con

sum

ptio

n R

ate,

TC

R(to

ols/

m2 )

for 7.4 m of arm lengthfor 3.4 m of arm length

1 2 3 4 5 6 7Chain Saw Tool Consumption Index, CSTCI

Fig. 14. Relationship between tool consumption rate and chain saw tool consu-

mption index.


using four-edge tools as follows (see Fig. 14):

TCR¼ 0:024CSTCIþ0:111 ð9Þ

The data for 7.4 m arm reach is also shown in Fig. 14; it is seen thattool consumption rate for long arm is quite high compared to shortarm machines. The field studies indicated that this might be due toinsufficient lacing design of the tools [27]. The data used for obtainingEq. (9) includes abrasive wear and premature breakages of four-edgetools made of tungsten carbide having similar metallurgical proper-ties based on long term records. Therefore, additional data is requiredfor a complete evaluation of the tool consumption issue. It is alsoknown that tool consumption rate for any type of tool is related toabrasivity of the rock or stone [29]. Unfortunately, there is insufficientdata for statistical inference and/or developing a prediction model fortool consumption based on stone abrasivity or Cerchar abrasivityindex, which is directly related to the hard mineral content [29]. Also,it should be noted that the data used for development of Eq. (9)includes both dry and wet cutting conditions; the effect of waterfeeding during the cutting operation on tool consumption should alsobe analyzed with additional data.

4.4. Predictions, validity, and discussions for the model based on

linear cutting experiments

Predictions of areal net cutting rate are presented in Table 5 for themodel based on linear cutting experiments together with measuredfield performance and relationships between specific energy andeffective depth of cut for each stone sample tested. The relationship

between measured and predicted performance is presented in Fig. 15for the model based on linear cutting experiments.

It is seen in Fig. 15 that a good trend is identified betweenpredicted and measured areal net cutting rate values, with a highcoefficient of determination (R2) of 0.90, indicating a strongrelationship. Statistical analysis by hypothesis testing with stu-dent’s t-test at 95% confidence level indicates that there is nosignificant difference between that predicted by the model given inEq. (6) and the measured areal net cutting rates. Therefore, themodel based on linear cutting experiments is accepted as statis-tically meaningful and reliable.

The results indicate that the method based on simplified linearcutting tests (unrelieved cutting with standard chisel tool) can beused for performance prediction purposes for chain saw machines,although over simplification due to some assumptions has someshortcomings. Additional data, including different stones and chainsaw machines (especially midsize machines) and more detailedanalysis, especially power consumption measurements for onlycutting the stones, are required for a complete evaluation of themodel based on linear cutting experiments.

A question arises about the model based on linear cuttingexperiments related to the effective depth of cut: Which effectivedepth of cut should be applied in the model? Effective depth of cutvalues vary between 0.3 mm (�0.5 mm/s cart movement speed) and0.7 mm (�1 mm/s cart movement speed) for the quarries visited. It isconsidered that this is a reasonable range for most of the chain sawmachines operated based on manufacturer’s directions and the mostof the stone types, which can be cut by chain saw machines. The effectof effective depth of cut on specific energy and ANCR predictions isquite limited, since the values of effective depth of cut are quite small,only fractions of a millimeter. Therefore, ANCR predictions can begiven for a range of 0.3–0.7 mm effective depths of cut, or effectivedepth of cut value of 0.5 mm, which is an average of 0.3 and 0.7 mmeffective depths of cut, can be used for average predictions. Manciniet al. [6,7] also used similarly the average 0.5 mm of indentation depthwhen applying the Knoop hardness test for geostatistical simulationof cutting action of chain saw machines. It should be noted that it isassumed in the model based on linear cutting experiments that thechain saw machines work at maximum capacity and arm cuttingdepth is not considered in this model.

5. Conclusions

Results of full-scale linear cutting tests, mechanical propertytests, empirical modeling studies, and field measurements are

Table 5Summary of the areal net cutting rate predictions based on linear cutting experiments.

Stone name Hmax (m) T (m) d (mm) Ptotal

(kW)

Pcutting

(kW)

SE (MJ/m3)a vs.

d (mm) Relationship

SE (kWh/m3) Measured ANCR

(m2/h)

Predicted ANCR

(m2/h)

Beige Marble 3.4 0.042 0.30 18.9 11.4 SE¼53.394e�0.238d 13.81 4.63 4.54

Travertine (B) 3.4 0.042 0.70 19.3 11.4 SE¼21.174e�0.174d 5.21 11.50 12.03

Travertine (P)b 3.4 0.038 0.48 – 11.4 SE¼43.743e�0.251d 10.77 5.70 5.82

Travertine (P)b 7.4 0.042 0.64 22.86c 15.6 SE¼43.743e�0.251d 10.35 11.00 9.16

Overburden (P) 7.4 0.038 0.63 22.6 15.6 SE¼61.667e�0.354d 13.71 8.10 6.91

Isparta Beige Marble 7.4 0.042 0.38 – 15.6 SE¼64.056e�0.387d 15.36 6.50 5.58

Hmax, maximum arm length (reach) of chain saw machine; T, arm thickness (chain width); d, effective depth of cut; Ptotal, total consumed power; Pcutting, power consumed for

only cutting the stone; SE, specific energy obtained by linear cutting tests in unrelieved mode with a standard chisel tool; ANCR, areal net cutting rate.

a MJ/m3 is divided by 3.6 for conversion to kWh/m3.b Same natural stone cut by different chain saw machines.c It is estimated based on a deterministic modeling defined in [11] after some simplifications and assumptions for some of the cutting modes/patterns.

y = 0.965x + 0.821R2 = 0.90

0

3

6

9

12

15

0

Mea

sure

d A

real

Net

Cut

ting

Rat

e(m

2 /h)

Predicted Areal Net Cutting Rate (m2/h)

3 6 9 12 15

Fig. 15. Relationship between measured and predicted areal net cutting rates by

using the model based on linear cutting experiments.


summarized as follows:

�
The most important physical and mechanical properties ofnatural stones affecting the cutting performance of chisel toolsare uniaxial compressive strength and Brazilian tensilestrength. It is indicated that using these stone properties,cutting characteristics and optimum cutting conditions ofnatural stones and optimum operational parameters of chainsaw machines can be identified. � The sideways angle does not have much effect on the maximum
tool forces from unrelieved cutting tests. The ratio of maximumto average normal force varies usually between 2 and 5, which ishigher in samples having large pores. The ratio of maximum toaverage cutting force varies usually between 2.5 and 5 fordepths of cut of 2–4 mm, while it reaches up to 8–10 for 1 mm ofdepth of cut, which might be due to the dominant effect of grainsize and inhomogeneities at very low depths of cut. The ratio ofmaximum to average tool force decreases with increase in depthof cut, especially for lower sideways angles for the range ofdepth of cut tested.
� The empirical model based on chain saw penetration index is
statistically verified and proved to be a very useful and reliabletool for prediction of areal net cutting rate of chain sawmachines. Uniaxial compressive strength of the stones, usefulcutting depth of the arms, and weight of the chain saw machinesare used as predictors in the model.
� The model based on linear cutting tests performed with a
standard chisel tool in the unrelieved cutting mode usingspecific energy as the predictor parameter is also statisticallyverified and proved to be a very useful and reliable tool forprediction of areal net cutting rate of chain saw machines. The

model should be improved by additional field studies especiallyfor midsize chain saw machines to establish its validity.

Acknowledgements

Scientific and Technological Research Council of Turkey (TUBI-TAK) is thanked for its support in Project 105M017. The authorswould also like to thank to Adnan Saracoglu (President of SETMakine Ltd. Sti.) for his contributions and help in this study. IlkeDuzyol is thanked for his help in the linear cutting experiments.Suayp Demirel (President of Demmak Makine, manufacturer ofchain saw machines) is thanked for contributions and providingsamples (Isparta Beige Marble) and field performance data. FahriEsenli is thanked for petrographical analysis of thin sections.

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field andlaboratorystudiesonnaturalstonesleadingtoempirical performancepredictionofchainsawmachines

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