Development of Predictive Models for the Specific ... - Springer Link

Rock Mech Rock Eng (2013) 46:767–783 DOI 10.1007/s00603-012-0290-6

ORIGINAL PAPER

Development of Predictive Models for the Specific Energy of Circular Diamond Sawblades in the Sawing of Granitic Rocks Gokhan Aydin • Izzet Karakurt • Kerim Aydiner

Received: 29 January 2012 / Accepted: 5 July 2012 / Published online: 27 July 2012 Ó Springer-Verlag 2012

Abstract This paper presents an experimental study on the sawing of granitic rocks by circular diamond sawblades. The influence of the operating variables and rock properties on the specific energy were initially investigated and analyzed. To determine the most significant operating variables and rock properties influencing the specific energy, statistical analyses were then employed and the models were built for the estimation of specific energy depending on the operating variables and the rock properties. Moreover, the derived models were validated through statistical tests such as the determination coefficient, t-test, F-test, and residuals. The results indicated that the specific energy decreased with the decreasing of peripheral speed and the increasing of traverse speed, cutting depth, and flow rate of cooling fluid, respectively. It was concluded that, rather than the physico-mechanical properties, the mineralogical properties were the dominant rock properties affecting the specific energy. Additionally, the peripheral speed was statistically determined as the most significant operating variable affecting the specific energy. The peripheral speed was followed by the cutting depth, traverse speed, and flow rate of cooling fluid with respect to their level of significance on the specific energy. Furthermore, the model results revealed that the developed models have high potentials as a guidance for practical applications. Keywords Diamond sawblades Granitic rock Specific energy Statistical analysis

G. Aydin (&) I. Karakurt K. Aydiner Maden Mu¨hendislig˘i Bo¨lu¨mu¨, Mu¨hendislik Faku¨ltesi, ¨ niversitesi (KTU ¨ ), 61080 Trabzon, Turkey Karadeniz Teknik U e-mail: [email protected]

List Fh Fv Fz Fn Ft Fc Ds d Vc Vp u ku Fc SE CR R1 R2 R3 R4 R5 R6 R7 R8 R9 A B C D X1 X2 X3 X4 X5 X6

of Symbols Horizontal force (N) Vertical force (N) Axial force (N) Normal force (N) Tangential force (N) Resultant cutting force (N) Disc diameter (mm) Cutting depth (mm) Workpiece traverse speed (m/s) Peripheral speed (m/s) Total included angle of the contact zone (°) Angle showing the location of the resultant force (°) Cutting force (N) Specific energy (kN/m3) Contribution rate (%) Verde Butterfly Giallo Fiorito Porto Rosa Crema Lal Giresun Vizon Balaban Green Bergama Gri Nero Zimbabwe Star Galaxy Peripheral speed Workpiece traverse speed Cutting depth Flow rate of cooling fluid Uniaxial strength (MPa) Density (kN/m3) Bending strength (MPa) Water absorption by volume (%) Porosity (%) Schmidt hammer hardness

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X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24

G. Aydin et al.

Ultrasonic velocity (m/s) Cerchar abrasion index Microhardness (HV) Shore hardness Mohs hardness Plagioclase content (%) Alkali feldspar content (%) Quartz content (%) Biotite content (%) Maximum grain size of plagioclase (mm) Maximum grain size of alkali feldspar (mm) Maximum grain size of quartz (mm) Maximum grain size of biotite (mm) Mean grain size of rock (mm) Mean grain size of plagioclase (mm) Mean grain size of alkali feldspar (mm) Mean grain size of quartz (mm) Mean grain size of biotite (mm)

1 Introduction As a constructional material, the use of granite due to its excellent features such as beautiful colors, splendid gloss, high durability, and resistance to scratches, cracks, stains, spills, heat, cold, and moisture has continually increased throughout the world (Hojamberdiev et al. 2011). As a result of this continual growing in recent years, there has been increasingly more attention for sustainability during the sawing of granite, since the complex nature of granite has created difficulties in sawing processes. Circular diamond sawblades have extensive applications in the sawing of granites. The performance of circular diamond sawblades depends on a series of factors associated with the technology and the characteristics of the rock itself. Among these factors, the characterization of technology itself and operating variables can be controlled in the sawing process; however, the characterization of rock due to heterogeneity can not. The specific energy is one of the most important performance indicators in sawing processes with circular diamond sawblades. It is derived from the amount of energy required to remove a given volume of rock and has been successfully used for the performance evaluation of circular diamond sawblades in rock sawing. The lower value of specific energy indicates that the sawing is performed more efficiently (Atici and Ersoy 2009). Because of its potential applications in sawing rocks, various attempts have been made in the relevant literature to investigate and optimize the sawblades’ performance, including the specific energy in rock sawing. For instance, Luo and Liao (1995); Luo (1997) investigated the worn

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surfaces of diamond segments in the sawing of hard and soft granites. They found that the worn particles were mainly of the macro-fractured crystal and/or pull-out hole type for the sawing of hard granite. The results of the study showed that, when cutting the relatively soft granite, the worn particles produced a greater portion of whole crystal and micro-fractured grit on the worn surface and the amount of crystal pull-out was also high. The author noted that the diamond breakdown and the pull-out of the sawblade should operate in the correct wear mode in order to be able to give an optimum blade performance. The kinematical behaviors of the frame sawing were discussed by Wang and Clausen (2002). The researchers indicated that the cutting depth per diamond grit increased as the blades moved forward. Only a few grits per segment could remove the material in the cutting process. The authors also emphasized that, when the direction of the stroke changed, the cutting forces did not decrease to zero due to the residual plastic deformation beneath the diamond grits. Additionally, the authors concluded that the plastic deformation and fracture chipping of material were the dominant removal processes. Xu et al. (2002) conducted an experimental study to investigate the characteristics of the force ratio (tangential force/normal force) in the circular sawing of several kinds of granites. They found that the cutting depth ranked first in governing the two force components compared to the workpiece velocity. The authors also noted that the force ratio increased linearly with increasing wheel speed, whereas the normal force decreased steeply and the tangential force almost remained stable. A group of rocks was sawn using three types of diamond circular saws at different feed rates (traverse speeds) (Ersoy and Atıcı 2004). The results of the study demonstrated that high feed rate was associated with low cutting energy for the diamond saws. Excellent relationships and correlations in terms of cutting energy between the cutting performance and material properties were also established in the study. Additionally, good correlation was obtained between cutting energy and grain size and quartz content of the rocks. Kahraman et al. (2004) conducted an experimental study to analyze the performance of large-diameter circular saws in the sawing of different carbonate rocks. The authors evaluated slab production as the performance criteria and developed models using multiple curvilinear regression analysis for the estimation of slab production from the rock properties. The results of the study showed that the slab production could be estimated using one of the models which were built. The author pointed out that the point load strength, Schmidt hammer value, P-wave velocity, and impact strength had practical and economical advantages for the stone industry. Luo and Liao (1995) investigated the influences of the types and sizes of the diamond on sawability performance in the sawing of

Development of Predictive Models for Specific Energy

granite. The results disclosed that the sawblades containing higher toughness grits resulted in a better blade performance, lower sawing forces, and a greater proportion of whole and pull-out grits occurring on the worn surface. Additionally, the blade performance was found to be better when sawblades containing smaller size grits of the same concentration were used, but the sawing forces were relatively larger, and a greater proportion of particles were pulled out, with a small number of polished grits appearing on the working segment surface. An experimental study for the investigation of sawing performances was carried out by Buyuksagis and Goktan (2005). Different types of marbles were used in the experimentation and the specific energy was considered as a criterion of sawing efficiency to determine the optimum sawing conditions for the tested marbles. They found that shallow cutting depths and low workpiece travel speeds were highly inefficient in terms of specific energy. The authors also noted that it was possible to predict the specific energy of sawing by combining the effects of dominant workpiece properties. In their study, Sańchez Delgado et al. (2005) indicated that the use of microhardness could provide more precise information in sawability studies. A study considering the specific wear rate of the sawblades and specific energy of cutting as the main performance criteria was carried out to investigate the influence of the cutting mode on the sawing performance (Buyuksagis 2007). The results of the study showed that the better performances were obtained in the up-cutting mode (the blade is traversing leftwards while it rotates anticlockwise or the blade is traversing rightwards while it rotates clockwise). Yılmaz and Go¨ktan (2008) investigated the effect of sawing rate on the force and energy requirements of two granite types using a fully instrumented circular side-cutting machine. The authors concluded that higher sawing rates and feed velocity, and lower cutting depth improved the efficiency of the process in terms of cutting forces, power, and specific energy, respectively. The authors also indicated that the magnitude of this improvement varied with respect to the mineralogical properties of the tested rock. In their study, Ucun et al. (2009) found that using boron oil coolant resulted in a decrease in power consumption, specific energy, and specific wear of the diamond segment. Yılmaz et al. (2011) carried out an experimental study to determine the most significant rock properties influencing sawblade wear performance. The results of the study indicated that the maximum grain size of quartz and alkali feldspar minerals were the most dominant factors influencing the specific wear rate. The author also emphasized that the quartz content alone might not be a major contributor to sawblade wear performance due to a relatively weak correlation between the quartz content and the specific wear rate.

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As can be understood from the literature summary, the influences of operating variables and material properties on the performance of the circular diamond sawblades have been investigated for wide ranges of rocks. Additionally, some statistically developed models provide performance predictions of circular diamond sawblades mainly as a function of some selected rock properties. As well known, it is very hard to build models for the performance prediction which is valid for all rock types, since the effect of process parameters and materials properties on sawing performance varies from one rock type to another, even in different samples of the same rock type. Therefore, the present study concentrated on a particular group of rocks (granitic rock). The lack of studies evaluating a variety of rock properties together in terms of the specific energy encouraged the authors to conduct the current study. This work aimed at investigating the relationship among the specific energy and operating variables and material properties of the rocks tested. The study also aimed at developing models for the estimation of the specific energy as a function of both operating variables and material properties.

2 Experimental Study 2.1 Experimental Set-Up The cutting tests were performed on a high-precision experimental cutting machine (Fig. 1). The machine consists of three major sub-systems: a cutting unit, instrumentation, and a PC. The diamond sawblade used in the tests was 40 cm in diameter, having 28 impregnated diamond segments (circumferential length 40 mm, width 3.5 mm, and height 10 mm). The diamonds were sized at 40/50 US mesh with a concentration of 30, which is recommended for the sawing of hard materials. Sawblade movements, forward–backward in the horizontal plane and up–down in the vertical plane, were driven with two 0.75kW AC motors, while the turns of the disc were driven with 4-kW AC motor. Moreover, a 0.75-kW AC motor was used to move the wagon through the cutting line. Operating variables such as peripheral speed, traverse speed, cutting depth, flow rate of cooling fluid, vertical, horizontal, and axial forces were measured using sensors, load cells, transducers, and an encoder in the monitoring system. All movements of the cutting machine were controlled by the computer and industrial electronic cards. Transmissions to the computer were carried out using processing software. 2.2 Material Characteristics For the execution of experiments, nine granitic rocks having different percentages of minerals, different grain

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difficulties in supplying enough samples having suitable dimensions, and preparing and testing for their mechanical properties, such as uniaxial compressive and bending strength. For these reasons, the uniaxial compressive and flexural strengths of the rocks were provided by the stone processing company where the rocks were supplied.

Fig. 1 Experimental set-up

size distributions, and substantial market potential were selected from a stone processing plant and dimensioned according to the requirements of experimental studies. The selected rocks included Verde Butterfly (R1), Giallo Fiorito (R2), Porto Rosa (R3), Crema Lal (R4), Giresun Vizon (R5), Balaban Green (R6), Bergama Gri (R7), Nero Zimbabwe (R8), and Star Galaxy (R9). The samples have a length of 30 cm and a 10-cm 9 3-cm section. 2.2.1 Physico-Mechanical Properties Some physico-mechanical properties of the selected rocks are presented in Table 1. The uniaxial compressive (MPa), bending strength (MPa), density (kN/m3), water absorption by volume (%), porosity (%), ultrasonic velocity (m/s), Cerchar abrasion index, Schmidt hammer hardness, microhardness (HV), Shore hardness, and Mohs hardness were determined. The processes for the laboratory tests are summarized below. 2.2.1.1 Uniaxial Compressive and Bending Strength It may be important to note that, in practice, there are serious

2.2.1.2 Density–Porosity In the density and porosity test, the ISRM-suggested method was used (Brown 1981) . In the porosity experiment, the ‘‘buoyancy method’’ was used. Through the buoyancy method, the bulk volume of samples was calculated with Archimedes’ principle. The weight of the specimen was determined by a balance, capable of weighing to an accuracy of 0.01 g or % of the sample weight. An electronic precision balance was used to weigh samples’ weight and a drying oven was used to dry samples. The density and porosity test was applied to ten samples prepared for each rock (Bilim 2011). 2.2.1.3 Water Absorption by Volume (%) The test samples were firstly subjected to a vacuum (about 0.7 mbar) for 3 h. After this period, the test samples were saturated in distilled water and subjected again to a vacuum for another period of 3 h. The detailed experimental procedure is explained elsewhere. 2.2.1.4 Ultrasonic Velocity The Pundit Plus model ultrasonic testing equipment was used for measuring the ultrasonic velocity. Piezoelectric transducers of a natural resonance frequency of 150 kHz were used in the measurements. The ultrasonic pulse velocity was obtained by direct transmission. The connection of the transducers to the sample was improved through the application of an appropriate coupling paste. The transit time was recorded for each sample as the average of ten independent readings. The mean values of the ultrasonic pulse velocity were

Table 1 Mechanical and intact properties of rocks used in the sawing tests Rock properties

R1

R2

R3

R4

R5

R6

R7

R8

R9

Uniaxial strength (MPa)

191.18

167.65

107.94

231.34

132.35

145.00

92.65

242.6

201.47

Bending strength (MPa)

13.14

22.06

15.00

19.42

18.14

15.20

14.90

24.02

19.61

Density (kN/m3)

27.60

26.60

26.40

25.9

26.7

26.6

26.09

30.30

28.40

Water absorption by volume (%)

0.20

0.28

0.30

0.86

0.20

0.19

0.30

0.14

0.10

Porosity (%)

1.50

0.80

1.50

1.50

3.30

2.20

1.80

0.30

1.00

Ultrasonic velocity (m/s) Cerchar abrasion index

4,130 4.348

3,917 4.166

4,196 4.508

4,140 5.2

5,866 3.868

4,849 4.356

4,836 4.622

6,054 3.412

6,863 4.29

Schmidt hammer hardness

47

48

51

56

54

55

54

64

65

Microhardness (HV)

502.04

543.47

538.73

539.55

505.5

559.03

537.93

501.84

463.18

Shore hardness

72.65

73.55

81.85

75.6

83.1

75.15

71.35

71.9

60.8

Mohs hardness

6.1

5.7

6.0

4.5

6.0

6.0

6.3

6.2

5.8

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obtained by dividing the path length by the average transit time of the ten measurements (Vasconcelos et al. 2007). 2.2.1.5 Schmidt Hardness Brown (1981) suggested that 20 rebound values from single impacts separated by at least a plunger diameter should be recorded and then the upper ten values averaged. The test method was carried out on all samples. All measurements were carried out in the direction perpendicular to the horizontal surface with an N-type Schmidt hammer.

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minerals. For this purpose, thin sections for each rock were prepared and examined under the polarizing microscope. Polished hand specimens were also examined for the grain size characterization for the coarse-grained rock samples. Petrographic descriptions, mineralogical compositions, and grain size ranges of the studied rocks are given in Table 2. As can be followed from the table, quartz, K-feldspar, plagioclase, and biotite were the main rock-forming minerals in all samples, varying in their percentage contents (see Fig. 2). 2.3 Experimental Procedure

2.2.1.6 Microhardness and Mohs Hardness The microhardnesses of the samples were measured by a Vickers Microhardness Meter, which is an average of 3–5 points for a mineral. In the experiment, it is difficult to identify the indentation diagonal of various hard and brittle minerals due to the fracture around the indentation; thus, a measure load of 100 g was chosen (Xie and Tamaki 2007). Microhardness stands for a weighted average value of granite microhardness as a whole, concerning mineral microhardness and its weight in granite. A similar procedure was applied for the determination of Mohs hardness of each rock sample. 2.2.1.7 Cerchar Abrasiveness Index (CAI) For Cerchar abrasiveness index testing, a pointed steel pin which has a 610 ± 5 Vickers hardness, 200 kg/mm2 tensile strength, and a cone angle of 90° was applied to the surface of a rock sample for approximately 1 s under a static load of 68.646 N to scratch a 10-mm-long groove. This procedure was repeated five times in various directions using a fresh pin for each repetition. The abrasiveness of the rock was determined by the resultant wear flat generated at the point of the stylus, which was measured in 0.1 mm units under a microscope. The unit of abrasiveness was defined as a wear flat of 0.1 mm, which is equal to 1 Cerchar abrasivity index, ranging from 0 to 6 (Yarali and Kahraman 2011; Valantin 1974). 2.2.1.8 Shore Scleroscope Hardness In order to perform the tests, samples having a diameter of 54 cm and a thickness of 3 cm were prepared. Then, the upper and lower surfaces were polished with emery. A ‘‘D’’ model scleroscope was used to perform the tests. Shore scleroscope hardness values were recorded 20 times in a 5-mm spacing on the surface and the average value was accepted as the Shore scleroscope hardness value. The tests were carried out according to the ISRM-suggested method (Yarali and Soyer 2011). 2.2.2 Petrographic Properties Petrographic studies conducted in the investigation include the determination of the composition and grain size of the

In order to determine the levels of the operating variables for the study, preliminary cutting tests were conducted by considering the instructions of diamond disc manufacturers and related studies. Consequently, valid for the type of tested rocks, the operating variables were varied at five levels (Table 3) and the experiment layout is given in Table 4. Each experiment was repeated five times in order to increase the accuracy of the results obtained. Additionally, the diamond sawblade was dressed by cutting a siliceous sedimentary tuff block before the cutting tests. The cutting experiments were then conducted in the down-cutting mode. The horizontal (Fh) and vertical (Fv) force components acting on the disk were measured using load cells. The tangential (Ft) and normal (Fn) forced were derived from Eqs. (1–11) considering the geometrical relations presented in Fig. 3. Cos d ¼

Fv Fc

ð1Þ

Sin d ¼

Fh Fc

ð2Þ

Fn ¼ Fc Cos ½ðkuÞ d Fv Fh Fn ¼ Fc Cos ðkuÞ þ Sin ðkuÞ Fc Fc

ð3Þ

Fn ¼ Fv Cos ðkuÞ þ Fh Sin ðkuÞ

ð5Þ

Ft ¼ Fc Sin ½ðkuÞ d Fv Fh Ft ¼ Fc Sin ðkuÞ Cos ðkuÞ Fc Fc

ð6Þ

Ft ¼ Fv Sin ðkuÞ Fh Cos ðkuÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fc ¼ Fn2 þ Ft2

ð8Þ

ð4Þ

ð7Þ

ð9Þ

where Fh is the horizontal force (N), Fv the vertical force (N), Fz the axial force (N), Fn the normal force (N), Ft the tangential force (N), Fc the resultant cutting force (N), Ds the disc diameter (mm), d the cutting depth (mm), Vc the workpiece traverse speed (m/s), Vp the peripheral speed (m/s), u the total included angle of the contact zone (°), and ku is the angle showing the location of the resultant force (°). The total included angle of the contact zone (u) and the angle (ku)

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G. Aydin et al.

Table 2 Mineralogical properties of the rocks Rock type

R1

R2

R3

R4

R5

R6

R7

R8

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Mineral

Alkali feldspar (orthoclase) Plagioclase Quartz Pyroxene Biotite Garnet Opaque Alkali feldspar (orthoclase, microcline) Quartz Plagioclase Biotite Secondary components Alkali feldspar (orthoclase, microcline) Quartz Plagioclase Biotite Other and secondary components (amphibole, apatite, zircon, opaque) Alkali feldspar (orthoclase, microcline) Quartz Plagioclase Biotite Secondary components Alkali feldspar (orthoclase) Plagioclase Quartz Amphibole Biotite Other and secondary components (pyroxene, apatite, zircon, opaque) Alkali feldspar (orthoclase, microcline) Quartz Plagioclase Amphibole Epidote Biotite Other and secondary components (mica, titanit. zircon, opaque) Plagioclase Alkali feldspar (orthoclase) Quartz Biotite Amphibole Other and secondary components (titanit, apatite, opaque) Plagioclase Pyroxene Biotite Opaque

Grain size (mm)

Prop. (%)

Summary of petrographic description (texture, grain size)

41 29 11 9 6 2 2 41 32 14 12 1 44 24 24 6 2

Allotriomorphic, very coarsegrained, grains between 0.08 and 20.0 mm

Min.

Max.

Mean

0.56 0.40 0.16 0.24 0.32 0.80 0.08 0.80 0.40 0.40 0.16 0.08 0.80 0.40 0.96 0.16 0.24

20.00 3.76 6.00 2.00 3.60 6.56 0.80 18.00 9.60 2.40 1.60 0.16 12.0 4.00 6.80 2.00 0.48

5.2 1.6 2.5 0.4 1.5 2.4

0.48 0.24 0.56 0.32 0.08 0.80 0.32 0.24 0.16 0.48 0.16

4.80 2.24 3.60 1.60 0.56 6.80 4.88 2.40 0.96 3.44 0.36

0.80 0.16 0.96 0.24 0.08 0.48 0.16

6.80 5.60 5.20 1.20 0.40 3.20 0.96

2.1 2.7 2.2 0.4 0.1 0.7

38 25 14 10 6 4 3

Hypidiomorphic, coarsegrained, grains between 0.08 and 6.80 mm

0.32 0.32 0.24 0.24 0.24 0.24

4.6 2.98 3.60 1.60 1.60 0.80

1.2 1.3 1.2 0.4 0.4

43 20 19 10 6 2

Hypidiomorphic, fine-grained, grains between 0.24 and 3.85 mm

0.24 0.24 0.16 0.04

3.36 2.40 0.32 0.80

1.7 1.6 0.2 0.1

48 40 4 8


12 4 1.8 0.7 8 0.7 1.7 0.7

0.8 1.7 2.0 0.4 1.1 2.2 1.9 0.2 1.4

39 27 22 10 2 47 27 16 4 4 2

Hypidiomorphic, very coarsegrained, grains between 0.08 and 18.0 mm

Allotriomorphic, very coarsegrained, grains between 0.16 mm and 12.0 mm

Hypidiomorphic, coarsegrained, grains between 0.08 and 4.80 mm

Allotriomorphic, coarsegrained, grains between 0.16 and 6.80 mm


773

Table 2 continued Rock type

R9

Mineral

Grain size (mm)

Plagioclase Pyroxene Biotite Amphibole Other and secondary components (quartz, opaque)

Min.

Max.

0.24 0.24 0.16 0.08 0.08

5.20 3.60 3.20 0.36 1.36

Prop. (%)

Summary of petrographic description (texture, grain size)

40 39 10 7 4


Mean 1.5 1.3 0.4 0.1

Fig. 2 Photomicrographs of the rocks tested

indicating the location of the resultant force can be calculated by the following formulas: 2d u ¼ Cos1 1 ð10Þ Ds ku ¼ 0:7u

ð11Þ

The specific energy (SE) was calculated as: SE ¼

Ft Vp dWVc

where W is the width of the sawblade segments.

ð12Þ

3 Experimental Results and Discussion The effect of the operating variables on the specific energy was first analyzed and then the contribution of each operating variable on the specific energy was investigated. Regression analysis was performed for the experimental data obtained from 19th test to determine the most important material properties in terms of the specific energy. In other words, a constant specific removal rate of 120 cm2/min was employed throughout the experiments so that all granite types could be easily sawn within the available power limits of the cutting machine. The same

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Table 3 Levels of operating variables

Operating variables

Level

Peripheral speed (m/s)

25

30

35

40

45

Traverse speed (cm/min)

60

70

80

90

100

Cutting depth (cm)

0.5

Flow rate of cooling fluid (ml/s)

Table 4 Experimental layout

1.0

1.5

100

150

2.0 200

2.5 250

Number of experiment

Peripheral speed (m/s)

Traverse speed (cm/min)

Cutting depth (cm)

Flow rate of cooling fluid (ml/s)

1

25

60

2.0

150

2

30

60

2.0

150

3

35

60

2.0

150

4

40

60

2.0

150

5

45

60

2.0

150

6

35

40

2.0

150

7

35

50

2.0

150

8

35

60

2.0

150

9

35

70

2.0

150

10

35

80

2.0

150

11 12

35 35

60 60

0.5 1.0

150 150

13

35

60

1.5

150

14

35

60

2.0

150

15

35

60

2.5

150

16

35

60

2.0

50

17

35

60

2.0

100

18

35

60

2.0

150

19

35

60

2.0

200

20

35

60

2.0

250

trends in the specific energy related to the specific removal rate at constant peripheral speed and flow rate of cooling fluid are also presented in Fig. 5 in a graphical form.

Fv

Fc

50

Fn Vp

3.1 Effect of the Operating Variables δ Vc

Ft

Fh Fz

d

Fig. 3 Kinematics of the cutting process for the down-cutting model (Konstanty 2002)

cutting rate enabled a direct comparison of results obtained for all the rock samples. The experimental results are presented in Fig. 4 as plots of the peripheral speed versus specific energy, workpiece travel speed versus specific energy, cutting depth versus specific energy, and flow rate of cooling fluid versus specific energy. Additionally, the

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Depending on the increase in the traverse speed, cutting depth, and flow rate of cooling fluid (especially for lower levels of flow rate of cooling fluid), a decrease was observed in the specific energy and it increased with respect to the increase in the peripheral speed. The critical levels of the peripheral speed in terms of the specific energy were determined as 35 m/s for the rock types R2 and R4, and 40 m/s for the other rocks tested. Above the critical levels defined for the peripheral speed, the specific energy increased dramatically. As also seen in Fig. 5, the specific energy generally decreased as a result of the increase in the specific removal rate, that is, the quantity of the material sawn in unit time or the area cut per unit time. The critical levels of the flow rate of cooling fluid in terms


775 4

Specific Energy (Nm/m )

3

3


5 4 3 2 1

3

2

1

0 25

30

35

40

40

45

60

70

80

4

3

3


5


50

Traverse Speed (cm/min.)

Peripheral Speed (m/s)

4 4 3 3 2

4 3 3 2

0.5

1

1.5

2

2.5

50

Cutting Depth (cm) R1

R2

100

150

200

250

Flow Rate of Cooling Fluid (ml/s)

R3

R4

R5

R6

R7

R8

R9

3


Fig. 4 Relation between operating variables and specific energy 5

4

3

2 30

60

80

90

100

120

140

150

160

Spesific Removal Rate (cm2/min.) R1

R2

R3

R4

R5

R6

R7

R8

R9

Fig. 5 Relation between specific removal rate and specific energy

of the specific energy were determined as 100 ml/s for the rock types R1, R3, R4, R5, and R7, and 150 ml/s for the other rocks tested. In the lower levels of flow rate of cooling fluid, the chips produced may not be efficiently removed from the cutting area and this may lead to obtaining higher specific energy due to increasing cutting force. Therefore, it is recommended that the flow rate of cooling fluid must be above the critical values for achieving effective cutting. 3.2 Effect of the Material Properties The relationships between physico-mechanical properties and specific energy were investigated on the basis of the

statistical approaches such as linear, logarithmic, exponent, and exponential, and the best relations established are depicted in Fig. 6 and presented in Table 5. The table indicates that, generally, there are moderate correlations between the specific energy and density, ultrasonic velocity, Schmidt hammer hardness, and microhardness. It may generally be possible to obtain higher specific energy values when cutting hard rocks having higher density, ultrasonic velocity, and Schmidt hammer hardness. However, unlike the expectations, lower specific energy was observed for these kinds of rocks in the current study. This phenomenon may be associated with mineralogical properties, since they were determined as being more dominant on the specific energy than physico-mechanical properties. Higher specific energy values were observed when cutting rocks having higher microhardness. This finding supports the observations of other researchers (Sańchez Delgado et al. 2005; Xie and Tamaki 2007). The relationships between mineralogical properties and specific energy are also illustrated in Fig. 7 and presented in Table 6 for the best relations. The table indicates that, generally, there are reliable correlations between the cutting force and quartz, plagioclase, and feldspar content. Generally, the higher specific energy obtained for the rocks including high percentages of quartz and alkali feldspar is due to their high resistance to wearing. Therefore, it may be important to note that, rather than the mechanical

123

Specific Energy (Nm/mm )

3

3

4

R2= 0.0823

3 2 1 0 50

100

150

200

250

Uniaxial strength (MPa)

2 1 0 10

15

20

25

2 1 0 24

26

28

32

4

R2= 0.4101

3 2 1 0 0

0,5

1

Water absorption by volume (%) 3


R2= 0.1989

4 3 2 1 0 0

1

2

3

4

Porosity (%)

R2= 0.5619

4 3 2 1 0 40

50

60

70

Schmidt hammer hardness 3


4

R2= 0.6099

3 2 1 0 2000

4000

6000

8000

R2= 0.3401

4 3 2 1 0 50

60

70

80

90

Shore hardness

3


Ultrasonic velocity (m/s) 4

R2= 0.2001

3 2 1 0 3

4

5

6

Cerchar abrasion index

4

R2= 0.5813

3 2 1 0 400

450

500

4

R2= 0.1728

3 2 1 0 4

5

550

Microhardness (HV)

3


123

30 3

Bending strength (MPa)

3


R2= 0.5843

3

3


R2= 0.0299

3

3


4

3


4

Density (kN/m )

3


Fig. 6 Relations between physico-mechanical rock properties and specific energy

G. Aydin et al.


776

6

Mohs hardness

7

600

Development of Predictive Models for Specific Energy Table 5 Correlations between specific energy and physicomechanical properties

777

Physico-mechanical properties

Regression equation

R2

X1

SE = 2.9567e-0.0005x

0.0823

X2

SE = 10.761e-0.0505x

0.5843

X3

SE = 2.9388e-0.0043x

0.0299

X4

SE = 3.1284x

0.0973

0.4101

X5

SE = 2.6765x0.0598

0.1989

X6

SE = 4.9781e-0.011x

0.5619

X7

SE = 3.832e-7E-05x

0.6099

X8

SE = 1.6303x0.3516

0.2001

0.0023x

X9

SE = 0.8047e

X10

SE = 0.212 x0.5933

0.3401

X11

SE = -0.1922x ? 3.8531

0.1728

properties of the rock, mineralogical properties could primarily be responsible for the specific energy. Additionally, it can be stated that some moderate correlations were found between the specific energy and the mean and maximum grain size of the quartz.

SER6 ¼ 3:3563 þ 0:0826A 0:0274B 0:5305C 0:0033D CR(%Þ : A : 35:64; B : 23:65; C : 26:63; D : 14:15

CR(%Þ : A : 38:77; B : 22:87; C : 26:38; D : 11:95

A computing package program (SPSS 11.5) was used for the statistical analysis. Multivariable linear regression analysis was carried out to predict the specific energy. A number of statistical parameters or terms are associated with the multivariable linear regression analysis. Some of the most important include the coefficient of multiple determination, the confidence level, standard error, model error, the significance level, the t distribution, the F distribution, and the residuals. Detailed explanations of these parameters or terms can be found from the related sources (Field 2009; C ¸ okluk et al. 2010; Akbulut 2011). The dependent and independent variables are denoted by specific energy (SE), the peripheral speed (A), the workpiece traverse speed (B), the cutting depth (C), and flow rate of cooling fluid (D). The best model (Eqs. 13–21) developed for the estimation of the specific energy from operating variables for each rock is given below, together with the contribution rates (CR) of each operating variable to the specific energy. SER1 ¼ 2:7855 þ 0:0778A 0:0222B 0:5190C 0:0027D CRð%Þ : A : 37:27; B : 21:27; C : 28:92; D : 12:74 ð13Þ SER2 ¼ 2:9867 þ 0:0888A 0:0247B 0:4695C 0:0028D ð14Þ

SER3 ¼ 2:7544 þ 0:0832A 0:0263B 0:4109C 0:0024D CR(%Þ : A : 40:15; B : 25:38; C : 23:06; D : 11:68 ð15Þ SER4 ¼ 3:3353 þ 0:0904A 0:0307B 0:5586C 0:0028D CR(%Þ : A : 36:90; B : 25:06; C : 26:52; D : 11:27

SER5 ¼ 3:0448 þ 0:0802A 0:0237B 0:5477C 0:0029D CR(%Þ : A : 36:32; B : 21:47; C : 28:85; D : 13:22 ð17Þ ð18Þ

SER7 ¼ 2:5702 þ 0:0746A 0:022B 0:4363C 0:0023D

4 Prediction of the Specific Energy

CR(%Þ : A : 40:18; B : 22:35; C : 24:71; D : 12:49

0.5813

ð16Þ

ð19Þ

SER8 ¼ 2:6100 þ 0:0746A 0:0260B 0:4239C 0:0027D CR(%Þ : A : 36:82; B : 25:66; C : 24:34; D : 13:13 ð20Þ SER9 ¼ 2:7456 þ 0:0658A 0:019B 0:5091C 0:0028D CR(%Þ : A : 34:61; B : 19:99; C : 31:15; D : 14:52:

ð21Þ

The CR was used to determine the significant process factors as a percentage. It is a tool to see which process factor has a significant effect on the process. Higher CRs indicate that there is a considerable change on the performance characteristic due to the variation of the related operating variables. As can be understood from the models, the most significant operating variable affecting the specific energy was determined as the peripheral speed. The peripheral speed was followed by the cutting depth, traverse speed (the order of cutting depth and traverse speed changes for some rocks), and flow rate of cooling fluid according to the order of importance in terms of specific energy. Predictive models of specific energy were also built by taking account of the material properties and some of these models (whose determination coefficients are 1) are presented below, together with the CRs of each material property to the specific energy (Eqs. 22–30). In the models, the independent variables (physico-mechanical and mineralogical properties) are denoted by the following: X1 uniaxial strength (MPa), X2 density (kN/m3), X3 bending strength (MPa), X4 water absorption by volume (%), X5 porosity (%), X6 Schmidt hammer hardness, X7 ultrasonic velocity (m/s), X8 Cerchar abrasion index, X9 microhardness

123

3


3

Fig. 7 Relations between mineralogical rock properties and specific energy

G. Aydin et al. Specific Energy (Nm/mm )

778

4

R2= 0.8552

3 2 1 0 10

20

30

40

50

4

R2= 0.7467

3 2 1 0 0

4

R2= 0.9031

3 2 1 0 0

10

20

30

40

4

R2= 0.0577

2 1 0 0

5

R2= 0.2778

3 2 1 0 1

1,5

2

2,5

4

R2= 0.4161

3 2 1 0 0

5

10

15

Mean grain size of alkali feldspar (mm) 3


3


15

3


3


4

4

R2= 0.5971

3 2 1 0 0

2

4

6

4

2

R = 0.2176 3 2 1 0 0

Mean grain size of quartz (mm)

0,5

1

1,5

2

Mean grain size of biotite (mm) 3


3


10

Biotite content (%)

Mean grain size of plagioclase (mm)

4

R2= 0.3767

3 2 1 0 0

2

4

6

8

Mean grain size of rock (mm)

4

R2= 0.0808

3 2 1 0 2

4

6

3


Maximum grain size of plagioclase (mm)

3


60

3

Quartz content (%)

4

R2= 0.3932

3 2 1 0 0

10

20

30

R2= 0.5758

3 2 1 0 0

5

3


4

R2= 0.1149

4 3 2 1 0 0

1

10

Maximum grain size of quartz (mm)

Maximum grain size of alkali feldspar (mm)

2

3

4

Maximum grain size of biotite (mm)

123

40

3


3


20

Alkali feldspar content (%)

Plagioclase content (%)

Development of Predictive Models for Specific Energy Table 6 Correlations between specific energy and mineralogical properties

779

Mineralogical properties

Regression equation

R2

X12

y = -0.0186x ? 3.2694

0.8552

X13

y = 2.392e0.0043x

0.7467

X14

y = 2.3872e0.0076x

0.9031 0.0577

X15

y = 0.0188x ? 2.5911

X16

y = -0.2294 Ln(x) ? 3.0606

0.0808

X17

y = 2.5537e0.0079x

0.3932

X18

y = 0.0651x ? 2.4772

0.5758

X19

y = 2.6474x0.0412

0.1149 0.3767

X20

y = 0.0816x ? 2.5259

X21

y = 2.094e0.1478x

0.2778

X22 X23

y = 0.0382x ? 2.5994 y = 0.1607x ? 2.4449

0.4161 0.5971

X24

y = 2.821x0.0709

0.2476

(HV), X10 Shore hardness, X11 Mohs hardness, X12 plagioclase content (%), X13 alkali feldspar content (%), X14 quartz content (%), X15 biotite content (%), X16 maximum grain size of plagioclase (mm), X17 maximum grain size of alkali feldspar (mm), X18 maximum grain size of quartz (mm), X19 maximum grain size of biotite (mm), X20 mean grain size of rock (mm), X21 mean grain size of plagioclase (mm), X22 mean grain size of alkali feldspar (mm), X23 mean grain size of quartz (mm), and X24 mean grain size of biotite (mm). In the statistical analysis where physico-mechanical and mineralogical properties were evaluated together, the following models (Eqs. 22–24) were established for the estimation of the specific energy.

In the analysis where only physico-mechanical properties were evaluated, the following models (Eqs. 25–27) were built. It was observed that porosity and Mohs hardness were included in the best models constructed.

SE(Nm=mm3 Þ ¼ 2:9132 0:0021 X1 0:0079X8

SE(Nm=mm3 Þ ¼ 2:1586 þ 0:0264X2 0:3912X4 0:0956X5 0:0743X6 þ 0:0004X7

þ 0:0029X10 0:2074X11 0:0464X16 þ 0:2757X21 CRð%Þ : X1 : 16:63; X8 : 7:86; X10 : 13:44; X11 : 17:03; X16 ð22Þ

SE(Nm=mm3 Þ ¼ 2:6474 þ 0:0087X3 þ 0:2809X4 þ 0:0940X5 0:0012X6 0:0097X12 þ 0:0352X18 0:0453X19 þ 0:0035X22 CRð%Þ : X3 : 6:78; X4 : 13:48; X5 : 17:24; X6 : 1:55; X12 : 25:23; X18 : 21:54; X19 : 10:78; X22 : 3:14

0:7909X4 þ 0:0677X5 0:0278X6 0:0046X8 þ 0:0045X10 0:4569X11 CR(%Þ : X1 : 2:95; X3 : 7:98; X4 : 19:39; X5 : 6:34; X6 : 18:80; X8 : 3:24; X10 : 14:78; X11 : 26:49 ð25Þ

þ0:0518X9 þ 0:0092X10 0:4978X11

þ 0:0218X22 þ 0:1143X24 : 9:23; X21 : 13:87; X22 : 13:96; X24 : 7:96

SE(Nm=mm3 Þ ¼ 4:7434 0:0005X1 þ 0:0201X3

ð23Þ

SE(Nm=mm3 Þ ¼ 2:3657 0:0014X1 þ 0:0138X3 þ 0:5318X4 þ 0:0005X10 0:0052X12 0:0170X15 þ 0:0120X22 þ 0:0957X23 CRð%Þ : X1 : 13:54; X3 : 9:33; X4 : 22:27; X10 : 2:80; X12 : 11:84; X15 : 9:94; X22 : 9:25; X23 : 21:06: ð24Þ

CR(%Þ : X2 : 2:20; X4 : 5:30; X5 : 4:95; X6 : 27:79; X7 ð26Þ

: 25:72; X9 : 1:53; X10 : 16:61; X11 : 15:94 SE(Nm=mm3 Þ ¼ 25:1383 þ 0:0087X1 0:7566X2 0:0575X3 0:3282X5 þ 0:0002X7 þ 0:0222X8 1:1509X9 þ 0:0739X11 CR(%Þ : X1 : 15:29; X2 : 35:09; X3 : 7:02; X5 : 9:46; X7 : 8:05; X8 : 4:80; X9 : 18:97; X11 : 1:32

ð27Þ

In the analysis where only mineralogical properties were evaluated, the following models (Eqs. 28–30) were built. It was noted that quartz content, plagioclase content, maximum grain size of plagioclase, mean grain size of alkali feldspar, and mean grain size of quartz were included in the best models constructed.

123

780

G. Aydin et al.

Table 7 Statistical results of the multiple linear regression analysis Rock type

Independent variables

R1

S

R2

R3

R4

R5

R6

R7

R8

R9

Coefficient 2.7855

Standard error

Standard error of estimate

0.548

0.169

t-value

5.081

A

0.0778

0.011

7.262

B

-0.0222

0.005

-4.144

C

-0.5190

0.092

-5.634

D

-0.0027

0.001

S

2.9867

0.428

A B

0.0888 -0.0247

0.008 0.004

10.614 -5.905

C

-0.4695

0.072

-6.527

D

0.0028

0.001

S

2.7544

0.534

6.977

0.534

0.0832

0.010

-0.0263

0.005

0.005

C

-0.4109

0.090

0.090

-0.0024

0.001

3.3353

0.551

A

0.0904

0.011

Determination coefficient (R2)

1.729

26.954

3.13

0.8998

1.729

50.253

3.13

0.9432

1.729

28.825

3.13

0.9062

1.729

36.474

3.13

0.9244

1.729

36.110

3.13

0.9229

1.729

44.908

3.13

0.9372

1.729

29.465

3.13

0.9065

1.729

34.725

3.13

0.9214

1.729

22.025

3.13

0.8791

0.010

0.001 0.170

6.051 8.393

B

-0.0307

0.005

-5.701

C

-0.5586

0.093

-6.032

D

-0.0028

0.001

S

3.0448

0.496

A B

0.0802 -0.0237

0.010 0.005

8.268 -4.887

C

-0.5477

0.083

-6.567

D

-0.0029

0.001

S

3.3563

0.463

A

0.0826

0.009

9.128

-2.562 0.153

6.135

-3.010 0.143

7.248

B

-0.0274

0.005

-6.056

C

-0.5305

0.078

-6.819

D

-0.0033

0.001

S

2.5702

0.485

A

0.0746

0.009

7.864

-3.625 0.150

5.295

B

-0.022

0.005

-4.638

C

-0.4363

0.082

-5.350

D

-0.0023

0.001

S

2.6100

0.464

A

0.0746

0.009

8.232

B C

-0.0260 -0.4239

0.005 0.078

-5.738 -5.441

D

-0.0027

0.001

S

2.7456

0.546

A

0.0658

0.011

6.163

-2.425 0.143

5.628

-2.935 0.169

5.025

B

-0.019

0.005

-3.559

C

-0.5091

0.092

-5.547

D

-0.0028

0.001

-2.585

123

Tabulated F-ratio

-3.299 0.165

B D

F-ratio

-2.483 0.132

A

S

Tabulated tvalue

781

0.4

0.4

0.2

0.2

0.2

0 -0.2

1

2

3

4

0 -0.2

1

R1

4

5

0 -0.2

0.2

0.2

0.2

-0.2

3

4

5

0 -0.2

1

2

3

4

Residuals

0.4

Residuals

0.4

2

-0.2

Predicted Specific Energy (Nm/mm 3 )

0.2

0.2

-0.2

3

4

0 -0.2

1

2

3

4

Residuals

0.2

Residuals

0.4

2

5

-0.2

1

2

3

4

R9

-0.4

-0.4


4

0

R8

R7

-0.4

3


0.4

0

2 R6

0.4

1

1

-0.4

-0.4


4

0

R5

R4

-0.4

3


0.4

0

2

-0.4


3

1

1 R3

-0.4

Predicted Specific Energy (Nm/mm )

Residuals

3

R2

-0.4

Residuals

2

Residuals

0.4

Residuals

Residuals




Fig. 8 Residuals against the predicted specific energy

SE(Nm=mm3 Þ ¼ 1:9831 þ 0:0144X14 þ 0:0097X15

5 Validation of the Models

0:0114X16 þ 0:0052X17 þ 0:2246X21 þ 0:0018X22 þ 0:0109X23 þ 0:0229X24 CR(%Þ : X14 : 46:75; X15 : 8:71; X16 : 4:20; X17 : 10:69; X21 : 20:87; X22 : 2:09; X23 : 3:67; X24 : 2:95

ð28Þ

SE(Nm=mm3 Þ ¼ 2:8881 0:0090X13 þ 0:0393X14 0:0268X15 0:1422X16 0:0664X18 þ 0:2090X19 þ 0:0469X22 0:0660X23 CR(%Þ : X13 : 10:51; X14 : 28:44; X15 : 5:34; X16 : 11:61; X18 : 12:07; X19 : 14:79; X22 : 12:35; X23 : 4:95 ð29Þ SE(Nm=mm3 Þ ¼ 2:9946 0:0155X12 0:0259X13 þ 0:0435 þ X14 þ 0:0157X17 0:0760 X18 0:0583 X19 þ 0:0143 X23 þ 0:6983X24 CR ð%Þ : X12 : 10:01; X13 : 25:34; X14 : 26:21; X17 : 6:01; X18 : 11:50; X19 : 3:43; X23 : 0:89; X24 : 16:64

ð30Þ

The predictive models derived from operating variables were verified by considering the following criteria: the behavior of determination coefficients (R2), and the t-test, the F-test, and the residual analysis (see Table 7). The models built from material properties were not tested since the determination coefficients of these model are 1. That means that 100 % of the variation of the experimental data is explained by the equations. R2 values for all models built from operating variables are around 0.90, indicating a high degree of relationship between the predicted and observed specific energy. As can be seen from Table 7, at the 95 % confidence level, the computed t-values and computed F-values are greater than the tabulated t-values and tabulated F-values, suggesting that the models built are statistically valid. A regression analysis is not completed by fitting a model on the basis of coefficients of determination, by providing confidence intervals, or by testing. These steps tell only half the story and give only the statistical inferences. A better test is to make a more direct comparison of the model and real data in the form of residuals (Ersoy et al. 2005). The plots of the residuals

123

782

against the predicted specific energy for the model case are shown in Fig. 8. The figure indicates that the residuals appear to be randomly scattered about the line, confirming the accuracy of the models. 6 Conclusions An experimental study on the specific energy in the sawing of granitic rocks was presented. It was determined that the specific energy decreased with increasing traverse speed, cutting depth, and flow rate of cooling fluid, while it increased with increasing peripheral speed (especially for lower levels of flow rates). The results also showed that the most significant operating variable affecting the specific energy was the peripheral speed. The peripheral speed was followed by the cutting depth, traverse speed, and flow rate of cooling fluid according to their significance on the specific energy. Moreover, the results indicated that the mineralogical properties could primarily be responsible for the specific energy rather than the physico-mechanical properties of the rock. Further, the results disclosed that the models derived from the operating variables and materials properties for the estimation of the specific energy have high potentials as a guidance for practical applications. Additionally, the results of the current study can provide opportunities to evaluate the sawability of granitic rocks without sawing tests involving complicated testing procedures. It is highly important to determine the unit cost of cutting, which must be minimized in an industrial production process. The economics of a sawing process, of course, are affected by several factors. One of the most important factors affecting the economics of the process is the specific energy. The wear rate of the blade elements also has an affect on the unit cost of cutting. Additionally, the surface quality of the cut is very important for the subsequent phases of the production (gauging, polishing). Therefore, it can be stated that the studies for the optimum setting of operational parameters are rather complicated. Consequently, before the cutting processes, determination of the intended use of the rock to be cut would be advantageous for defining the optimal cutting conditions. Acknowledgments The authors would like to thank the Scientific Research Fund of Karadeniz Technical University (KTU) for the financial support of this work (Project No. 2009.112.008.3). Additionally, the authors are most grateful to Granitas¸ A.S¸ . stone processing company for supporting this research by providing dimensioned rock samples for the sawing experiments.

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