Rock Mech. Rock Engng. (2007) 40 (5), 505–517 DOI 10.1007/s00603-006-0110-y Printed in The Netherlands
Technical Note Performance Prediction of Circular Diamond Saws from Mechanical Rock Properties in Cutting Carbonate Rocks By 1
M. Fener , S. Kahraman2 , and M. O. Ozder1 1
Geological Engineering Department, University of Nigde, Nigde, Turkey 2 Mining Engineering Department, University of Nigde, Nigde, Turkey Received April 28, 2005; accepted July 25, 2006 Published online October 17, 2006 # Springer-Verlag 2006
Keywords: Rock sawability, diamond saws, mechanical rock properties, statistical analysis.
1. Introduction Large-diameter circular diamond saw is one of the principal machines used for the slab production in stone processing plants. The prediction of rock sawability is important in the cost estimation and the planning of the plants. Rock sawability depends on machine characteristics, type and diameter of saw, depth of cut, rate of sawing and toolwear, and rock properties. Although some researchers (Burgess, 1978; Wright and Cassapi, 1985; Ceylanoglu and Gorgulu, 1997; Brook, 2002; Wei et al., 2003; Gunaydin et al., 2004; Kahraman et al., 2004; Delgado et al., 2005) have studied the relations between sawability and rock properties, none of them investigated the correlations between sawability and mechanical rock properties, such as compressive strength and tensile strength. Recently, Kahraman et al. (2005) derived artificial neural networks models for the sawability prediction of carbonate rocks with large-diameter circular saws from shear strength parameters and compared with simple and multiple regression models. They concluded that applicability of artificial neural networks for the sawability prediction is more reliable than the statistical models. The main objective of this study is to investigate the possibility of estimating the sawability of carbonate rocks from some mechanical rock properties. For this purpose, hourly production of circular saws was firstly correlated with rock properties and then, multiple regression analysis was performed.
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2. Field Studies Marble factories in Kayseri, Konya and Antalya areas of Turkey were visited and the sawing performances of large-diameter circular saws were measured on eight different carbonate rocks. Performance studies were carried out on the machines operating approximately in same conditions. The diameter and the round per minute of the saw in cutting, the advancing rate of the saw, the depth of the cut, the dimensions of the slabs, the number of slabs cut per hour etc. were recorded in the performance forms (Table 1) during performance studies. The round per minute of the saws was measured with a stroboscope produced by Bamberg þ Bormann-Electronics Company. Factory names, the locations and the names of the rocks sawed and hourly slab productions are given in Table 2.
3. Laboratory Studies Rock blocks were collected from the factories for laboratory tests. An attempt was made to collect rock samples that were large enough to obtain all of the test specimens of a given rock type from the same piece. Each block sample was inspected for Table 1. The performance form for observation number 1 Observation number Date Factory name Factory location Machine model Saw diameter Saw model Rotational speed of saw Advancing rate of saw Motor current for saw Rock type Rock location Slab dimension Slab number cut in per hour Hourly slab production
1 25 October 2003 Kamer Mermer Kayseri (Turkey) MKS-four footed 1200 mm Sonmak 2418 rpm 2.3 cm=s 105 A Dolomitic limestone Yahyali=Kayseri 135 30 cm 26.5 10.7 m2 =h
Table 2. The results of performance studies Factory name and location
Rock location
Rock type
Slab production (m2 =h)
Kamer Mermer=Kayseri Derinkok Mermer=Kayseri Toros Mermer=Kayseri Akmeras° Mermer=Konya Model Mermer=Antalya Kombassan Mermer=Konya Kombassan Mermer=Konya Kombassan Mermer=Konya
Yahyali=Kayseri Bunyan=Kayseri Yildizeli=Sivas Godene=Konya Bucak=Burdur Karaman Sogutalan=Bursa Mut=Icel
Dolomitic limestone Limestone (Bunyan rose) Travertine Travertine Travertine (Limra) Travertine Limestone (Bursa beige) Travertine
10.7 13.2 12.5 17.4 19.6 18.7 13.5 16.8
Saw diameter: 1200–1400 mm; rotational speed of saw: 2200–2600 rpm; advancing rate of saw: 2.2–2.8 cm=s; depth of cut: 30 cm.
Performance Prediction of Circular Diamond Saws from Mechanical Rock Properties 507 Table 3. The results of laboratory tests Rock location
Rock type
Uniaxial compressive strength (MPa)
Brazilian tensile strength (MPa)
Schmidt hammer value
Point load strength (MPa)
Impact strength (%)
Los Angeles abrasion loss (%)
P-wave velocity (km=s)
Yahyali= Kayseri Bunyan= Kayseri Yildizeli=Sivas Godene=Konya Bucak= Burdur Karaman Bursa
Dolomitic limestone Limestone (Bunyan rose) Travertine Travertine Travertine (Limra) Travertine Limestone (Bursa beige) Travertine
136.7
10.2
58.5
6.5
81.4
25.0
6.1
175.0
7.4
57.7
7.1
86.6
24.7
6.0
83.3 45.4 50.3
5.8 4.6 2.8
51.2 57.0 38.9
5.2 4.8 3.0
76.4 75.2 71.3
31.4 40.1 75.9
5.4 5.4 3.7
50.3 128.8
4.1 5.6
54.7 59.7
4.5 5.4
76.5 78.8
39.0 33.3
5.4 6.1
60.0
2.2
35.2
1.6
66.6
61.9
4.0
Mut=Icel
macroscopic defects so that it would provide test specimens free from fractures, partings or alteration zones. Then, standard test samples were prepared from these block samples, and uniaxial compressive strength, Brazilian tensile strength, Schmidt hammer, point load, impact strength, Los Angeles (LA) abrasion and sound velocity tests were conducted. The summaries of the test results are given in Table 3.
3.1 Uniaxial Compressive Strength Uniaxial compression tests were performed on trimmed core samples, which had a diameter of 38 mm and a length-to-diameter ratio of 2. The stress rate was applied within the limits of 0.5–1.0 MPa=s.
3.2 Brazilian Tensile Strength Brazilian tensile strength tests were conducted on core samples having a diameter of 38 mm and a height to diameter ratio of 1. The tensile load on the specimen was applied continuously at a constant stress rate such that failure will occur within 5 min of loading.
3.3 Schmidt Hammer Test Schmidt hammer tests were carried out on the test samples having an approximate dimension of 30 30 20 cm. The tests were performed with an N-type hammer having impact energy of 2.207 Nm. All tests were conducted with the hammer held vertically downwards and at right angle to the horizontal rock surface. In the tests, ISRM (Brown, 1981) method was applied for each rock type. ISRM suggested that twenty rebound values from single impacts separated by at least a plunger diameter should be recorded and averaged the upper ten values. The test was repeated at least three times on any rock type and average value was recorded as Schmidt hammer value.
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3.4 Point Load Test The diametral point load test was carried out on cores having a diameter of 38 mm. The core specimens had a length-to-diameter ratio of 1.2. For testing, a specimen was positioned between the platens, taking care that the minimum distance to either end was 0.5 times the core diameter. The load on the sample was then increased to failure with the maximum load being recorded. The calculated point load strength was corrected to a specimen diameter of 50 mm according to the method proposed by ISRM (1985). 3.5 Impact Strength Test The device designed by Evans and Pomeroy (1966) was used in the impact strength test. A 100 g sample of rock in the size range 3.175–9.525 mm was placed inside a cylinder of 42.86 mm diameter and a 1.8 kg weight dropped 20 times from a height of 30.48 cm onto the rock sample. The amount of rock remaining in the initial size range after the test is termed as the impact strength index. 3.6 Los Angeles Abrasion Test ASTM method C 131 was used for the LA abrasion test. Test samples were oven-dried at 105–110 C for 24 hr and then cooled to room temperature before they were tested. There are four aggregate sizes grading to choose from in the ASTM method. Grading D was used in the tests. Six steel spheres were placed in a steel drum along with approximately 5000 g aggregate sample and the drum was rotated for 500 revolutions at a rate of 30–33 rev=min. After the revolution was complete, the sample was sieved through the No. 12 sieve (1.7 mm). The amount of material passing the sieve, expressed as a percentage of the original weight, is the LA abrasion loss or percentage loss. 3.7 Sound Velocity Test P-wave velocities were measured on cores having a diameter of 54 mm and a length of 110 mm. End surfaces of the core samples were polished sufficiently smooth and plane to provide good coupling. In the tests, the E48 Pulse Generator Unit made by Controls and two transducers (a transmitter and a receiver) having a frequency of 54 kHz were used. 4. Statistical Analysis 4.1 Simple Regression Analysis Performance results and rock properties were analysed using the method of least squares regression. Hourly production values were correlated with the corresponding rock property values. Linear, logarithmic, exponential and power curve fitting approximations were tried and the best approximation equation with the highest correlation coefficient was determined for each regression.
Performance Prediction of Circular Diamond Saws from Mechanical Rock Properties 509
Fig. 1. Production versus uniaxial compressive strength
A strong correlation between hourly production and compressive strength was found (Fig. 1). The relation follows a logarithmic function. Hourly production decreases with increasing compressive strength. The equation of the curve is: Ph ¼ 5:22 ln c þ 38:23;
R2 ¼ 0:73;
ð1Þ
where Ph is the production, m2=h, and c is the uniaxial compressive strength, MPa. Hourly production strongly correlated with Brazilian tensile strength (Fig. 2). The relation follows an exponential function. Hourly production decreases with increasing tensile strength. The equation of the curve is: Ph ¼ 22:23e0:074t ;
R2 ¼ 0:77;
where Ph is the production, m2=h, and t is the Brazilian tensile strength, MPa.
Fig. 2. Production versus tensile strength
ð2Þ
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Fig. 3. Production versus Schmidt hammer value
A weak correlation between hourly production and Schmidt hammer value was found (Fig. 3). The equation of the line is: Ph ¼ 0:19Rn þ 24:2;
R2 ¼ 0:29;
ð3Þ
2
where Ph is the production, m =h, and Rn is the Schmidt hammer value. The main reason behind the weakness of the correlation is probably that the Schmidt hammer values of different rocks tested in this study are very similar. Most of the Schmidt hammer values fall within the range of 51.2–58.5. If a wider range of Schmidt hammer values is included in the study, the correlation may be improved. There is a significant correlation between hourly production and point load strength (Fig. 4). The relation follows an exponential function. Hourly production decreases with increasing point load strength. The equation of the curve is: Ph ¼ 22:57e0:086Is ;
R2 ¼ 0:50;
2
where Ph is the hourly production, m =h, and Is is the point load strength, MPa.
Fig. 4. Production versus point load strength
ð4Þ
Performance Prediction of Circular Diamond Saws from Mechanical Rock Properties 511
Fig. 5. Production versus impact strength
Fig. 6. Production versus Los Angeles abrasion loss
The correlation between hourly production and impact strength index is weak (Fig. 5). The equation of the curve is: Ph ¼ 85:19e0:023ISI ;
R2 ¼ 0:40;
ð5Þ
2
where Ph is the production, m =h, and ISI is the impact strength index, %. A strong correlation between hourly production and LA abrasion loss was found (Fig. 6). The relation follows a logarithmic function. Hourly production increases with increasing abrasion loss. The equation of the curve is: Ph ¼ 6:61 ln LA 8:83;
R2 ¼ 0:68;
ð6Þ
2
where Ph is the hourly production, m =h, and LA is the LA abrasion loss, %. There is a significant correlation between hourly production and P-wave velocity (Fig. 7). The relation follows a linear function. Hourly production decreases with increasing P-wave velocity. The equation of the line is: Ph ¼ 2:51Vp þ 28:49;
R2 ¼ 0:52;
where Ph is the production, m2=h, and Vp is the P-wave velocity, km=s.
ð7Þ
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Fig. 7. Production versus P-wave velocity
4.2 Multiple Regression Analysis To produce more significant and more practical equations, multiple regression analysis was performed using a computing package called Statgraphics V.5. The regression model including all independent variables is: Ph ¼ 38:8 0:02c 0:02t þ 0:7Rn 4:9Is þ 1:2ISI 0:08LA 8:1Vp ; R2 ¼ 1; ð8Þ where Ph is the production, m2=h, c is the uniaxial compressive strength, MPa, t is the Brazilian tensile strength, MPa, Rn is the Schmidt hammer value, Is is the point load strength, MPa, ISI is the impact strength index, %, LA is the LA abrasion loss, %, and Vp is the P-wave velocity, km=s. Although Eq. (8) has the highest possible correlation coefficient, this equation is not useful due to the complexity and impracticality. To develop simple and practical equations, multiple regression analysis including two and three variables was carried out. For practical considerations, the following three equations were selected among the all possible equations: Ph ¼ 28:21 þ 0:69Rn 8:92Vp ;
R2 ¼ 0:81;
ð9Þ
Ph ¼ 23:67 þ 0:72Rn 1:03Is 7:72Vp ;
R2 ¼ 0:86;
ð10Þ
Ph ¼ 32:59 þ 0:67Rn 0:09ISI 8:5Vp ;
R2 ¼ 0:81;
ð11Þ
where Ph is the production, m2=h, Rn is the Schmidt hammer value, Vp is the P-wave velocity, km=s, Is is the point load strength, MPa, and ISI is the impact strength index, %. Equations (9), (10) and (11) were derived from Schmidt hammer, point load, impact strength and sound velocity tests. These tests are easy to use, practical and economical. Also, they are portable and can be used in the field.
Independent variables
Constant Schmidt ham. value P-wave velocity
Constant Schmidt ham. value Point load strength P-wave velocity
Constant Schmidt ham. value Impact strength P-wave velocity
Model
Eq. (9)
Eq. (10)
Eq. (11)
32.59 0.67 0.09 8.50
23.67 0.72 1.03 7.72
28.21 0.69 8.92
Coefficient
11.37 0.27 0.23 2.87
4.97 0.23 0.81 2.50
3.67 0.24 2.46
Standard error
1.85
1.59
1.69
Standard error of estimate
2.87 2.51 0.41 2.96
4.76 3.08 1.27 3.09
7.69 2.72 3.63
t-value
2.02
2.02
1.94
Tabulated t-value
5.81
8.29
10.34
F-ratio
5.79
5.79
5.99
Tabulated F-ratio
Table 4. Statistical results of the selected multiple regression models
0.81
0.86
0.81
Correlation coefficient (R2)
0.67
0.76
0.73
Adjusted correlation coefficient (R2adj )
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4.2.1 Confirmation of the Models Confirmation of the selected models (Eqs. (9), (10) and (11)) were done by considering correlation coefficient, the F-test, the t-test, residuals analysis and the plots of predicted versus observed values. The statistical results of the three models are given in Table 4. The correlation coefficients (R2) of Eqs. (9), (10), and (11) are 0.81, 0.86, and 0.81, respectively. These values are good, but they do not necessarily identify the valid model. The significance of R2-values can be determined by the t-test, assuming that both variables are normally distributed and the observations are chosen randomly. The test compares computed t-value with tabulated t-value using the null hypothesis. In this test, a 95% level of confidence was chosen. If the computed t-value is greater than the tabulated t-value, the null hypothesis is rejected. This means that r is significant. If the computed t-value is less than the tabulated t-value, the null hypothesis is not rejected. In this case, r is not significant. Since a 95% confidence level was chosen in this test, a corresponding critical t-value 1.94 for Eq. (9) and 2.02 for Eqs. (10) and (11), respectively, were obtained. As it is seen in Table 4, the computed t-values are greater than the tabulated t-values for Eq. (9). However, one of the t-values for Eqs. (10) and (11) is lower than the tabulated t-values, indicating some doubt, about the models. To test the significance of regressions, analysis of variance was employed. This test follows an F-distribution with degrees of freedom 1 ¼ 1 and 2 ¼ 6 for Eq. (9) and 1 ¼ 2 and 2 ¼ 5 for Eqs. (10) and (11), so that the critical region will consist of values exceeding 5.99 and 5.79, respectively. In this test, a 95% level of confidence was chosen. If the computed F-value is greater than the tabulated F-value, the null hypothesis is rejected and there is a real relation between dependent and independent variables. Since the computed F-values are greater than the tabulated F-values, the null hypothesis is rejected. Therefore, it is concluded that the model is valid. To check the assumptions of the models, residual analysis was used. The residuals are the difference between the real and the estimated data. The symmetric distribution of the residuals about the zero line verifies the correctness of the model. It was shown that the plots of the residuals versus individual independent variables of the three models indicated nearly symmetrical distribution about the zero line. To see the estimation capability of the derived equations, the scatter diagrams of the observed and estimated values can be plotted. Ideally, on a plot of observed versus estimated value, the points should be scattered around the 1:1 diagonal straight line. A point lying on the line indicates an exact estimation. A systematic deviation from this line may indicate, for example, that larger errors tend to accompany larger estimations, suggesting non-linearity in one or more variables. The plots of estimated versus observed values for the three equations are shown in Figs. 8, 9 and 10, respectively. In the plots for the Eqs. (10) and (11) (Figs. 9 and 10) the points are scattered uniformly about the diagonal line, suggesting that the models are reasonable. However, the points in the plot for Eq. (9) (Fig. 8) deviate somewhat from the diagonal line, showing that there may be some doubts about the model. Although there is some doubt, about Eqs. (10) and (11) (Figs. 9 and 10) according to t-test, the prediction capability of these equations is stronger than Eq. (9).
Performance Prediction of Circular Diamond Saws from Mechanical Rock Properties 515
Fig. 8. Estimated production versus observed production for Eq. (9)
Fig. 9. Estimated production versus observed production for Eq. (10)
Fig. 10. Estimated production versus observed production for Eq. (11)
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4.2.2 Generalization of the Models The derived equations in this study are valid for 1200–1400 mm saw diameter, 2200– 2600 rpm rotational speed of saw, 2.2–2.8 cm=s advancing rate of saw and 30 cm depth of cut. These equations can be generalized using the relations presented by Ersoy and Atici (2004). They recently examined the influence of operational variables on the performance characteristics of circular diamond saws. They correlated the specific cutting energy with operational variables and found valuable relations. They also found strong correlations between the cutting rate, which is the area cut per unit time, and the specific cutting energy. 5. Conclusions The sawing performances of large-diameter circular saws and some properties of carbonate rocks were evaluated using simple and multiple regression analysis. Simple regression analysis shows that compressive strength, tensile strength and LA abrasion loss exhibit strong correlation with production. For practical considerations, some models were selected among the numerous multiple regression models. These models include index tests, such as Schmidt hammer, point load, impact strength and sound velocity tests. These index tests are practical, economical and suitable for field use. It is therefore concluded that sawability of carbonate rocks can reliably be predicted from compressive strength, tensile strength and LA abrasion loss using simple regression equations. However, selected multiple regression models have the advantages of using index tests. Acknowledgement Authors are deeply grateful to Nigde University Research Fund for the financial support. This work has been partially supported by the Turkish Academy of Sciences, in the framework of the Young Scientist Award Program (EA-TUBA-GEBIP=2001-1-1). The authors also wish to acknowledge to Kamer Mermer, Derinkok Mermer, Toros Mermer, Akmeras Mermer, Kombassan Mermer, Antalya Mermer, Model Mermer, Derinoglu Mermer and Detay Mermer due to providing facilities for the performance measurements.
References Brook, B. (2002): Principles of diamond tool technology for sawing rock. Int. J. Rock Mech. Min. Sci. 39, 41–58. Brown, E. T. (ed.) (1981): ISRM Suggested Methods. Rock characterization testing and monitoring. Pergamon Press, Oxford. Burgess, R. B. (1978): Circular sawing granite with diamond saw blades. In: Proc., 5th Industrial Diamond Seminar, 3–10. Ceylanoglu, A., Gorgulu, K. (1997): The performance measurement results of stone cutting machines and their relations with some material properties. In: Strakos, V., Kebo, V., Farana, L., Smutny, L. (eds.) Proc., 6th Int. Symp. on Mine Plann. and Equip. Selection. Balkema, Rotterdam, pp 393–398.
Performance Prediction of Circular Diamond Saws from Mechanical Rock Properties 517 Delgado, N. S., Rodriguez-Rey, A., Rio, L. M. S., Sarria, I. D., Calleja, L., Argandona, V. G. R. (2005): The influence of microhardness on the sawability of Pink Porrino granite (Spain). Int. J. Rock Mech. Min. Sci. 42, 161–166. Evans, I., Pomeroy, C. D. (1966): The strength fracture and workability of coal. Pergamon Press, Oxford. Gunaydin, O., Kahraman, S., Fener, M. (2004): Sawability prediction of carbonate rocks from brittleness indexes. J. S. Afr. Inst. Min. Metallurgy 104, 239–243. ISRM (1985): Suggested method for determining point load strength. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 22(2), 53–69. Kahraman, S., Fener, M., Gunaydin, O. (2004): Predicting the sawability of carbonate rocks using multiple curvilinear regression analysis. Int. J. Rock Mech. Min. Sci. 41, 1123–1131. Kahraman, S., Altun, H., Tezekici, B. S., Fener, M. (2005): Sawability prediction of carbonate rocks from shear strength parameters using artificial neural networks. Int. J. Rock Mech. Min. Sci. 43(1), 157–164. Wie, X., Wang, C. Y., Zhou, Z.-H. (2003): Study on the fuzzy ranking of granite sawability. J. Mater. Process. Techn. 139, 277–280. Wright, D. N., Cassapi, V. B. (1985): Factors influencing stone sawability. Ind. Diamond Rev. 2, 84–87. Authors’ address: Dr. S. Kahraman, Mining Engineering Department, University of Nigde, 51100 Nigde, Turkey; e-mail:
[email protected]
