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Prediction of Performance of Diamond Wire Saw with Respect to Texture Characteristics of Rock / Prognozowanie Wydajności Pracy Strunowej Piły Diamentowej W Odniesieniu Do Charakterystyki Tekstury Skał

Prediction of Performance of Diamond Wire Saw with Respect to Texture Characteristics of Rock /... Arch. Min. Sci., Vol. 57 (2012), No 4, p. 887­900 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/v10267-012-0058-6 N. GHAYSARI*, M. ATAEI*1, F. SERESHKI*, R. MIKAIEL* PREDICTION OF PERFORMANCE OF DIAMOND WIRE SAW WITH RESPECT TO TEXTURE CHARACTERISTICS OF ROCK PROGNOZOWANIE WYDAJNOCI PRACY STRUNOWEJ PILY DIAMENTOWEJ W ODNIESIENIU DO CHARAKTERYSTYKI TEKSTURY SKAL In this study, prediction of production rate in diamond wire saw has been investigated. Performance measurements of diamond wire saw carried out in 7 different quarries of carbonate rocks in Iran. For determination textural properties, rock samples were collected from these quarries. At first, a thin section was prepared for each rock and then 5 digital photographs were taken from each section. After this, all images were digitized using AutoCAD software. Then, area, perimeter, longest diameter and shortest diameter were assigned. According to these parameters, all of the other textural characteristics and texture coefficient were determined too. The correlation between sawing rate and textural characteristics were evaluated using multiple and simple regression analyses. Then developed model was validated by P-value test. It was concluded that area, perimeter, diameter equivalent and index of grain size homogeneity are very effective on production rate. Production rate using diamond wire saw can reliably be predicted using developed model. Keywords: Diamond wire saws, production rate, texture coefficient W pracy prognozowano wydajno pracy strunowej pily diamentowej. Badania wydajnoci prowadzono w 7 kamieniolomach na terenie Iranu, w których wydobywane s skaly wglanowe. W celu okrelenia tekstury skal zebrano próbki wszystkich skal wydobywanych w kamieniolomach. Przygotowano zglady i wykonano 5 fotografii cyfrowych kadej analizowanej próbki. Uzyskane obrazy poddano nastpnie obróbce cyfrowej przy uyciu oprogramowania AutoCAD. Okrelono nastpujce parametry: powierzchnia, obwód, najdlusza i najkrótsza rednica. W oparciu o powysze parametry przeprowadzono analiz tekstury i wyznaczono odpowiednie wspólczynniki. Korelacj pomidzy wydajnoci pracy pily a wlaciwociami powierzchni (tekstur) okrelono przy uyciu prostej regresji liniowej oraz regresji wielokrotnej. Otrzymany model poddano nastpnie walidacji przy pomocy odpowiednich testów statystycznych. Stwierdzono, e pole powierzchni, obwód, równowane rednice oraz wskanik jednorodnoci uziarnienia maj wplyw na wydajno pracy pily. Opracowany model moe by skutecznie wykorzystywany dla wiarygodnego prognozowania postpu prac prowadzonych z wykorzystaniem pily diamentowej. Slowa kluczowe: strunowa pila diamentowa, wydajno pracy, tekstura * 1 SHAHROOD UNIVERSITY OF TECHNOLOGY, SHAHROOD, IRAN Corresponding author: Faculty of Mining Engineering, Petroleum & Geophysics, Shahrood University of Technology, Shahrood, Iran. Address: Shahrood Uni. of Tech., University Ave., Hafte-Tir Square, Shahrood, Iran; E-mail: ataei@shahroodut.ac.ir, Tel./Fax: +98273-3395509 1. Introduction There are several methods for block production in carbonate rocks. Nowadays, diamond wire cutting is a widely used method in carbonate rocks. It is very important that extraction is carried out at minimum cost and high yield of good quality blocks. Therefore prediction of rock sawability is significant in the cost estimation and rate of production. Diamond wire is rotated with the drive wheel movement. Required tension and rotation force for cutting is provided by the movement of a diamond wire saw machine away from the cut surface on the rail. Water is applied with spin direction of the wire as a coolant and as a means of removing the participles. Diamond wire is simply a steel cable on which small beads bonded with abrasive are mounted at a regular interval with spacing material placed between the beads (Figure 1). There are several parameters affecting on diamond wire cutting operation. These parameters are given in Table 1. The beads provide the actual cutting action in diamond wire saw operation. The important point efficient usage of diamond wire cutting is to produce blocks at minimum cost by adjusting to effective cutting parameters adequately. Non-controlled parameters such as physical, mechanical and textural properties should be determined before cutting operation. After determination of non-controlled parameters, it should be possible that efficient cutting should be achieved with adjusting of partially-controlled parameters under consideration of non-controlled (Ozcelik, 2004). Up to now, any serious study has not been done on relation between textural properties and production rate of diamond wire saws. In rock engineering, selection of optimum machine and operation technique mostly depend on textural and mechanical properties. The textural characteristics of rocks significantly affect the mechanical behavior, performance of cutting and drilling equipments. The main textural properties are grain size, shape and orientation, proportion of grain and matrix material. These features resulted in a texture coefficient represented by a single number for each rock specimen (Ersoy, 1995). Rock texture has been defined as "the degree of crystalline, grain size or granularity and the fabric or geometrical relationship between the constituents of a rock" (Williams et al., 1982). In this study, effects of textural properties on production rate in diamond wire saws were investigated. Fig. 1. Typical illustration of diamond wire and cross-section of diamond bead (Ozcelik, 2004) TABLE 1 Parameters affect cutting efficiency in diamond wire cutting method (Ozcelik, 2004) Non-controlled parameters Partially-controlled parameters · · · · · · Rock properties Rock hardness Rock strength Water content Degree of alteration Discontinuities Mineralogical composition and texture · · · · · · · Cutting machine properties Machine power Wire speed Structure of diamond bead Dimension of block Geometry of wire during cutting Vibration of machine Water consumption Operating condition · Technical personal · Used techniques 2. Quantitative analysis of rock texture To study of texture rock, a thin section is prepared and digital photographs are taken from each sample. Individual analysis consisted of selecting a reference area or observation window, containing a number of grains which depend on the size of the grains in rock. Quantitative analysis of texture of rock is done by following parameters: · Area (Ai): It is simplest parameter to evaluate texture of rock. Observed area of each grain in thin section is grain`s area. · Perimeter (Lp): It is showing length of boundary of grain in rock. In fact it is perimeter of grain. · Maximum and minimum diameter: these parameters are so useful that they are always used to study texture of rock. Length and breadth have been defined as being maximum and minimum diameter. These parameters represent the perpendicular distance between two parallel outer tangents to an object. The longest distance is defined as maximum diameter and the shortest distance is defined as minimum diameter. · Diameter equivalent: This parameter introduces grain size. It is obtained by below equation (Petruk, 1986): Dequi = 4 Ai p (1) where, Dequi -- Diameter equivalent (mm), Ai -- Area of grain (mm2); · Compactness: This parameter is as shape of section in grain. It is calculated by below equation: C= where, C -- compactness, Lp -- Perimeter of grain (mm), Ai -- Area of grain (mm2); 2 Lp Ai (2) · Shape factor: At textural observations this parameter is as amount of round of section in grain. It is calculated by below equation: SF = 4p Ai 2 Lp (3) where, SF -- Shape factor, Ai -- Area of grain (mm2), Lp -- Perimeter of grain (mm); · Aspect ratio: It is obtained by dividing maximum diameter to minimum diameter. AR = Dmax Dmin (4) where, AR -- Aspect ratio, Dmax -- Maximum diameter (mm), Dmin -- Minimum diameter (mm); · Interlocking index: at first, this index was presented by Dreyer in 1973. In fact this parameter shows relation between area of grain and part of perimeter that is neighbor with other grain. Actually this index explains complexity of relation between grains. To obtain this index, below equation was presented: g= where, L pi 1 ×å n Ai (5) g -- Interlocking index, n -- Number of grains, Lpi -- Length of grain that is neighbor with other grains (mm), Ai -- Area of grain (mm); · Grain size homogeneity index: This index was presented by Dreyer in 1973. It is introduced as explanation of distribution grain packing in texture of rock. Below equation was presented to obtain index of grain size homogeneity: t= were, Aavg å (Ai - Aavg )2 (6) t -- Grain size homogeneity index, Aavg -- Average of area of grains (mm2), Ai -- Area of grain (mm2); · Texture coefficient: The method of quantitative analysis of geometrical properties of rock particles or rock texture comprises the following component: a. To measure and analyze grain shape. b. To measure and analyze grain elongation (to calculate shape factor and aspect ratio). c. To measure and quantify grain angle (orientation). d. To calculate total grain area to total references area (including matrix) or weighting factors based on the degree of grain packing. The results can be derived from the following formula which was suggested by Howarth and Rowlands in 1987: é ì N0 üù 1 ü ì N1 TC = AW ê í ´ ´ AR 1 ´ AF1 ý ú ý+í N0 + N1 FF0 þ î N0 + N1 êî þú ë û where, TC N0 N1 FFo AR1 AF1 AW -- -- -- -- -- -- -- texture coefficient, Number of grains with aspect ratio less than 2, Number of grains with aspect ratio greater than 2, Arithmetic mean of shape factor of all N0 grains, Arithmetic mean of aspect ratio of N1 grains, Angle factor orientation which were computed for all N1 grains, Area weighting (grain packing density), which calculated: Total grain area within reference are boundary Total area enclosed by the reference area boundary (including matrix area) (7) AW = Angle factor is defined as angle between the maximum diameter and horizon. The maximum value of angle is 180°. Angular orientation of grains was quantified by the development of the angle factor. This factor was only calculated for elongated grains where their aspect ratio was greater than 2. The angle factors AF1 has been calculated by a class weighted system applied to the absolute, acute angular differences (0° < < 90°), between each and every elongated grain (Howarth & Rowlands, 1987). Therefore, for a group of N grains the number of unique angular difference is: N (N - 1) 2 Thus, four grains will have: 3 + 2 + 1 = 6 unique angular difference ( ). The angular differences are grouped into nine classes, each of which is weighted (Table 2). (N ­ 1) + (N ­ 2) + ... + 2 + 1= TABLE 2 Classes and weighting for absolute, acute angular differences (Ersoy, 2004) Number Class range (°) Weighting (i) 0 < DMAX 10 10 < DMAX 20 20 < DMAX 30 30 < DMAX 40 40 < DMAX 50 50 < DMAX 60 60 < DMAX 70 70 < DMAX 80 80 < DMAX 90 The angle factor has been calculated by summing of the class weighting and fractions of the total number of angular differences in each class. é ù ê ú Xi AF = å ê ú i =1 N (N - 1) ê ú ê ú ë û 2 (8) where, AF1 N Xi i -- -- -- -- Angle factor, Total number of elongated grains, Number of angular differences in each class, Weighting factor and class number. 3. Field studies During the field study, 7 marble quarries in West of Iran were visited and the sawing performances of diamond wire saws on their different carbonate rocks were measured. In Iranian mines, usually very similar machines are used. Therefore in the studied quarries many technical features of wire saws machines were nearly same. In this paper properties of wire saws machine are considered to be constant and were not used in the prediction model. Characteristics of wire saws machines which were usually used in Iranian quarries are shown in Table 3. TABLE 3 Operational parameters of wire saws machine Parameter Description Main motor power (KW) Length of wire (m) Linear speed (m/s) Rotator diameter (cm) Beads per meter Bead type 45 65-80 30-35 60 33-36 Special for soft rocks 4. Laboratory studies The most important parameters of rock are its textural characteristics. In this study, in order to evaluation of the effects of texture on production rate in diamond saws wire, a thin section was prepared for each rock and then digital photographs were taken from each section. Then, all images were digitized using Auto CAD software Fig 2. Then area, perimeter, longest diameter and shortest diameter were assigned. After all above stages, relationships between textural characteristics and production rate of rocks have been evaluated and the related mathematical equations have presented. In all sections, basic information has been determined. Table 4 shows them. In respect to basic information, other textural parameters have been determined. Results are shown Fig. 2. Digital format of thin section in Table 5. The results of performance studies (record rates) are given in Table 6. Parameters relevant to texture coefficient have been calculated and results are given in Table 7. TABLE 4 Mean of basic textural information Mine name Perimeter (mm) Area (mm2) Maximum diameter (mm) Minimum diameter (mm) TABLE 5 Textural characteristics for samples Mine name g t SF C Dequi AR TABLE 6 The result of performance studies Mine name Production rate (m2/h) TABLE 7 Texture coefficient derivation determined for rocks Mine name AW N0 N0 + N1 N1 N0 + N1 1 FF0 AR1 AF1 TC 5. Statistical analysis 5.1. Simple regression analysis Performance results and textural characteristics were analyzed using the method of least squares regression. Hourly production values were correlated with the corresponding textural characteristic values. Linear, logarithmic, exponential and power curve fitting approximation equation with the highest correlation coefficient (R2) was determined for each equation (Fig. 3-11). A strong correlation between texture coefficient and production rate was found (Fig 2). The relation follows an exponential function. Hourly production decreases with increase texture coefficient. The equation of curve is: Ph = 54.78e ­1.9TC R 2 = 0.82 (9) where Ph is production per hour (m /h), and TC is texture coefficient. A strong correlation between area of grain and production rate was found (Fig. 3). The relation follows an exponential function. Hourly production decreases with increase area of grain. The equation of curve is: Ph = 11.47e ­2.7A R 2 = 0.84 (10) where Ph is production per hour (m2/h), and A is area of grain. Fig. 3. Relation between production rate and texture coefficient Fig. 4. Relation between production rate and Area of grain Fig. 5. Relation between Production rate and Perimeter of grain Fig. 6. Relation between production rate and Aspect Ratio Fig. 7. Relation between production rate and Diameter equivalent Fig. 8. Relation between production rate and Compactness Fig. 9. Relation between production rate and texture coefficient Fig. 10. Relation between production rate and texture coefficient Fig. 11. Relation between production rate and texture coefficient A strong correlation between perimeter of grain and production rate was found (Fig. 4). The relation follows an exponential function. Hourly production decreases with increase perimeter of grain. The equation of curve is: Ph = 14.84e ­2.7Lp R 2 = 0.79 (11) where Ph is production per hour (m2/h), and Lp is perimeter of grain. A strong correlation between diameter equivalent and production rate was found (Fig. 6). The relation follows an exponential function. Hourly production decreases with increase diameter equivalent. The equation of curve is: Ph = 14.25e ­1.5Dequi R 2 = 0.77 (12) where Ph is production per hour (m2/h), and Dequi is diameter equivalent. A strong correlation between grain size homogeneity and production rate was found (Fig. 10). The relation follows an exponential function. Hourly production decreases with increase grain size homogeneity. The equation of curve is: Ph = 12.49e ­2.13t R 2 = 0.77 (13) where Ph is production per hour (m2/h), and t is grain size homogeneity. Correlations between textural traits are given in Table 8. Respect to this Table, multiple regressions have been done for parameters that have well correlation (more 0.5) at single regression and also correlation between them in above table is less 0.9. Therefore multiple regressions have been done for texture coefficient with area, perimeter, and diameter equivalent and grain size homogeneity. TABLE 8 Correlation between textural traits TC TC Area Perimeter AR Dequi C SF g t Pr Area Perimeter AR Dequi C SF g t Pr 1 0.89 0.88 0.15 0.87 ­0.41 0.41 ­0.3 0.89 ­0.91 1 0.99 ­0.14 0.99 ­0.52 0.53 ­0.44 0.97 ­.091 1 0.15 0.99 ­0.52 0.53 ­0.42 0.97 ­0.88 1 ­0.56 0.59 ­0.49 0.98 ­0.86 1 ­0.98 0.98 0.6 0.23 1 ­0.97 ­0.61 0.31 1 ­0.53 0.26 1 ­0.86 5.2. Multiple regression analysis To present more significant and more practical equation, multiple regression analysis was performed. The regression models including two and three independent variables are shown in Table 9. Equation 6 has the highest determination coefficient and it is the best model to predict production rate. TABLE 9 Results of the multiple regression models Model 1 2 R2 3 Equ. 1 Equ. 2 Equ. 3 Equ. 4 + 17.97 + 20.23 + 20.73 + 20.73 Equ. 5 Equ. 6 Equ. 7 Equ. 8 Equ. 9 Equ. 10 Equ.11 Equ.12 Equ.13 Pr = ­94.32A ­ 6.1TC + 14.63Lp + 7.94 Pr = ­87.44A ­ 5.24TC + 44.83Dequi + 8.89 Pr = ­23.47A ­ 9.25TC + 11.76t + 18.25 Pr = ­10.2Lp ­ 9.41TC + 29.24Dequi + 20.36 Pr = ­2.19Lp ­ 10.46TC + 3.88t + 20.83 Pr = ­4.10Dequi ­ 10.19TC + 0.1t + 20.47 Pr = 36.01Dequi ­ 5.1TC + 4.99Lp ­ 100.48A + 7.26 Pr = 6.47t ­ 6.79TC + 13.75Lp ­ 96.28A + 7.26 Pr = ­7.43t ­ 8.34TC ­ 11.54L +38,37Dequi 19.24 0.1t 6. Model validation Validation of model was carried out by considering the determination coefficient, the t-test, F-test and the plot of observed production versus predicted production. The statistical result of model for Equ. 6 is given in Table 10. The determination coefficient (R2) of the model is higher than 0.95. This value is good, but it does not necessarily identify the valid model. To test the significance of the regressions, analysis of variance was employed. This test follows an F-distribution for the model. 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 that there is a real relationship between dependant and independent variables. Since the computed F-value is greater than tabulated F-value for the model, the null hypothesis is rejected. Therefore it is concluded that the model is valid. The predicted and observed production values for all data are given in Table 11. The predicted production values for these data were plotted against the observed production values and are shown in Fig. 12. The error in predicted values is represented by the distance that each data point plots for the diagonal line. A point lying on the line indicates an exact prediction. In the plots for the model, the points are scattered uniformly about the diagonal line, suggesting that the model is good. It is concluded that the sawing speed for carbonate rocks using diamond wire saws can reliably be predicted using the developed model. TABLE 10 Statistical results for model of Equ. 6 Model Independent variables Coefficient Standard error Standard error of estimate t-value F ratio Tabulated F ratio R2 Adjusted R2 Equ. 6 constant A TC Dequi 8.89 ­87.44 ­5.24 44.83 2.16 ­3.62 ­1.42 3.24 TABLE 11 The predicted and observed values for all data (Equ. 6) Mine Name Observed production (m2/h) Predicted production (m2/h) Fig. 12. The predicted production values VS the observed production values for Equ. 6 7. Conclusion The diamond wire saw is one of the important machines used in carbonate stones extraction. Performance prediction of these saws is important in the cost estimation and the planning of the quarries. A correct estimation of saw ability helps to make the stone sawing more efficient. In this paper the relationship between production rate and textural traits was evaluated using multiple linear regression analysis and estimation model was developed. Are, diameter equivalent and texture coefficient are suggested for the estimation of the saw ability in carbonate rocks. The result shows that production rate has a strong relationship with area of grain, diameter equivalent and texture coefficient. It was concluded that the sawing rate of carbonate rocks using diamond wire saw can reliably be predicted using the developed model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Mining Sciences de Gruyter

Prediction of Performance of Diamond Wire Saw with Respect to Texture Characteristics of Rock / Prognozowanie Wydajności Pracy Strunowej Piły Diamentowej W Odniesieniu Do Charakterystyki Tekstury Skał

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Arch. Min. Sci., Vol. 57 (2012), No 4, p. 887­900 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/v10267-012-0058-6 N. GHAYSARI*, M. ATAEI*1, F. SERESHKI*, R. MIKAIEL* PREDICTION OF PERFORMANCE OF DIAMOND WIRE SAW WITH RESPECT TO TEXTURE CHARACTERISTICS OF ROCK PROGNOZOWANIE WYDAJNOCI PRACY STRUNOWEJ PILY DIAMENTOWEJ W ODNIESIENIU DO CHARAKTERYSTYKI TEKSTURY SKAL In this study, prediction of production rate in diamond wire saw has been investigated. Performance measurements of diamond wire saw carried out in 7 different quarries of carbonate rocks in Iran. For determination textural properties, rock samples were collected from these quarries. At first, a thin section was prepared for each rock and then 5 digital photographs were taken from each section. After this, all images were digitized using AutoCAD software. Then, area, perimeter, longest diameter and shortest diameter were assigned. According to these parameters, all of the other textural characteristics and texture coefficient were determined too. The correlation between sawing rate and textural characteristics were evaluated using multiple and simple regression analyses. Then developed model was validated by P-value test. It was concluded that area, perimeter, diameter equivalent and index of grain size homogeneity are very effective on production rate. Production rate using diamond wire saw can reliably be predicted using developed model. Keywords: Diamond wire saws, production rate, texture coefficient W pracy prognozowano wydajno pracy strunowej pily diamentowej. Badania wydajnoci prowadzono w 7 kamieniolomach na terenie Iranu, w których wydobywane s skaly wglanowe. W celu okrelenia tekstury skal zebrano próbki wszystkich skal wydobywanych w kamieniolomach. Przygotowano zglady i wykonano 5 fotografii cyfrowych kadej analizowanej próbki. Uzyskane obrazy poddano nastpnie obróbce cyfrowej przy uyciu oprogramowania AutoCAD. Okrelono nastpujce parametry: powierzchnia, obwód, najdlusza i najkrótsza rednica. W oparciu o powysze parametry przeprowadzono analiz tekstury i wyznaczono odpowiednie wspólczynniki. Korelacj pomidzy wydajnoci pracy pily a wlaciwociami powierzchni (tekstur) okrelono przy uyciu prostej regresji liniowej oraz regresji wielokrotnej. Otrzymany model poddano nastpnie walidacji przy pomocy odpowiednich testów statystycznych. Stwierdzono, e pole powierzchni, obwód, równowane rednice oraz wskanik jednorodnoci uziarnienia maj wplyw na wydajno pracy pily. Opracowany model moe by skutecznie wykorzystywany dla wiarygodnego prognozowania postpu prac prowadzonych z wykorzystaniem pily diamentowej. Slowa kluczowe: strunowa pila diamentowa, wydajno pracy, tekstura * 1 SHAHROOD UNIVERSITY OF TECHNOLOGY, SHAHROOD, IRAN Corresponding author: Faculty of Mining Engineering, Petroleum & Geophysics, Shahrood University of Technology, Shahrood, Iran. Address: Shahrood Uni. of Tech., University Ave., Hafte-Tir Square, Shahrood, Iran; E-mail: ataei@shahroodut.ac.ir, Tel./Fax: +98273-3395509 1. Introduction There are several methods for block production in carbonate rocks. Nowadays, diamond wire cutting is a widely used method in carbonate rocks. It is very important that extraction is carried out at minimum cost and high yield of good quality blocks. Therefore prediction of rock sawability is significant in the cost estimation and rate of production. Diamond wire is rotated with the drive wheel movement. Required tension and rotation force for cutting is provided by the movement of a diamond wire saw machine away from the cut surface on the rail. Water is applied with spin direction of the wire as a coolant and as a means of removing the participles. Diamond wire is simply a steel cable on which small beads bonded with abrasive are mounted at a regular interval with spacing material placed between the beads (Figure 1). There are several parameters affecting on diamond wire cutting operation. These parameters are given in Table 1. The beads provide the actual cutting action in diamond wire saw operation. The important point efficient usage of diamond wire cutting is to produce blocks at minimum cost by adjusting to effective cutting parameters adequately. Non-controlled parameters such as physical, mechanical and textural properties should be determined before cutting operation. After determination of non-controlled parameters, it should be possible that efficient cutting should be achieved with adjusting of partially-controlled parameters under consideration of non-controlled (Ozcelik, 2004). Up to now, any serious study has not been done on relation between textural properties and production rate of diamond wire saws. In rock engineering, selection of optimum machine and operation technique mostly depend on textural and mechanical properties. The textural characteristics of rocks significantly affect the mechanical behavior, performance of cutting and drilling equipments. The main textural properties are grain size, shape and orientation, proportion of grain and matrix material. These features resulted in a texture coefficient represented by a single number for each rock specimen (Ersoy, 1995). Rock texture has been defined as "the degree of crystalline, grain size or granularity and the fabric or geometrical relationship between the constituents of a rock" (Williams et al., 1982). In this study, effects of textural properties on production rate in diamond wire saws were investigated. Fig. 1. Typical illustration of diamond wire and cross-section of diamond bead (Ozcelik, 2004) TABLE 1 Parameters affect cutting efficiency in diamond wire cutting method (Ozcelik, 2004) Non-controlled parameters Partially-controlled parameters · · · · · · Rock properties Rock hardness Rock strength Water content Degree of alteration Discontinuities Mineralogical composition and texture · · · · · · · Cutting machine properties Machine power Wire speed Structure of diamond bead Dimension of block Geometry of wire during cutting Vibration of machine Water consumption Operating condition · Technical personal · Used techniques 2. Quantitative analysis of rock texture To study of texture rock, a thin section is prepared and digital photographs are taken from each sample. Individual analysis consisted of selecting a reference area or observation window, containing a number of grains which depend on the size of the grains in rock. Quantitative analysis of texture of rock is done by following parameters: · Area (Ai): It is simplest parameter to evaluate texture of rock. Observed area of each grain in thin section is grain`s area. · Perimeter (Lp): It is showing length of boundary of grain in rock. In fact it is perimeter of grain. · Maximum and minimum diameter: these parameters are so useful that they are always used to study texture of rock. Length and breadth have been defined as being maximum and minimum diameter. These parameters represent the perpendicular distance between two parallel outer tangents to an object. The longest distance is defined as maximum diameter and the shortest distance is defined as minimum diameter. · Diameter equivalent: This parameter introduces grain size. It is obtained by below equation (Petruk, 1986): Dequi = 4 Ai p (1) where, Dequi -- Diameter equivalent (mm), Ai -- Area of grain (mm2); · Compactness: This parameter is as shape of section in grain. It is calculated by below equation: C= where, C -- compactness, Lp -- Perimeter of grain (mm), Ai -- Area of grain (mm2); 2 Lp Ai (2) · Shape factor: At textural observations this parameter is as amount of round of section in grain. It is calculated by below equation: SF = 4p Ai 2 Lp (3) where, SF -- Shape factor, Ai -- Area of grain (mm2), Lp -- Perimeter of grain (mm); · Aspect ratio: It is obtained by dividing maximum diameter to minimum diameter. AR = Dmax Dmin (4) where, AR -- Aspect ratio, Dmax -- Maximum diameter (mm), Dmin -- Minimum diameter (mm); · Interlocking index: at first, this index was presented by Dreyer in 1973. In fact this parameter shows relation between area of grain and part of perimeter that is neighbor with other grain. Actually this index explains complexity of relation between grains. To obtain this index, below equation was presented: g= where, L pi 1 ×å n Ai (5) g -- Interlocking index, n -- Number of grains, Lpi -- Length of grain that is neighbor with other grains (mm), Ai -- Area of grain (mm); · Grain size homogeneity index: This index was presented by Dreyer in 1973. It is introduced as explanation of distribution grain packing in texture of rock. Below equation was presented to obtain index of grain size homogeneity: t= were, Aavg å (Ai - Aavg )2 (6) t -- Grain size homogeneity index, Aavg -- Average of area of grains (mm2), Ai -- Area of grain (mm2); · Texture coefficient: The method of quantitative analysis of geometrical properties of rock particles or rock texture comprises the following component: a. To measure and analyze grain shape. b. To measure and analyze grain elongation (to calculate shape factor and aspect ratio). c. To measure and quantify grain angle (orientation). d. To calculate total grain area to total references area (including matrix) or weighting factors based on the degree of grain packing. The results can be derived from the following formula which was suggested by Howarth and Rowlands in 1987: é ì N0 üù 1 ü ì N1 TC = AW ê í ´ ´ AR 1 ´ AF1 ý ú ý+í N0 + N1 FF0 þ î N0 + N1 êî þú ë û where, TC N0 N1 FFo AR1 AF1 AW -- -- -- -- -- -- -- texture coefficient, Number of grains with aspect ratio less than 2, Number of grains with aspect ratio greater than 2, Arithmetic mean of shape factor of all N0 grains, Arithmetic mean of aspect ratio of N1 grains, Angle factor orientation which were computed for all N1 grains, Area weighting (grain packing density), which calculated: Total grain area within reference are boundary Total area enclosed by the reference area boundary (including matrix area) (7) AW = Angle factor is defined as angle between the maximum diameter and horizon. The maximum value of angle is 180°. Angular orientation of grains was quantified by the development of the angle factor. This factor was only calculated for elongated grains where their aspect ratio was greater than 2. The angle factors AF1 has been calculated by a class weighted system applied to the absolute, acute angular differences (0° < < 90°), between each and every elongated grain (Howarth & Rowlands, 1987). Therefore, for a group of N grains the number of unique angular difference is: N (N - 1) 2 Thus, four grains will have: 3 + 2 + 1 = 6 unique angular difference ( ). The angular differences are grouped into nine classes, each of which is weighted (Table 2). (N ­ 1) + (N ­ 2) + ... + 2 + 1= TABLE 2 Classes and weighting for absolute, acute angular differences (Ersoy, 2004) Number Class range (°) Weighting (i) 0 < DMAX 10 10 < DMAX 20 20 < DMAX 30 30 < DMAX 40 40 < DMAX 50 50 < DMAX 60 60 < DMAX 70 70 < DMAX 80 80 < DMAX 90 The angle factor has been calculated by summing of the class weighting and fractions of the total number of angular differences in each class. é ù ê ú Xi AF = å ê ú i =1 N (N - 1) ê ú ê ú ë û 2 (8) where, AF1 N Xi i -- -- -- -- Angle factor, Total number of elongated grains, Number of angular differences in each class, Weighting factor and class number. 3. Field studies During the field study, 7 marble quarries in West of Iran were visited and the sawing performances of diamond wire saws on their different carbonate rocks were measured. In Iranian mines, usually very similar machines are used. Therefore in the studied quarries many technical features of wire saws machines were nearly same. In this paper properties of wire saws machine are considered to be constant and were not used in the prediction model. Characteristics of wire saws machines which were usually used in Iranian quarries are shown in Table 3. TABLE 3 Operational parameters of wire saws machine Parameter Description Main motor power (KW) Length of wire (m) Linear speed (m/s) Rotator diameter (cm) Beads per meter Bead type 45 65-80 30-35 60 33-36 Special for soft rocks 4. Laboratory studies The most important parameters of rock are its textural characteristics. In this study, in order to evaluation of the effects of texture on production rate in diamond saws wire, a thin section was prepared for each rock and then digital photographs were taken from each section. Then, all images were digitized using Auto CAD software Fig 2. Then area, perimeter, longest diameter and shortest diameter were assigned. After all above stages, relationships between textural characteristics and production rate of rocks have been evaluated and the related mathematical equations have presented. In all sections, basic information has been determined. Table 4 shows them. In respect to basic information, other textural parameters have been determined. Results are shown Fig. 2. Digital format of thin section in Table 5. The results of performance studies (record rates) are given in Table 6. Parameters relevant to texture coefficient have been calculated and results are given in Table 7. TABLE 4 Mean of basic textural information Mine name Perimeter (mm) Area (mm2) Maximum diameter (mm) Minimum diameter (mm) TABLE 5 Textural characteristics for samples Mine name g t SF C Dequi AR TABLE 6 The result of performance studies Mine name Production rate (m2/h) TABLE 7 Texture coefficient derivation determined for rocks Mine name AW N0 N0 + N1 N1 N0 + N1 1 FF0 AR1 AF1 TC 5. Statistical analysis 5.1. Simple regression analysis Performance results and textural characteristics were analyzed using the method of least squares regression. Hourly production values were correlated with the corresponding textural characteristic values. Linear, logarithmic, exponential and power curve fitting approximation equation with the highest correlation coefficient (R2) was determined for each equation (Fig. 3-11). A strong correlation between texture coefficient and production rate was found (Fig 2). The relation follows an exponential function. Hourly production decreases with increase texture coefficient. The equation of curve is: Ph = 54.78e ­1.9TC R 2 = 0.82 (9) where Ph is production per hour (m /h), and TC is texture coefficient. A strong correlation between area of grain and production rate was found (Fig. 3). The relation follows an exponential function. Hourly production decreases with increase area of grain. The equation of curve is: Ph = 11.47e ­2.7A R 2 = 0.84 (10) where Ph is production per hour (m2/h), and A is area of grain. Fig. 3. Relation between production rate and texture coefficient Fig. 4. Relation between production rate and Area of grain Fig. 5. Relation between Production rate and Perimeter of grain Fig. 6. Relation between production rate and Aspect Ratio Fig. 7. Relation between production rate and Diameter equivalent Fig. 8. Relation between production rate and Compactness Fig. 9. Relation between production rate and texture coefficient Fig. 10. Relation between production rate and texture coefficient Fig. 11. Relation between production rate and texture coefficient A strong correlation between perimeter of grain and production rate was found (Fig. 4). The relation follows an exponential function. Hourly production decreases with increase perimeter of grain. The equation of curve is: Ph = 14.84e ­2.7Lp R 2 = 0.79 (11) where Ph is production per hour (m2/h), and Lp is perimeter of grain. A strong correlation between diameter equivalent and production rate was found (Fig. 6). The relation follows an exponential function. Hourly production decreases with increase diameter equivalent. The equation of curve is: Ph = 14.25e ­1.5Dequi R 2 = 0.77 (12) where Ph is production per hour (m2/h), and Dequi is diameter equivalent. A strong correlation between grain size homogeneity and production rate was found (Fig. 10). The relation follows an exponential function. Hourly production decreases with increase grain size homogeneity. The equation of curve is: Ph = 12.49e ­2.13t R 2 = 0.77 (13) where Ph is production per hour (m2/h), and t is grain size homogeneity. Correlations between textural traits are given in Table 8. Respect to this Table, multiple regressions have been done for parameters that have well correlation (more 0.5) at single regression and also correlation between them in above table is less 0.9. Therefore multiple regressions have been done for texture coefficient with area, perimeter, and diameter equivalent and grain size homogeneity. TABLE 8 Correlation between textural traits TC TC Area Perimeter AR Dequi C SF g t Pr Area Perimeter AR Dequi C SF g t Pr 1 0.89 0.88 0.15 0.87 ­0.41 0.41 ­0.3 0.89 ­0.91 1 0.99 ­0.14 0.99 ­0.52 0.53 ­0.44 0.97 ­.091 1 0.15 0.99 ­0.52 0.53 ­0.42 0.97 ­0.88 1 ­0.56 0.59 ­0.49 0.98 ­0.86 1 ­0.98 0.98 0.6 0.23 1 ­0.97 ­0.61 0.31 1 ­0.53 0.26 1 ­0.86 5.2. Multiple regression analysis To present more significant and more practical equation, multiple regression analysis was performed. The regression models including two and three independent variables are shown in Table 9. Equation 6 has the highest determination coefficient and it is the best model to predict production rate. TABLE 9 Results of the multiple regression models Model 1 2 R2 3 Equ. 1 Equ. 2 Equ. 3 Equ. 4 + 17.97 + 20.23 + 20.73 + 20.73 Equ. 5 Equ. 6 Equ. 7 Equ. 8 Equ. 9 Equ. 10 Equ.11 Equ.12 Equ.13 Pr = ­94.32A ­ 6.1TC + 14.63Lp + 7.94 Pr = ­87.44A ­ 5.24TC + 44.83Dequi + 8.89 Pr = ­23.47A ­ 9.25TC + 11.76t + 18.25 Pr = ­10.2Lp ­ 9.41TC + 29.24Dequi + 20.36 Pr = ­2.19Lp ­ 10.46TC + 3.88t + 20.83 Pr = ­4.10Dequi ­ 10.19TC + 0.1t + 20.47 Pr = 36.01Dequi ­ 5.1TC + 4.99Lp ­ 100.48A + 7.26 Pr = 6.47t ­ 6.79TC + 13.75Lp ­ 96.28A + 7.26 Pr = ­7.43t ­ 8.34TC ­ 11.54L +38,37Dequi 19.24 0.1t 6. Model validation Validation of model was carried out by considering the determination coefficient, the t-test, F-test and the plot of observed production versus predicted production. The statistical result of model for Equ. 6 is given in Table 10. The determination coefficient (R2) of the model is higher than 0.95. This value is good, but it does not necessarily identify the valid model. To test the significance of the regressions, analysis of variance was employed. This test follows an F-distribution for the model. 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 that there is a real relationship between dependant and independent variables. Since the computed F-value is greater than tabulated F-value for the model, the null hypothesis is rejected. Therefore it is concluded that the model is valid. The predicted and observed production values for all data are given in Table 11. The predicted production values for these data were plotted against the observed production values and are shown in Fig. 12. The error in predicted values is represented by the distance that each data point plots for the diagonal line. A point lying on the line indicates an exact prediction. In the plots for the model, the points are scattered uniformly about the diagonal line, suggesting that the model is good. It is concluded that the sawing speed for carbonate rocks using diamond wire saws can reliably be predicted using the developed model. TABLE 10 Statistical results for model of Equ. 6 Model Independent variables Coefficient Standard error Standard error of estimate t-value F ratio Tabulated F ratio R2 Adjusted R2 Equ. 6 constant A TC Dequi 8.89 ­87.44 ­5.24 44.83 2.16 ­3.62 ­1.42 3.24 TABLE 11 The predicted and observed values for all data (Equ. 6) Mine Name Observed production (m2/h) Predicted production (m2/h) Fig. 12. The predicted production values VS the observed production values for Equ. 6 7. Conclusion The diamond wire saw is one of the important machines used in carbonate stones extraction. Performance prediction of these saws is important in the cost estimation and the planning of the quarries. A correct estimation of saw ability helps to make the stone sawing more efficient. In this paper the relationship between production rate and textural traits was evaluated using multiple linear regression analysis and estimation model was developed. Are, diameter equivalent and texture coefficient are suggested for the estimation of the saw ability in carbonate rocks. The result shows that production rate has a strong relationship with area of grain, diameter equivalent and texture coefficient. It was concluded that the sawing rate of carbonate rocks using diamond wire saw can reliably be predicted using the developed model.

Journal

Archives of Mining Sciencesde Gruyter

Published: Dec 1, 2012

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