Open access peer-reviewed chapter

Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine

By Gencay Sariisik

Submitted: September 20th 2018Reviewed: March 4th 2019Published: May 23rd 2019

DOI: 10.5772/intechopen.85622

Downloaded: 167

Abstract

This study used a four-axis computer controlled machine to determine the cutting forces (Cf), specific cutting energy (Sc) and specific energy (Se) affecting the processability of natural rocks. A total of 17 types of natural rocks were categorized according to their geological formations. This study consisted of three parts: (1) experimental measurement of the Cf resulting from processing natural rocks using a 6.0-mm diameter end mill cutting tool and a four-axis machine; (2) calculation of Cf, Sc and Se values; and (3) statistical analysis of the parameters. In terms of Cf, Sc and Se values, a statistically significant difference (P < 0.001) was observed among a depth of cut (dp) and feed speed (Va). It was found that the parameters that affected the processability of natural rocks were dp and Va. Accordingly, the processability of natural rocks processing type, dp and Va was found that affected. Simple linear regression was performed to examine the relationship between physicomechanical properties, and between Cf, Se and Sc values. As a result, regression equations were developed in consideration of the physicomechanical properties of natural rocks and the Cf, Sc and Se equation for the prediction of the efficiency of computer numerical control (CNC) machines.

Keywords

  • natural rock
  • CNC machine
  • efficiency
  • Cf
  • Sc
  • Se

1. Introduction

Natural stone industry is one of the most effective actors of the Turkish mining industry economy. With its 4000-year history of natural stone production, Turkey is one of the oldest natural stone producers in the world. Natural stones are classified as metamorphic, sedimentary and magmatic according to their formations [1]. Marble is a metamorphic rock formed by recrystallization of limestone. Marble is a metamorphic stone composed of calcite (CaCO3) and formed as a result of the recrystallization of the limestone under excessive pressure and heat [2, 3, 4, 5, 6]. CNC machines are electromechanical systems that process the materials according to the logical operation unit of numerical control (NC) codes defined by numbers, letters, and symbols of a product designed using a computer-aided design and manufacturing (CAD/CAM) program. Nowadays, 3D design in the natural stone industry can be processed with high accuracy, precision series and quality the use of CNC machine [7, 8]. Various processing technologies are used at natural stone quarries and factories to manufacture as building materials. In quarries, in the production of natural stone blocks, diamond wire cutting and chain arm cutting machines are widely used in factories, plates and panels manufacturing in the production of block cutter ST and gangsaw machines [9, 10, 11, 12, 13, 14, 15, 16, 17, 18].

CNC machine is used to process natural stone blocks and wastes in 3D design products to be used in buildings. Many studies have been found on the Cf in circular saws depending on the physicomechanical properties of natural rocks, modeling of the Se and socket [19, 20, 21, 22, 23], the definition of the theoretical chip geometry [24], and connections between tangential cutting force and chip thickness [25, 26, 27]. Some other studies address the effect of processing parameters on tool wear [28, 29, 30, 31], the modeling of natural stone cutting with diamond cutting tools [32] and specific grinding energy of chip samples under a scanning microscope [33] in order to determine specific cutting energy and power consumption [34, 35]. Energy and the type of cutting mechanism used in the production of end products from natural rocks lead to the wear of cutting tools. Energy consumption and wear of cutting edges are the important factors affecting processing costs. These factors should be efficiently to reduce processing costs. It is therefore important to determine the cutting performance of natural rocks according to their characteristics. Cut tools should be selected carefully and performance forecast should be proper in order to improve the processing efficiency of natural rocks and reduce costs. Different from the manufacture of plates and panels in which gangsaw and cutter ST are deep cut on the x (length), z (depth) axis, this process requires few depth cut and precision tools with a CNC machine on the x (length), y (width) and z (depth) axis. Cf, Sc and wear of diamond cut tools have a low spindle and Va in the processability of rocks in the CNC machine with internally cooled cut tools. Carbide coated end mills tools are widely used in the natural stones sectors. In addition, the number of studies on parameters affecting the processability of natural rocks in the CNC machine is less [36, 37, 38, 39, 40].

This study investigated the relationship between the values of the Cf, Se and Sc obtained from the processing of rocks using CNC, and related parameters (i.e., cutting parameters and physicomechanical properties). Cf, Se and Sc values depending on the dp and Va of natural rocks have been analyzed (ANOVA) statistically. Results show that 1.0, 1.2 and 1.6 mm at the dp and 2000, 2500, 3000 mm/min at the Va are important cutting parameters in the processability of natural rocks. Regression models were developed for the estimation of Cf, Se and Sc of the with measured by power and load meter tester. Regression analyses were performed to determine the optimum relationship between the Cf, Se and Sc dependent variable and physicomechanical properties independent variable in three different groups of natural rocks. Regression models developed in this study can be used by planners and natural stone manufacturing companies for cost analysis and mill cut tool processing programs in natural rocks. We recommend that it be considered in further studies use a larger database to analyze the possibility of regression analyses the Cf, Se and Sc any of the physico-mechanical parameters of natural rocks.

2. Materials and method

2.1 Materials

These natural rock samples were obtained from the companies operating a quarry in Afyon. The surface of each series was adjusted with the cutting process as a square (30 by 30-cm) and 1 cm thickness. Furthermore, these rock samples were polished on one side. Table 1 shows sample code, pertographic name, dimensions, main modal compositions, sample number and surface processing of the rocks used in the test.

Natural rocksSample codePertographic nameMain modal compositionsDimensions (mm)NSurface processing
TravertineT1-T5SedimentaryCalcite300 × 300 × 3015Polished
MarbleM1-M7MetamorphicCalcite300 × 300 × 3015Polished
LimestoneK1-K5SedimentaryCalcite300 × 300 × 3015Polished

Table 1.

Characteristics of natural rocks used in experimental tests.

Cut tool (carbide-coated end-mill cutting edge tool) was used in the processing of natural rocks by CNC machine. Figure 1 shows the image of the end mill cut tool. Table 2 shows the technical specifications of the end mill cut tool.

Figure 1.

Image of the end mill cutting edge tool.

Technical propertiesUnitValues
CodeMFR-6
Cutting tool diameter/d1mm6
Stem diameter/d2mm6
Cutting length/l2mm25
End length/l1mm76
Milling end36,677
Edge number4
Helix angle(°)25

Table 2.

Technical properties of end-mill cutting edge tool.

2.2 Method

Figure 2 shows that the CNC consists of the machine, electric motors, pneumatic or hydraulic power units, control panel and software.

Figure 2.

CNC natural stone processing machines.

A 4-Axis CNC (Megatron) machine designed for the natural stone industry in Afyon Kocatepe University Natural Stone Processing Laboratory was used for the tests. The technical features of the machine are given in Table 3.

Technical properties/unitValues
Spindle motor (kW)9.0
Number of axis (number)4.0
Motor speed (rpm)24.000
Processing speed (rpm)24.000
Vamotor x axis (mm/dk)80.000
Voltage (V)380
Processing length (mm)4.000–4.500
Processing width (mm)2.000–2.500
Processing height (mm)500–600
Lathe height (mm)700–750
Lathe length (mm)2.500–3.000
Coolant (l/dk)3.0
Automatic number of teams (adet)8.0

Table 3.

Technical properties of CNC natural stone processing machine.

Processability tests were performed on natural rocks according to the dp and Va cutting parameters by using CNC machine. Alpha CAM drawing program was used to determine the cutting parameters of natural rocks. As shown in Figure 3, 120 × 25 mm in size 18 rectangular samples were produced using a 3D modeling and simulation program for the processability tests.

Figure 3.

Test specimens on (a) alpha CAM drawing program, (b) modeling, (c) simulation.

A power meter, also known as load meter, built in the CNC machine was used in the processability tests. This testing tool consists of a measurement unit, a load cell, a controller unit and Defne Lab Soft program (Figure 4).

Figure 4.

Processability tests (a) vector representation of forces (Fx, Fy, Fc and Ft), cutting speed (Vt) and Va(Va), (b) power and load meter tester and load cells, (c) control unit, (d) Defne lab-soft natural stone test program interface, (e) recon program interface, (f) views of database.

Natural stone samples were bond and stabilized to the platform on the measurement unit with cut tools. There were 4 on the Z axis, 4 on the X and Y axis total 8 load cells on the testing machine to calculate the Cf. Defne Lab-Soft program was recorded into the data input screen of types and sizes of natural rocks, cutter information, and constant and variable parameters. NC codes from Alphacam drawing program were transferred to the CNC machine with Recon program interface. The cut tool was balanced to the engine of the CNC machine connected to the tool holder. The reset operation was performed when the cutting tool was guided by the function and operation keys to the reference point on the test specimen surface. NC code was selected using the function and operation keys on the control unit and the measurement was performed by pressing the start button. Depending on the different process parameters, the natural stones were processed in the cooling process from the water flow rate of 1 l/min. A rectangle of 120 × 25 mm was processed for 40 s to obtain 100 data per second. All samples were processed in a total of 84 min. Figure 4 shows a schematic view of the test apparatus.

In the processability tests, variable and constant parameters were taken into consideration. Constant cutting parameters were the cut tool diameter of 6.0 mm, spindle speed of 10,000 d/min, cutting width of 3.0 mm and plunge speed of 1000 d/min. Variable cutting parameters were the dp of 1.20, 1.60 and 2.0 mm and Va of 2500, 3000, 3500 mm/min. Table 4 shows the CNC cutting parameters for the natural rocks processed in the tests.

Processing parametersUnitValues
Cutting tool diametermm6.0
Depth of cutmm1.20–1.60–2.00
Spindle speedd/min10,000
Feed speedmm/min2000–2500–3000
Plunge speedd/min1000
Cutting speedm/min188.4
Cutting widthmm3.0

Table 4.

CNC processing parameters.

Figure 5 explains the vector representation of the forces (Fx, Fy, Fc and Ft), Vt and Va that occurred during the processing of the natural rocks.

Figure 5.

Vector representation of the forces (Fx, Fy, Fc and Ft), Vt and Va that occur during the processing.

Calculation of Fx cutting force according to CNC processing parameters is as shown in Eq. (1).

Fx cutting force Eq. (1);

Fx=Fx1+Fx2E1

Fx = cutting force (N); Fx1 = absolute forward cutting force (N); Fx2 = absolute back cutting force (N).

Fy cutting force Eq. (2);

Fy=Fy1+Fy2E2

Fy = cutting force (N); Fy1 = absolute forward cutting force (N); Fy2 = absolute back cutting force (N).

Calculation by using R resultant force, Fx and Fy cutting forces, Eq. (3):

R=Fx2+Fy2E3

R = resultant force (N); Fx = cutting force (N); Fy = cutting force (N).

β angle between R and Fx, Eq. (4),

β=tan1FyFxE4

Contact angle θ between tool diameter (d) and natural rocks, Eq. (5);

θ=cos112dpdE5

Calculating Fc tangential force and radial force Ft components of the cutting forces with the R value obtained.

Eqs. (6) and (7):

Fc=RsinδE6
Ft=RcosδE7

δ angle between Ft and Fc.

Eq. (8):

δ=βE8

Parameter Z depends on the location of the application point of the compound forces R on the arc AC, which is contact between cutting edges and natural rocks.

Parameter Z, Eq. (9):

Z=ABACE9

Vt cutting speed Eq. (10):

Vt=π×D×n1000E10

Vt = cutting speed (m/min); n = spindle speed (d/min); D = cutter diameter (mm).

Specific cutting energy depending on tangential force and cutting speed is shown in Eq. (11).

Sc=Fc×VtVa×dp×bE11

Fc = tangential cutting force (N); Vt = cutting speed (m/min); Va = feed speed (mm/min); dp = cutting depth (mm); b = cutting width (mm).

Se values were calculated using the power P and Qw obtained from the main electric motor of 7.5 kW where the cutting end of the natural rocks was connected during the processability time (t).

The chip volume is shown in Eq. (12).

Qw=b×l×dp123E12

Qw = chip volume (mm3); b = size of the sample (mm); l = the width of the sample (mm); dp(1,2,3) = cutting depth (mm).

The total specific energy is shown in Eq. (13).

Se=j=1nPjn×j=1ntjQw123E13

Se = total specific energy (J/mm3); P = power consumption (W); t = total time (s); Qw = chip volume (mm3).

3. Findings and evaluations

3.1 Petrographic, chemical and physicomechanical properties

The petrographic analysis was carried out in the MTA (General Directorate Mineral Research and Exploration) mineralogical and petrographic analysis laboratory in Ankara/Turkey. Chemical properties of natural rocks were performed using the XRF (X-ray fluorescence) method in ACME (Analytical Laboratory in Turkey/Ankara). The metamorphic (marble) and sedimentary (travertine, and limestone) origin natural rocks used in this study had different textures. All natural rock types were composed of CaO as main calcite crystals and at least 99.0% calcite minerals ranging from 53.10 to 55.70%. The petrographic analysis results and chemical analysis of the samples are presented in Tables 5 and 6, respectively. Petrographic and chemical analysis results of samples are given in Tables 5 and 6, respectively.

Natural RocksPetrographic descriptionsMinerals
T1Fine-grained calcite is the dominant mineral. Consist of micro-mesocrystalline calcite minerals with a little amount of clay. Often contains pores. Micritic (intraclast) texture. Travertines77% Calcite (mic), 22% Calcite (spr)
T278% Calcite (mic), 21% Calcite (spr)
T379% Calcite (mic), 20% Calcite (spr)
T478% Calcite (mic), 21% Calcite (spr)
T577% Calcite (mic), 22% Calcite (spr)
M1Fine, medium, medium-coarse and coarse-grained with polysynthetic twins, granoblastic texture. Marbles98.5% Calcite
M297.5% Calcite
M398% Calcite
M498.5% Calcite
M598.5% Calcite
M699% Calcite
M797% Calcite, 2% dolomite
K1Fine-grained. Consists of cryptocrystalline calcite within crypto microcrystalline calcite. Micritic texture. Limestones96% Calcite (mic), 2% Calcite (spr)
K296% Calcite (mic), 2% Calcite (spr)
K395% Calcite (mic), 3% Calcite (spr)
K495% Calcite (mic), 3% Calcite (spr)
K595% Calcite (mic), 3% Calcite (spr)

Table 5.

Petrographic descriptions of natural rock samples.

Natural RocksCaO (%)SiO2 (%)Al2O3 (%)Fe2O3 (%)MgO (%)K2O (%)TiO2 (%)P2O5 (%)MnO (%)LoI (%)
T155.700.010.010.010.010.0150.010.030.0243.96
T255.440.060.010.020.060.110.010.020.0344.02
T355.450.010.010.010.280.120.010.020.0144.08
T455.470.010.010.010.210.100.010.020.0144.01
T555.480.060.010.020.090.110.010.020.0343.95
M155.590.010.010.010.110.210.010.040.0144.00
M254.400.950.310.050.210.040.010.010.0144.00
M354.160.890.270.090.810.080.020.010.0443.60
M453.371.570.570.290.750.270.030.030.0443.06
M555.380.170.030.090.310.210.010.020.0143.76
M655.080.270.030.190.330.190.010.020.0143.86
M753.100.550.300.191.920.050.010.030.0343.81
K155.570.100.020.010.370.160.010.040.0143.71
K254.920.100.010.010.410.130.010.040.0144.36
K354.800.220.010.010.400.110.010.040.0144.39
K454.680.460.010.010.560.120.010.030.0144.11
K554.370.750.010.010.350.140.010.040.0144.31

Table 6.

Chemical characteristics of natural rock samples.

The CNC processability tests were conducted in the Rock Mechanics and Technology Application and Research Center Laboratory of the Department of Mining Engineering of Afyon Kocatepe University. The tests were performed in accordance with Standard No. TS EN 1936: 2010 [41], Standard No. TS EN 13755: 2014 [42], Standard No. TS EN 14205: 2004 [43], Standard No. TS EN 1926: 2007 [44], Standard No. TS EN 13161: 2014 [45], Standard No. TS 699 [46] and Standard No. TS EN 1341 (Appendix-C: 2013) [47]. The physicomechanical properties of the natural rocks are presented in Table 7. The rock samples were 40 × 40 mm3, 70 × 70 × 70 mm3 and 30 × 50 × 180 mm3. The tests were carried out using at least six samples.

Natural RocksD (kg/m3)P (%)WA (%)KHUCS (MPa)FS (MPa)IS (MPa)AR (cm3/50 cm2)
T126401.521.38113.3854.567.9217.0024.01
T226501.461.24117.9655.258.0919.0023.48
T326601.281.06122.5456.858.4621.0023.05
T426701.150.94126.2857.948.8922.0022.61
T526801.040.87129.3558.658.9523.0022.04
M126900.960.82131.1459.859.0324.0021.79
M227000.880.78135.7662.169.2825.0019.95
M327050.750.66137.8964.859.4626.0019.01
M427100.710.55141.5266.859.8627.0018.72
M527150.680.43143.7868.759.9828.0018.13
M627200.660.38145.7870.4510.1229.0017.79
M727300.520.32155.4577.0410.9431.0017.58
K127350.380.28168.2584.1012.8533.0017.29
K227450.250.21173.5687.2513.9434.0016.57
K327550.230.18178.2490.8414.9636.0016.05
K427750.200.16184.5893.2616.2438.0015.34
K528000.160.14190.9597.0818.4540.0014.12

Table 7.

Physico-mechanical properties of natural rocks.

D, density; P, porosity; WA, water absorption; KH, knoop hardness; UCS, uniaxial compressive strength; FS, flexural strength; IS, impact strength; AR, abrasion strength.

3.2 Variance analysis (ANOVA) of cutting forces

In processability tests, the Fc and Ft measurements were conducted using two-factor analysis of variance (ANOVA) (17 natural rocks × 2 Cf × 3 dp × 3 Va) randomized experimental design with 100 replications (n = 100). A total of 30,600 data were obtained on the rocks. In terms of the Cf (Fc, Ft), among the dp and Va there was a statistically significant difference (P < 0.001) (Table 8).

Cf (N) dependent variabledp (mm)Mean difference (I-J)Std. ErrorSig.95% confidence interval
Mean (I)Mean (J)Lower boundUpper bound
Fc1.201.00−3.8214*0.27897<0.001−4.4787−3.1642
2.00−7.4694*0.27897<0.001−81267−6.8122
1.601.203.8214*0.27897<0.0013.16424.4787
2.00−3.6480*0.27897<0.001−4.3052−2.9907
2.001.207.4694*0.27897<0.0016.81228.1267
1.603.6480*0.27897<0.0012.99074.3052
Ft1.201.60−3.7896*0.27690<0.001−4.4420−3.1372
2.00−7.5726*0.27690<0.001−8.2250−6.9202
1.601.203.7896*0.27690<0.0013.13724.4420
2.00−3.7830*0.27690<0.001−4.4354−3.1306
2.001.207.5726*0.27690<0.0016.92028.2250
1.603.7830*0.27690<0.0013.13064.4354
Va(mm/dk)
Fc20002500−2.2064*0.27897<0.001−2.8637−1.5491
3000−3.7687*0.27897<0.001−4.4259−3.1114
250020002.2064*0.27897<0.0011.54912.8637
3000−1.5623*0.27897<0.001−2.2195−0.9050
300020003.7687*0.27897<0.0013.11144.4259
25001.5623*0.27897<0.0010.90502.2195
Ft20002500−2.1094*0.27690<0.001−2.7618−1.4570
3000−3.3713*0.27690<0.001−4.0236−2.7189
250020002.1094*0.27690<0.0011.45702.7618
3000−1.2619*0.27690<0.001−1.9142−0.6095
300020003.3713*0.27690<0.0012.71894.0236
25001.2619*0.27690<0.0010.609519142

Table 8.

Statistical analysis of Cf of natural rocks depending on the dp and Va.

The mean difference is significant at the, 05 level.


In processability tests for natural rocks, the mean Fc and Ft increase with an increase in the dp and Va was given in Figure 6. K4 and K5 samples have high values of the Cf at the dp of 2.0 mm while T1, T2, and T3 samples have low values of the Cf at the dp of 1.2 mm. Processability of the Cf values of K4 and K5 samples the dp of 2.0 mm is more forced than that of the other samples. K4 and K5 samples have high values of the Cf at a Va of 3.000 mm/min while T1, T2, and T3 samples have low values of the Cf at a Va of 2.000 mm/min. Processability of the Cf of K4 and K5 samples at a Va of 3.000 mm/min is more forced than that of the other samples.

Figure 6.

Cf according to the dp and Va in natural rocks.

3.3 Variance analysis (ANOVA) of specific cutting energy and specific energy

In processability tests, the Sc and Se measurements were conducted using two-factor analysis of variance (ANOVA) (Sc and Se for 12 natural rocks × 3 dp × 3 Va) randomized experimental design with 100 replications (n = 100). A total of 30,600 data were obtained on the rocks. In terms of the Sc and Se, among the dp and Va there was a statistically significant difference (P < 0.001) (Table 9).

Sc and Se dependent variabledp (mm)Mean difference (I-J)Std. ErrorSig.95% confidence interval
Mean (I)Mean (J)Lower boundUpper bound
Sc1.201.6072898*0.70556<0.00156.27589.521
2.0010.9091*0.70556<0.00192.46812.5714
1.601.20−72898*0.70556<0.001−89.521−56.275
2.0036193*0.70556<0.00119.56952.816
2.001.20−10.9091*0.70556<0.001−12.5714−92.468
1.60−36193*0.70556<0.001−52.816−19.569
Va(mm/dk)
Sc2000250045448*0.70556<0.00128.82562.071
300095051*0.70556<0.00178.42711.1674
25002000−45448*0.70556<0.001−62.071−28.825
300049603*0.70556<0.00132.98066.226
30002000−95051*0.70556<0.001−11.1674−78.427
2500−49603*0.70556<0.001−66.226−32.980
Se1.201.6014500*0.02103<0.00114.00414.996
2.0023077*0.02103<0.00122.58223.573
1.601.20−14500*0.02103<0.001−14.996−14.004
2.00.8577*0.02103<0.001.80820.9073
2.001.20−23077*0.02103<0.001−23.573−22.582
1.60−0.8577*0.02103<0.001−0.9073−0.8082
Va(mm/dk)
Se200025000.6747*0.02103<0.0010.62520.7243
300011701*0.02103<0.00111.20512.197
25002000−0.6747*0.02103<0.001−0.7243−0.6252
30000.4954*0.02103<0.0010.44580.5449
30002000−11701*0.02103<0.001−12.197−11.205
2500−0.4954*0.02103<0.001−0.5449−0.4458

Table 9.

Statistical analysis of Sc and Se of natural rocks depending on the dp and Va.

The mean difference is significant at the, 05 level.


In processability tests for natural rocks, the mean Sc and Se values at the dp of 1.2 mm are lower than those at the dp of 1.6 and 2.0 mm was given in Figure 7. Sc and Se values at the Va of 2000 mm/min are higher than those at the Va of 2500 and 3000 mm/min. Sc and Se values at the Va of 3000 mm/min are lower for T1, T2, and T3 samples while those at the Va of 2000 mm/min are higher for both K4 and K5 samples. The natural rocks should have the Va of 3000 mm/min according to the Sc and Se values.

Figure 7.

Sc and Se values according to the dp in processability tests of rocks.

3.4 Relationships between cutting forces and specific cutting energy

Regression models were applied to examine the relationship between the Cf and Sc values for each of the natural rocks. The results of the simple linear regression analysis are given in Figure 8.

Figure 8.

Relationship between the Cf of natural rocks and Sc according to cutting depth and feed speed.

Figure 8 shows that there is a statistically significant relationship between Sc and Cf values. Correlation coefficient (R2) values obtained from the natural rocks in the Fc at depths of cut of 1.2, 1.6 and 2.0 mm are 0.895, 0.871 and 0.859, respectively. Correlation coefficient (R2) values obtained from the natural rocks in the Ft at depths of cut of 1.2, 1.6 and 2.0 mm are 0.890, 0.878 and 0.880, respectively. Correlation coefficient (R2) values obtained from the natural rocks in the Fc at the Va of 2000, 2500 and 3000 mm/min are 0.771, 0.780 and 0.780, respectively. Correlation coefficient (R2) values obtained from the natural rocks in the Ft at the Va of 2000, 2500 and 3000 mm/min are 0.745, 0.781 and 0.781, respectively.

3.5 Relationships between specific cutting energy and specific energy

The results of the correlation coefficient and regression model are given in Figure 9. Correlation coefficient (R2) obtained from the natural rocks is 0.784, indicating that there is a linear relationship between the Sc and Se.

Figure 9.

Relationship between the Sc and Se of natural rocks.

3.6 Relationships between cutting forces, specific cutting energy and specific energy natural rocks properties

The relation between the Fc, Ft, Sc and Se values, and the physico-mechanical properties of the natural stones were evaluated through regression analysis. The results of the regression analysis are given in Tables 10 and 11, respectively.

Independents/CfDependents/physico-mechanical propertiesCustom equationR2 Linear Model
FcDy = 3.506 * x + 2625.9620.931
Py = −0.035 * x + 1.5950.923
WAy = −0.031 * x + 1.3560.887
KHy = 1.982 * x + 99.0070.976
UCSy = 1.842 * x + 53.3650.981
FSy = 0.244 * x + 5.1290.889
ISy = 0.547 * x + 14.6120.968
ARy = −0.245 * x + 25.1890.932
FtDy = 3.588* x + 2627.8380.930
Py = −0.035 * x + 1.5750.919
WAy = −0.031 * x + 1.3380.883
KHy = 2.030 * x + 100.0260.978
UCSy = 1.217 * x + 42.8610.983
FSy = 0.251 * x + 5.2370.896
ISy = 0.560 * x + 14.9020.968
ARy = −0.251 * x + 25.0470.928

Table 10.

Relationships between Fc and Ft cutting forces natural rock properties.

Independents/Sc and SeDependents/physico-mechanical propertiesCustom equationR2 linear model
ScDy = 2.017* x + 2630.8040.929
Py = −0.020*x + 1.5470.922
WAy = −0.017 * x + 1.3140.887
KHy = 1.142 * x + 101.6960.977
UCSy = 0.684 * x + 43.8580.983
FSy = 0.140 * x + 5.4560.892
ISy = 0.315 * x + 15.3570.968
ARy = −0.141 * x + 24.8450.929
SeDy = 115.7 * x + 2166.1490.858
Py = −1.032 * x + 5.6100.686
WAy = −0.883 * x + 4.7660.616
KHy = 63.347 * x + −151.2190.844
UCSy = 37.511 * x + −105.5780.829
FSy = 8.647 * x + −29.6630.944
ISy = 17.500 * x + −54.5200.837
ARy = −7.476 * x + 54.4450.732

Table 11.

Relationships between Sc and Se natural rock properties.

Correlation coefficient (R2) values of the natural rock samples, a linear relationship between the Cf values and the physicomechanical characteristics is observed. As a result of the analysis, the following correlation coefficient (R2) values have been obtained: R2 coefficient range from 0.887 to 0.981 in the Fc and from 0.883 to 0.983 in the Ft. All values confirm the linear relationship among physicomechanical properties in natural rocks with the Cf. Accordingly, as porosity, water absorption and abrasion strength decrease in the natural rocks, Cf values increases. Moreover, as knoop hardness, uniaxial compressive strength, flexural strength and impact strength increase, the Cf values also increase.

Correlation coefficient (R2) values of the natural rock samples, a linear relationship between the Sc and Se values and the physicomechanical characteristics is observed. As a result of the analysis, the following correlation coefficient (R2) values have been obtained: R2 coefficient range from 0.887 to 0.977 in Sc and from 0.616 to 0.858 in the Se. All values confirm the linear relationship among physicomechanical characteristics in natural rocks with the Sc and Se. Accordingly, as porosity, water absorption and abrasion strength decrease in the natural rocks, Sc and Se value increases. Moreover, as Knoop hardness, uniaxial compressive strength, flexural strength and impact strength increase, the Sc and Se values also increases.

Proper selection and performance estimation of mill cutting tools are important factors in improving the efficiency of processability and decrease costs in natural rocks. Performance cutting parameters and 3D design of mill cutting tools are cutting tool diameter, dp, Va, Fc, and Ft, Sc and Se. A contribution was made to the literature by proposing new correlation coefficients (R2) for natural rocks.

4. Conclusion

The rocks in this study were determined according to by taking into account the Cf, Sc and Se. value in accordance with the statistical analyses. Cf, Sc and Se values vary depending on the dp and Va used in natural rocks. Results of the experimental study are summarized below:

  • Fc and Ft values are high at the dp of 2.0 mm and Va of 3.000 mm/min.

  • Sc and Se, values are high at the dp of 1.2 mm and Va of 2.000 mm/min.

  • Due to the increased friction force due to the increase in the amount of natural rock chips to be cut by the cutter edge at the dp of 2.0 mm, the processability is most difficult.

  • The cutting parameters with the highest specific energy volume are considered to be the toughest moments of the CNC machine.

  • The values of Sc and Se are reduced and the efficiency increases with an increase in the dp which results from the increase in the cutting edge of the chip volume in natural rocks. Sc and Se are significantly increased at the dp of 1.2 mm.

  • There is a significant relationship between Cf, Sc and Se depending on the dp and Va, the correlation coefficient (R2) values of which are 0.859 to 0.895, and 0.745 to 0.781 respectively.

  • A significant relationship between the Sc and Se was identified as R2 (0.784).

  • There is a significant relationship between the Cf and physicomechanical properties. R2 ranges from 0.887 to 0.981 in the Fc and from 0.883 to 0.983 in the Ft.

  • There is a significant relationship between the Sc, Se, and physicomechanical properties. R2 ranges from 0.887 to 0.983 in the Sc and from 0.616 to 0.944 in the Se.

Acknowledgments

This study was supported (Project number: 13.GÜZSAN.01 and TR33/12/SKMDP/0104). We would like to thank them for their (Afyon Kocatepe University and Zafer Development Agency) support and contributions.

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Gencay Sariisik (May 23rd 2019). Force and Specific Energy in Natural Rocks Cutting by Four-Axis Machine, Earth Crust, Muhammad Nawaz, Farha Sattar and Sandeep Narayan Kundu, IntechOpen, DOI: 10.5772/intechopen.85622. Available from:

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