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Forces and wear in high-speed machining of granite by circular sawing
Diamond & Related Materials 100 (2019) 107579
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Forces and wear in high-speed machining of granite by circular sawing ⁎
T
S. Turchetta , L. Sorrentino Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, 03043 Cassino, Italy
A R T I C LE I N FO
A B S T R A C T
Keywords: Forces Wear Diamond tools Cutting efficiency Speed cutting
In stone sawing process, the most adopted tool type is the circular diamond blade, whose duration and performance are influenced by various elements. These factors can be grouped into four categories: the mineralogical characteristics of the material to be machined; the working conditions, such as the depth of cut, the feed rate and the cutting speed; the production process of the diamond segment and the characteristics of both the matrix and the diamond, such as the size, the type and the concentration of the diamonds and the metal bonding formulation hardness. A key factor to increase productivity and reduce processing costs is cutting speed. In fact, the current trend is to adopt ever higher cutting speeds in order to reduce production times and costs. The purpose of this work is to evaluate over time the efficiency of the granite cutting process using diamond discs according to the cutting speed. The analysis was carried out for cutting speeds higher than the parameters conventionally used in the industrial field which is about 25 m/s. The efficiency of the processing was assessed by measuring the forces and wear of the tool according to the main process parameters for different working stages. In particular, the impact of working parameters modifications on the cutting operation of an ornamental stone was studied by experimental tests carried out on a CNC working centre equipped with a data acquisition system, suitable for the registration of all the three components of the cutting force.
1. Introduction Cutting temperature, tool wear and surface integrity depend on cutting energy and forces. During cutting operation mineral stone elements are removed from the surface being machined by the movement of the abrasive grit. Realizing the interactions between the stone and the abrasive tool is necessary to optimize the machining process of stone. The causal connection between control parameters and cutting performances can be simulated by models derived from the analysis of the events happening during machining operations; a model is necessary to establish the connection between control parameters and the cutting operation as to predict the wear of the abrasive tool. In literature there are not many works dealing with cutting operation of stones. The ideal chipping geometries were studied by Jerro et al. who introduced a mathematical model; they defined the connection between the thickness and the area of chips by realizing the ideal chip shape and they studied the connection between chip thickness and the tangential cutting force [1]. Branch et al. investigated the method to calculate power required for machining operation from the cutting forces and energies detected by a dynamometer [2], while Asche et al. carried out a study to define a practical relationship between tool wear and process parameters [3]. The specific grinding
⁎
energy was correlated to chip shape by Pai et al., who observed chip samples by a scanning microscope [4]. One of the most adopted models was proposed by Tönshoff et al. and it was suitable for cutting operation of stone by means of a diamond disk [5]; even if a thorough test campaign was not carried out to validate it, according to the suggested model the friction among diamonds, stone, matrix and swarf and the deformation of both the grits and the material being machined govern the interactions between workpiece and tool. Another ideal model for the study of natural stone cutting was introduced by Konstanty and it was suitable for the analysis of diamond impregnated tools mounted on both circular and frame saw, even if experimental tests to validate it were not carried out [6]. A further model, suitable for the definition of cutting forces under several machining conditions, was proposed by Turchetta [7–9]. The diamond grit cutting process was simulated by Wang and Clausen through the study of the single point cutting tool; they saw that the grooves characters were comparable to the cutting forces tendency [10]. An analytical model suitable for the prediction of the maximum wear rates of both matrix and grit was proposed by Di Ilio et al. who studied the wear mechanism too [11]. Two were the fundamental elements at the basis of the tool wear rate indicated by the model: the grain characteristic and the matrix one, that had to be calculated through experimental tests. The diamond grit wear of a sintered
Corresponding author. E-mail address: [email protected] (S. Turchetta).
https://doi.org/10.1016/j.diamond.2019.107579 Received 24 June 2019; Received in revised form 9 October 2019; Accepted 12 October 2019 0925-9635/ © 2019 Elsevier B.V. All rights reserved.
Diamond & Related Materials 100 (2019) 107579
S. Turchetta and L. Sorrentino
Fig. 1. CNC milling machine and stone machining test.
machine spindle and the abrasive grit, it cushions the forces arising during the machining process and it gives the desired shape to diamond tool. Support is generally made up of corrosion resistant Cr-steel. Steel bodies are heat treated (quench and tempering) to reach approx. 43–45 HRC hardness. Super-abrasive particles have the task of removing the material: its properties and parameters to be defined are granulometry, shape and concentration of the bonding. Granulometry expresses the measurement of the super-abrasive grain size. The shape of the diamond particles may be regular or irregular according to their quality. Concentration is the quantity, in weight, of the diamond particles for sector unit volume. Increasing in concentration leads to cost increase and, therefore, price one. The bonding is an alloy which blocks the super-abrasive grains to the tool support so that it can carry out cutting, milling, sharpening, smoothening and profiling economically and in a technically correct manner. The bonding must guarantee two contrasting requisites: cutting capacity and long tool life. At last, the wear resistance of the bonding must be proper for the abrasive grit type, in order to warrant the correct protrusion as a function of the characteristics of the stone to be machined and the process, and it must essentially guarantee the worn grain release in order to assure the grit renewal, exposing the unaltered grains that are embedded in the matrix. The metal powders making up the bonding mixture are iron, copper, tungsten, cobalt and nickel.
tool was studied by Carrino et al. [12], while the diamond saw wear and the material properties were connected to the cutting specific energy by Ersoy et al. for various stone types [13]. Cu-based diamond tools were developed and produced through powder metallurgy by Wang et al. [14], while the configuration of the diamond tool for various CNC machining processes was studied by Kenda and. Kopač, who described the forces and the tool wear mechanism operating in different type of machining technologies [15]. Zhang J. et al. show an innovative frame saw machine to cut granite. A sawing test and a simulation were carried out to analyse the sawing trajectory, the surface topography of the segments and the percentage of worn diamond particles [16]. Turchetta et al. show an innovative prototype machine to cut stone by a diamond wire. The developed prototype was provided by a sensory system to measure both the cutting power and the tensile force of the diamond wire during experimental tests. In this way it was possible to verify the functionality of the prototype plant and, in the same time, to evaluate the productivity of the implemented cutting process [17,18]. Wang P. shows the modelling and estimation of production rate in ornamental stones sawing based on brittleness indexes [19]. Denkena B. et al. study thin tools for the high speed cutting of granite; in particular the application of thinner discs is the aim to achieve the standard market quality while working with lower tool stiffness at higher rotational speeds. Investigations on the influence of the shape, the different alloys of the steel core and of different bonding systems on process forces, tool wear and cut quality [20,21]. All these works lack a systematic study for the evaluation of high-speed machining performance in cutting granite with diamond disks. Current state of studies points out how cutting efficiency depends on cutting speed in natural stones machining. The current trend in all cutting processes is to work at high cutting speeds with the aim of reducing processing times and costs. This requires a careful analysis of the performance of the tool that varies with the cutting speed. In cutting granite with diamond disks, conventional cutting speeds are around 20–25 m/s. The objective of this paper is to analyse the performance of the tool in cutting granite at high cutting speeds, i.e. speeds higher than those conventionally used. In particular, the machining conditions that are most interesting by an industrial point of view were investigated. An ornamental stone was machined on a CNC machining centre, retrofitted with a dynamometer and data acquisition systems, to investigate the effects of variations in machining parameters. The sensor data included cutting force measurements further divided into measurable components.
3. Experimental setup Fig. 1a shows a CNC milling machine chosen to perform the experimental tests; it is characterized by a 15 kW spindle power, while the tests have been carried out at a maximum spindle speed of 15,000 rpm. The material chosen for this study is the Sardinian granite, while the adopted tool is a sintered diamond disk commonly selected for natural stone cutting, whose properties are reported in Table 1. As concerns the process parameters, two values of feed per revolution and four ones of Table 1 Tool properties. Tool properties
Diamond disk
Diamond mesh [#] Diamond concentration [Kts/cm3] Tool diameter [mm] Tool thickness [mm]
40/50 4.4 180 5
2. Sintered diamond tools for natural stone machining Chemical composition of bonding (%)
Natural stone machining occurs by using diamond tools for cutting such as wires, blades disks and for surface machining such as grinders and mills of different shapes and profiles. Commonly the tool is made of a super-abrasive grit anchored on a support by means of a bonding. Support is very important since it transfers the energy between the
Co Cu C O Al
2
42.80 28.40 20.44 5.14 2.24
Diamond & Related Materials 100 (2019) 107579
S. Turchetta and L. Sorrentino
out taking into account the Fy and the Fz components of the cutting force. The highest readings obtained for each tool revolution readings have been considered from acquired force signals for each test. For each signal acquired have been calculated the highest values of components of the cutting force Fy and Fz obtained as average value of the peaks measured. Fig. 3 shows the highest values of Fy and Fz component of the cutting force as a function of cutting speed for both levels of feed per revolution: both components increased with feed per revolution and they decreased with cutting speed increment. This is due to the fact that the quantity of material removed by the single abrasive grain decreased with the increase of the cutting speed, other conditions being equal, so the components of the cutting force were reduced. Likewise, the chip section removed by the single abrasive grain increases as the advancement per revolution increases, with a consequent increase in the components of the cutting force. The graph also shows results dispersion very low, which demonstrates repeatability of the test method and of the tool characteristics. The graph in Fig. 3 denotes also that the Fy component of cutting force was lower than Fz one that reached maximum values of about 220 N and about 120 N for a feed per revolution of 0.10 mm and 0.05 mm, respectively, while the maximum value of the Fy was about 90 N for a feed per revolution of 0.10 mm. Moreover, in Fig. 3 the relations of linear type between the component of the cutting force and the cutting speed are reported. As can be seen from the graph, the regression curves obtained show an excellent value of R2. The results show that adopting high cutting speeds allows to increase productivity by reducing process times and to reduce process forces and, consequently, the stresses acting on the workpiece and the diamond grains.
Table 2 Experimental plan. Factors
# Levels
Levels
Cutting speed “Vc” [m/s] Feed per revolution “f” [mm] Radial cutting depth “dr” [mm]
4 2 1
35–45–55–65 0.05–0.10 25
Working stage 0, 1, 2, 3,4,5 Working stage 0
Working stage 1
Working stage 2
Working stage 3
Working stage 4
Working stage 5
Material removed 0 cm3
Material removed 600 cm3
Material removed 1200 cm3
Material removed 1800 cm3
Material removed 2400 cm3
Material removed 3000 cm3
cutting speed are considered; in addition, 6 stages of working are considered. A total of 192 experimental runs are performed, as four replications are run for each parameter set, as the experimental plan shows in Table 2. As regards cutting speed, higher values have been used compared to the maximum speeds conventionally used in the industrial sector for the tested granite, which are around 20–25 m/s, and in particular in a range that varies between 35 and 65 m/s. As showed in Fig. 1b, a piezoelectric dynamometer has been employed to evaluate the three components of the cutting force, that are Fx, Fy and Fz. The acquisition system is suitable to acquire the signals of the dynamometer for various time intervals and frequencies in order to analyse the entire information about the signal of force. It has been observed that the signal along the three axes is periodic, so the entire signal information has been collected with 32,768 points. The acquisition system has been completed by an A/D converter and a PC that sampled the signal at 10 kHz; therefore, each inspection lasted 3.2768 s.
4.2. High-speed cutting of granite: wear analysis The behavior of a diamond tool in respect to wear is the consequence of wear progressions of the single diamonds grain and the bonding constituting the tool (see Fig. 4). This classification and the related experimental method have been described in previous works [12]. At first, the bonding erosion increases the diamond grain protrusion so as to come into contact with the material being machined (intact grain). Once in contact, the grain is rounded so as to form a plateau (smoothed grain). Intermittent contact with the workpiece due to tool rotation leads to cyclical load on the diamond grain which, amplified by the inhomogeneity of the stone and the vibrations, causes deterioration of grain capacity to resist the cut forces and consequently its disintegration after a certain interval of time (fractured grain). The wear progression leads finally to a completely fractured particle or to a matrix enough eroded to allow the release of diamond grain (pull-out). Other grains will come to the tool cutting surface and the wear cycle starts again. The test conditions are given in Table 2. A representative sample was extracted from the diamond grain population scattered on tool surface and its behaviour with regard to wear has been observed. The sample has been selected considering at least 20 grains to be contained on the reference segment surface. The univocal identification of the diamond grain on the reference surface has been obtained by LAICA microscope mapping with a magnification of 200×. In order to plan the cuts sequence, i.e. to determine the material volume to be removed for each cut, the average life of a diamond grain through preliminary tests has been determined. Each cut removes the same volume of material corresponding to a specific processing condition defined working stage. The amount of the material removed has been set for each working stage and it is equal to 600 cm3. At the end of each working stage, components of cutting force have been measured. For each force signal, the highest value obtained has been considered as the average value of the signal peaks, moreover since the
4. Results and discussion This section shows the forces and wear analysis as a function of high-speed cutting of granite. 4.1. High-speed cutting of granite: forces analysis
F [N]
A monitoring strategy has been adopted based on time-domain characteristics. Fig. 2 shows typical time domain signals monitored in Y (feed) and Z(vertical) directions. Stone cutting has been performed at a cutting speed of 45 m/s and at a feed per revolution of 0.10 mm. As figures show, force signals are periodic and regular. Fx component of cutting force is negligible compared to Fy and Fz ones since cut takes place in the plane. Therefore, cutting forces analysis has been carried
220 200 180 160 140 120 100 80 60 40 20 0
Fz
0
5
10
15
20 25 time [ms]
Fy
30
35
40
45
50
Fig. 2. Time domain signal monitored in Y and Z direction. 3
Diamond & Related Materials 100 (2019) 107579
S. Turchetta and L. Sorrentino
Fy (f=0.05 [mm])
Fy (f=0.10 [mm])
Fz (f=0.05[mm])
Fz (f=0.10 [mm])
240 220 200 180
Fy, Fz [N]
160 140 120 100 80 60 40 20 0 20
25
30
35
40
45
50
55
60
65
70
75
cung speed [m/s] f=0.05 mm Fy=69.70-0.6075Vc Fz=160.75-1.065Vc R2=0.806 R2=0.978
f=0.10 mm Fy=123.31-1.0275Vc Fz=286-2.27Vc R2=0.9145 R2=0.9527
Fig. 3. Fy and Fz component vs. cutting speed for the two values of f (0.05–0.10 mm); working stage 0.
cutting speed of 35 m/s and 45 m/s, while it increases significantly with working progression for cutting speed of 55 m/s and 65 m/s. This increasing is particularly evident for cutting speed of 65 m/s. Similar results have been obtained for Fz component of cutting force. Fig. 6 shows Fy and Fz components trend of cutting force as a function of cutting speed and as a function of working stages, for a fixed feed per
dispersion obtained after four replications is always limited (< 7%), in the following graphs have been reported only the average value. Fig. 5 shows the trend of Fy and Fz component of cutting force as a function of cutting speed and working stages for a fixed feed per revolution of 0.05 mm. In Figure are showed the average force values: Fy component of cutting force remains almost constant over time for
intact grain
smoothed grain
fractured grain
pull-out grain Fig. 4. Wear states of a diamond grain. 4
Diamond & Related Materials 100 (2019) 107579
S. Turchetta and L. Sorrentino
240 Fy (working stage 1)
220
Fy (working stage 2)
Fy,Fz [N]
200 180
Fy (working stage 3)
160
Fy (working stage 4)
140
Fy (working stage 5)
120
Fz (working stage 1)
100
Fz (working stage 2)
80
Fz (working stage 3)
60 Fz (working stage 4) 40 Fz (working stage 5) 20 30
35
40
45
50
55
60
65
70
cung speed [m/s]
Fy,Fz [N]
Fig. 5. Fy and Fz component vs. cutting speed for different working stages; f = 0.05 mm.
360 340 320 300 280 260 240 220 200 180 160 140 120 100 80 60 40
Fy (working stage 1) Fy (working stage 2) Fy (working stage 3) Fy (working stage 4) Fy (working stage 5) Fz (working stage 1) Fz (working stage 2) Fz (working stage 3) Fz (working stage 4) Fz (working stage 5) 30
35
40
45
50
55
60
65
70
cung speed [m/s] Fig. 6. Fy and Fz component vs. cutting speed for different working stages; f = 0.10 mm.
percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 7. Percentage of diamond grains morphology for different working stage; Vc = 35 [m/s] and f = 0.05; 0.10 [mm].
5
Diamond & Related Materials 100 (2019) 107579
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percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 8. Percentage of diamond grains morphology for different working stage; Vc = 45 [m/s] and f = 0.05; 0.10 [mm].
percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 9. Percentage of diamond grains morphology for different working stage; Vc = 55 [m/s] and f = 0.05; 0.10 [mm].
percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 10. Percentage of diamond grains morphology for different working stage for Vc = 65 [m/s] and f = 0.05; 0.10 [mm].
occurs; its increase is probably due to a greater wear of the diamond grains. In order to better understand this phenomenon, for each working stage have been monitored the characteristics of a single diamond grain
revolution of 0.10 mm; the components of cutting force is almost constant with the working progress for cutting speed of 35 m/s, 45 m/s and 55 m/s. By reaching the cutting speed of 65 m/s a considerable increase of Fy and Fz component of the cutting force with the working progress
6
Diamond & Related Materials 100 (2019) 107579
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Fig. 11. Performance index as a function of the cutting speed; f = 0.05 [mm].
Fig. 12. Performance index as a function of the cutting speed; f = 0.10 [mm].
removed by a single diamond during the cutting process combined with the low process forces in working stage 0 exerted on the diamond and on the matrix. Figs. 11 and 12 show the performance index obtained as the ratio between the number of damaged grains (smoothed grains, fractured grains, pull-out grains) and the intact grains as a function of the cutting speed, for both level of feed. As it can be seen from Fig. 11, for a feed of 0.05 mm the smoothed/intact grains performance index increases drastically with cutting speeds above 45 m/s, going from about 0.4 to about 1.6, while the pull-out/intact grains performance index remains almost constant with the cutting speed and the fractured/intact grains performance index presents a fluctuating trend between 0.4 and 1. For higher feeds, the performance index trends are similar, even if the values reached are lower.
belonging to a two-sector taken as a reference on the disc for minimum 40 grains. In particular, the diamonds were classified according to the different working stages (intact grain, smoothed grain, fractured grain, pull-out grain, as visible in Fig. 4) characterized using a procedure reported in (test protocol for micro-geometric wear of sintered diamond tools [12]). Figs. 7–10 show the percentage values of diamonds morphology for different working stage: for all tests a low dispersion was found (< 5%). In Fig. 7 (cutting speed of 35 mm/s), for f = 0.05 mm, the percentage of intact grains is about 42%, the percentage of smoothed grains is about 13%, the percentage of fractured grains is about 32% and finally the percentage of pull-out grains is about 13%; for f = 0.10 mm, the percentage of intact grains is about 47%, the percentage of smoothed grains is about 12%, the percentage of fractured grains is about 27% and finally the percentage of pull-out grains is about 14%. This high percentage of intact and fractured grains, combined with a low percentage of the smoothed ones, indicates a good cutting behaviour of the tool; during the working progress a constant and optimal renewal of diamond grits occurs. Similar results have been obtained with a cutting speed of 45 mm/s, see Fig. 8. Figs. 9–10 show the percentage values of diamonds morphology for different working stage and cutting speed of 55/65 m/s. It is noticed a considerable increase of the percentage of smoothed grain (> 30%), tending to increase with the working stages; the percentage of intact grains is < 35% and it tends to decrease with the working stages. It is clear that working with a cutting speed of 55 and 65 m/s is not possible to obtain a good renewal of diamond grits, so it is possible to increase the cutting speed up to 45 m/s. This low renewal of diamond grits for high cutting speed are essentially due to the maximum chip section
5. Conclusions This work points out the relation between the cutting force components and the main process parameters (feed per revolution and cutting speed) for granite cutting by diamond disk. In particular, the cutting force components increase with feed per revolution and they decrease with cutting speed raising. The results obtained point out how it is possible to improve the process efficiency by working with cutting speed higher than conventional value of about 35 m/s with considerable productivity growth. However, the tool wear is compatible for cutting speed ≤45 m/s as higher values can cause problems due to the poor renewal of diamond grits, which is important for the effective use of any sintered diamond tool. This phenomenon is highlighted by the performance index, that is obtained as the ratio between the number of smoothed grains and intact 7
Diamond & Related Materials 100 (2019) 107579
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grains. This index undergoes a significant increase due to the poor renewal of the abrasive grits passing from a cutting speed of 45 m/s to 55 m/s. In conclusion, increasing the cutting speed is possible in natural stone machining processes using diamond tools in order to increase productivity; however, there is a limit value beyond which the tool suffers an evident loss of its cutting capacity.
[9] S. Turchetta, Cutting force and diamond tool wear in stone machining, Int. J. Adv. Manuf. Technol. 61 (2012) 441–448, https://doi.org/10.1007/s00170-0113717-04. [10] C.Y. Wang, R. Clausen, Marble cutting with single point cutting tool and diamond segments, Int J Mach Tool Manu 42 (2002) 1045–1054. [11] A. Di Ilio, A. Togna, A theoretical wear model for diamond tools in stone cutting, Int J Mach Tool Manu 43 (2003) 1171–1177. [12] L. Carrino, W. Polini, S. Turchetta, Test protocol for micro-geometric wear of sintered diamond tools, Wear 257 (2004) 246–256. [13] A. Ersoy, S. Buyuksagic, U. Atici, Wear characteristics of circular diamond saws in the cutting of different hard abrasive rocks, Wear (2005) 1422–1436. [14] C. Wang, X. Zhang, C. Jia, Current research situation and development of Cu-based diamond tools made by powder metallurgy, FenmoYejinJishu/Powder Metall. Technol. 30 (2) (2012) 140–143. [15] J. Kenda, J. Kopac, Diamond tools for machining of granite and their wear, StrojniskiVestnik/J. Mech. Eng. 55 (12) (2009) 775–780. [16] H. Zhang, J. Zhang, Z. Wang, Q. Sun, J. Fang, A new frame saw machine by diamond segmented blade for cutting granite, Diam. Relat. Mater. 69 (2016) 40–48. [17] S. Turchetta, G. Gelfusa, W. Polini, E. Venafro, A new sawing machine by diamond wire, Adv. Manuf. Technol. 70 (2014) 73–78. [18] S. Turchetta, L. Sorrentino, C. Bellini, A method to optimize the diamond wire cutting process, Diam. Relat. Mater., Vol. 71, 1 January 2017, Pages 90–97. [19] P. Wang, Modeling and estimation of production rate in ornamental stones sawing based on brittleness indexes, Math. Probl. Eng. 4 (2019) 1–12 3232517. [20] B. Denkena, H.K. Tönshoff, T. Friemuth, T. Glatzel, Development of advanced tools for economic and ecological grinding of granite, Key Eng. Mater. 250 (2003) 21–32. [21] B. Denkena, D. Boehnke, J. Bockhorst, Thin tools for the high speed cutting of granite, Int. J. Abras. Technol. 2 (2) (2009) 173–183.
References [1] H.D. Jerro, S.S. Pamg, C. Yang, R.A. Mirshams, Kinematics analysis of the chipping process using the circular diamond saw blade, Trans. ASME J. Manuf. Sci. Eng. 121 (1999) 257–264. [2] K. Brach, D.M. Pai, E. Ratterman, M.C. Shaw, Grinding forces and energy, Trans. ASME J. Eng. Ind. 110 (1998) 25–31. [3] J. Asche, H.K. Tönshoff, T. Friemuth, Cutting principles, wear and applications of diamond tools in the stone and civil engineering industry, Proceedings of Diamond Tools Conference, 1999, pp. 151–157. [4] D.M. Pai, E. Ratterman, M.C. Shaw, Grinding swarf, Wear 131 (1989) 329–339. [5] Tönshoff HK, Warnecke G (1982) Research on stone sawing. Advances in Ultrahard Materials Applications Technology, P. Daniel, Hornbeam ed. England vol. 1:36-29. [6] J. Konstanty, Theoretical analysis of stone sawing with diamonds, J. Mater. Process. Technol. 123 (2002) 146–154. [7] S. Turchetta, Cutting force on a diamond grit in stone machining, Int. J. Adv. Manuf. Technol. 44 (2009) 854–861. [8] S. Turchetta, Cutting force in stone machining by diamond disk, Adv. Mater. Sci. Eng. (2010) 631437, , https://doi.org/10.1155/2010/631437.
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Forces and wear in high-speed machining of granite by circular sawing ⁎
T
S. Turchetta , L. Sorrentino Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, 03043 Cassino, Italy
A R T I C LE I N FO
A B S T R A C T
Keywords: Forces Wear Diamond tools Cutting efficiency Speed cutting
In stone sawing process, the most adopted tool type is the circular diamond blade, whose duration and performance are influenced by various elements. These factors can be grouped into four categories: the mineralogical characteristics of the material to be machined; the working conditions, such as the depth of cut, the feed rate and the cutting speed; the production process of the diamond segment and the characteristics of both the matrix and the diamond, such as the size, the type and the concentration of the diamonds and the metal bonding formulation hardness. A key factor to increase productivity and reduce processing costs is cutting speed. In fact, the current trend is to adopt ever higher cutting speeds in order to reduce production times and costs. The purpose of this work is to evaluate over time the efficiency of the granite cutting process using diamond discs according to the cutting speed. The analysis was carried out for cutting speeds higher than the parameters conventionally used in the industrial field which is about 25 m/s. The efficiency of the processing was assessed by measuring the forces and wear of the tool according to the main process parameters for different working stages. In particular, the impact of working parameters modifications on the cutting operation of an ornamental stone was studied by experimental tests carried out on a CNC working centre equipped with a data acquisition system, suitable for the registration of all the three components of the cutting force.
1. Introduction Cutting temperature, tool wear and surface integrity depend on cutting energy and forces. During cutting operation mineral stone elements are removed from the surface being machined by the movement of the abrasive grit. Realizing the interactions between the stone and the abrasive tool is necessary to optimize the machining process of stone. The causal connection between control parameters and cutting performances can be simulated by models derived from the analysis of the events happening during machining operations; a model is necessary to establish the connection between control parameters and the cutting operation as to predict the wear of the abrasive tool. In literature there are not many works dealing with cutting operation of stones. The ideal chipping geometries were studied by Jerro et al. who introduced a mathematical model; they defined the connection between the thickness and the area of chips by realizing the ideal chip shape and they studied the connection between chip thickness and the tangential cutting force [1]. Branch et al. investigated the method to calculate power required for machining operation from the cutting forces and energies detected by a dynamometer [2], while Asche et al. carried out a study to define a practical relationship between tool wear and process parameters [3]. The specific grinding
⁎
energy was correlated to chip shape by Pai et al., who observed chip samples by a scanning microscope [4]. One of the most adopted models was proposed by Tönshoff et al. and it was suitable for cutting operation of stone by means of a diamond disk [5]; even if a thorough test campaign was not carried out to validate it, according to the suggested model the friction among diamonds, stone, matrix and swarf and the deformation of both the grits and the material being machined govern the interactions between workpiece and tool. Another ideal model for the study of natural stone cutting was introduced by Konstanty and it was suitable for the analysis of diamond impregnated tools mounted on both circular and frame saw, even if experimental tests to validate it were not carried out [6]. A further model, suitable for the definition of cutting forces under several machining conditions, was proposed by Turchetta [7–9]. The diamond grit cutting process was simulated by Wang and Clausen through the study of the single point cutting tool; they saw that the grooves characters were comparable to the cutting forces tendency [10]. An analytical model suitable for the prediction of the maximum wear rates of both matrix and grit was proposed by Di Ilio et al. who studied the wear mechanism too [11]. Two were the fundamental elements at the basis of the tool wear rate indicated by the model: the grain characteristic and the matrix one, that had to be calculated through experimental tests. The diamond grit wear of a sintered
Corresponding author. E-mail address: [email protected] (S. Turchetta).
https://doi.org/10.1016/j.diamond.2019.107579 Received 24 June 2019; Received in revised form 9 October 2019; Accepted 12 October 2019 0925-9635/ © 2019 Elsevier B.V. All rights reserved.
Diamond & Related Materials 100 (2019) 107579
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Fig. 1. CNC milling machine and stone machining test.
machine spindle and the abrasive grit, it cushions the forces arising during the machining process and it gives the desired shape to diamond tool. Support is generally made up of corrosion resistant Cr-steel. Steel bodies are heat treated (quench and tempering) to reach approx. 43–45 HRC hardness. Super-abrasive particles have the task of removing the material: its properties and parameters to be defined are granulometry, shape and concentration of the bonding. Granulometry expresses the measurement of the super-abrasive grain size. The shape of the diamond particles may be regular or irregular according to their quality. Concentration is the quantity, in weight, of the diamond particles for sector unit volume. Increasing in concentration leads to cost increase and, therefore, price one. The bonding is an alloy which blocks the super-abrasive grains to the tool support so that it can carry out cutting, milling, sharpening, smoothening and profiling economically and in a technically correct manner. The bonding must guarantee two contrasting requisites: cutting capacity and long tool life. At last, the wear resistance of the bonding must be proper for the abrasive grit type, in order to warrant the correct protrusion as a function of the characteristics of the stone to be machined and the process, and it must essentially guarantee the worn grain release in order to assure the grit renewal, exposing the unaltered grains that are embedded in the matrix. The metal powders making up the bonding mixture are iron, copper, tungsten, cobalt and nickel.
tool was studied by Carrino et al. [12], while the diamond saw wear and the material properties were connected to the cutting specific energy by Ersoy et al. for various stone types [13]. Cu-based diamond tools were developed and produced through powder metallurgy by Wang et al. [14], while the configuration of the diamond tool for various CNC machining processes was studied by Kenda and. Kopač, who described the forces and the tool wear mechanism operating in different type of machining technologies [15]. Zhang J. et al. show an innovative frame saw machine to cut granite. A sawing test and a simulation were carried out to analyse the sawing trajectory, the surface topography of the segments and the percentage of worn diamond particles [16]. Turchetta et al. show an innovative prototype machine to cut stone by a diamond wire. The developed prototype was provided by a sensory system to measure both the cutting power and the tensile force of the diamond wire during experimental tests. In this way it was possible to verify the functionality of the prototype plant and, in the same time, to evaluate the productivity of the implemented cutting process [17,18]. Wang P. shows the modelling and estimation of production rate in ornamental stones sawing based on brittleness indexes [19]. Denkena B. et al. study thin tools for the high speed cutting of granite; in particular the application of thinner discs is the aim to achieve the standard market quality while working with lower tool stiffness at higher rotational speeds. Investigations on the influence of the shape, the different alloys of the steel core and of different bonding systems on process forces, tool wear and cut quality [20,21]. All these works lack a systematic study for the evaluation of high-speed machining performance in cutting granite with diamond disks. Current state of studies points out how cutting efficiency depends on cutting speed in natural stones machining. The current trend in all cutting processes is to work at high cutting speeds with the aim of reducing processing times and costs. This requires a careful analysis of the performance of the tool that varies with the cutting speed. In cutting granite with diamond disks, conventional cutting speeds are around 20–25 m/s. The objective of this paper is to analyse the performance of the tool in cutting granite at high cutting speeds, i.e. speeds higher than those conventionally used. In particular, the machining conditions that are most interesting by an industrial point of view were investigated. An ornamental stone was machined on a CNC machining centre, retrofitted with a dynamometer and data acquisition systems, to investigate the effects of variations in machining parameters. The sensor data included cutting force measurements further divided into measurable components.
3. Experimental setup Fig. 1a shows a CNC milling machine chosen to perform the experimental tests; it is characterized by a 15 kW spindle power, while the tests have been carried out at a maximum spindle speed of 15,000 rpm. The material chosen for this study is the Sardinian granite, while the adopted tool is a sintered diamond disk commonly selected for natural stone cutting, whose properties are reported in Table 1. As concerns the process parameters, two values of feed per revolution and four ones of Table 1 Tool properties. Tool properties
Diamond disk
Diamond mesh [#] Diamond concentration [Kts/cm3] Tool diameter [mm] Tool thickness [mm]
40/50 4.4 180 5
2. Sintered diamond tools for natural stone machining Chemical composition of bonding (%)
Natural stone machining occurs by using diamond tools for cutting such as wires, blades disks and for surface machining such as grinders and mills of different shapes and profiles. Commonly the tool is made of a super-abrasive grit anchored on a support by means of a bonding. Support is very important since it transfers the energy between the
Co Cu C O Al
2
42.80 28.40 20.44 5.14 2.24
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out taking into account the Fy and the Fz components of the cutting force. The highest readings obtained for each tool revolution readings have been considered from acquired force signals for each test. For each signal acquired have been calculated the highest values of components of the cutting force Fy and Fz obtained as average value of the peaks measured. Fig. 3 shows the highest values of Fy and Fz component of the cutting force as a function of cutting speed for both levels of feed per revolution: both components increased with feed per revolution and they decreased with cutting speed increment. This is due to the fact that the quantity of material removed by the single abrasive grain decreased with the increase of the cutting speed, other conditions being equal, so the components of the cutting force were reduced. Likewise, the chip section removed by the single abrasive grain increases as the advancement per revolution increases, with a consequent increase in the components of the cutting force. The graph also shows results dispersion very low, which demonstrates repeatability of the test method and of the tool characteristics. The graph in Fig. 3 denotes also that the Fy component of cutting force was lower than Fz one that reached maximum values of about 220 N and about 120 N for a feed per revolution of 0.10 mm and 0.05 mm, respectively, while the maximum value of the Fy was about 90 N for a feed per revolution of 0.10 mm. Moreover, in Fig. 3 the relations of linear type between the component of the cutting force and the cutting speed are reported. As can be seen from the graph, the regression curves obtained show an excellent value of R2. The results show that adopting high cutting speeds allows to increase productivity by reducing process times and to reduce process forces and, consequently, the stresses acting on the workpiece and the diamond grains.
Table 2 Experimental plan. Factors
# Levels
Levels
Cutting speed “Vc” [m/s] Feed per revolution “f” [mm] Radial cutting depth “dr” [mm]
4 2 1
35–45–55–65 0.05–0.10 25
Working stage 0, 1, 2, 3,4,5 Working stage 0
Working stage 1
Working stage 2
Working stage 3
Working stage 4
Working stage 5
Material removed 0 cm3
Material removed 600 cm3
Material removed 1200 cm3
Material removed 1800 cm3
Material removed 2400 cm3
Material removed 3000 cm3
cutting speed are considered; in addition, 6 stages of working are considered. A total of 192 experimental runs are performed, as four replications are run for each parameter set, as the experimental plan shows in Table 2. As regards cutting speed, higher values have been used compared to the maximum speeds conventionally used in the industrial sector for the tested granite, which are around 20–25 m/s, and in particular in a range that varies between 35 and 65 m/s. As showed in Fig. 1b, a piezoelectric dynamometer has been employed to evaluate the three components of the cutting force, that are Fx, Fy and Fz. The acquisition system is suitable to acquire the signals of the dynamometer for various time intervals and frequencies in order to analyse the entire information about the signal of force. It has been observed that the signal along the three axes is periodic, so the entire signal information has been collected with 32,768 points. The acquisition system has been completed by an A/D converter and a PC that sampled the signal at 10 kHz; therefore, each inspection lasted 3.2768 s.
4.2. High-speed cutting of granite: wear analysis The behavior of a diamond tool in respect to wear is the consequence of wear progressions of the single diamonds grain and the bonding constituting the tool (see Fig. 4). This classification and the related experimental method have been described in previous works [12]. At first, the bonding erosion increases the diamond grain protrusion so as to come into contact with the material being machined (intact grain). Once in contact, the grain is rounded so as to form a plateau (smoothed grain). Intermittent contact with the workpiece due to tool rotation leads to cyclical load on the diamond grain which, amplified by the inhomogeneity of the stone and the vibrations, causes deterioration of grain capacity to resist the cut forces and consequently its disintegration after a certain interval of time (fractured grain). The wear progression leads finally to a completely fractured particle or to a matrix enough eroded to allow the release of diamond grain (pull-out). Other grains will come to the tool cutting surface and the wear cycle starts again. The test conditions are given in Table 2. A representative sample was extracted from the diamond grain population scattered on tool surface and its behaviour with regard to wear has been observed. The sample has been selected considering at least 20 grains to be contained on the reference segment surface. The univocal identification of the diamond grain on the reference surface has been obtained by LAICA microscope mapping with a magnification of 200×. In order to plan the cuts sequence, i.e. to determine the material volume to be removed for each cut, the average life of a diamond grain through preliminary tests has been determined. Each cut removes the same volume of material corresponding to a specific processing condition defined working stage. The amount of the material removed has been set for each working stage and it is equal to 600 cm3. At the end of each working stage, components of cutting force have been measured. For each force signal, the highest value obtained has been considered as the average value of the signal peaks, moreover since the
4. Results and discussion This section shows the forces and wear analysis as a function of high-speed cutting of granite. 4.1. High-speed cutting of granite: forces analysis
F [N]
A monitoring strategy has been adopted based on time-domain characteristics. Fig. 2 shows typical time domain signals monitored in Y (feed) and Z(vertical) directions. Stone cutting has been performed at a cutting speed of 45 m/s and at a feed per revolution of 0.10 mm. As figures show, force signals are periodic and regular. Fx component of cutting force is negligible compared to Fy and Fz ones since cut takes place in the plane. Therefore, cutting forces analysis has been carried
220 200 180 160 140 120 100 80 60 40 20 0
Fz
0
5
10
15
20 25 time [ms]
Fy
30
35
40
45
50
Fig. 2. Time domain signal monitored in Y and Z direction. 3
Diamond & Related Materials 100 (2019) 107579
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Fy (f=0.05 [mm])
Fy (f=0.10 [mm])
Fz (f=0.05[mm])
Fz (f=0.10 [mm])
240 220 200 180
Fy, Fz [N]
160 140 120 100 80 60 40 20 0 20
25
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40
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50
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60
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cung speed [m/s] f=0.05 mm Fy=69.70-0.6075Vc Fz=160.75-1.065Vc R2=0.806 R2=0.978
f=0.10 mm Fy=123.31-1.0275Vc Fz=286-2.27Vc R2=0.9145 R2=0.9527
Fig. 3. Fy and Fz component vs. cutting speed for the two values of f (0.05–0.10 mm); working stage 0.
cutting speed of 35 m/s and 45 m/s, while it increases significantly with working progression for cutting speed of 55 m/s and 65 m/s. This increasing is particularly evident for cutting speed of 65 m/s. Similar results have been obtained for Fz component of cutting force. Fig. 6 shows Fy and Fz components trend of cutting force as a function of cutting speed and as a function of working stages, for a fixed feed per
dispersion obtained after four replications is always limited (< 7%), in the following graphs have been reported only the average value. Fig. 5 shows the trend of Fy and Fz component of cutting force as a function of cutting speed and working stages for a fixed feed per revolution of 0.05 mm. In Figure are showed the average force values: Fy component of cutting force remains almost constant over time for
intact grain
smoothed grain
fractured grain
pull-out grain Fig. 4. Wear states of a diamond grain. 4
Diamond & Related Materials 100 (2019) 107579
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240 Fy (working stage 1)
220
Fy (working stage 2)
Fy,Fz [N]
200 180
Fy (working stage 3)
160
Fy (working stage 4)
140
Fy (working stage 5)
120
Fz (working stage 1)
100
Fz (working stage 2)
80
Fz (working stage 3)
60 Fz (working stage 4) 40 Fz (working stage 5) 20 30
35
40
45
50
55
60
65
70
cung speed [m/s]
Fy,Fz [N]
Fig. 5. Fy and Fz component vs. cutting speed for different working stages; f = 0.05 mm.
360 340 320 300 280 260 240 220 200 180 160 140 120 100 80 60 40
Fy (working stage 1) Fy (working stage 2) Fy (working stage 3) Fy (working stage 4) Fy (working stage 5) Fz (working stage 1) Fz (working stage 2) Fz (working stage 3) Fz (working stage 4) Fz (working stage 5) 30
35
40
45
50
55
60
65
70
cung speed [m/s] Fig. 6. Fy and Fz component vs. cutting speed for different working stages; f = 0.10 mm.
percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 7. Percentage of diamond grains morphology for different working stage; Vc = 35 [m/s] and f = 0.05; 0.10 [mm].
5
Diamond & Related Materials 100 (2019) 107579
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percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 8. Percentage of diamond grains morphology for different working stage; Vc = 45 [m/s] and f = 0.05; 0.10 [mm].
percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 9. Percentage of diamond grains morphology for different working stage; Vc = 55 [m/s] and f = 0.05; 0.10 [mm].
percentage of diamond grains
60% 55%
intact grain-f=0.05
50%
smoothed grain-f=0.05
45% 40%
fractured grain-f=0.05
35%
pull-out grain-f=0.05
30% intact grain-f=0.10
25% 20%
smoothed grain-f=0.10
15% fractured grain-f=0.10
10% 5%
pull-out grain-f=0.10
0% 0
1
2
3 working stage
4
5
Fig. 10. Percentage of diamond grains morphology for different working stage for Vc = 65 [m/s] and f = 0.05; 0.10 [mm].
occurs; its increase is probably due to a greater wear of the diamond grains. In order to better understand this phenomenon, for each working stage have been monitored the characteristics of a single diamond grain
revolution of 0.10 mm; the components of cutting force is almost constant with the working progress for cutting speed of 35 m/s, 45 m/s and 55 m/s. By reaching the cutting speed of 65 m/s a considerable increase of Fy and Fz component of the cutting force with the working progress
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Diamond & Related Materials 100 (2019) 107579
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Fig. 11. Performance index as a function of the cutting speed; f = 0.05 [mm].
Fig. 12. Performance index as a function of the cutting speed; f = 0.10 [mm].
removed by a single diamond during the cutting process combined with the low process forces in working stage 0 exerted on the diamond and on the matrix. Figs. 11 and 12 show the performance index obtained as the ratio between the number of damaged grains (smoothed grains, fractured grains, pull-out grains) and the intact grains as a function of the cutting speed, for both level of feed. As it can be seen from Fig. 11, for a feed of 0.05 mm the smoothed/intact grains performance index increases drastically with cutting speeds above 45 m/s, going from about 0.4 to about 1.6, while the pull-out/intact grains performance index remains almost constant with the cutting speed and the fractured/intact grains performance index presents a fluctuating trend between 0.4 and 1. For higher feeds, the performance index trends are similar, even if the values reached are lower.
belonging to a two-sector taken as a reference on the disc for minimum 40 grains. In particular, the diamonds were classified according to the different working stages (intact grain, smoothed grain, fractured grain, pull-out grain, as visible in Fig. 4) characterized using a procedure reported in (test protocol for micro-geometric wear of sintered diamond tools [12]). Figs. 7–10 show the percentage values of diamonds morphology for different working stage: for all tests a low dispersion was found (< 5%). In Fig. 7 (cutting speed of 35 mm/s), for f = 0.05 mm, the percentage of intact grains is about 42%, the percentage of smoothed grains is about 13%, the percentage of fractured grains is about 32% and finally the percentage of pull-out grains is about 13%; for f = 0.10 mm, the percentage of intact grains is about 47%, the percentage of smoothed grains is about 12%, the percentage of fractured grains is about 27% and finally the percentage of pull-out grains is about 14%. This high percentage of intact and fractured grains, combined with a low percentage of the smoothed ones, indicates a good cutting behaviour of the tool; during the working progress a constant and optimal renewal of diamond grits occurs. Similar results have been obtained with a cutting speed of 45 mm/s, see Fig. 8. Figs. 9–10 show the percentage values of diamonds morphology for different working stage and cutting speed of 55/65 m/s. It is noticed a considerable increase of the percentage of smoothed grain (> 30%), tending to increase with the working stages; the percentage of intact grains is < 35% and it tends to decrease with the working stages. It is clear that working with a cutting speed of 55 and 65 m/s is not possible to obtain a good renewal of diamond grits, so it is possible to increase the cutting speed up to 45 m/s. This low renewal of diamond grits for high cutting speed are essentially due to the maximum chip section
5. Conclusions This work points out the relation between the cutting force components and the main process parameters (feed per revolution and cutting speed) for granite cutting by diamond disk. In particular, the cutting force components increase with feed per revolution and they decrease with cutting speed raising. The results obtained point out how it is possible to improve the process efficiency by working with cutting speed higher than conventional value of about 35 m/s with considerable productivity growth. However, the tool wear is compatible for cutting speed ≤45 m/s as higher values can cause problems due to the poor renewal of diamond grits, which is important for the effective use of any sintered diamond tool. This phenomenon is highlighted by the performance index, that is obtained as the ratio between the number of smoothed grains and intact 7
Diamond & Related Materials 100 (2019) 107579
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grains. This index undergoes a significant increase due to the poor renewal of the abrasive grits passing from a cutting speed of 45 m/s to 55 m/s. In conclusion, increasing the cutting speed is possible in natural stone machining processes using diamond tools in order to increase productivity; however, there is a limit value beyond which the tool suffers an evident loss of its cutting capacity.
[9] S. Turchetta, Cutting force and diamond tool wear in stone machining, Int. J. Adv. Manuf. Technol. 61 (2012) 441–448, https://doi.org/10.1007/s00170-0113717-04. [10] C.Y. Wang, R. Clausen, Marble cutting with single point cutting tool and diamond segments, Int J Mach Tool Manu 42 (2002) 1045–1054. [11] A. Di Ilio, A. Togna, A theoretical wear model for diamond tools in stone cutting, Int J Mach Tool Manu 43 (2003) 1171–1177. [12] L. Carrino, W. Polini, S. Turchetta, Test protocol for micro-geometric wear of sintered diamond tools, Wear 257 (2004) 246–256. [13] A. Ersoy, S. Buyuksagic, U. Atici, Wear characteristics of circular diamond saws in the cutting of different hard abrasive rocks, Wear (2005) 1422–1436. [14] C. Wang, X. Zhang, C. Jia, Current research situation and development of Cu-based diamond tools made by powder metallurgy, FenmoYejinJishu/Powder Metall. Technol. 30 (2) (2012) 140–143. [15] J. Kenda, J. Kopac, Diamond tools for machining of granite and their wear, StrojniskiVestnik/J. Mech. Eng. 55 (12) (2009) 775–780. [16] H. Zhang, J. Zhang, Z. Wang, Q. Sun, J. Fang, A new frame saw machine by diamond segmented blade for cutting granite, Diam. Relat. Mater. 69 (2016) 40–48. [17] S. Turchetta, G. Gelfusa, W. Polini, E. Venafro, A new sawing machine by diamond wire, Adv. Manuf. Technol. 70 (2014) 73–78. [18] S. Turchetta, L. Sorrentino, C. Bellini, A method to optimize the diamond wire cutting process, Diam. Relat. Mater., Vol. 71, 1 January 2017, Pages 90–97. [19] P. Wang, Modeling and estimation of production rate in ornamental stones sawing based on brittleness indexes, Math. Probl. Eng. 4 (2019) 1–12 3232517. [20] B. Denkena, H.K. Tönshoff, T. Friemuth, T. Glatzel, Development of advanced tools for economic and ecological grinding of granite, Key Eng. Mater. 250 (2003) 21–32. [21] B. Denkena, D. Boehnke, J. Bockhorst, Thin tools for the high speed cutting of granite, Int. J. Abras. Technol. 2 (2) (2009) 173–183.
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