# Numerical Investigation of the Rock Cutting Performance of a Circular Sawblade

Authors: Zhiwen Wang; Qingliang Zeng; Zhenguo Lu; Zhihai Liu; Xu Li
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

The rock cutting process with a circular sawblade and the rock breaking mechanism of rock are studied with a numerical simulation method in this paper. The influence of cutting parameters of the circular sawblade on cutting force, rock damage, and specific cutting energy in the process of circular sawblade cutting rock is researched. The cutting force increases with the feed speed and an increase in cutting depth and decline in rotation speed. Cutting rock with double circular sawblades can reduce cutting force. However, the specific cutting energy declines with the increase in cutting depth and the decline in the distance between the double circular sawblades. Cutting parameters have a great influence on the damage range of rock. The research results can be applied to rock processing with a circular sawblade.


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## Body

## 1. Introduction

Natural stone is an important building material, and the circular sawblade is widely applied in natural stone processing. The influences of circular sawblade cutting parameters on the cutting performance are studied. Many experts and scholars at home and abroad have penetrated into research on cutting rock with a sawblade.The brittleness of the rock makes rock processing very difficult. Diamond sawblade is the best choice in rock processing. Therefore, many scholars have investigated cutting rock with a sawblade. Zhang et al. explored the wear performance of diamond tools with different sawing trajectories in stone processing with experiments [1]. Yan et al. established the mathematical model to research the influence of a diamond-coated tool on cutting characteristics in machining of natural marble [2]. Oh et al. researched the effect of the abrasive feed rate and the particle size distribution on the rock cutting performance [3]. Wang et al. investigated the effect of the cutting parameters and abrasive angle on a rock fragment and cutting forces and demonstrated the feasibility and reliability of FDEM in simulating rock machining [4]. Dong et al. applied the scanning electron microscopy and the 3D laser microscope in sawing experiments to study the wear characteristics of diamond tools during cutting granite [5]. Jerro et al. built the theoretical chip morphology and the relationship between the force and cutting parameters [6]. Turchetta et al. expressed the influence of pretwisting and tensioning of wire on the cutting force and optimized [7]. Zhong et al. discussed the influence of fluid and the shale rock interaction on rock [8]. Karakurt et al. expressed the influence of cutting parameters and the petrophysical parameters on cutting force [9]. Buyuksagis and Goktan conducted experiments of a circular sawblade cutting seven types of marble to investigate the influence of cutting parameters on specific cutting energy [10]. Ersoy and Atici researched the influence of operation and rock parameters on the performance of saw with experiments [11]. Fener et al. studied the rock cutting process with a circular diamond sawblade to predict the performance of cutting carbonate rocks [12]. Tumac investigated the rock parameters of Turkish carbonate rock cutting with a large diameter circular saw to predict the cutting performance [13]. Wang et al. performed single cutting experiments to research the influence of milling parameters on marble fragments and cutting force [14].Kahraman et al. predicted the sawability of carbonated rock with the artificial network from shear strength parameters [15]. Tumac researched the cutting performance of a circular sawblade with the artificial neural network and geological origin of the rock [16, 17]. Wie et al., based on a new method of fuzzy mathematics, established the relationship between the sawability and the mechanical properties of granite [18]. Kahraman et al. carried out experiments of cutting rock with large diameter diamond saws and analyzed with multiple curvilinear regression analysis to build the predicting model of sawability of carbonate rock [19]; besides, they researched the relationship between sawability and undertaken hardness [20]. According to operation and rock parameters, Yurdakul and Akdas established the predicting model using statistical methods to predict the specific cutting energy [21]. Güney established the performance prediction model of a larger diameter saw based on rock parameters [22].Many scholars have researched the influence of operation and rock parameters on the diamond saws cutting performance and specific cutting energy with experimental and theoretical methods. However, few research studies are based on the method of numerical simulation to investigate the damage of rock with a circular sawblade cutting rock. Therefore, this paper establishes the numerical simulation models to research the influence of various parameters on the cutting performance of a circular sawblade, with feed speeds of 0.10, 0.15, 0.20, 0.25, and 0.30 m/min and rotation speeds of 1000, 1500, 2000, 2500, and 3000 r/min, the cutting depths set as 10, 20, 30, 40, 50, and 60 mm, and the distance of double diamond sawblades set as 10, 20, 30, 40, and 50 mm.


## 2. The Cutting Force Components Demonstration

The rotation speed direction of a circular sawblade has a great effect on the cutting performance. It is defined that the feed speed and the rotation speed in the same direction is the forward cutting while the opposite direction is the reverse cutting. There are two kinds of cutting force models of circular sawblade cutting rock with two directions of rotation speed, as is shown in Figure1. The cutting thickness of the forward cutting is from thin to thick. When circular sawblade contacts the rock which immediately cuts the rock, the circular sawblade will slide on the rock surface and the cutting thickness increases slowly, which is advantageous to cutting rock. However, the cutting thickness of the circular sawblade reverse cutting is from thick to thin, and the circular sawblade cuts rock from the uncutting surface to the cutting surface. In addition, the reverse cutting is starting from the uncutting surface into the surface of the hard layer, and the circular sawblade is subject to a great impact load. The cutting thickness and the contact time of the forward cutting and reverse cutting are different, and the damage of rock is different in the process of a circular sawblade cutting rock. According to experience, the cutting performance of the circular sawblade with forward cutting is obviously higher than that of the reverse cutting. When the circular sawblade cuts hard rock, the forward cutting is more suitable to the rock cutting.Figure 1
Force model of a circular sawblade cutting rock: (a) The force model of a circular sawblade cutting rock with forward cutting; (b) the force model of a circular sawblade cutting rock with reverse cutting.
(a)(b)The tangential force and normal force are the main components of cutting force in a circular sawblade cutting rock. However, the axial force is much smaller than tangential force and normal force. The axial force is neglected during a circular saw cutting rock in the calculation for formulas. The cutting force can be obtained by the equation as follows:(1)Fc=Fv2+Fh2,where Fc is the cutting force, Fv is the vertical force, and Fh is the horizontal force.The contact angleθ between the circular sawblade and rock is shown as follows:(2)θ=cos−11−2lpd,where lp is the cutting depth and d is the diameter of the circular sawblade.The angleμ between the cutting force and the vertical force is as follows:(3)μ=cos−1FvFc.The tangential forceFt and the normal force Fn are the components of the cutting force Fc.(4)Ft=Fcsinγ,Fn=Fccosγ,where(5)γ=μ−Aθ,A=γ±μθ.The value ofA depends on the location of the circular sawblade with rock. The application point of the cutting force on the arc θ of the contact between the sawblade and the rock decides the value of A. However, the cutting depth and the length of the contact between the circular sawblade and rock are small, which makes A difficult to obtain. For the slow cutting, A = 0.67 is consistent with the distribution of triangular force intensity along the grinding zone [23, 24].


## 3. Establishing a Numerical Simulation Model

### 3.1. Geometric Model and Boundaries

In order to research the rock damage and the circular sawblade cutting performance, the geometric model of a circular sawblade cutting rock is established with Solidworks software, and then, the geometric model is imported to the ANSYS/LS-DYNA software to establish the circular sawblade cutting rock numerical simulation model.The diameter of the circular sawblade is 380 mm, and it has 24 segments with the length of 40 mm, height of 15 mm, and thickness of 3.4 mm. The rock is a cuboid which is 500 mm in length, 150 mm in width, and 125 mm in height. The hexahedral element SOLID164 is used to mesh the circular sawblade and the rock, and the smallest size of rock element is 1 mm. The model is meshed by local mesh refinement that can reduce the number of grids to improve calculation speed, as well as to ensure the computation accuracy. The key parameters of rock material are plotted in Table1.Table 1
The related parameters of rock material [25].
ParametersMass density (kg/m3)Young’s modulus (GPa)Uniaxial compressive strength (MPa)Brazilian tensile strength (MPa)Value2.7e345.5120.712.1Constrains are applied to the numerical simulation model. The full constraints are applied to the bottom surface, the displacements constraints in theX- and Y-direction are applied to right and left surfaces, and the displacements constraints in the Y- and Z-direction are applied to the front and back surfaces. The displacements constraints in the X- and Y-direction and the rotation constraints around the Y- and Z-axis are added to the circular sawblade, as shown in Figure 2. By adding the nonboundary reflection condition to the noncutting surface of the rock, the small rock model can be used to simulate the large rock. The contact types between the circular sawblade and rock are defined as the ERODING_SURFACE_AND_SURFACE and AUTOMATIC_GENERAL. The simulation time is set as 5 minutes, and a d3plot file is exported with each step lasting 1 s. The solver in LS-DYNA/ANSYS has no limits for CPU cores, and the circular sawblade cutting rock simulation model is efficiently performed on the workstation for 45 hours.Figure 2
The numerical simulation model of a circular sawblade cutting rock.


### 3.2. The RHT Constitutive Model

The RHT model is divided into three stages: the elastic stage, linear strengthening stage, and damage softening stage. The standardized pressure expression isp∗=p/fc, where fc is the uniaxial compressive stress. The equivalent stress intensity expression for the failure surface is(6)σfailp,θ,ε˙=fc⋅σTXC∗ps⋅R3θ⋅Frateε˙,where σTXC∗ps is the equivalent stress intensity of the compressive meridian of the quasistatic failure surface equation, R3θ is the load angle factor, ps=p/Frateε˙ is the quasistatic pressured, and Frateε˙ is the compressive strain rate dynamic increase factor, with the expression as follows:(7)Frateε˙=ε˙ε0c˙βc,p≥fc3,p+ft/3fc/3+ft/3ε˙ε0c˙βc+p−fc/3−fc/3−ft/3ε˙ε0c˙βc,−ft3<p<fc3,ε˙ε0t˙βt,p≤−ft3,where ft is the uniaxial tensile strength; ε0c˙=30×10−6s−1; ε0t˙=3×10−6s−1; ε0˙=1.0s−1; βc is the compressive strain rate-dependent exponent, βc=4/20+3fc; βt is the tensile strain rate-dependent exponent, βt=2/20+fc; and fc is the uniaxial compressive strength.The equivalent stress of the elastic limit plane of the initial material is obtained by the equivalent stress on the failure plane, with the expression as follows:(8)σelasticp,θ,ε˙=fc⋅σTXC∗ps,el⋅R3θ⋅Frateε˙⋅Felastic⋅Fcap,where Felastic is the elastic scaling function, Fcap is the cap function, and ps,el=ps/Felastic is the quasistatic elastic limit pressure.(9)Felastic=gc∗,p≥fc,el3p+ft,el/3fc,el/3+ft,el/3gc∗+p−fc,el/3−fc,el/3−ft,el/3gt∗,−ft,el3<p<fc,el3,gc∗,p≤−ft,el3,where gc∗ is the compression yield surface parameter, gc∗=fc,el/fc, fc,el is the uniaxial compression elastic extreme pressure; gt∗ is the tensile yield surface parameter, gt∗=ft,el/fc; and ft,el is the uniaxial tensile elastic extreme pressure. The cap function is expressed as(10)Fcap=1,p≤pu=fc3,1−p−pup0−pu2,pu<p<p0,gc∗,p≥p0=pel,where p0=pel is the material porosity break compressive pressure.Because the RHT constitutive model introduces the linear reinforcement phase equation, it can describe the strain hardening effect of brittle materials such as concrete and rock. In the linear strengthening stage, the yield stress obeys the linear strengthening model. The function expression is(11)σYhard=σelastic+εplεpl−presoftening×σfail+σelastic,where σfail is the equivalent stress strength and σelastic is the equivalent elastic strength.(12)εpl−presoftening=GelasticGelastic−Gplastic×σfail+σelastic3G,while G is the shear modulus, Gelastic is the elastic modulus, and Gplastic is the plastic modulus. Combining formulas (11) and (12), the following is obtained:(13)σYhard=σelastic+3GRGεp,where εp is the plastic strain accumulated in the linear strengthening period and RG=Gelastic/Gelastic−Gplastic.At the beginning of the elastic phase and the linear reinforcement of the plastic strain, there is no accumulated damage. Only when the equivalent stress strength exceeds the equivalent stress beyond the failure stress intensity, the material begins to accumulate damage and, then, enters the softening stage of damage. The ratio of the cumulative equivalent plastic strain increase to the ultimate failure equivalent plastic strain is defined as the damage variableD, and the expression is given as(14)0≤D=∑Δεpεpfailure≤1,with(15)εpfailure=D1p∗−HTL∗D2≥εpm.The stress state equation with various different load angles is as follows:(16)R3θ=21−Q2cosθ+2Q−141−Q2cos2θ+5Q24Q41−Q2cos2θ+2Q−12,where Q is the ratio of tension to compression and θ is the load angle.(17)HTL∗=HTLfc,HTL=ft3fs/fcR3sfs/fcR3s−ftfcQ,where Δεp is the equivalent random strain increase, D1 and D2 are the parameters of the material, and εpm is the minimum equivalent plastic strain when the material is destroyed.The residual stress surface is introduced in the RHT concrete model, and the equivalent stress intensity isσdamage. The expression of σdamage is shown in the following formula:(18)σdamage=1−Dσfailure+Dσresidual.In the process of circular sawblade cutting rock, the failure modes of rock elements is complex, including compressive failure, tensile failure, and shear failure. Under the action of compressive, tensile, and shear stresses, the damage of rock element appears and increases, while with the rock damage reaching 1, the rock element will fail and be deleted. The rock fragments are difficult to be presented; therefore, the amount of the rock fragments is a positive correlation with rock removal volume. Therefore, the rock fragments are evaluated by rock removal volume.


### 3.3. Grid Independence Validation

Owing to the grid independence of the simulation model having great influence on the accuracy of simulation results, it is necessary to verify the grid independence. When the relative change rate of cutting force is within the set range scope, the results can be considered reliable and accurate. Finally, the appropriate rock mesh density is selected for the numerical simulation. The relative change rate curve of cutting force under different mesh densities is presented in Figure3.Figure 3
Independence test of the rock mesh density.When the mesh number reaches 144330, the relative change rate is less than 0.11%, which is within 0.15%. The increase of mesh number has little effect on the relative change rate of the cutting force. Therefore, when the mesh number is more than 144330, the results of numerical simulation can be considered accurate.


### 3.4. Calibration and Verification

In order to verify the numerical simulation of a circular sawblade cutting rock, in this paper, the experimental results [26] are applied to compare with the numerical simulation with a peripheral speed of 30 m/s, cutting depth of 15 mm, and feed speed of 3 m/min, as shown in Figure 4. The mining values of the vertical and horizontal force at the stable cutting stage are 190.06 N and 137.12 N, respectively, in the experimental results and 195.26 N and 131.25 N, respectively, in the numerical simulation results. The difference ratio of vertical and horizontal force between experiments and numerical simulation is 2.735% and 4.28%, respectively. The results indicate that the numerical simulation results are in agreement with experimental results, which proves the numerical simulation in this paper is reliable.Figure 4
The results of numerical simulation and experiment.


## 3.1. Geometric Model and Boundaries

In order to research the rock damage and the circular sawblade cutting performance, the geometric model of a circular sawblade cutting rock is established with Solidworks software, and then, the geometric model is imported to the ANSYS/LS-DYNA software to establish the circular sawblade cutting rock numerical simulation model.The diameter of the circular sawblade is 380 mm, and it has 24 segments with the length of 40 mm, height of 15 mm, and thickness of 3.4 mm. The rock is a cuboid which is 500 mm in length, 150 mm in width, and 125 mm in height. The hexahedral element SOLID164 is used to mesh the circular sawblade and the rock, and the smallest size of rock element is 1 mm. The model is meshed by local mesh refinement that can reduce the number of grids to improve calculation speed, as well as to ensure the computation accuracy. The key parameters of rock material are plotted in Table1.Table 1
The related parameters of rock material [25].
ParametersMass density (kg/m3)Young’s modulus (GPa)Uniaxial compressive strength (MPa)Brazilian tensile strength (MPa)Value2.7e345.5120.712.1Constrains are applied to the numerical simulation model. The full constraints are applied to the bottom surface, the displacements constraints in theX- and Y-direction are applied to right and left surfaces, and the displacements constraints in the Y- and Z-direction are applied to the front and back surfaces. The displacements constraints in the X- and Y-direction and the rotation constraints around the Y- and Z-axis are added to the circular sawblade, as shown in Figure 2. By adding the nonboundary reflection condition to the noncutting surface of the rock, the small rock model can be used to simulate the large rock. The contact types between the circular sawblade and rock are defined as the ERODING_SURFACE_AND_SURFACE and AUTOMATIC_GENERAL. The simulation time is set as 5 minutes, and a d3plot file is exported with each step lasting 1 s. The solver in LS-DYNA/ANSYS has no limits for CPU cores, and the circular sawblade cutting rock simulation model is efficiently performed on the workstation for 45 hours.Figure 2
The numerical simulation model of a circular sawblade cutting rock.


## 3.2. The RHT Constitutive Model

The RHT model is divided into three stages: the elastic stage, linear strengthening stage, and damage softening stage. The standardized pressure expression isp∗=p/fc, where fc is the uniaxial compressive stress. The equivalent stress intensity expression for the failure surface is(6)σfailp,θ,ε˙=fc⋅σTXC∗ps⋅R3θ⋅Frateε˙,where σTXC∗ps is the equivalent stress intensity of the compressive meridian of the quasistatic failure surface equation, R3θ is the load angle factor, ps=p/Frateε˙ is the quasistatic pressured, and Frateε˙ is the compressive strain rate dynamic increase factor, with the expression as follows:(7)Frateε˙=ε˙ε0c˙βc,p≥fc3,p+ft/3fc/3+ft/3ε˙ε0c˙βc+p−fc/3−fc/3−ft/3ε˙ε0c˙βc,−ft3<p<fc3,ε˙ε0t˙βt,p≤−ft3,where ft is the uniaxial tensile strength; ε0c˙=30×10−6s−1; ε0t˙=3×10−6s−1; ε0˙=1.0s−1; βc is the compressive strain rate-dependent exponent, βc=4/20+3fc; βt is the tensile strain rate-dependent exponent, βt=2/20+fc; and fc is the uniaxial compressive strength.The equivalent stress of the elastic limit plane of the initial material is obtained by the equivalent stress on the failure plane, with the expression as follows:(8)σelasticp,θ,ε˙=fc⋅σTXC∗ps,el⋅R3θ⋅Frateε˙⋅Felastic⋅Fcap,where Felastic is the elastic scaling function, Fcap is the cap function, and ps,el=ps/Felastic is the quasistatic elastic limit pressure.(9)Felastic=gc∗,p≥fc,el3p+ft,el/3fc,el/3+ft,el/3gc∗+p−fc,el/3−fc,el/3−ft,el/3gt∗,−ft,el3<p<fc,el3,gc∗,p≤−ft,el3,where gc∗ is the compression yield surface parameter, gc∗=fc,el/fc, fc,el is the uniaxial compression elastic extreme pressure; gt∗ is the tensile yield surface parameter, gt∗=ft,el/fc; and ft,el is the uniaxial tensile elastic extreme pressure. The cap function is expressed as(10)Fcap=1,p≤pu=fc3,1−p−pup0−pu2,pu<p<p0,gc∗,p≥p0=pel,where p0=pel is the material porosity break compressive pressure.Because the RHT constitutive model introduces the linear reinforcement phase equation, it can describe the strain hardening effect of brittle materials such as concrete and rock. In the linear strengthening stage, the yield stress obeys the linear strengthening model. The function expression is(11)σYhard=σelastic+εplεpl−presoftening×σfail+σelastic,where σfail is the equivalent stress strength and σelastic is the equivalent elastic strength.(12)εpl−presoftening=GelasticGelastic−Gplastic×σfail+σelastic3G,while G is the shear modulus, Gelastic is the elastic modulus, and Gplastic is the plastic modulus. Combining formulas (11) and (12), the following is obtained:(13)σYhard=σelastic+3GRGεp,where εp is the plastic strain accumulated in the linear strengthening period and RG=Gelastic/Gelastic−Gplastic.At the beginning of the elastic phase and the linear reinforcement of the plastic strain, there is no accumulated damage. Only when the equivalent stress strength exceeds the equivalent stress beyond the failure stress intensity, the material begins to accumulate damage and, then, enters the softening stage of damage. The ratio of the cumulative equivalent plastic strain increase to the ultimate failure equivalent plastic strain is defined as the damage variableD, and the expression is given as(14)0≤D=∑Δεpεpfailure≤1,with(15)εpfailure=D1p∗−HTL∗D2≥εpm.The stress state equation with various different load angles is as follows:(16)R3θ=21−Q2cosθ+2Q−141−Q2cos2θ+5Q24Q41−Q2cos2θ+2Q−12,where Q is the ratio of tension to compression and θ is the load angle.(17)HTL∗=HTLfc,HTL=ft3fs/fcR3sfs/fcR3s−ftfcQ,where Δεp is the equivalent random strain increase, D1 and D2 are the parameters of the material, and εpm is the minimum equivalent plastic strain when the material is destroyed.The residual stress surface is introduced in the RHT concrete model, and the equivalent stress intensity isσdamage. The expression of σdamage is shown in the following formula:(18)σdamage=1−Dσfailure+Dσresidual.In the process of circular sawblade cutting rock, the failure modes of rock elements is complex, including compressive failure, tensile failure, and shear failure. Under the action of compressive, tensile, and shear stresses, the damage of rock element appears and increases, while with the rock damage reaching 1, the rock element will fail and be deleted. The rock fragments are difficult to be presented; therefore, the amount of the rock fragments is a positive correlation with rock removal volume. Therefore, the rock fragments are evaluated by rock removal volume.


## 3.3. Grid Independence Validation

Owing to the grid independence of the simulation model having great influence on the accuracy of simulation results, it is necessary to verify the grid independence. When the relative change rate of cutting force is within the set range scope, the results can be considered reliable and accurate. Finally, the appropriate rock mesh density is selected for the numerical simulation. The relative change rate curve of cutting force under different mesh densities is presented in Figure3.Figure 3
Independence test of the rock mesh density.When the mesh number reaches 144330, the relative change rate is less than 0.11%, which is within 0.15%. The increase of mesh number has little effect on the relative change rate of the cutting force. Therefore, when the mesh number is more than 144330, the results of numerical simulation can be considered accurate.


## 3.4. Calibration and Verification

In order to verify the numerical simulation of a circular sawblade cutting rock, in this paper, the experimental results [26] are applied to compare with the numerical simulation with a peripheral speed of 30 m/s, cutting depth of 15 mm, and feed speed of 3 m/min, as shown in Figure 4. The mining values of the vertical and horizontal force at the stable cutting stage are 190.06 N and 137.12 N, respectively, in the experimental results and 195.26 N and 131.25 N, respectively, in the numerical simulation results. The difference ratio of vertical and horizontal force between experiments and numerical simulation is 2.735% and 4.28%, respectively. The results indicate that the numerical simulation results are in agreement with experimental results, which proves the numerical simulation in this paper is reliable.Figure 4
The results of numerical simulation and experiment.


## 4. Results and Discussion

### 4.1. The Process of a Circular Sawblade Cutting Rock

The circular sawblade cuts rock with constant rotation speed and feed speed, with the feed speed of 0.30 m/min, rotation speed of 2000 r/min, and the cutting depth of 30 mm. It is obvious that the force appears and increases as the circular sawblade contacts the rock. The rock element is damaged with circular sawblade compression and tension. The damage value of some rock elements reaches 1 which is acted by the circular sawblade with continuing cutting. While the damage value of rock element reaches 1, the element would fail and be deleted. The rock damage nephograms in the process of circular sawblade cutting rock are plotted in Figure5. In the initial stage of rock cutting with a circular sawblade, the deformation and damage of rock appear under compression and tension, as shown in Figure 5(a). With the circular sawblade cutting further, fail elements appear in the first layer elements on the upper surface of the rock and are deleted, as shown in Figure 5(b). While the circular sawblade advances to a certain distance, the rock damage extends outward, and the broken area extends beyond the contacting area. The depth of rock damage increases with the increase in the cutting distance of circular sawblade cutting and reaches a stable depth. Meanwhile, damage ranges also extend and increase downward. When the cutting distance of circular sawblade is large, the damage element on the both sides of saw slot cut by the circular sawblade fail under the interaction of circular sawblade.Figure 5
Rock damage nephograms of a circular sawblade cutting rock at various cutting distances: (a) Rock damage nephogram of 7 mm cutting distance; (b) rock damage nephogram of 9 mm cutting distance; (c) rock damage nephogram of 12 mm cutting distance; (d) rock damage nephogram of 21 mm cutting distance; (e) rock damage nephogram of 27 mm cutting distance; (f) rock damage nephogram of 45 mm cutting distance; and (g) rock damage nephogram of 70 mm cutting distance.The cutting force has a larger peak value when the circular sawblade cuts the rock at the beginning, as shown in Figure6. The circular sawblade cuts rock at a constant rotation speed and feed speed; at the moment when the circular sawblade contacts the rock which produces a greater impact, the cutting force increases sharply and the peak cutting force is larger than that of stable cutting. It is obvious that the cutting force is closely related to the tangential and normal force, and the wave shape of the normal force curve is similar to the cutting force. The similarity between axial force and cutting force is lower. The values of the normal force and the tangential force are larger than the axial force of a circular sawblade. The fluctuation ranges of the normal force curve and the cutting force are lager; however, the fluctuation of the tangential force curve around the fixed value is relatively stable.Figure 6
Force curves of rock cutting with a circular sawblade.


### 4.2. The Influence of the Rotation Speed Direction of a Circular Sawblade on the Cutting Performance

The circular sawblade cuts rock with the feed speed of 0.30 m/min, rotation speed of 2000 r/min, and the cutting depth of 30 mm. The direction of rotation speed has great effects on the cutting performance. The rock damage nephograms with different rotation speed directions are shown in Figure7. However, in the numerical simulation results of circular sawblade cut rock with forward cutting, the rock damage area is smaller than that of the reverse cutting. The rock damage ranges of the circular sawblade forward cutting are smaller and more irregular. The broken area is random which is determined by the rock properties. The cutting surface of the circular sawblade is rough, and the quality of rock processing is poor with the circular sawblade reverse cutting, as shown in Figure 7(b). The forward cutting of the circular sawblade can achieve perfect quality and the relatively smooth cutting surface. In the left view, the damage area of forward cutting is smaller than that of reverse cutting. Also, the circular sawblade cutting rock with the same cutting parameters, the width and depth of damage area with forward cutting is smaller and more regular than that of the reverse cutting. The damage area of rock is irregular with the reverse cutting, and the quality of rock processing is poor which cannot meet processing requirement. Therefore, the forward cutting is more suitable for rock processing.Figure 7
The rock damage nephograms with various cutting models: (a) the rock damage nephogram with forward cutting; (b) the rock damage nephogram with reverse cutting.The force curves of the circular sawblade cutting rock with the forward cutting and reverse cutting are presented in Figure8. The cutting force of the forward cutting is smaller than that of the reverse cutting. The force fluctuates steadily with the forward cutting during steady cutting, which is much smaller than that of the reverse cutting. In the process of the circular sawblade cutting rock of the forward cutting, the cutting thickness of each circular grit increases slowly from 0 to the maximum, which makes the amplitude of cutting force smaller. However, when the cutting thickness of the reverse cutting declines from the maximum value to zero slowly and the compressive strength of rock is large, the fluctuation of cutting force is larger. The wave shape of normal force is basically the same as that of cutting force. Comparing the normal force of the circular sawblade with the forward and reverse cutting, it can be seen that the normal and tangential force amplitude of the forward cutting is smaller than that of the reverse cutting. However, the axial force of forward cutting and the reverse cutting are basically the same.Figure 8
Force curves of the circular sawblade cut rock with forward and reverse cutting: (a) the cutting force of the circular sawblade cutting rock; (b) the normal force of the circular sawblade cutting rock; (c) the tangential force of the circular sawblade cutting rock; and (d) the axial force of the circular sawblade cutting rock.
(a)(b)(c)(d)


### 4.3. The Influence of Cutting Parameters on Cutting Force

#### 4.3.1. The Influence of Feed Speed on Cutting Force

To investigate the influence of feed speed on the cutting force, the circular sawblade cutting rock numerical with the rotation speed of 2000 r/min, the cutting depths of 10, 30, and 50 mm, and the feed speeds of 0.10, 0.15, 0.20, 0.25, and 0.30 m/min are built. The average force curves with various feed speeds are presented in Figure9. It is obvious that the force increases with the increase of feed speed. While a circular sawblade cuts rock with constant rotation speed, the rock removal volume per circle increases with feed speed increasing, which causes tangential and normal force to increase obviously. The variation trend of the average force curves of cutting force and tangential force is similar. The feed speed increase causes the volume of the rock removal to increase. The difficulty of discharging fragments increasing causes the average axial force increase. However, the growth rate of force with a cutting depth from 30 to 50 mm is larger than that of a cutting depth from 10 to 30 mm. According to Figure 10, the force increases with the cutting depth increasing, and the relationship between the force of circular sawblade and cutting depth is quadratic.Figure 9
Force curves of the circular sawblade cutting rock with various feed speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.
(a)(b)(c)(d)Figure 10
Force curves of the circular sawblade cutting rock with various rotation speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.
(a)(b)(c)(d)


#### 4.3.2. The Influence of Rotation Speed on Cutting Force

The results of the circular sawblade cutting rock with the feed speed of 0.3 m/min, rotation speed of 1000, 1500, 2000, 2500, and 3000 r/min, and cutting depth of 10, 30, and 50 mm are shown in Figure10. The average force curves of the circular sawblade cutting rock with various rotation speed are presented in Figure 10. It is obvious that the force declines with the rotation speed increasing. The increasing rotation speed reduces the removal volume of rock by a circle of the circular sawblade, which causes the cutting force, normal force, and tangential force to decline, as shown in Figures 10(a)–10(c). Meanwhile, the removal volume of rock will be decreased by a circle of the circular sawblade cutting rock with the rotation speed increasing, causing the discharge efficiency of rock fragments increasing and the axial force to decrease, as shown in Figure 10(d).


#### 4.3.3. The Influence of Cutting Depth on Cutting Force

Cutting depth is an important cutting parameter which influences cutting force and rock damage. The simulation models with the feed speed of 0.30 m/min, the cutting depths of 10, 20, 30, 40, 50, and 60 mm at the rotation speeds of 1000, 2000, and 3000 r/min are applied to researching influence of cutting depth on cutting force. The cutting force of the circular sawblade cutting rock increases obviously with the increase in cutting depth, as shown in Figure11. With the increase of cutting depth of the circular sawblade, the rock removal volume by one circle of circular sawblade increasing causes the cutting force, tangential force, and normal force to increase obviously, as presented in Figures 11(a)–11(c). The increasing cutting depth causes the increase of the overlap area between the circular sawblade and rock, which reduces the discharge velocity of rock fragments, and the direct extrusion of rock fragments between circular sawblade and rock increases the axial force of the sawblade, as shown in Figure 11(d).Figure 11
Force curves of the circular sawblade cutting rock with various cutting depths: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of circular sawblade cutting rock.
(a)(b)(c)(d)


#### 4.3.4. The Influence of the Distance of Double Circular Sawblades on Cutting Force

The average force curves of double circular sawblades cutting rock with various distances between the double circular sawblades are shown in Figure12. Also, the distance of the double circular sawblades has a great effect on cutting force, as shown in Figure 12. It is obvious that the cutting force, normal force, and the tangential force increase with the increase in the distance of the circular sawblades, and the cutting force, normal force, and the tangential force of double circular sawblades are smaller than that of a single circular sawblade by comparison, as shown in Table 2. Owing to stress superposition, the force of the double circular sawblades is less than that of the single circular sawblade. Therefore, with the distance between the double circular sawblades increasing, the stress superposition effect of the circular sawblades decreases, which causes the cutting force of double circular sawblades to increase. Meanwhile, the average axial force declines with the increase in the distance of double circular sawblades. When the distance is small, the double circular sawblades will affect each other, which causes large axial force.Figure 12
Force curves of the average value of double circular sawblades with various distances: (a) the cutting force curve of double circular sawblades cutting rock; (b) the normal force curve of double circular sawblades cutting rock; (c) the tangential force curve of double circular sawblades cutting rock; and (d) the axial force curve of double circular sawblades cutting rock.
(a)(b)(c)(d)Table 2
The forces of the single and double circular sawblades
Single sawbladeCutting force (N)Normal force (N)Tangential force (N)Axial force (N)501.51227.85446.716.91Distance1#2#1#2#1#2#1#2#Double circular sawblade10317.6309.9107.5106.3297.4289.514.815.615335.3323.0115.0118.8313.9299.313.212.820341.9363.6134.7131.7313.5338.211.010.625396.7378.3142.2140.4369.9350.89.49.230408.2387.1159.1158.1375.6352.98.08.335426.5421.5168.0163.0391.8388.56.66.540429.7441.8175.0177.6392.3404.36.25.850464.1468.6179.5185.2427.9430.35.66.1The results of a single circular sawblade cutting rock are shown in Table2, with the rotation speed of 2000 r/min, feed speed of 0.30 m/min, and cutting depth of 50 mm, and the double circular sawblades cut rock with the same cutting parameters. The results of single circular sawblade show that the cutting force is 501.51 N, the normal force is 227.85 N, the tangential force is 446.71 N, and the axial force is 6.91 N. However, the results of the double circular sawblade are lower than that of the single sawblade. When the distance between the double circular sawblades reaches 50 mm, the results are close to that of the single circular sawblade. Therefore, it can be concluded that the cutting rock with double circular sawblades can reduce the cutting force.


### 4.4. The Influence of Cutting Parameters on Rock Damage

#### 4.4.1. The Influence of Feed Speed on Rock Damage

The rock damage area is greatly affected by feed speed, as shown in Figure13. The damage area in front of the rock with a circular sawblade cutting direction becomes serious with the feed speed increasing. The width of rock damage in front of the cutting direction of the circular sawblade is obviously wider than that behind the circular sawblade. Also, the width of the rock damage area increases with the increase in feed speed. However, the distribution of rock damage is obviously uncertain. Rock removal volume increases with the increase of the feed speed. With constant rotation speed, the higher the feed speed of the circular sawblade, the rougher the sawing seam formed by the circular sawblade cutting rock.Figure 13
Rock damage nephogram with various feed speeds: (a) feed speed of 0.10 m/min; (b) feed speed of 0.15 m/min; (c) feed speed of 0.20 m/min; (d) feed speed of 0.25 m/min; and (e) feed speed of 0.30 m/min.
(a)(b)(c)(d)(e)


#### 4.4.2. The Influence of Rotation Speed on Rock Damage

In order to research the influence of rotation speed on rock damage, it is defined in the circular sawblade cutting rock in the rotation speeds as 1000, 1500, 2000, 2500, and 3000 r/min, as shown in Figure14. With the increase in rotation speed, the rock damage area decreases. The width of the rock damage area extends to both sides of the sawing slot decreased at the same cutting depth with the increasing rotation speed. The rock removal volume decreases, and the sawing gap formed by the circular sawblade cutting is smoother. It is obvious that the rock damage area with circular sawblade cutting tends to decrease with the increase of rotation speed. However, the damage of rock in front of the circular sawblade cutting direction is more serious than that behind the circular sawblade.Figure 14
Rock damage nephogram with various rotation speeds: (a) rotation speed of 1000 r/min; (b) rotation speed of 1500 r/min; (c) rotation speed of 2000 r/min; (d) rotation speed of 2500 r/min; and (e) rotation speed of 3000 r/min.
(a)(b)(c)(d)(e)


#### 4.4.3. The Influence of Cutting Depth on Rock Damage

With the increase in cutting depth, the damage of rock increases. As shown in Figure15, it is obvious that the rock damage is greatly affected by the cutting depth. The rock damage area increases greatly, and the damage area is gradually connected with the increase in cutting depth of the circular sawblade. The rock damage increases with the cutting depth increasing. The width of rock damage increases with the increase in cutting depth, and the deleted amount of rock increases. Meanwhile, the regularity of the rock saw joint is improved. Therefore, increasing the cutting depth of the circular sawblade can improve the processing quality of rock to a certain extent.Figure 15
Rock damage nephogram with various cutting depths: (a) cutting depth of 10 mm; (b) cutting depth of 20 mm; (c) cutting depth of 30 mm; (d) cutting depth of 40 mm; (e) cutting depth of 50 mm; and (f) cutting depth of 60 mm.
(a)(b)(c)(d)(e)(f)


#### 4.4.4. The Influence of the Distance between Double Circular Sawblades on Rock Damage

The distance of the double circular sawblades affects the cutting performance. The damage field distributions of the double circular sawblades with various distances between the double circular sawblades are shown in Figure16. It is obvious that the damage field of rock is superposed by two single damage fields of the circular sawblade. When the distance between the double circular sawblades is small, the overlapping part of damage field of rock between the circular sawblades is large, as shown in Figure 16(a). With the increase of the distance between the circular sawblades, the superimposed damage field changes reduce obviously. When the distance of the double circular sawblades reaches 25 mm, the overlap of the rock damage field disappears, as shown in Figure 16(d). The damage field of rock with circular sawblades cutting affects the area of the rock removal area directly. When the two circular sawblades are close to each other, the overlap of rock damage is larger, which causes the rock slab between the circular sawblades hard to form.Figure 16
Rock damage nephogram with various distances between double circular sawblades: (a) distance between doubled circular sawblades of 10 mm; (b) distance between doubled circular sawblades of 15 mm; (c) distance between doubled circular sawblades of 20 mm; (d) distance between doubled circular sawblades of 25 mm; and (e) distance between doubled circular sawblades of 30 mm.
(a)(b)(c)(d)(e)The distance between the double circular sawblades affects the rock damage during circular sawblade cutting rock, as shown in Figure16. The distance of double circular sawblades affects the formation of rock plate directly. The large stress superposition makes the rock plate between the double circular sawblades difficult to form. When the distance of the double circular sawblades is small, it is difficult to form a relatively complete rock plate between the double circular sawblades. With the increase of the distance between the double circular sawblades, the damage superposition of the double circular sawblades would be weakened, and the rock plate in the middle of the circular sawblades is easier to form. The amount of rock removal volume of the double circular sawblade cutting declines with the increase of the distance between the double circular sawblades.


### 4.5. The Influence of the Cutting Parameter on Specific Cutting Energy

The specific energy consumption is an important index to evaluate the cutting performance of a circular sawblade. The cutting energy of a circular sawblade cutting rock is defined as the product of tangential force and relative moving distance of the circular sawblade, and the specific cutting energy is defined as the ratio of the cutting energy consumption to rock removal volume.(19)SE=Ft⋅sV,where SE is the specific cutting energy, s is the relative moving distance of the circular sawblade and rock, and V is the rock removal volume.The specific cutting energy of the circular sawblade cutting rock with various cutting parameters is shown in Figures17 and 18. The relationship between the specific energy consumption and the cutting depth of the circular sawblade is presented in Figure 17. The specific cutting energy consumption declines with cutting depth increasing. The relationship between the specific cutting energy and distance between the double circular sawblades is shown in Figure 18. The specific cutting energy of the double circular sawblades increases with the increase in distance between double circular sawblades, the increasing trend slows down, and the specific cutting energy tends to be stable. The specific cutting energy consumption of the double circular sawblades is less than that of the single circular sawblade. The expressions of the fitting relationship between the specific cutting energy consumption and cutting depth and the distance between the double circular sawblades are shown in Table 3. The specific cutting energy consumption decreases, and the specific cutting energy consumption increases with the increase in circular sawblade spacing, to a certain extent.Figure 17
The relationship of the specific cutting energy and cutting depth.Figure 18
Relationship between the specific cutting energy consumption and the distance between the circular sawblades.Table 3
The regression results to predict the specific cutting energy.
VariablesCutting parametersRegression equationCorrelation coefficientF valueP valueSE-CDRS = 1000 r/miny = 0.00246x2 − 0.04554x + 0.428470.89530602.26631.2383E – 4SE-CDRS = 2000 r/miny = 0.0024x2-0.05062x + 0.499670.959131556.8792.8962E – 5SE-CDRS = 3000 r/miny = 0.00567x2 − 0.07476x + 0.586710.990087631.3712.7548E – 6SE-DDFS = 0.3 m/miny = −0.000128x2 + 0.01443x + 0.308790.952393850.3991.0724E − 8RS = 2000 r/minSE = specific energy, CD = cutting depth, DD = distance between the double circular sawblades


## 4.1. The Process of a Circular Sawblade Cutting Rock

The circular sawblade cuts rock with constant rotation speed and feed speed, with the feed speed of 0.30 m/min, rotation speed of 2000 r/min, and the cutting depth of 30 mm. It is obvious that the force appears and increases as the circular sawblade contacts the rock. The rock element is damaged with circular sawblade compression and tension. The damage value of some rock elements reaches 1 which is acted by the circular sawblade with continuing cutting. While the damage value of rock element reaches 1, the element would fail and be deleted. The rock damage nephograms in the process of circular sawblade cutting rock are plotted in Figure5. In the initial stage of rock cutting with a circular sawblade, the deformation and damage of rock appear under compression and tension, as shown in Figure 5(a). With the circular sawblade cutting further, fail elements appear in the first layer elements on the upper surface of the rock and are deleted, as shown in Figure 5(b). While the circular sawblade advances to a certain distance, the rock damage extends outward, and the broken area extends beyond the contacting area. The depth of rock damage increases with the increase in the cutting distance of circular sawblade cutting and reaches a stable depth. Meanwhile, damage ranges also extend and increase downward. When the cutting distance of circular sawblade is large, the damage element on the both sides of saw slot cut by the circular sawblade fail under the interaction of circular sawblade.Figure 5
Rock damage nephograms of a circular sawblade cutting rock at various cutting distances: (a) Rock damage nephogram of 7 mm cutting distance; (b) rock damage nephogram of 9 mm cutting distance; (c) rock damage nephogram of 12 mm cutting distance; (d) rock damage nephogram of 21 mm cutting distance; (e) rock damage nephogram of 27 mm cutting distance; (f) rock damage nephogram of 45 mm cutting distance; and (g) rock damage nephogram of 70 mm cutting distance.The cutting force has a larger peak value when the circular sawblade cuts the rock at the beginning, as shown in Figure6. The circular sawblade cuts rock at a constant rotation speed and feed speed; at the moment when the circular sawblade contacts the rock which produces a greater impact, the cutting force increases sharply and the peak cutting force is larger than that of stable cutting. It is obvious that the cutting force is closely related to the tangential and normal force, and the wave shape of the normal force curve is similar to the cutting force. The similarity between axial force and cutting force is lower. The values of the normal force and the tangential force are larger than the axial force of a circular sawblade. The fluctuation ranges of the normal force curve and the cutting force are lager; however, the fluctuation of the tangential force curve around the fixed value is relatively stable.Figure 6
Force curves of rock cutting with a circular sawblade.


## 4.2. The Influence of the Rotation Speed Direction of a Circular Sawblade on the Cutting Performance

The circular sawblade cuts rock with the feed speed of 0.30 m/min, rotation speed of 2000 r/min, and the cutting depth of 30 mm. The direction of rotation speed has great effects on the cutting performance. The rock damage nephograms with different rotation speed directions are shown in Figure7. However, in the numerical simulation results of circular sawblade cut rock with forward cutting, the rock damage area is smaller than that of the reverse cutting. The rock damage ranges of the circular sawblade forward cutting are smaller and more irregular. The broken area is random which is determined by the rock properties. The cutting surface of the circular sawblade is rough, and the quality of rock processing is poor with the circular sawblade reverse cutting, as shown in Figure 7(b). The forward cutting of the circular sawblade can achieve perfect quality and the relatively smooth cutting surface. In the left view, the damage area of forward cutting is smaller than that of reverse cutting. Also, the circular sawblade cutting rock with the same cutting parameters, the width and depth of damage area with forward cutting is smaller and more regular than that of the reverse cutting. The damage area of rock is irregular with the reverse cutting, and the quality of rock processing is poor which cannot meet processing requirement. Therefore, the forward cutting is more suitable for rock processing.Figure 7
The rock damage nephograms with various cutting models: (a) the rock damage nephogram with forward cutting; (b) the rock damage nephogram with reverse cutting.The force curves of the circular sawblade cutting rock with the forward cutting and reverse cutting are presented in Figure8. The cutting force of the forward cutting is smaller than that of the reverse cutting. The force fluctuates steadily with the forward cutting during steady cutting, which is much smaller than that of the reverse cutting. In the process of the circular sawblade cutting rock of the forward cutting, the cutting thickness of each circular grit increases slowly from 0 to the maximum, which makes the amplitude of cutting force smaller. However, when the cutting thickness of the reverse cutting declines from the maximum value to zero slowly and the compressive strength of rock is large, the fluctuation of cutting force is larger. The wave shape of normal force is basically the same as that of cutting force. Comparing the normal force of the circular sawblade with the forward and reverse cutting, it can be seen that the normal and tangential force amplitude of the forward cutting is smaller than that of the reverse cutting. However, the axial force of forward cutting and the reverse cutting are basically the same.Figure 8
Force curves of the circular sawblade cut rock with forward and reverse cutting: (a) the cutting force of the circular sawblade cutting rock; (b) the normal force of the circular sawblade cutting rock; (c) the tangential force of the circular sawblade cutting rock; and (d) the axial force of the circular sawblade cutting rock.
(a)(b)(c)(d)


## 4.3. The Influence of Cutting Parameters on Cutting Force

### 4.3.1. The Influence of Feed Speed on Cutting Force

To investigate the influence of feed speed on the cutting force, the circular sawblade cutting rock numerical with the rotation speed of 2000 r/min, the cutting depths of 10, 30, and 50 mm, and the feed speeds of 0.10, 0.15, 0.20, 0.25, and 0.30 m/min are built. The average force curves with various feed speeds are presented in Figure9. It is obvious that the force increases with the increase of feed speed. While a circular sawblade cuts rock with constant rotation speed, the rock removal volume per circle increases with feed speed increasing, which causes tangential and normal force to increase obviously. The variation trend of the average force curves of cutting force and tangential force is similar. The feed speed increase causes the volume of the rock removal to increase. The difficulty of discharging fragments increasing causes the average axial force increase. However, the growth rate of force with a cutting depth from 30 to 50 mm is larger than that of a cutting depth from 10 to 30 mm. According to Figure 10, the force increases with the cutting depth increasing, and the relationship between the force of circular sawblade and cutting depth is quadratic.Figure 9
Force curves of the circular sawblade cutting rock with various feed speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.
(a)(b)(c)(d)Figure 10
Force curves of the circular sawblade cutting rock with various rotation speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.
(a)(b)(c)(d)


### 4.3.2. The Influence of Rotation Speed on Cutting Force

The results of the circular sawblade cutting rock with the feed speed of 0.3 m/min, rotation speed of 1000, 1500, 2000, 2500, and 3000 r/min, and cutting depth of 10, 30, and 50 mm are shown in Figure10. The average force curves of the circular sawblade cutting rock with various rotation speed are presented in Figure 10. It is obvious that the force declines with the rotation speed increasing. The increasing rotation speed reduces the removal volume of rock by a circle of the circular sawblade, which causes the cutting force, normal force, and tangential force to decline, as shown in Figures 10(a)–10(c). Meanwhile, the removal volume of rock will be decreased by a circle of the circular sawblade cutting rock with the rotation speed increasing, causing the discharge efficiency of rock fragments increasing and the axial force to decrease, as shown in Figure 10(d).


### 4.3.3. The Influence of Cutting Depth on Cutting Force

Cutting depth is an important cutting parameter which influences cutting force and rock damage. The simulation models with the feed speed of 0.30 m/min, the cutting depths of 10, 20, 30, 40, 50, and 60 mm at the rotation speeds of 1000, 2000, and 3000 r/min are applied to researching influence of cutting depth on cutting force. The cutting force of the circular sawblade cutting rock increases obviously with the increase in cutting depth, as shown in Figure11. With the increase of cutting depth of the circular sawblade, the rock removal volume by one circle of circular sawblade increasing causes the cutting force, tangential force, and normal force to increase obviously, as presented in Figures 11(a)–11(c). The increasing cutting depth causes the increase of the overlap area between the circular sawblade and rock, which reduces the discharge velocity of rock fragments, and the direct extrusion of rock fragments between circular sawblade and rock increases the axial force of the sawblade, as shown in Figure 11(d).Figure 11
Force curves of the circular sawblade cutting rock with various cutting depths: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of circular sawblade cutting rock.
(a)(b)(c)(d)


### 4.3.4. The Influence of the Distance of Double Circular Sawblades on Cutting Force

The average force curves of double circular sawblades cutting rock with various distances between the double circular sawblades are shown in Figure12. Also, the distance of the double circular sawblades has a great effect on cutting force, as shown in Figure 12. It is obvious that the cutting force, normal force, and the tangential force increase with the increase in the distance of the circular sawblades, and the cutting force, normal force, and the tangential force of double circular sawblades are smaller than that of a single circular sawblade by comparison, as shown in Table 2. Owing to stress superposition, the force of the double circular sawblades is less than that of the single circular sawblade. Therefore, with the distance between the double circular sawblades increasing, the stress superposition effect of the circular sawblades decreases, which causes the cutting force of double circular sawblades to increase. Meanwhile, the average axial force declines with the increase in the distance of double circular sawblades. When the distance is small, the double circular sawblades will affect each other, which causes large axial force.Figure 12
Force curves of the average value of double circular sawblades with various distances: (a) the cutting force curve of double circular sawblades cutting rock; (b) the normal force curve of double circular sawblades cutting rock; (c) the tangential force curve of double circular sawblades cutting rock; and (d) the axial force curve of double circular sawblades cutting rock.
(a)(b)(c)(d)Table 2
The forces of the single and double circular sawblades
Single sawbladeCutting force (N)Normal force (N)Tangential force (N)Axial force (N)501.51227.85446.716.91Distance1#2#1#2#1#2#1#2#Double circular sawblade10317.6309.9107.5106.3297.4289.514.815.615335.3323.0115.0118.8313.9299.313.212.820341.9363.6134.7131.7313.5338.211.010.625396.7378.3142.2140.4369.9350.89.49.230408.2387.1159.1158.1375.6352.98.08.335426.5421.5168.0163.0391.8388.56.66.540429.7441.8175.0177.6392.3404.36.25.850464.1468.6179.5185.2427.9430.35.66.1The results of a single circular sawblade cutting rock are shown in Table2, with the rotation speed of 2000 r/min, feed speed of 0.30 m/min, and cutting depth of 50 mm, and the double circular sawblades cut rock with the same cutting parameters. The results of single circular sawblade show that the cutting force is 501.51 N, the normal force is 227.85 N, the tangential force is 446.71 N, and the axial force is 6.91 N. However, the results of the double circular sawblade are lower than that of the single sawblade. When the distance between the double circular sawblades reaches 50 mm, the results are close to that of the single circular sawblade. Therefore, it can be concluded that the cutting rock with double circular sawblades can reduce the cutting force.


## 4.3.1. The Influence of Feed Speed on Cutting Force

To investigate the influence of feed speed on the cutting force, the circular sawblade cutting rock numerical with the rotation speed of 2000 r/min, the cutting depths of 10, 30, and 50 mm, and the feed speeds of 0.10, 0.15, 0.20, 0.25, and 0.30 m/min are built. The average force curves with various feed speeds are presented in Figure9. It is obvious that the force increases with the increase of feed speed. While a circular sawblade cuts rock with constant rotation speed, the rock removal volume per circle increases with feed speed increasing, which causes tangential and normal force to increase obviously. The variation trend of the average force curves of cutting force and tangential force is similar. The feed speed increase causes the volume of the rock removal to increase. The difficulty of discharging fragments increasing causes the average axial force increase. However, the growth rate of force with a cutting depth from 30 to 50 mm is larger than that of a cutting depth from 10 to 30 mm. According to Figure 10, the force increases with the cutting depth increasing, and the relationship between the force of circular sawblade and cutting depth is quadratic.Figure 9
Force curves of the circular sawblade cutting rock with various feed speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.
(a)(b)(c)(d)Figure 10
Force curves of the circular sawblade cutting rock with various rotation speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.
(a)(b)(c)(d)


## 4.3.2. The Influence of Rotation Speed on Cutting Force

The results of the circular sawblade cutting rock with the feed speed of 0.3 m/min, rotation speed of 1000, 1500, 2000, 2500, and 3000 r/min, and cutting depth of 10, 30, and 50 mm are shown in Figure10. The average force curves of the circular sawblade cutting rock with various rotation speed are presented in Figure 10. It is obvious that the force declines with the rotation speed increasing. The increasing rotation speed reduces the removal volume of rock by a circle of the circular sawblade, which causes the cutting force, normal force, and tangential force to decline, as shown in Figures 10(a)–10(c). Meanwhile, the removal volume of rock will be decreased by a circle of the circular sawblade cutting rock with the rotation speed increasing, causing the discharge efficiency of rock fragments increasing and the axial force to decrease, as shown in Figure 10(d).


## 4.3.3. The Influence of Cutting Depth on Cutting Force

Cutting depth is an important cutting parameter which influences cutting force and rock damage. The simulation models with the feed speed of 0.30 m/min, the cutting depths of 10, 20, 30, 40, 50, and 60 mm at the rotation speeds of 1000, 2000, and 3000 r/min are applied to researching influence of cutting depth on cutting force. The cutting force of the circular sawblade cutting rock increases obviously with the increase in cutting depth, as shown in Figure11. With the increase of cutting depth of the circular sawblade, the rock removal volume by one circle of circular sawblade increasing causes the cutting force, tangential force, and normal force to increase obviously, as presented in Figures 11(a)–11(c). The increasing cutting depth causes the increase of the overlap area between the circular sawblade and rock, which reduces the discharge velocity of rock fragments, and the direct extrusion of rock fragments between circular sawblade and rock increases the axial force of the sawblade, as shown in Figure 11(d).Figure 11
Force curves of the circular sawblade cutting rock with various cutting depths: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of circular sawblade cutting rock.
(a)(b)(c)(d)


## 4.3.4. The Influence of the Distance of Double Circular Sawblades on Cutting Force

The average force curves of double circular sawblades cutting rock with various distances between the double circular sawblades are shown in Figure12. Also, the distance of the double circular sawblades has a great effect on cutting force, as shown in Figure 12. It is obvious that the cutting force, normal force, and the tangential force increase with the increase in the distance of the circular sawblades, and the cutting force, normal force, and the tangential force of double circular sawblades are smaller than that of a single circular sawblade by comparison, as shown in Table 2. Owing to stress superposition, the force of the double circular sawblades is less than that of the single circular sawblade. Therefore, with the distance between the double circular sawblades increasing, the stress superposition effect of the circular sawblades decreases, which causes the cutting force of double circular sawblades to increase. Meanwhile, the average axial force declines with the increase in the distance of double circular sawblades. When the distance is small, the double circular sawblades will affect each other, which causes large axial force.Figure 12
Force curves of the average value of double circular sawblades with various distances: (a) the cutting force curve of double circular sawblades cutting rock; (b) the normal force curve of double circular sawblades cutting rock; (c) the tangential force curve of double circular sawblades cutting rock; and (d) the axial force curve of double circular sawblades cutting rock.
(a)(b)(c)(d)Table 2
The forces of the single and double circular sawblades
Single sawbladeCutting force (N)Normal force (N)Tangential force (N)Axial force (N)501.51227.85446.716.91Distance1#2#1#2#1#2#1#2#Double circular sawblade10317.6309.9107.5106.3297.4289.514.815.615335.3323.0115.0118.8313.9299.313.212.820341.9363.6134.7131.7313.5338.211.010.625396.7378.3142.2140.4369.9350.89.49.230408.2387.1159.1158.1375.6352.98.08.335426.5421.5168.0163.0391.8388.56.66.540429.7441.8175.0177.6392.3404.36.25.850464.1468.6179.5185.2427.9430.35.66.1The results of a single circular sawblade cutting rock are shown in Table2, with the rotation speed of 2000 r/min, feed speed of 0.30 m/min, and cutting depth of 50 mm, and the double circular sawblades cut rock with the same cutting parameters. The results of single circular sawblade show that the cutting force is 501.51 N, the normal force is 227.85 N, the tangential force is 446.71 N, and the axial force is 6.91 N. However, the results of the double circular sawblade are lower than that of the single sawblade. When the distance between the double circular sawblades reaches 50 mm, the results are close to that of the single circular sawblade. Therefore, it can be concluded that the cutting rock with double circular sawblades can reduce the cutting force.


## 4.4. The Influence of Cutting Parameters on Rock Damage

### 4.4.1. The Influence of Feed Speed on Rock Damage

The rock damage area is greatly affected by feed speed, as shown in Figure13. The damage area in front of the rock with a circular sawblade cutting direction becomes serious with the feed speed increasing. The width of rock damage in front of the cutting direction of the circular sawblade is obviously wider than that behind the circular sawblade. Also, the width of the rock damage area increases with the increase in feed speed. However, the distribution of rock damage is obviously uncertain. Rock removal volume increases with the increase of the feed speed. With constant rotation speed, the higher the feed speed of the circular sawblade, the rougher the sawing seam formed by the circular sawblade cutting rock.Figure 13
Rock damage nephogram with various feed speeds: (a) feed speed of 0.10 m/min; (b) feed speed of 0.15 m/min; (c) feed speed of 0.20 m/min; (d) feed speed of 0.25 m/min; and (e) feed speed of 0.30 m/min.
(a)(b)(c)(d)(e)


### 4.4.2. The Influence of Rotation Speed on Rock Damage

In order to research the influence of rotation speed on rock damage, it is defined in the circular sawblade cutting rock in the rotation speeds as 1000, 1500, 2000, 2500, and 3000 r/min, as shown in Figure14. With the increase in rotation speed, the rock damage area decreases. The width of the rock damage area extends to both sides of the sawing slot decreased at the same cutting depth with the increasing rotation speed. The rock removal volume decreases, and the sawing gap formed by the circular sawblade cutting is smoother. It is obvious that the rock damage area with circular sawblade cutting tends to decrease with the increase of rotation speed. However, the damage of rock in front of the circular sawblade cutting direction is more serious than that behind the circular sawblade.Figure 14
Rock damage nephogram with various rotation speeds: (a) rotation speed of 1000 r/min; (b) rotation speed of 1500 r/min; (c) rotation speed of 2000 r/min; (d) rotation speed of 2500 r/min; and (e) rotation speed of 3000 r/min.
(a)(b)(c)(d)(e)


### 4.4.3. The Influence of Cutting Depth on Rock Damage

With the increase in cutting depth, the damage of rock increases. As shown in Figure15, it is obvious that the rock damage is greatly affected by the cutting depth. The rock damage area increases greatly, and the damage area is gradually connected with the increase in cutting depth of the circular sawblade. The rock damage increases with the cutting depth increasing. The width of rock damage increases with the increase in cutting depth, and the deleted amount of rock increases. Meanwhile, the regularity of the rock saw joint is improved. Therefore, increasing the cutting depth of the circular sawblade can improve the processing quality of rock to a certain extent.Figure 15
Rock damage nephogram with various cutting depths: (a) cutting depth of 10 mm; (b) cutting depth of 20 mm; (c) cutting depth of 30 mm; (d) cutting depth of 40 mm; (e) cutting depth of 50 mm; and (f) cutting depth of 60 mm.
(a)(b)(c)(d)(e)(f)


### 4.4.4. The Influence of the Distance between Double Circular Sawblades on Rock Damage

The distance of the double circular sawblades affects the cutting performance. The damage field distributions of the double circular sawblades with various distances between the double circular sawblades are shown in Figure16. It is obvious that the damage field of rock is superposed by two single damage fields of the circular sawblade. When the distance between the double circular sawblades is small, the overlapping part of damage field of rock between the circular sawblades is large, as shown in Figure 16(a). With the increase of the distance between the circular sawblades, the superimposed damage field changes reduce obviously. When the distance of the double circular sawblades reaches 25 mm, the overlap of the rock damage field disappears, as shown in Figure 16(d). The damage field of rock with circular sawblades cutting affects the area of the rock removal area directly. When the two circular sawblades are close to each other, the overlap of rock damage is larger, which causes the rock slab between the circular sawblades hard to form.Figure 16
Rock damage nephogram with various distances between double circular sawblades: (a) distance between doubled circular sawblades of 10 mm; (b) distance between doubled circular sawblades of 15 mm; (c) distance between doubled circular sawblades of 20 mm; (d) distance between doubled circular sawblades of 25 mm; and (e) distance between doubled circular sawblades of 30 mm.
(a)(b)(c)(d)(e)The distance between the double circular sawblades affects the rock damage during circular sawblade cutting rock, as shown in Figure16. The distance of double circular sawblades affects the formation of rock plate directly. The large stress superposition makes the rock plate between the double circular sawblades difficult to form. When the distance of the double circular sawblades is small, it is difficult to form a relatively complete rock plate between the double circular sawblades. With the increase of the distance between the double circular sawblades, the damage superposition of the double circular sawblades would be weakened, and the rock plate in the middle of the circular sawblades is easier to form. The amount of rock removal volume of the double circular sawblade cutting declines with the increase of the distance between the double circular sawblades.


## 4.4.1. The Influence of Feed Speed on Rock Damage

The rock damage area is greatly affected by feed speed, as shown in Figure13. The damage area in front of the rock with a circular sawblade cutting direction becomes serious with the feed speed increasing. The width of rock damage in front of the cutting direction of the circular sawblade is obviously wider than that behind the circular sawblade. Also, the width of the rock damage area increases with the increase in feed speed. However, the distribution of rock damage is obviously uncertain. Rock removal volume increases with the increase of the feed speed. With constant rotation speed, the higher the feed speed of the circular sawblade, the rougher the sawing seam formed by the circular sawblade cutting rock.Figure 13
Rock damage nephogram with various feed speeds: (a) feed speed of 0.10 m/min; (b) feed speed of 0.15 m/min; (c) feed speed of 0.20 m/min; (d) feed speed of 0.25 m/min; and (e) feed speed of 0.30 m/min.
(a)(b)(c)(d)(e)


## 4.4.2. The Influence of Rotation Speed on Rock Damage

In order to research the influence of rotation speed on rock damage, it is defined in the circular sawblade cutting rock in the rotation speeds as 1000, 1500, 2000, 2500, and 3000 r/min, as shown in Figure14. With the increase in rotation speed, the rock damage area decreases. The width of the rock damage area extends to both sides of the sawing slot decreased at the same cutting depth with the increasing rotation speed. The rock removal volume decreases, and the sawing gap formed by the circular sawblade cutting is smoother. It is obvious that the rock damage area with circular sawblade cutting tends to decrease with the increase of rotation speed. However, the damage of rock in front of the circular sawblade cutting direction is more serious than that behind the circular sawblade.Figure 14
Rock damage nephogram with various rotation speeds: (a) rotation speed of 1000 r/min; (b) rotation speed of 1500 r/min; (c) rotation speed of 2000 r/min; (d) rotation speed of 2500 r/min; and (e) rotation speed of 3000 r/min.
(a)(b)(c)(d)(e)


## 4.4.3. The Influence of Cutting Depth on Rock Damage

With the increase in cutting depth, the damage of rock increases. As shown in Figure15, it is obvious that the rock damage is greatly affected by the cutting depth. The rock damage area increases greatly, and the damage area is gradually connected with the increase in cutting depth of the circular sawblade. The rock damage increases with the cutting depth increasing. The width of rock damage increases with the increase in cutting depth, and the deleted amount of rock increases. Meanwhile, the regularity of the rock saw joint is improved. Therefore, increasing the cutting depth of the circular sawblade can improve the processing quality of rock to a certain extent.Figure 15
Rock damage nephogram with various cutting depths: (a) cutting depth of 10 mm; (b) cutting depth of 20 mm; (c) cutting depth of 30 mm; (d) cutting depth of 40 mm; (e) cutting depth of 50 mm; and (f) cutting depth of 60 mm.
(a)(b)(c)(d)(e)(f)


## 4.4.4. The Influence of the Distance between Double Circular Sawblades on Rock Damage

The distance of the double circular sawblades affects the cutting performance. The damage field distributions of the double circular sawblades with various distances between the double circular sawblades are shown in Figure16. It is obvious that the damage field of rock is superposed by two single damage fields of the circular sawblade. When the distance between the double circular sawblades is small, the overlapping part of damage field of rock between the circular sawblades is large, as shown in Figure 16(a). With the increase of the distance between the circular sawblades, the superimposed damage field changes reduce obviously. When the distance of the double circular sawblades reaches 25 mm, the overlap of the rock damage field disappears, as shown in Figure 16(d). The damage field of rock with circular sawblades cutting affects the area of the rock removal area directly. When the two circular sawblades are close to each other, the overlap of rock damage is larger, which causes the rock slab between the circular sawblades hard to form.Figure 16
Rock damage nephogram with various distances between double circular sawblades: (a) distance between doubled circular sawblades of 10 mm; (b) distance between doubled circular sawblades of 15 mm; (c) distance between doubled circular sawblades of 20 mm; (d) distance between doubled circular sawblades of 25 mm; and (e) distance between doubled circular sawblades of 30 mm.
(a)(b)(c)(d)(e)The distance between the double circular sawblades affects the rock damage during circular sawblade cutting rock, as shown in Figure16. The distance of double circular sawblades affects the formation of rock plate directly. The large stress superposition makes the rock plate between the double circular sawblades difficult to form. When the distance of the double circular sawblades is small, it is difficult to form a relatively complete rock plate between the double circular sawblades. With the increase of the distance between the double circular sawblades, the damage superposition of the double circular sawblades would be weakened, and the rock plate in the middle of the circular sawblades is easier to form. The amount of rock removal volume of the double circular sawblade cutting declines with the increase of the distance between the double circular sawblades.


## 4.5. The Influence of the Cutting Parameter on Specific Cutting Energy

The specific energy consumption is an important index to evaluate the cutting performance of a circular sawblade. The cutting energy of a circular sawblade cutting rock is defined as the product of tangential force and relative moving distance of the circular sawblade, and the specific cutting energy is defined as the ratio of the cutting energy consumption to rock removal volume.(19)SE=Ft⋅sV,where SE is the specific cutting energy, s is the relative moving distance of the circular sawblade and rock, and V is the rock removal volume.The specific cutting energy of the circular sawblade cutting rock with various cutting parameters is shown in Figures17 and 18. The relationship between the specific energy consumption and the cutting depth of the circular sawblade is presented in Figure 17. The specific cutting energy consumption declines with cutting depth increasing. The relationship between the specific cutting energy and distance between the double circular sawblades is shown in Figure 18. The specific cutting energy of the double circular sawblades increases with the increase in distance between double circular sawblades, the increasing trend slows down, and the specific cutting energy tends to be stable. The specific cutting energy consumption of the double circular sawblades is less than that of the single circular sawblade. The expressions of the fitting relationship between the specific cutting energy consumption and cutting depth and the distance between the double circular sawblades are shown in Table 3. The specific cutting energy consumption decreases, and the specific cutting energy consumption increases with the increase in circular sawblade spacing, to a certain extent.Figure 17
The relationship of the specific cutting energy and cutting depth.Figure 18
Relationship between the specific cutting energy consumption and the distance between the circular sawblades.Table 3
The regression results to predict the specific cutting energy.
VariablesCutting parametersRegression equationCorrelation coefficientF valueP valueSE-CDRS = 1000 r/miny = 0.00246x2 − 0.04554x + 0.428470.89530602.26631.2383E – 4SE-CDRS = 2000 r/miny = 0.0024x2-0.05062x + 0.499670.959131556.8792.8962E – 5SE-CDRS = 3000 r/miny = 0.00567x2 − 0.07476x + 0.586710.990087631.3712.7548E – 6SE-DDFS = 0.3 m/miny = −0.000128x2 + 0.01443x + 0.308790.952393850.3991.0724E − 8RS = 2000 r/minSE = specific energy, CD = cutting depth, DD = distance between the double circular sawblades


## 5. Conclusions

The process of the circular sawblade cutting rock is studied in this paper. The influence of cutting parameters and the direction of the circular sawblade on the cutting performance are explored.(1)
Cutting parameters have a great effect on the cutting performance. The cutting force increases with the feed speed, and cutting depth increasing and declines with the increase of rotation speed. The increasing distance of double sawblades causes the cutting force to increase and, then, maintain stable.(2)
The damage and rock removal volume of the rock are influenced by the cutting parameters of the circular sawblade. When the damage of rock reaches 1, the rock elements will fail and be deleted. Therefore, the rock removal volume is closely related to rock damage. The forward cutting and reverse cutting have different influences on rock damage and cutting force. The fluctuation of the forward cutting force curve is much smaller than that of the reverse cutting force curve.(3)
The cutting parameters of the circular sawblade influence the specific cutting energy. The specific cutting energy decreases with the increase in cutting depth, and the specific cutting energy increases with the increase of the distance between double circular sawblades.The results of the researches could be used to guide rock processing.



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*Source: 9706183-2020-09-25.xml*