Simulation of the Working Performance of a Shearer Cutting Coal Rock

Taking the MG2∗55/250-BWD shearer as the research object and considering the influence of the rock on the working performance of the shearer, the shearer-coal-rock coupled discrete element model was established and its dynamic working process has been studied. 0e single-factor analysis method was used to study the variation law of the cutting depth, traction speed, and the drum’s rotational speed on the three-way force acting on the drum, the coal loading rate, and the trajectory of the coal particles. 0e simulation showed that the coal loading rate fluctuated during the start-up phase of the shearer, and it was then constant as the time increased.0e value of the cutting resistance was the largest, the traction resistance was the second largest, the axial force was the smallest, and the fluctuation coefficient of the axial force was the largest of all of them. 0e research showed that the coal loading rate of the drum decreased with the increase of the cutting depth, increased with the increase of the rotating speed of the drum, and decreased with the increase of the traction speed. 0e three-way force of the drum increased with the increase of the traction speed, decreased with the increase of the drum’s rotational speed, and increased with the increase of the cutting depth. According to the analysis of the coal cutting force and the coal loading rate, the drum could achieve high-efficiency cutting if the cutting depth, rotational speed, and traction speed of the dynamic were matched.


Introduction
e working mechanism of a shearer has two functions: coal cutting and coal loading.Most of the research on the coal cutting rules of the spiral cutters of coal mining machines has been based on theoretical formulas or experience.However, for shearers that cut coal rock, the loads have strong nonlinear and time-varying properties.
e theoretical parameters of the formula have large fluctuations, and the calculation of the load suffers from inevitable human error [1].LS-DYNA was used in the literature to simulate the drum cutting coal, and the unit was automatically removed after failure [2]; it is difficult to reflect the influence of the reaction on the drum during coal loading, and the discrete element method has certain advantages [3].
e discrete element method was used in the literature to simulate the cutting head [4], and the cutting force variation law of the pick was obtained.e discrete element method was used in the literature to simulate the performance of the cutting head [5], and the cutting force variation law of the pick was obtained, and the reliability of the simulation was verified experimentally.e influence of the roof pressure on the cutting performance was considered in the literature [6], and the discrete element method was used to study the dynamic process of the drum cutting coal rock, and the coal loading rate and force were obtained under different drum motion parameters.
e PCF was used in the literature [7] to simulate the uniform linear cutting process of the pick, and the theoretical results of the simulation result are consistent.
e discrete element method was used in the literature [8] to study the performance of coal drum loading, and the effects of the spiral drum structure and kinematic parameters on the motion law of the coal loading were obtained.e threedimensional discrete element software was used in the literature [9] to simulate the vertical screw conveyor, and the effects of speed, blade clearance, and material parameters on the conveying e ect are obtained.e discrete element method was used in the literature [10] to analyze the coal loading performance of the shearer, and the in uence of the drum motion parameters on the drum coal loading rate was obtained.e discrete element analysis software PFC3D was used in the literature [11] to simulate the process of the pick breaking the coal, and the force of the pick and the relationship between the force of the pick and the cutting thickness were obtained.e discrete element software was used in the literature [12] to simulate the process of the drum breaking the coal, and the variation law of the coal wall and the force of the drum were obtained during the working process of the double drum shearer.e discrete element software was used in the literature [13] to simulate the charging process of the drum and analyze the factors affecting the drum loading.EDEM was used in literature [14] to simulate the rock fracture problem and obtain the rock failure mechanism.e discrete element software was used in the literature [15] to study the dynamic process of the coal rock being cut by the coal mining machine, and the in uence of di erent cutting angles on the coal loading rate, cutting resistance, and the cutting energy consumption of shearer was studied.EDEM software was used in the literature [16] to establish a discrete element simulation model of the shearer's cutting section, and the relationship between the drum speed, the traction speed, and the coal loading rate was analyzed.e discrete element method was used in the literature [17] to study the dynamic process of picks cutting coal, and the e ect of the di erent cutting thickness on the cutting force was obtained.

Discrete Element Theory Analysis
According to the theory of discrete elements [18,19], the coal wall model uses the Hertz-Mindlin bonding contact model.e bonding of particles 1 and 2 is achieved by the bond as shown in Figure 1; a certain bonding force must be existent between the coal particles by the bond.
In Figure 1, r 1 and r 2 are the radii of particles 1 and 2, respectively, r n1 and r n2 are the contact radii of particles 1 and 2, U n is the normal overlap between particles, C n and C t are the normal and tangential damping, and S n and S t are the normal contact sti ness and tangential contact sti ness between particles, respectively. where )/E 2 , E 1 and E 2 are the macroscopic elastic moduli of particles 1 and 2, respectively, μ 1 and μ 2 are the macroscopic Poisson ratios of particles 1 and 2, G * is the equivalent elastic modulus, 1/G * (2 2 )/G 2 , and G 1 and G 2 are the macroscopic shear moduli of particles 1 and 2. r * is the equivalent radius of particles, 1/r * 1/r 1 + 1/r 2 .m * is the equivalent mass of particles, 1/m * 1/m 1 + 1/m 2 .e is the restitution coe cient of particles in Table 1.
e mathematical expressions of the bonding force and the torque between the particles are shown in the following formula: where δ t is the time step, υ n is the normal velocity of the particles, υ t is the tangential velocity of the particles, ω n is the normal angular velocity of the particles, ω t is the tangent angular velocity of the particles, S n is the normal contact sti ness of the particles, and S t is the tangential contact sti ness.Due to the bonding force, the particles can withstand certain stretching and shearing e ects.When the force between the particles exceeds the bonding strength, the bond is broken [18], and the breaking conditions are shown in the following formula:

Modelling and Simulation in Engineering
where A � πR 2 , J � (1/2)πR 4 , and . R is the bonding radius, F n and F t are the normal and tangential forces between the particles, T n and T t are the normal and tangential moments between the particles, A is the contact area, and J is the polar moment of inertia.

Simulation Model of the Drum Cutting
Coal Rock

Establishment of the Discrete Element Method of the Coal
Rock Model.In order to accurately establish the coal wall model, the coal seam samples and rock samples were tested [20], including density, tensile strength, compressive strength, elastic modulus, Poisson's ratio, cohesion, and internal friction angle.e test results of the physical and mechanical parameters of the coal rock are shown in Table 2.
Both the coal and rock used the Hertz-Mindlin bonding contact models.
e normal contact stiffness S n and the tangential contact stiffness S t were calculated by using equations (1) and (2) and the relevant parameters from Tables 1 and 2. e normal stress σ and tangential stress τ can be calculated by Mohr-Coulomb theory.When the stress value exceeds σ or τ, the corresponding tensile or shear failure or shear failure occurs [21], as shown in the following formula: where σ is the normal stress on the failure surface (MPa), τ is the shear stress of the failure surface (MPa), σ 1 is the maximum principal stress (MPa), σ 3 is the minimum principal stress (MPa), α is the shear failure angle ( °), φ is the internal friction angle ( °), and C is the cohesion of coal rock (MPa).Among them, σ 1 and σ 3 can be calculated by McClintock and Walsh's modified Griffith formula, as shown in the following formula: where σ t is the tensile strength of the material (MPa), σ c is the compressive strength of the material (MPa), and f is the coefficient of friction.e normal stress σ and tangential stress τ were calculated by using equations ( 7) and ( 8) and the relevant parameters from Table 2. e parameters of the particle contact model [20] are shown in Table 3. e coal particles were nonuniform and spherical, and the radius of the sphere varied from 6 mm to 18 mm [18].To establish the coal rock model, it was necessary to first establish a coal wall particle factory and fill it with the coal particles.When the coal particles had been introduced, a virtual rock particle factory was built and the rock particles were introduced.Finally, a virtual coal particle factory was built and the coal particles were introduced. is completed the filling process of the coal wall containing a layer of rock.
e filled coal rock model was compressed, so that the distance between the particles reached the contact radius, and the particles were bonded according to the parameters of Table 3, and a three-dimensional model of the bond contact with the rock wall was obtained.

Establishment of the Drum Model.
Taking the spiral drum of the MG2 * 55/250-BWD type coal mining machine as the prototype, the three-dimensional solid model of the drum was established in Pro/E, as shown in Figure 2(a), and the picking arrangement diagram of the drum was established as shown in Figure 2(b).e drum model was imported into the discrete element model in the IGES file format.

Simulation Setup and Solution.
According to the actual working conditions, the rotational speed of the drum was 95 r/min, and the traction speed was 4 m/min.In order to ensure the stability of the simulation, the time step should be Modelling and Simulation in Engineering appropriate, and the Rayleigh time step [22] is the maximum of the time step of particle set, determined by where T R is the Rayleigh time step, r is the coal particle radius, ρ is the particle density, G is the shear modulus, and μ is the Poisson ratio.e time step is usually set from the range of 10 to 40%T R .In this paper, the time step was 20%T R .Rayleigh time step was calculated as 3.42e − 06 s. e simulation time was 6 s, the target storage time interval was 0.01 s, and the grid size was 5 times that of the minimum particle radius, and the coal mining machine cutting coal rock process is shown in Figure 3.

Analysis of the ree-Dimensional Force of the Drum.
In the EDEM postprocessing, the three-directional force and the total force of the drum were extracted and exported as a .CVS le, and the three-dimensional force curve was obtained in MATLAB, as shown in Figure 4.It can be seen from Figure 4(a) that when the drum cut the coal rock, the total force uctuated irregularly within a certain range.is was because the position, number, and declination of the picks involved in the cutting were constantly changing with time, and the coal rock was not regular.In the threedirectional force, the Z-direction force was the cutting resistance, the X-direction force was the traction resistance, and the Y-direction force was the axial force.Among them, the value of the cutting resistance was the largest, the traction resistance was second, and the axial force was the smallest, as shown in Figure 4(b).e Y-direction force of the drum uctuated above and below zero, but its average value was not zero.In order to obtain the relationship between the rotational speed and the triaxial force, the simulations were carried out with di erent rotational speeds of 75 r/min, 85 r/ min, 95 r/min, and 105 r/min and a traction speed of 4 m/ min.e load uctuation coe cient [23,24] can measure the cutting performance of the drum.e load uctuation coe cient is  4 Modelling and Simulation in Engineering where F i is the instantaneous value of the drum load and F is the average of the drum load.e three-way extraction force is shown in Table 4.It can be seen from Table 4 that the average value of the three-way resultant force decreased with the increase of the rotational speed; when the traction speed and the depth of the cut were constant, the rotational speed of the drum increased, the cutting thickness decreased, and the corresponding cutting resistance decreased.5.It can be seen from Table 5 that the average value of the resultant three-way force increased with the increase of the traction speed.Due to the increase of the traction speed, when the rotational speed was constant, the maximum cutting thickness of the drum increased, and the force received by the drum cutter per unit time also increased, so the resultant force increased.

In uence of the Cutting Depth on the ree-Way Force of the Drum.
In order to obtain the relationship between the cutting depth and the triaxial force, simulations were carried out with di erent cutting depths of 480 mm, 530 mm,   Modelling and Simulation in Engineering 580 mm, and 630 mm, and the traction speed was 4 m/min, and the drum's speed was 95r/min.e three-way resultant force of the extraction drum was extracted and sorted by MATLAB.e results are shown in Table 6.It can be seen from Table 6 that the average value of the three-way force of the drum increased with the increase of the cutting depth.When the cutting depth of the cut increased, the number of picks involved in the cut increased, causing the resultant force of the drum to increase.

Research on the Performance of Drum Loading.
Statistics on the particle mass of the floating coal zone I and the effective coal loading area II have been shown in Figure 6(a).e total amount of coal falling was the sum of the particle mass in the effective coal loading zone and the floating coal zone [25].e coal loading rate η is the mass of the effective coal loading area divided by the total mass of falling coal, as shown in the following equation: where m e is the particle mass of the loading coal zone and m f is the particle mass of the floating coal zone.When the drum's rotational speed was 95 r/min, the traction speed was 4 m/min and the cutting depth was 580 mm; the drum's coal loading rate curve is shown in Figure 6(b).It can be seen from Figure 6(b) that the coal loading rate fluctuated a certain amount during the start-up phase of the shearer, and the coal loading rate became constant as the time increased.

Influence of Rotational Speed on the Drum Loading
Rate.In order to study the effect of the rotational speed on the drum loading rate, the rotational speeds used were 75 r/ min, 85 r/min, 95 r/min, and 105 r/min, the cutting depth was 630 mm, the traction speed was 4 m/min, and the simulation was then carried out.In the EDEM posttreatment, the coal flow velocity of 4.45 s in the four working conditions was obtained [26] as shown in Figure 7.It can be seen from Figure 7 that the rotational speed increased from 75 r/min to 105 r/min, and the instantaneous maximum velocity of the coal particles increased from 9.81 m/s to 15.6 m/s, mainly because the cut coal rock was driven by the drum.When the rotational speed of the drum was large, the particles were thrown outward under the frictional force of the drum, and the maximum throwing speed of the particles increased.
In order to analyze the instantaneous velocity and the throwing position of the particles, the distance vs. velocity diagram of the particles obtained for each working condition in the postprocessing is shown in Figure 8.As can be seen from Figure 5, the maximum number of particles of the instantaneous velocity of the coal flow in Figure 8 was small.At most, the instantaneous velocity of the particles    Modelling and Simulation in Engineering did not exceed 7 m/s at the same time.e drum had a depth of 630 mm and the coal wall had a width of 800 mm.It can be seen from Figure 5 that the number of e ective coal loading zones was di erent when the cylinder speed was di erent.e coal loading rate statistics are shown in Table 7.As can be seen from Table 7, as the drum's rotational speed increased, the coal loading rate gradually increased.Since the speed of the drum was low, the movement of the particles in the drum was mainly sliding, and the speed of particle ejection was small.As the rotational speed of the drum increased, the movement of the particles was more a ected by the rotation of the drum, so that the particles were thrown into the effective coal loading area, so the coal loading rate improved.In order to study the in uence of the traction speed of the drum on the coal loading rate of the drum, the drum speed was set to 95 r/min, the cutting depth was 630 mm, the traction speeds used were 3 m/min, 4 m/min, 5 m/min, and 6 m/min, and the simulation was then carried out.e coal particle velocity of the drum obtained in the posttreatment is shown in Figure 9.It can be seen from Figure 9 that as the traction speed increased, the number of coal rock particles falling into the e ective coal loading zone gradually increased.However, the traction speed was too large so the amount of coal falling into the oating coal zone increased, so the coal charging rate was lowered.e distance vs. speed of the coal ow is shown in Figure 10.As can be seen from Figure 10, as the traction speed increased, the velocity of most of the particles in each working condition gradually increased.Mainly due to the higher traction speed, the thickness of the drum cutting layer per unit time increased, and the corresponding instantaneous throwing particle speed increased.
e coal loading rate of the abovementioned working condition for the drum is shown in Table 7.It can be seen from Table 7 that as the traction speed of the drum increased, the loading rate of the drum decreased.As the traction speed increased, the coal ow rate in the drum blades increased, which reduced the amount of coal rock that could not be discharged by the coal wall and the picks due to the low traction speed.As the traction speed continued to increase, the unit interception coal volume of the shearer exceeded the coal retention space in the drum blade, causing the coal rock ow to block the drum, and it could not be discharged in time, which greatly reduced the coal loading rate of the drum.

In uence of the Cutting Depth on the Drum Loading
Rate.In order to study the e ect of the cutting depth on the speed of the coal particles, the rotational speed of the drum was set to 95r/min, the traction speed was set to 4 m/min, and the di erent depths used were 480 mm, 530 mm, 580 mm, and 630 mm. e coal particle velocity and coal particle distance were obtained for the di erent depths.e speeds are shown in Figures 11 and 12.It can be seen from Figures 11 and 12 that as the depth of cut increased, the amount of coal particles thrown into the coal charging zone gradually decreased.It can be seen from Table 5 that as the   Modelling and Simulation in Engineering cutting depth of the shearer deepened, the coal loading rate of the drum was reduced.e main reason for this was that the mining depth of the shearer drum was too large, resulting in a cumulative increase of the amount of coal falling in the capacity space of the drum blade, causing longterm blockage, which was di cult to clear, and increased the drum's resistance.Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.

4. 2 .
Force Analysis of Each Intercept Pick.It can be seen from the pick arrangement diagram of the drum that the barrel had 7 sections and the end plate had 5 sections.In the postprocessing of EDEM, the force of each pick was extracted and collated by MATLAB Figure 5.4.3.e In uence of the Rotational Speed, the Traction Speed, and the Cutting Depth on the Triaxial Force of the Drum 4.3.1.In uence of the Rotational Speed on the Triaxial Force of the Drum.

Figure 2 :Figure 3 :
Figure 2: (a) e picking arrangement diagram of the drum (b) ree-dimensional model of the drum.
Speed on the ree-Way Force of the Drum.In order to obtain the relationship between the traction speed and the triaxial force, the simulations were carried out with di erent traction speeds of 3 m/min, 4 m/min, 5 m/min, and 6 m/min, and the speed of the drum was 95 r/min.e three directions of the drum were extracted in postprocessing.e force and the three-way force were collated by MATLAB, as shown in Table

Figure 4 :
Figure 4: (a) e total force of the drum.(b) ree-directional force of the drum.

( 1 )
e discrete element analysis software was used to study the dynamic cutting process of coal mining with a shearing coal drum, and it could dynamically observe the rock fragmentation and coal rock velocity trajectory, and it has provided a new

Table 1 :
Particle parameters of coal rock.

Table 2 :
Physical and mechanical parameters of coal.

Table 3 :
Particle contact model parameters.

Table 4 :
e relationship between the rotational speed and the three-directional force of the drum.

Table 5 :
e relationship between the traction speed and the three-directional force of the drum.

Table 6 :
e relationship between the cutting depth and the three-directional force of the drum.

Table 7 :
e statistics of the coal loading rate.