Discrete Element Simulation of Conical Pick ’ s Coal Cutting Process under Different Cutting Parameters

To explore how the cutting parameters affect the conical pick’s cutting force in coal cutting process, some simulation tests were carried with EDEM based on analysis of coal cutting process of conical pick and micro mechanical characteristic of coal particles. In this paper, traction speed, drum angular velocity, and installation angle of conical pick were considered as the main coal cutting parameters. The discrete element simulations were conducted under 7 sets of various cutting parameters, which were determined in the range of empirical parameters. From the results of the simulation tests, it can be concluded that the fragmentation of coal particles appears in a compacted, squeezed, and crumbling state in coal cutting process; the traction speed has the greatest impact on the conical pick’s cutting force and cutting force fluctuation and the influence of drum angular velocity and installation angle reduce in turn; the force and force fluctuation tend to decrease and obviously increase, respectively, with the increase of drum angular velocity and traction speed; and they will reach theminimumwhen the pick’s installation angle is 45 under certain traction speed and drum angular velocity.


Introduction
Various coal cutting works are carried out in mining engineering by means of different machines and cutting tools [1].The shearer and conical pick, as the core device and main cutting tool, are widely used in mining engineering, and the basic physical phenomenon occurring during coal cutting process is fracturing and fragmentation of the coal under mechanical action of conical picks, of which the cutting parameters not only affect the cutting efficiency of shearer, but also influence the cutting power and abrasion of the conical picks.Therefore, the research on the cutting parameters of conical pick in coal cutting process has become a hotspot in this field.
From the cutting force model of conical pick proposed by Evans on the basis of tensile stress theory [2], the cutting force was considered to be related to tensile stress of coal, semitip angle of conical pick, cutting angle, and cutting thickness and was proportional to the square of the cutting thickness.According to analyzing the friction between conical picks and coal, the theoretical model of the conical picks has been obtained based on Evans theory by Roxborough and Liu [3].When the cutting friction angle and front angle of pick were introduced into Evans' model, the value of cutting force was modified under semitip angle at 0 degree, and then a semiempirical cutting model was proposed by Göktan [4] and Göktan and Gunes [5] with regression method on the basis of a large number of experiments.A theoretical model to estimate the cutting force of conical pick based on fracture mechanics was presented by Bao et al. [6], in which the cutting force work was considered to be proportional to the square of the depth of cut, and the cutting peak force and the depth of cut have a power law relationship with the component equal to 4/3.A mathematical model on the lateral force of conical pick under different cutting conditions has been developed by Liu and Li [7] based on cutting mechanism and mechanics principle; then spectrum of the lateral force load at different slope angles and cutting thicknesses was decomposed in frequency domain and time domain.
With the development of computer technology and modern engineering technology, a number of numerical tests of rock cutting utilized the finite element method have been explored [8][9][10][11][12].However, the finite element method based on the continuum mechanics theory of material modeling has some drawbacks in representing properly discontinuities of the material occurring during rock cutting [13].The discrete element method was pioneered by Cundall [14], which has a wide range of application in rock mechanics [15,16] and soil mechanics [17,18], as well as various penetration conditions in granular media [19,20].
The discrete element method that treats coal or rock as being composed of separate rigid particles has extensive prevalence in coal cutting process.Particle Flow Code (PFC) was used to study the cutting force of the picks in linear [21][22][23] and rotary [1,24] cutting process when the cutting thickness was constant and to develop the crack propagation [22,23,25] of coal and rock in the linear cutting process.Extended Discrete Element Method (EDEM) was used to establish linear conical pick cutting coal model to study the cutting process with different cutting thickness and different installation angles [26], which showed that the cutting force of conical pick increases linearly with the cutting thickness and varied nonlinearly with the installation angle.
In the coal mining operation, conical picks, installed on the shearer drum at different installation angles, are driven by traction speed of the shearer and the angular velocity of the drum to cut the coal.However, the cutting condition, like the prolate cycloid cutting trajectory and the varying cutting thickness, is not distinctly considered in the above scholars' research [21][22][23][24][25][26] based on simplified assumptions.Based on the coal mining operation, this paper simulated the coal cutting process of conical pick at various traction speed, drum angular velocity, and installation angle in EDEM, to analyze the phenomenon of coal fragmentation and the cutting force of conical pick, as well as the relation between cutting force and the cutting parameters mentioned above.

Cutting Parameters of Conical Pick
2.1.Determination of Cutting Parameters. Figure 1 presents the coal cutting process of conical pick.The pick is mounted on shearer drum with the installation angle  and it is driven by the shearer traction speed V and the drum angular velocity  to cut the coal, where  is cutting radius, the points  and  1 are coordinate origins located at the drum center axis at the beginning and ending of the coal cutting process, trajectories 1 and 2 are formed by the first and the second cutting cycle, respectively, in coal cutting process, between which is the cutting thickness, the formula of cutting trajectory is given in (1), and ℎ max is the maximum cutting thickness in cutting process.
In coal cutting process, the cutting thickness varies with the traction speed of shearer, drum angular velocity, and cutting radius.If (1) represents trajectory 1, the formula of trajectory 2 can be deduced as follows: where ℎ max = 2V/,  is the number of picks on the same transversal.Then the change of cutting thickness in coal cutting process can be obtained as The detailed formula of cutting thickness can be calculated according to (1), (2), and (3).
Under certain working condition of shearer, this paper selected the semitip angle of conical pick equal to the optimum value of 38 degrees [2], and the drum diameter was set as 1 m (cutting radius  is 0.5 m) for the tests.Then the traction speed of shearer V, angular velocity of drum , and installation angle  were selected as the parameters to be studied in the coal cutting process.

The Range of Cutting Parameters.
At present, the above three parameters have formed the empirical range, respectively, [27].In this paper, 7 sets of various parameters were selected to simulate the cutting process on the basis of empirical ranges, which were classified as different angular velocity, traction speed, and installation angle, as shown in Table 1.

Materials and Contact Model of Coal and Conical Pick.
Conical pick and coal materials were selected, respectively, as steel and coal from EDEM material database, and the contact model between coal and conical pick was chosen as Hertz-Mindlin (with no slip) contact model in this paper.The parameters of contact property [28] are given in Table 2.

Parameters of Coal Particle.
The structural and mechanical properties of coal are complex, which present certain regularity bedding, joints, and random waste, pores, cracks, and so on.In order to simplify the modeling and simulation experiments, the circular particles with   Where  1 ,  2 are the radius of particles 1 and 2, respectively,  1 ,  2 are the contact radius of particles 1 and 2,   is the normal overlap between particles,   ,   are normal and tangential damping, and   ,   are normal contact stiffness and tangential contact stiffness between particles.Their relations [32] are obtained: where  * is equivalent elastic modulus, 2 )/ 2 ,  1 and  2 are macroscopic elastic modulus of coal particles 1 and 2, respectively,  1 and  2 are macroscopic Poisson ratio of coal particles 1 and 2,  * is equivalent elastic modulus, 2 )/ 2 , and  1 ,  2 are macroscopic shear modulus of coal particles 1 and 2.  * is equivalent radius of coal particles, 1/ * = 1/ 1 + 1/ 2 . * is equivalent mass of coal particles, 1/ * = 1/ 1 + 1/ 2 . is the restitution coefficient of coal particles in Table 2.And the macro mechanical characteristic parameters of coal particles are shown in Table 4 [33].
The normal contact stiffness   and the tangential contact stiffness   were calculated by the ( 5) and ( 6) and the relevant parameters from Tables 3 and 4. Then the Micro mechanical parameters of coal particles were set up in EDEM, which were shown in Table 5, where the critical normal stress   and the critical shear stress   are equal to the compressive strength and shear strength of the coal, respectively.

Building of the Geometric Model.
In this paper, a simplified three-dimensional drum geometric model with a single conical pick was established using UG, and the model was imported into the EDEM geometry module to simulate the coal cutting process of conical pick.
In order to simulate the coal cutting process showed in Figure 1, every simulation test was carried under different coal cutting surface, which was determined by the cutting trajectory (1) based on the cutting parameters shown in Table 1.In EDEM, the length, width, and height of coal model were determined as 0.68 m, 0.15 m, and 1.30 m according to the drum diameter, physical dimension of conical pick, and the related cutting parameters, and its geometry model is consisted by 90000 coal particles, which were dynamically deposited by Rain Drop Method.When the micro mechanical parameters of coal particles were set according to Table 5, the bonding between coal particles was generated.The model of coal cutting process of conical pick in EDEM was given in Figure 3.

Time Step of Simulation.
If the time step is not appropriate, it may cause particle divergence and affect the accuracy of simulation results.The Rayleigh time should be set reasonably for the simulation tests to go smoothly in EDEM.According to the literature [32], the Rayleigh time step is the maximum of the time step of particle set, determined by where   is the Rayleigh time step,  is coal particle radius,  is particle density,  is shear modulus, and  is Poisson ratio.Rayleigh time step was calculated as 1.55×10 −5 according to the related parameters in Tables 3 and 4. In the actual simulation test, the time step is usually set from the range of 10-40%   .In this paper the time step was 20%   .

Analysis of Coal Cutting Process. The simulation of coal cutting process of conical pick under the parameters
A from Table 1 is shown in Figure 4, where (a)∼(i) are cutting state, particle velocity vector, and sectional of bonding diagrams when conical pick is at the beginning, middle, and end position of the cutting process.In the particle velocity vector diagrams, the direction of the arrows indicates the instantaneous velocity direction of the coal particles, and the color of the arrows represents the instantaneous velocity of particles, which increases gradually with blue, green, and red in turn.And in the section of bonding diagrams, the strip represents the bonding between the coal particles, which constitutes bond networks; the red and blue color represent large and little cohesive force, respectively.
As indicated in Figure 4, the cutting thickness is small at the beginning of coal cutting process, and the pick causes small clumps of coal particles, when the internal velocity pattern of coal tends to be more stable than that at the tip of the conical pick, and the falling massive coal particles appear irregular motion state; meanwhile, the bonding between coal particles has few fractures that belong to compaction state of coal.With the continuous cutting of the conical pick, the cutting thickness increases, and the cutting thickness reaches the maximum at the middle position of cutting process, and near this position, coal particles are gradually piled up at the joint between the conical pick and pick holder, where the bonding is extruded and deformed, and then a large degree of fracture occurs, showed by blue colored bonding, which results in coal gliding fracture.And the velocity of the coal particles is high at the tip and the end of the conical pick, which causes coals to collapse along the movement direction of the conical pick.When the pick is close to the end of the coal cutting process, cutting thickness decreases gradually, and velocity of coal particles is still high at the tip of conical pick.The falling coal moves with cutting direction of conical pick.The particle velocity vector and bonding diagram proposed in this paper shows fracture mechanism and movement direction of coal particles, which strengthen and prove the rationality of results on coal cutting state [34,35].conical pick in the cutting coal process with the parameters A, B, C, D, E, F, and G, respectively.It can be seen from the diagram that the traction speed is the primary factor affecting the cutting force of the conical pick, and the drum angular velocity is the secondary and the installation angle is the least.In coal cutting process, the cutting force of the conical pick, which tends to increase first and then decrease with the change of cutting thickness, shows irregular fluctuations on the whole because of randomness of the lump coal fragmentation.This trend is consistent with the experimental results [24] and theoretical calculation results [27] in the literature.

Analysis of Cutting Force under
The general trend of cutting force is similar to the cutting thickness obtained from (4) and the larger the cutting thickness, the greater the cutting force.At the initial stage of coal cutting process, the coal was effected by cutting force of conical pick, and the coal fragmentation occurs when the cutting force is accumulated to a certain extent, then the cutting force is obviously reduced until the end of cutting process.

Force Analysis at Different Angular Velocity.
According to the comparison of the cutting force curves in Figures 5,  6, and 7, the cutting force of conical pick decreases with the increase of the angular velocity , and the smaller the angular velocity of the drum, the greater the variation of the cutting force.When the drum angular velocity is 5.23 rad/s, the maximum fluctuation of the cutting force is about 8000 N. To analyze this phenomenon, the coal particles are easily piled up when the angular velocity of the drum is small, and great pressure is formed before caving; the coal fragmentation is obviously larger than the cutting thickness, which results in sudden increase in cutting force.There will be a temporary no-load phenomenon that occurs after the coal was cut.8, 6, and 9, it can be seen that the cutting force of conical pick increases obviously with the increase of the traction speed.Also, the fluctuation of cutting force increases with the increase of traction speed; the maximum fluctuation of the cutting force is about 9000 N when the traction speed is 0.09 m/s.

Force Analysis at Different Installation Angle.
The installation angle has little effect on the cutting force, and the average cutting forces of the conical pick are about 6500 N, 6000 N, and 6300 N when the installation angle is set as 40 ∘ , 45 ∘ , and 50 ∘ , respectively, by comparing the cutting force curves in Figures 10, 6, and 11.The interference of extrusion between coal and conical pick and its holder is not prone to happen because the conical pick has an advantage position to cut the coal when the installation angle is 45 ∘ .Therefore, the

Figure 2 :
Figure 2: Schematic illustration of the Hertz-Mindlin contact model of coal particles.

Figure 3 :
Figure 3: EDEM model of coal cutting process of conical pick.

Figure 6 :Figure 7 :
Figure 6: Cutting force of conical pick under the cutting parameter B.

Figure 8 :Figure 9 :
Figure 8: Cutting force of conical pick under the cutting parameter D.

Figure 10 :Figure 11 :
Figure 10: Cutting force of conical pick under the cutting parameter F.

Table 1 :
7 sets of various parameters.Notes.The data in the Table 1 are the cutting parameters range of single pick.

Table 2 :
The parameters of contact properties of coal and steel.

Table 3 :
Parameters of coal particles.
[29][30][31]ical Parameters of Coal Particles.Since the coal is massive structure state before cutting and appears crumbling during the cutting process, certain bonding force must be existent between the coal particles.The Hertz-Mindlin with bonding was selected as the contact model between coal particles in this paper.The bonding model was depicted in Figure 2[29][30][31].

Table 4 :
Macro mechanical characteristic parameters of coal particles.

Table 5 :
Micro mechanical parameters of coal particles.