Finite element simulation study on cutting coal and rock by cutting head of roadheader

In order to improve the cutting efficiency of the roadheader and address the challenge of monitoring the load of the cutting head and pick, a load simulation method was proposed using ABAQUS finite element software to simulate the cutting head at different cutting depths under various cutting conditions. According to the coal cutting test, a finite element simulation model was developed using Drucker-Prager as the constitutive model of coal to simulate the conical pick cutting of coal. The results of the finite element analysis were compared with the cutting test results, and the reliability of the former was confirmed. The study further involved establishing a model of cutting coal with different depths under various working conditions, and the torque waveform was obtained through finite element simulation. MATLAB was employed to program the theoretical formula, the theoretical waveforms of the force and torque of the cutting head were obtained. Additionally, the mean value of the cutting force of each pick in the finite element simulation results under different working conditions was statistically analyzed, and its distribution law was obtained. The results showed that the finite element simulation results were in good consistency with the theoretical calculation results, indicating that the simulation method was both reasonable and feasible for simulating the coal cutting process. Finite element simulation combined with theoretical calculation can be used in the stability control of cutting head dynamic load, and provide a basis for improving cutting efficiency.


Introduction
The cutting object of the roadheader is coal and rock with high hardness grade and wide range of variation, which has large working load and challenging construction environment.Due to the complex and changeable characteristics of coal seams, the load of the roadheader changes sharply during the cutting process, causing the cutting mechanism of the roadheader to bear frequent alternating impact load during the work.Also, the pick collides and rubs with the hard rock of the coal seam, resulting in pick wear, breakage, fall-off and other phenomena.Such issues not only cause the unstable operation of the roadheader, but also seriously affect the cutting efficiency.To improve the cutting performance and efficiency, the operating parameters such as cutting head rotation speed or cantilever swing speed can be adjusted according to the cutting state of cutting head [1].
Many domestic scholars have conducted research on the load calculation and simulation of the cutting head.Li Xiaohuo et al. [2] established the calculation formula of pick and cutting head load based on experimental and theoretical research.Liu Chunsheng et al. [3]  platform and simulated the process of straight and rotary cutting of coal with picks using ABAQUS.Liu Weihuang [4] used the finite element simulation method to establish a model in which the two picks of the cutting head cut coal rocks in sequence to simulate the process of cutting coal rocks by the cutting head.Although domestic scholars have conducted extensive research and simulation on the cutting process of the cutting head, most have carried out simulation research on the process of cutting coal with single or double picks.Few have done finite element simulation research on the entire cutting process of the cutting head.
Since the cutting process of coal and rock by the cutting head is relatively complicated in actual operation, it is necessary to analyze and simulate the cutting process of the cutting head at different cutting depths under different working conditions.In this paper, referring to the test conditions and process of the coal-rock cutting test of the pick [5], the feasibility and effectiveness of finite element simulation are verified by establishing a model and setting relevant parameters, and then performing finite element simulation.Combined with the theoretical calculation of the cutting head load and finite element simulation, the load of the cutting head at different cutting depths under different cutting conditions is simulated using MATLAB and ABAQUS respectively.Obtained the load variation pattern and the force distribution of picks.The results of finite element simulation can be used to revise the load calculation formula and lay the foundation for calculating the load in load control of roadheader.

Theoretical calculation of cutting head load
When the cutting head cuts coal and rock, the load on the pick is a pulsating impact load, which can be regarded as a stable random load [6].The load on the cutting head is the vector sum of the loads on all the picks in the cutting state.By calculating the force on the pick, the force on the cutting head can be obtained.

Load calculation of pick and cutting head
When the pick cuts coal and rock, the reaction force it receives can be decomposed into cutting resistance Z (along the cutting direction), traction resistance Y (along the cutting head radius direction), lateral resistance X (along the cutting head axis direction), as shown in Figure 1.The formula for calculating the force of conical pick [7][8] is: where, Z i , Y i , X i are the cutting resistance, traction resistance and lateral resistance of the ith pick on the cutting head; P k is the contact strength of the rock (MPa), usually taken as P k =44f 1.5 ; f is the solidity coefficient of the rock; k T , k g , k '  y are the type coefficient of the picks, geometric shape influence coefficient of the picks and intercept influence coefficient of the picks respectively; t is the average cutting distance (mm); h i is the average cutting thickness of the ith pick (mm); S j is the projected area of pick back-edge after dull along the line of traction (mm 2 ); C 1 , C 2 , C 3 are the influence coefficients of breakout patterns.
Under different cutting conditions, the calculation method of the average cutting thickness h i of the pick is different.Under horizontal cutting or vertical cutting conditions: (4) Under drilling cutting conditions: ( where v b and v k are the swing velocity and drilling velocity of the cutting head (m/min); n is the cutting head rotating velocity (r/min); m is the number of picks at the same cut line;  i is the position angle of the ith pick, β i is the angle between the axis of the ith pick and the rotation plane of the pick tip.
The force on the cutting head can be decomposed into traversing force R a (along the vertical cutting direction), vertical force R b (along the horizontal cutting direction), and axial force R c (along the axial direction), as shown in Figure 2. The load of cutting head can be obtained by Formula (6) (6) (7) (8) The torque calculation formula at the cutting head axis is: (9) where r i is the cutting radius of the pick.

Load simulation of cutting head
The cutting head has three cutting conditions: horizontal cutting, vertical cutting and drilling cutting, as shown in Figure 3.
In order to calculate the resultant force on the cutting head, it is necessary to judge whether the pick participates in cutting.Under horizontal cutting condition, when the distance from the tip of the pick to the top of the cutting head is less than the cutting depth h and between 0 ° and 180 °, the pick is in cutting state; under vertical cutting condition, when ,position angle 90° 90° , , the pick is in the cutting state, when , and 90° 90°, the pick is in cutting state; under the drilling cutting condition, when the distance from the tip of the pick to the top of the cutting head is less than the cutting depth h, the pick is in the cutting state; MATLAB is used to program the above theoretical model.The cutting depth is set to 200 mm, 400 mm, and 600 mm under the horizontal cutting condition, and set the corresponding simulation angle under the vertical cutting and drilling cutting conditions, the force change curve of the cutting head is obtained, as shown in Figure 4.

Finite element simulation of cutting head cutting coal and rock
The finite element simulation is a main method used to study the cutting process of cutting head and picks.The simulation can simulate the load changes occurring during coal and rock cutting by the cutting head, and provide the basis for the stability control of the cutting head.Firstly, UG NX is used to model the cutting head model.Hexahedral element meshes are generated using HyperMesh, and the model is imported into ABAQUS for finite element simulation.

Single pick cutting simulation
Cutting test is the main method to study coal and rock cutting [9].The consistency between the cutting force and the test results is a measure of the reliability of the finite element simulation results.The coal sample used in the test is made by mixing cement and sand in a ratio of 3:1, and an appropriate amount of water is added.The protodyakonov coefficient f=28.94/10=2.894,and the density is 2.4×10-9 t/mm 3 , the elastic modulus is 39800 MPa, the Poisson's ratio is 0.257, the uniaxial compressive strength is 28.94 MPa, and the uniaxial tensile strength is 6.56 MPa.A U135-25 pick is selected, with a cutting angle of 45°, a cutting speed of 0.158 m/s, and a cutting depth of 5 mm, 10 mm, and 15 mm.The force curves of the pick at different cutting depths are obtained, as shown in Figure 5.To verify the reliability of the finite element analysis, the finite element simulation is carried out based on the single pick cutting test.Models are designed according to different cutting depths, and hexahedral element meshes are generated using HyperMesh.The element type selected is C3D8R.Import the mesh model into ABAQUS for material definition.
The Extended Liner Drucker-Prager model [10][11] is adopted for coal rock, and the parameters are set according to the mechanical properties of the coal rock sample; the material density of the pick is 1.46×10 -8 t/mm 3 , the elastic modulus is 600.000MPa, and the Poisson's ratio is 0.22.The simulation time is set to 1s, and the finite element simulation is performed.The model of single pick cutting coal under the cutting depth of 10 mm is shown in Figure 6.After simulation, the picks gradually contact and intrude into the coal rock within 0s to 0.15s, and the cutting force gradually increases.After 0.15s, the picks completely penetrate into the coal rock, and the magnitude and fluctuation of the cutting force tend to stabilize.The results shown in Figure 7.
The comparison of the average cutting resistance obtained by finite element simulation with the cutting test, and the results are shown in Table 1.
Through comparison, it is found that the finite element simulation results are consistent with the test results, and the error is small.Using Drucker-Prager as the constitutive model of coal rock conforms to its mechanical properties, and the finite element simulation can accurately simulate the process of cutting coal and rock by the pick.Therefore, the finite element model can be used for the simulation of cutting head cutting coal rock.

Cutting simulation of cutting head
After simplifying the cutting head model, models are established for the cutting head invasion depths of 200 mm, 400 mm, 600 mm under horizontal cutting conditions; the cutting head invasion depths of 0 mm, 200 mm, 400 mm under vertical cutting and drilling cutting conditions.A hexahedral element mesh is generated and imported into ABAQUS for related settings.Figure 8 shows the mesh model of the cutting head with a cutting depth of 200 mm.After the material definition is completed in ABAQUS, the contact between the surface of each pick and the internal nodes of coal and rock is set in turn.The type used is surface-to-surface contact, and the friction coefficient is set to 0.3.The pick is constrained to be a rigid body, which does not deform during the cutting process.The reference point is selected at the center of the bottom of the cutting head.The cutting head body and picks seat are constrained to be display body, which does not participate in the analysis calculations, reducing simulation time.The surface of the coal rock that does not participate in cutting is constrained by boundary conditions to constrain its six degrees of freedom.At the reference point, the cutting head is set to rotate around the z-axis at a speed of 30.6 r/min.The cutting head is set to swing at a speed of 1 m/min along the x-axis under the horizontal cutting and vertical cutting conditions, and the drilling cutting condition is set the drilling speed of the cutting head along the z-axis to 1.5 m/min.The simulation time is set to 2s.
The reaction moment at the central axis of the cutting head is selected to reflect the change of the overall load of the cutting head, and the results are shown in Figure 9.The torque waveform of 1 to 2 seconds of finite element simulation is selected to compare with the waveform calculated theoretically, as shown in Figure 10.The cutting depths of 0 mm, 200 mm, and 400 mm in the vertical cutting condition correspond to 0 s, 12 s, and 24 s of the MATLAB simulation The torque results from 1 s to 2 s of finite element simulation are in good agreement with the theoretical calculation results on average.However, the fluctuation range of the load torque waveform of finite element simulation is larger.The comparison results of the average load torque are shown in Table 2.When the cutting depth is small, the error between the mean value of simulated torque and the mean value of theoretical torque is relatively large, but still within a reasonable range.As the cutting depth increases, the error decreases, and the simulation results are in good agreement with the theoretical results.Due to the complex and changeable coal rock, the load torque of the cutting head fluctuates randomly when cutting coal and rock.Theoretical calculations cannot simulate the random fluctuation of the load torque, and its waveform presents a certain periodicity, while the finite element simulation results are more consistent with the actual working conditions.The results show that it is reasonable and feasible to use finite element simulation to simulate the coal rock cutting process.

Force statistics of picks
To achieve stable control of cutting head load, it is necessary to ensure that the cutting force of the pick when cutting coal and rock is less than the maximum allowable force.
When calculating the load torque of the cutting head using Formula (9), the maximum value of cutting resistance Z i of all picks under horizontal and vertical cutting conditions is the same.Under the condition of drilling cutting, the resistance Z i of each pick is different but remains a constant value.However, in actual working conditions, the load on the pick is a pulsating impact load, and the theoretically calculated cutting force cannot reflect the actual situation.Therefore, to obtain the distribution law of the cutting force of the pick, the force waveform of each pick is extracted from the finite element simulation results, and the mean value of the cutting force is calculated.
To analyze the results of pick cutting force, the picks need to be numbered from 1 to 60 based to the distance from each pick to the bottom of the cutting head.The cutting head has 3 spiral lines, with 20 picks distributed in each line.Figure 11 shows the cutting head model.It can be seen from Figure 13 that when the statistics are carried out according to the number sequence of picks, the average value of cutting force of adjacent picks differs greatly, resulting in a highly fluctuating curve.This is because when the cutting head rotates to cut coal and rock, the picks on the same spiral line cut coal in sequence, and their forces are relatively close, while the picks with adjacent numbers are distributed on the other two spiral lines, resulting in different forces.Therefore, the picks should be grouped according to the spiral line before conducting statistics.The picks on each spiral line from 1 to 20 are renumbered, and the statistical results of the maximum cutting depth under each working condition are shown in Figure 13.The results indicate that the average cutting force of the picks on the same spiral line are relatively close.Under horizontal and vertical cutting conditions, the average cutting force gradually decreases with an increase of the number of picks, and the force at the bottom of the cutting head is relatively higher.Under the drilling condition, the average cutting force gradually increases with an increase of the number of picks, and the picks at the top of the cutting head bear a greater force.

Conclusions
(1) By comparing the results of single pick cutting test and finite element simulation, it has been verified that the Drucker-Prager constitutive model adopted conforms to the mechanical properties of coal rock, and that the simulation model is reliable.
(2) By comparing the simulation of single pick cutting test and theoretical calculation, it has been verified that it is feasible to use ABAQUS to simulate the actual cutting conditions, and the results are reliable.
(3) The force and torque of the cutting head increase in varying degrees with an increase in cutting depth and the number of working picks.The mean value of the load obtained by the finite element simulation is in good agreement with the theoretical calculation, and the simulation of the random load is more consistent with the actual load fluctuation.
(4) The force distribution law of the picks obtained from the finite element simulation can be used to correct the theoretical calculation.By establishing the mapping relationship between the force on the pick, the torque of the cutting head and the current of the cutting motor, the load on the pick can be controlled to reduce the loss of the pick and improve the cutting efficiency.

Figure 1 .
Figure 1.Force analysis of conical pick.

Figure 2 .
Figure 2. Force analysis of cutting head.

Figure 5 .
Figure 5. Cutting force curves with displacement at different cutting depths.

Figure 6 .
Figure 6.Meshed model of conical pick cutting coal.

Figure 7 .
Figure 7. Simulation results of conical pick cutting coal.

Figure 8 .
Figure 8. Meshed model of cutting head cutting coal rock at 200mm depth.

Figure 10 .
Figure 10.Finite element simulation and theoretical calculation of load torque curve.

Figure 11 .Figure 12 .
Figure 11.Cutting head model.The mean value of pick cutting force is shown in Figure 12.

Figure 13 .
Figure 13.Average cutting force of pick on each spiral line.
established a coal cutting test

Table 1 .
Finite element simulation and cutting test results.

Table 2 .
Mean value of finite element simulation and theoretical calculation results.