Numerical Simulation of Dynamic Response Characteristics of Cutting Coal and Rock by a Roller Coal Cutter

College of Electronic and Electrical Engineering, Henan Normal University, Xinxiang 453007, Henan, China Henan Key Laboratory of Optoelectronic Sensing Integrated Application, Xinxiang 453007, Henan, China Academician Workstation of Electromagnetic Wave Engineering of Henan Province, Xinxiang 453007, Henan, China College of international Education, Henan Normal University, Xinxiang 453007, Henan, China Henan Institute of Metrology, Zhengzhou 450000, Henan, China


Introduction
Automatic identification technology of coal and rock properties of the working face is not only the basis of automatic control of coal-winning machine but also the need for intelligent and unmanned mining. Due to the effect of large coal dust, poor visibility, complex environment, and other shortcomings [1][2][3][4][5], it is difficult to accurately judge the coal and rock properties in front of the drum of the coalwinning machine by direct visual observation, cutting noise, and other information. If one can distinguish the cutting medium in front of the shearer in real time, then one can automatically control the coal machine, reducing (or eliminating) the damage to the cutting teeth or avoiding gas explosion accident caused by friction spark. At the same time, treatment measures, such as preloosening fracturing, can be done for the hard rock if encountered at an earlier time [6][7][8][9][10][11]. In Chinese Energy Science and Technology Development Plan of the twelfth five-year plan, it is also clearly pointed out that the unmanned mining technology of fully mechanized coal face is an important development direction, and the focus is on the automatic identification technology of coal and rock properties to realize unmanned and automatic mining of the working face.
According to the existing literature, there are no less than 20 research methods for coal and rock identification, for example, the gamma-ray methods, which contain radioactive elements in coal rocks, the image recognition based on color and grain difference of coal and rock surface, the current and voltage threshold judgment method of cutting motor, the mechanical vibration analysis based on signal strength and spectral difference, the memory cutting, the infrared reflection, and so on [12][13][14][15][16][17][18][19][20][21][22][23]. Although these methods have achieved certain scientific research results, some methods have also been applied to production practices and most of the technologies have low reliability, low practicability, and hysteresis. For example, it cannot judge the cutting state of the coal mining machine in real time when the working face encounters sudden changes, such as working fault. erefore, it is necessary to make further exploration on the basis of the existing automatic identification technology of coal and rock. e relevant theory [24][25][26] of cut rocks point out that if coal and rock medium changes, the dynamic response generated by certain dynamic excitation will also change. Also, its dynamic characteristics can reflect features of physical and mechanical parameters, such as density and strength of coal and rock. erefore, by means of numerical simulation, this study investigated the dynamic response characteristics of the coal cutter roller when cutting coal and rock and analyzed the variation rules of the characteristics, such as displacement, speed, and reverse torsion of the roller when cutting coal and rock. We can identify the cutting state of the roller in real time by the characteristic information of the cutting medium. At the same time, if the property of the medium in front of the working face is known, the dynamic characteristics can be predicted in advance. is will have very important theoretical significance and engineering value.

Breaking Mechanism of Coal and Rock by Truncated
Tooth. e process of cutting coal and rock is described in detail as follows. When the truncated tooth just touches the coal body, stress concentration phenomenon occurs. When stress increases to certain degree, the local coal which is in contact will be crushed into powder. After further compression, the pulverized coal will be in the intact coal body in front of the truncated tooth, forming a compact core structure, which is shown in Figure 1.
When the truncated tooth moves forward, the stress inside the dense nuclear will increase, causing the breakage of I in Figure 1 and presenting notch on the surface of coal body.
en the powder is ejected from the dense core structure. When the truncated tooth moves forward over the small caved block I, it recontacts the coal and forms a dense core structure. Meanwhile, the volume and pressure increase, leading to small parts of II to break up again. As the cycle goes on, the rate of caved coal increases and finally falls into large chunks III along the crack AB. e mechanism of breaking coal by the truncated tooth is summarized as follows. At first, the truncated tooth produces a crushing effect to the partial coal body under compressive stress. Under the shear stress effect, the coal rock body produces cracks. After the cracks are fully expanded and developed, brittle fracture occurs in the coal rock [27][28][29][30].

Coal and Rock Failure Criteria.
e failure criterion of the rock represents the relationship between stress and rock strength in the state of ultimate stress. Shear failure is the main form of breaking coal and rock, and the frictional strength is equal to the bonding force against shear friction and the friction produced by the normal force on the shear surface. Although the Mohr-Coulomb failure criterion can reflect the essence of rock material failure by compression and shear, it ignores the influence of the intermediate main stress σ2.
e Dracker-Prager failure criterion makes up for this defect and can simulate the equivalent softening and hardening of rock materials as well as the inelastic bulk deformation. erefore, this study adopts D-P failure criterion. e cutting failure of coal and rock samples is not a transient process, but a dynamic continuous process. erefore, failure criteria include initial failure criteria and progressive failure criteria [31].
(1) Initial failure criteria for coal and rock: the shear failure criterion predicts the initial failure state according to the shear behavior. It is assumed that the equivalent plastic strain of the rock in the initial failure state is ε s pl , and ε s pl (θ s , ε · pl ) is a function related to the shear stress rate θ s and the plastic strain rate ε · pl . When the following criterion is met, the rock begins to break down: Among them, ω s is a state variable. When the plastic deformation increases with the proportion of equivalent plasticity, ω s increases at the same time.
For each incremental step in the analysis, the increment Vω s of ω s is calculated according to the following equation: (2) Criterion for progressive failure of coal and rock: during the process of coal and rock being cut and broken, the strength of coal and rock decreases continuously at first and finally leads to the breaking of coal and rock (as shown in Figure 2). e solid line represents the failure stress-strain curve, and the dotted line represents the corresponding nonfailure stress-strain curve. When the rock element is subjected to a stress greater than its yield stress σ 0 , the rock element begins to move from the elastic phase to the plastic hardening phase, but it is not destroyed at this time. Under the continuous action of the truncated tooth, when the stress value of the rock is greater than the critical yield stress σ y0 and the corresponding critical plastic strain ε 0 pl , the rock enters the stage of strain softening and the damage factor D increases continuously. When the equivalent plastic strain value reaches ε f pl , the damage factor D � 1, the rock element completely fails, and spalling from the rock mass forms a groove.

Basic Assumptions.
It is a complicated process to cut the coal wall of the working face with the coal cutter roller's truncated tooth, which is affected by the mechanical parameters of coal and rock, the power and model number of the coal cutter, and the stress state of coal and rock. In order to facilitate the numerical calculation, the following basic assumptions are made: (1) Because the process of coal cutter cutting coal and rock is completed through the roller's truncated tooth, in order to reduce the amount of calculation without affecting the calculation results, we can ignore the motor, rocker, base, and other components of the coal cutter, only to establish the coal cutter roller model. (2) Because the coal cutter roller has a high strength and hardness compared with the coal rock mass, the model can be assumed as a rigid body. (3) e cutting of coal and rock by the roller is carried out parallel to the direction of the working face. e track of the roller cuts coal, and the rock is well controlled. It moves forward along a straight line and the roller rotates around the axis. (4) After the coal and rock units are cut and broken, the problem of repeated destruction is no longer considered, and the broken coal and rock units no longer affect the subsequent cutting process.

Building the Cutting Model.
rough a lot of investigations on the common rocks in the coal face, it is found that there are mainly mudstone, sandstone, sandy mudstone, and other materials. Coal sample, mudstone, and sandstone are taken from Luszigou Coal Mine in Zhongneng, Shanxi Province, China. e standard specimens were made (as shown in Figure 3). Relevant mechanical parameters were tested in the State Key Laboratory of Efficient Mining and Clean Utilization of Coal Resources. e results are shown in Table 1.
e coal cutter roller and the coal wall model of the working face established by CAE software are shown in Figure 4. e left side is a coal cutter roller model with a diameter of 2 m and a width of 0.8 m. e right side is a coal rock model of the working face with a length of 10 m, width of 2 m, and height of 4 m. e coal rock model and the roller model are divided by a tetrahedral free grid. In order to ensure the calculation accuracy and save the calculation time, the grid was refined in the areas that had a great influence on the roller cutting of coal and rock, whereas the grid size was appropriately increased in other areas [32].

e Failure Process of Coal Rock Cut by Roller.
e central position of the roller at point o is selected and a constant forward traction of 200 kN and a rotation speed of 4.18 rad/s are applied. e traction provides forward power for the roller to cut coal and rock by the truncated tooth. e rotation speed provides the original rotation speed for the roller, which is driven to the coal and rock interface under dynamic conditions. e truncated tooth is in contact with the interface of the coal and rock wall at first, and then, friction is generated between the truncated tooth and the coal and rock. e rotation of the truncated tooth starts to cut the coal and rock. en, the coal and rock will be subject to friction, pressure, and cutting force of the truncated tooth. When the force of coal and rock is greater than its yield strength, it will produce yield change and enter the stage of plastic hardening.
When the truncated tooth continuously acts on the coal and rock mass, the stress is greater than the failure strength of the coal and rock, which will be destroyed and cut off by the truncated tooth. is process is simulated by setting up units in CAE software. e above process reciprocates and causes the coal and rock wall of the working face to be continuously cut. Figure 5 shows the cutting displacement and plastic zone distribution of the roller at different time periods in the process of cutting the coal seam.    As can be seen from Figure 5, the position of the roller at different time periods goes from shallow to deep. When t � 30 s, the roller was cut to the position of 2.3 m. When t � 60 s, it was cut to the position of 3.97 m. When t � 90 s, the position was cut to 5.8 m. When t � 120 s, it was cut to 7.71 m position. According to the cutting position of the roller at different time periods, the average cutting speed can be calculated. e average cutting speed of 2.9∼30 s is 0.07 m/s, 30∼60 s is 0.058 m/s, 60∼90 s is 0.061 m/s, and 90∼120 s is 0.064 m/s. at is to say, the average cutting speed is between 0.058 and 0.07 m/s, and the roller does not completely cut coal in the first 30 seconds, so the average cutting speed will be higher. It can be seen that the average cutting speed presents a slight fluctuation trend, with a small range of variation. It can be speculated that if the coal cutter roller cuts the coal and rock medium of the same nature, it will cut forward with an average speed.

Dynamic Characteristics of Cutting a Single Medium.
If dynamic conditions, such as traction f, rotation speed r, and boundary conditions, remain unchanged, dynamic response characteristics of coal seam, mudstone, and sandstone are obtained by numerical simulation.

Analysis of Inverse Moment Response When Cutting a
Single Medium. As we know, if the roller rotates to cut coal and rock medium, it is necessary to overcome resistance of the medium to roller's truncated tooth. en, the roller generates an inverse torque to the truncated tooth. e reaction torque curves of three media obtained by simulation are shown in Figure 6.
According to Figure 6, there are two inflection points A and B in the curve between inverse torque and time relationship. Before point A, the inverse torque is 0. e inverse torque between points A and B fluctuates slightly. After point B, the inverse torque decreases to 0 again. According to this feature, it can be concluded that the roller does not contact with the coal and rock medium before point A. Between points A and B, it is the cutting process of the roller. Finally, the cutting process is over after point B. e reverse moment of cutting the same medium shows a phenomenon of big and small. e reason is that the process of breaking the coal rock medium needs to go through three stages of elastic deformation, plastic deformation, and crushing. e resistance of the medium to the roller's truncated tooth in each stage is inconsistent. e rock element suffers the least resistance in the elastic stage. At the same time, resistance in the plastic stage increases gradually, and the resistance is greatest before failure occurs at the ultimate stress state. After the failure of the element, the new element is cut and this process will be repeated and continued.
But when cutting a different medium, the change of resistance to the roller is not consistent. e inverse torque of coal is mostly concentrated in the range of 0∼600 kN·m, mudstone torque is in the range of 0∼1200 kN·m, and sandstone torque is in the range of 0∼1685 kN·m. e average inverse torque relationship can be obtained by taking the inverse torque linear trend line of three media. e relationship is "sandstone > mudstone > coal seam." e change reason of the inverse torque is that the strength and hardness of medium are inconsistent.
at is to say, the strength of the coal is small and the strength of the sandstone is larger. e above coal and rock failure criterion theory points out that only when the stress subjected to the medium reaches its critical yield stress, the failure of the rock unit occurs. erefore, the failure of coal needs to overcome the smaller working resistance, whereas the failure of sandstone needs to overcome larger working resistance.

Displacement Response Analysis When Cutting a Single
Medium. Cutting displacement refers to the depth of the center point of the drum into the medium when cutting the medium. e simulated cutting displacements and time curves of coal, mudstone, and sandstone are shown in Figure 7.
e relation curve between cutting displacement and time in is shown in Figure 7. Point A (the roller is not in contact with coal and rock medium) indicates that roller is in a state of free rotation. en, displacement parameters increase significantly. e displacement and time images between A and B (when the roller is cutting the medium) show an approximate linear "step up" growth, but the displacement and time slopes are lower than in the stage of free rotation. e reason is that the roller cutting the medium needs to overcome the resistance and apply work. Figure 7 shows that the displacements-time curve of the cutting medium fluctuates up and down near a straight line with a certain slope. erefore, the average cutting speed of the medium can be figured out by the line slope. e average cutting speed of the three media is 0.064 m/s, 0.031 m/s, and 0.012 m/s, respectively. at is to say, the general relationship of the average cutting speed is "coal seam > mudstone > sandstone." erefore, the average cutting speed is a good reflection of medium type.

Velocity Response Analysis When Cutting a Single
Medium.
e curve of instantaneous cutting speed and time among the three media obtained by simulation is shown in Figure 8. Figure 8 shows that the instantaneous velocity rose rapidly before point A (the roller did not contact with the medium). It fluctuates greatly between A and B (during cutting) and suddenly increases in A straight line after point B (after cutting). It can be seen that no matter what kind of media the drum cuts, the cutting speed fluctuates all the time. e changing rule of the cutting speed is exactly the reflection of the resistance during the cutting process analyzed above. But when the cutting medium is different, the wave fluctuation is different, which is reflected in the velocity amplitude and the number of rebounds (that is, the number of vibrations with the velocity below 0″). For example, the instantaneous velocity of coal seam cutting is between 0 and 0.11 m/s, and no rebound is found. e instantaneous velocity of mudstone cutting is between −0.1 and 0.14 m/s. ere is a small amount of rebound, and a small part of the instantaneous velocity is less than 0. e instantaneous Shock and Vibration 5 velocity of sandstone cutting is between −0.27 and 0.29 m/s, and a large number of springback are found. at is to say, half of the total instantaneous velocity is less than 0. e instantaneous velocity fluctuation of different media is inconsistent because the mechanical properties of coal and rock of the cutting media change. When the cutting medium varies, the roller needs to overcome different working resistance. According to the analysis of inverse moment response, it is pointed out that the largest resistance needs to be overcome when cutting the sandstone and the smallest   resistance needs to be overcome when cutting the coal seam. erefore, the instantaneous velocity fluctuation is the largest when cutting the sandstone and the smallest when cutting the coal seam.
When the traction force suffered by the roller is small, it is not enough to instantly destroy the medium with greater strength.
e phenomenon of "falling-forward-refallingback" will be generated, and repeated destruction of the medium will not be carried out until the rock unit is completely destroyed, which is also the reason for the springback phenomenon during cutting. Due to the high strength of the sandstone, it is not easy to be damaged. When the traction force is relatively small, a complete rock unit needs repeated cutting to be destroyed, so the number of springback is more. However, the strength of mudstone and coal seam is small and relatively easy for destruction, so there are fewer times of rebound. Or only the speed decreases, and no rebound phenomenon occurs. erefore, if the strength and hardness of the coal rock affect the cutting speed of the roller, different instantaneous cutting speeds can precisely reflect the type of cutting medium and springback during cutting is also a reflection of mechanical parameters of the medium rock.

Dynamic Characteristics of Cutting the Coal-Rock Combination Model.
Due to fluctuation variation of the coal seam, the roller often cuts some gangue when the coal cutter roller cuts the coal seam in the working face, so the phenomenon of "cutting the top" appears. erefore, the dynamic characteristic of the roller cutting coal seam is different from gangue, which will change with the change in the thickness of "cutting the top" at the same time. e above analysis indicates that lithology of cutting the medium can be distinguished according to the dynamic characteristics of single medium. In order to explore the dynamic characteristics of the roller when the phenomenon of "cutting the top" occurs, the coal and rock medium combination model is established for numerical analysis.

Coal and Rock Combination Scheme Design.
e CAE finite element software is used to establish the three-dimensional combination model of coal-mudstone and coalsandstone medium. e overall height of the model is 4 m, and the coal cutter height remains unchanged (2 m). According to different proportions of coal and rock medium, four scheme models are designed, which are shown in Figure 9. e first scheme is that the coal seam thickness cut by the roller is 1.67 m and mudstone is 0.33 m. erefore, the proportion of mudstone is 1/6. e second scheme is that coal seam is 1.33m and mudstone is 0.67 m thick. erefore, the proportion of mudstone is 1/3. e third plan is that coal seam is 1.67 m thick and sandstone is 0.33 m thick. erefore, the proportion of sandstone is 1/6. e fourth plan is that coal seam is 1.33 m thick and the sandstone is 0.67 m thick. erefore, the proportion of sandstone is 1/3.

Analysis of Inverse Moment Response When Cutting Coal and Rock Assemblage.
e dynamic characteristics of different combined models were obtained through numerical calculation. e reaction moment curves of the obtained models are shown in Figure 10.
As can be seen from Figure 10, there is a great difference in the reverse torque characteristics of the combination Shock and Vibration model. Among them, the reverse torque of plan (i) is concentrated in the range of 0∼650 kN·m, plan (ii) in the range of 0∼700 kN·m, plan (iii) in the range of 0∼700 kN·m, and plan (iv) in the range of 0∼1200 kN·m. It can be seen that the reaction force suffered by the roller cutting the coal and rock combination model is larger than that suffered by roller cutting the single coal seam medium (Figure 6(a)). e reverse torque of plans (ii) and (iii) is larger than that of plan (i). e reverse torque of plan (iv) is larger than that of plans (ii) and (iii). By comparing the characteristics of the reverse torque, it can be concluded that the roller reverse torque is between the cutting single coal seam and rock stratum. e more parts of mudstone or sandstone are cut, the greater the reaction force will be. When the truncated mudstone and sandstone parts are equal, the truncated coal-sandstone combination model is subjected to greater reaction force than the coal-mudstone model. e reason that reverse torque presents this characteristic is that different media have different strengths. Based on the above analysis of the coal and rock failure process, it is found that cutting the sandstone needs to overcome the largest resistance, followed by mudstone , and the smallest being coal seam. Since the resistance to be overcome in cutting the coal seam is same, the total resistance to be    Shock and Vibration overcome in cutting the coal and rock combination model is determined by the strata.

Analysis of Displacement Response in Cutting the Coal-Rock
Assemblage. e displacement dynamic responses of different scheme models obtained by numerical calculation are shown in Figure 11.
As can be seen from the relation curve between cutting displacement and time in Figure 11, the combination model of coal and rock cutting by the cylinder is similar to that of cutting a single medium. e relation between displacement and time is still nearly linear; that is, the roller maintains a certain average speed of forward cutting. It can be seen from the variation of the average cutting velocity that the average cutting velocity of the combined model is between the coal seam and rock strata with a single cutting medium. e greater the proportion of the cutting strata, the lower the average cutting speed. When the proportion of the truncated mudstone or sandstone is the same, the average velocity of the truncated coal-sandstone assemblage is lower than that of the truncated coal-mudstone assemblage model. e change of the average cutting velocity is the reflection of the characteristic of the cutting reverse torque.

Velocity Response Analysis When Cutting the Coal-Rock Assemblage.
e instantaneous velocity responses of different scheme models obtained by numerical calculation are shown in Figure 12.
e relation curve between cutting speed and time is shown in Figure 12. Although the instantaneous cutting velocity of each model shows obvious difference, which is similar to that of cutting a single coal rock medium, it fluctuates up and down near the average cutting velocity. Compared with the single cutting of coal seam medium (Figure 8(a)), the fluctuation range of instantaneous velocity in scheme 1 is smaller because the average velocity in cutting scheme 1 model is smaller. In scheme 1, the instantaneous velocity of some position points is less than 0, indicating the springback phenomenon occurred because the mudstone part cannot be destroyed at the same time.
Compared with the instantaneous velocity of plan (i), the amplitude of instantaneous velocity of plan (iii) increases and the number of rebounds increases. It shows that when the cut part of the mudstone increases, the instantaneous velocity changes greatly. en, the model can be destroyed only when more rebound phenomenon occurs. At the same time, the change in instantaneous velocity in schemes (ii) and (iv) is similar to that in schemes (i) and (iii), which indicate that when the cutting gangue part increases, it is more difficult to cut the combined medium of coal and rock by the roller, resulting in larger amplitude fluctuation of instantaneous velocity and increase in the number of springback.

Summary of Dynamic Characteristics.
According to the dynamic characteristics of different coal and rock media obtained through the above numerical calculation and analysis, the summary is shown in Table 2.
As can be seen from Table 2, when a single medium is cut by a roller coal cutter, the larger the medium strength is, or when cutting the combined medium of coal and rock, the more the coal and rock parts are cut, the greater the reaction torque on the roller will be. e lower the average cutting velocity is, the larger the instantaneous velocity fluctuation is and the more the number of rebounds is. Because the average cutting speed is the most important index of the Shock and Vibration 9 medium cut by the roller. In order to qualitatively study the change of average cutting speed with coal and rock medium, the numerical simulation method is adopted on the basis of the abovementioned way. e change of the average cutting speed of the roller coal cutter was further studied when the proportion of mudstone and sandstone was 1/2, 2/3, and 5/6, as shown in Figure 13. As can be seen from Figure 13, with the increase of the proportion of gangue cut by the roller, the average cutting speed decreases gradually and presents a nonlinear relationship. When cutting a single coal seam medium, the average velocity is 0.64 m/s. When cutting a part of gangue, which accounts for only 16.7%, the average velocity drops suddenly. When the gangue is mudstone, the average velocity dropped to 0.45 m/s; when the gangue is sandstone, the average velocity dropped to 0.28 m/s. With the increase in the cutting gangue part, the average velocity decreases gradually, and when the proportion of cutting gangue part increased to 66.7%, the average speed was almost close to that of cutting single gangue medium. e working resistance to be overcome by the roller cutting gangue is much larger than that of cutting coal seam. When the phenomenon  of top cutting occurs, even if there is only a small part of gangue, it will produce a large working resistance to the roller, leading to a sudden drop in the average speed.

Conclusions
e conclusions drawn from this study are summarized as follows: (1) When taking the dynamic condition to keep the traction force and the rotation speed is unchanged, the roller always maintains a certain average speed of cutting forward. However, the instantaneous velocity fluctuates up and down in a small amplitude near the average velocity, presenting a "jump" phenomenon. e larger the medium strength is, the larger the jump amplitude is.
(2) If the roller traction force is small and the medium strength of coal and rock is large, the roller will produce negative instantaneous velocity, which can cut the medium repeatedly in the way of forward, backward, and forward again. at is to say, the phenomenon of "springback" occurs and springback is a reflection of the mechanical properties of coal and rock itself.
(3) When the phenomenon of "cutting top" of the coal cutter roller appears, the average cutting speed will decrease gradually with the increase of the gangue part, which presents a "nonlinear" relationship. e average velocity of cutting a small part of gangue will lead to a sudden drop, whereas cutting a large part of gangue will be close to that of cutting a single gangue medium. (4) e average cutting speed and reverse torque are good indices to evaluate the cutting medium's type.
If the relevant sensors can be used to capture the dynamic response characteristics of the field of drum cutting medium, the coal rock medium type ahead of the roller can be determined in real time according to the dynamic parameters. At the same time, if the lithology of the medium ahead of the working face is known, the dynamic response characteristics of the roller coal cutter can also be predicted in advance.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.