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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 the minimum when the pick’s installation angle is 45° under certain traction speed and drum angular velocity.

Various coal cutting works are carried out in mining engineering by means of different machines and cutting tools [

From the cutting force model of conical pick proposed by Evans on the basis of tensile stress theory [

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 [

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 [

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 [

Figure

The diagram of conical pick cutting coal progress.

In coal cutting process, the cutting thickness varies with the traction speed of shearer, drum angular velocity, and cutting radius. If (

where

The detailed formula of cutting thickness can be calculated according to (

Under certain working condition of shearer, this paper selected the semitip angle of conical pick equal to the optimum value of 38 degrees [

At present, the above three parameters have formed the empirical range, respectively, [

7 sets of various parameters.

Cutting parameters | Traction speed/m/s | Drum angular velocity/rad/s | Installation angle |
---|---|---|---|

Different angular velocity | ① 0.07 | 5.23 | 45 |

② 0.07 | 5.76 | 45 | |

③ 0.07 | 6.28 | 45 | |

Different traction speed | ④ 0.05 | 5.76 | 45 |

② 0.07 | 5.76 | 45 | |

⑤ 0.09 | 5.76 | 45 | |

Different installation angle | ⑥ 0.07 | 5.76 | 40 |

② 0.07 | 5.76 | 45 | |

⑦ 0.07 | 5.76 | 50 |

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 [

The parameters of contact properties of coal and steel.

Materials parameters | Coefficient of restitution | Coefficient of static friction | Coefficient of rolling friction |
---|---|---|---|

Coal to coal | 0.5 | 0.6 | 0.05 |

Coal to steel | 0.5 | 0.4 | 0.05 |

Steel to steel | 0.7 | 0.2 | 0.01 |

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 equal radius were simulated as coal particle in EDEM. The parameters of coal particles are shown in Table

Parameters of coal particles.

Coal particle parameters | Particle radius [m] | Contact radius [m] | Density [kg/m^{3}] | Mass [kg] |
---|---|---|---|---|

Value | | | | |

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

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

Where

where

Macro mechanical characteristic parameters of coal particles.

Macro mechanical parameters of coal particles | Compressive strength | Shear strength | Elastic modulus | Shear modulus | Poisson ratio |
---|---|---|---|---|---|

Value | | | | | |

The normal contact stiffness

Micro mechanical parameters of coal particles.

Micro mechanical parameters of coal particles | Normal stiffness [N·m^{−1}] | Shear stiffness [N·m^{−1}] | Critical normal stress [pa] | Critical shear stress [pa] |
---|---|---|---|---|

Value | | | | |

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

EDEM model of coal cutting process of conical pick.

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 [

where

Rayleigh time step was calculated as

The simulation of coal cutting process of conical pick under the parameters ① from Table

Dynamic coal cutting process of conical pick.

Cutting state at the beginning position

Particle velocity vector diagram at the beginning position

Section of bonding diagram at the beginning position

Cutting state at the middle position

Particle velocity vector diagram at the middle position

Section of bonding diagram at the middle position

Cutting state at the end position

Particle velocity vector diagram at the end position

Section of bonding diagram at the end position

As indicated in Figure

Figures

Cutting force of conical pick under the cutting parameter ①.

Cutting force of conical pick under the cutting parameter ②.

Cutting force of conical pick under the cutting parameter ③.

Cutting force of conical pick under the cutting parameter ④.

Cutting force of conical pick under the cutting parameter ⑤.

Cutting force of conical pick under the cutting parameter ⑥.

Cutting force of conical pick under the cutting parameter ⑦.

The general trend of cutting force is similar to the cutting thickness obtained from (

According to the comparison of the cutting force curves in Figures

Comparing the cutting force curves in Figures

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

The simulation tests are further studied based on theoretical study [

The structural characteristics of coal, such as fracture, joint, and pore, are not taken into account because of the software limitations and the particularities of the generated particles method (Rain Drop Method), as well as the vibration, abrasion of conical pick, and the smoothness of cutting surface formed by cutting trajectory. These factors will impact the cutting force of conical pick, but the impact will be far less than the impact of the parameters discussed in this paper.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was supported by the National Nature Science Fund (Grant no. 51674155) and High Educational Institution of Shandong Science and Technology Project (Grant no. YB06).