Based on a Chinese enterprise's single-mouth crusher, the ‘waterfall flow’ inlet crusher is developed from a foreign two-flow crusher. The two-inlet crushing mode has advantages of continuous particle feeding, controlled particle flow and low wear of housing. By analysing the working principle of the equipment, the three-dimensional model of the crusher is established. Based on the discrete element method, the simulation data are obtained by EDEM simulation software. The crushing energy, the wear of the housing and the counter boards are analysed to obtain the optimal parameters. The crushing efficiency is significantly improved and the wear of the housing is controlled to some extent. The overall performance of the crusher is improved and the cost is reduced.

#### Keywords

- DEM
- waterfall flow
- two-flow crushing
- crushing energy

The fine processing technology of sand and gravel aggregate is mainly completed by impact crusher [1]. As shown in Figure 1(a), the amount of sand and gravel processed by an ordinary impact crusher is less than the two-flow crushing shown in Figure 1(b). More and more enterprises are beginning to pay attention to two-flow crushing, but the research on the mechanism of two-flow crushing is still relatively few.

The discrete element method (DEM) is an effective method to solve the problem of particle dispersion [2,3]. There are two contact modes: rock to rock mode and rock to metal mode. The collision of particles and the counter board as well as the chamber makes rock to metal mode, while the collisions of particles make a rock to rock mode. The studies show that rock to rock mode is the main way to shape particles [4, 5], while the rock to metal mode is the way to particle breakage [6, 7].

In the field of two-flow crushing, some researchers also call the two-flow crushing as ‘waterfall’ flow inlet crushing. Podvysotskii et al. [8] established a model of non-equilibrium two-phase flow analysis with flocculation. Li et al. [9] designed the SVS system to test the particle layer. Qiang Zhao et al. [10] simulated the flow field of the cyclone separator with different cyclone diameters and inlet sizes. But, there are few literature on two-flow crushing.

This paper used the DEM to simulate and analyse feed mouth, input particle size, feed rate, rotating speed and counter boards of the two-flow crusher. The optimal structure parameters were obtained, improving the crusher's operation efficiency, which provides a reference for parameter adjustment and machine improvement in actual production.

DEM is a numerical method of display solution. Like the finite element method, the DEM also divides the region into units. However, because the unit is controlled by discontinuities such as joints, in the later movement process, the unit nodes can be separated, that is, a unit and its adjacent units can be contacted or separated.

The displacement can be calculated using Newton's second law, as follows:

In the formula, _{k}_{k}_{k}_{k}

In the setting interface of global, the physical property parameters and contact parameters of the stacking particles and geometry materials are set. According to the relevant research results and empirical parameters, the specific discrete element physical parameters of the uniaxial compression particle connection model are shown in Table 1. To bring particle deposition to steady state faster, you set the coefficient of recovery, coefficient of static friction and coefficient of rolling friction to 0.001, and you can moderately reduce the material's shear modulus to shorten the stack simulation time. After the accumulation of particles, the contact parameters should be reset to the exact value for subsequent simulation. The specific contact parameters are shown in Table 2.

The physical parameters of particles and the inner wall of the crusher

Poisson's ratio | 0.3 | 0.3 |

Shear modulus/GPa | 0.56 | 70 |

Density/kg/m^{3} |
2630 | 7,800 |

Particle contact parameter settings

The recovery coefficient | 0.2 | 0.25 |

Static friction coefficient | 0.5 | 0.7 |

Rolling friction coefficient | 0.001 | 0.001 |

As suggested in reference 13, it creates a cylinder with a base diameter of 50 mm and a height of 120 mm on the geometry setting interface, and creates a grain factory with a radius of 2 mm with the number of grains generated at 3,650 on the grain factory interface. In order to make particle accumulation reach a steady state faster, the upper limit of a particle falling speed was set at 1 m/s. The simulation of particle accumulation can be carried out after the corresponding simulation time step and grid size are set up. The effect diagram of the particle stacking process and completion is shown in Figures 2-1 and 2-2.

In order to make the stress distribution within the uniaxial compression specimen uniform, after the specimen model is compactified, it is necessary for it to stand for a period of time to make the accumulated particles inside reach a steady state. In general, when the particle velocity is less than 0.002 m/s, it can be regarded as having reached the steady state. It can be seen from Figure 2–3 that the particle velocities of uniaxial compression specimens are generally less than 0.002 m/s. Therefore, the uniaxial compression specimen stacking model can be regarded as reaching a steady state.

According to the crushing form of a foreign two-flow system, the simulation was carried out by changing the positions of the waterfall inlet and the original feed mouth. The simulation has two forms: small particles hitting large particles (the waterfall inlet for small particles and the original feed mouth for large particles) and large particles hitting small particles (the waterfall inlet for large particles and the original feed mouth for small particles). The data were compared, mainly by analysing the energy between particles and the housing wear (i.e., the force on the housing) to determine the position for the best crushing effect. Due to the randomness of the simulation results, the final results are the average of the data from two-set simulations.

Particle size usually falls into three categories: less than 3.7 mm, 3.7–20 mm and 20–50 mm. Generally, a gravel crusher deals with the stone with particle size below 50 mm. In this simulation, the particle sizes of small particles are 3.75 mm and 7.5 mm, and the particle sizes of large particles are 12.5 mm, 17.5 mm and 22.5 mm.

With the same particle size, the distance between the waterfall inlet and the impeller was changed and the influence of the distance on the crushing effect was analysed through simulation. The distances between the waterfall inlet and the impeller are 250 mm, 500 mm and 700 mm, respectively, as shown in Figure 3.

At three different waterfall inlet positions, when large particles hit small particles (the waterfall inlet for large particles, and the original feed mouth for small particles), the energy generated by the collision between particles and the force on the housing are shown in Figure 4, wherein 25–7.5 means that the particle size of the particles through the waterfall inlet is 25 mm, the size of the particles through the original feed mouth is 7.5 mm and large particles hit small particles. The following data are all based on this.

When small particles hit large particles (the waterfall inlet for small particles, and the original feed mouth for large particles) the energy generated by the collision between particles and the force on the housing are shown in Figure 5.

We simulate small particles hitting large particles at position 1. We carry out two groups of experiments, namely 7.5–25 to 7.5–45 and 15–25 to 15–45. It can be seen from Figures 5 and 6 that in both groups of 7.5–25 to 7.5–45 and 15–25 to 15–45, the force on the housing shows an increasing trend, but the energy peaks at 7.5–35 and 15–35, and then decreases. The trends in the two intervals are similar. Through the analysis of the above data and graphs (Figure 6), the particle size at the original feed mouth is the main factor influencing the force on the housing. Comparing the two cases of 7.5–35 and 15–35, the collision energies between particles are close. The difference is just over 150 J, and the energy is greater at 15–35. However, at 7.5–35 when the force on the housing is lower than that at 15–35, the difference in force F is more than 4,000 N, and the force is lower at 7.5–35, which is 27,357.2 N. The energies of the two cases are similar, but the wear of the housing is less at 7.5–35. Based on the above analysis, at position 1 when the particle size of the particles through the waterfall inlet is 7.5 mm and the particle size of the particles through the original feed mouth is 35 mm, the crushing effect is the best.

We simulate small particles hitting large particles at position 2 (Figure 7). The data shows that the collision energy between particles is the largest at 15–35, which is 24,952.6 J. At 7.5–35, the energy is close to the largest but in other cases, the energy is much lower, that is, with small crushing force and poor crushing effect. Comparing the forces on the housing, although the forces are smaller at 7.5–25 and 15–25 and the housing wear is low, the collision energies between particles are too low to have a good crushing effect. It also can be seen from the graphs (Figure 7) that at 7.5–25 to 7.5–45 and 15–25 to 15–45, the force on the housing shows an increasing trend, but the energy peaks at 7.5–35 and 15–35, and then decreases. The two graphs have similar trends. Through the analysis of the above data and graphs in Figure 7, in this simulation, the particle size at the original feed mouth is the main factor influencing the force on the housing. Comparing the two cases of 7.5–35 and 15–35, the collision energy between particles differs by more than 600 J in value, and it is larger at 15–35. However, at 15–35 when the force on the housing is lower than that at 7.5–35, the difference in force F is more than 2,200 N and at 15–35, the housing wear is lower. Therefore, at position 2, when the particle size of the particles through the waterfall inlet is 15 mm and the particle size of the particles through the original feed mouth is 35 mm, the collision energy between particles is larger, the housing wear is lower, and the crushing effect is the best.

In the simulation at position 3 (Figure 8), the data results are also analysed according to the above situation. The two cases of 7.5–35 and 15–35 are mainly compared. The energy at 7.5–35 is larger, slightly greater than 150 J, and the force on the housing is lower by 8,000 N. Therefore, it is considered that at position 3, when the particle size of the particles through the waterfall inlet is 7.5 mm and the particle size of the particles through the original feed mouth is 35 mm, the crushing effect is the best.

Through the analysis of the three sets of positions and particle sizes, the three sets of optimal cases are listed. Position 1 is used as a comparison to calculate the growth rate of each data. The specific values are shown in Table 3.

Growth rate of the data

Position 1 (7.5–35) | 25,001.8 | 27,351.2 |

Position 2 (15–35) | 24,952.6 (−0.20%) | 34,496.7 (16.13%) |

Position 3 (7.5–35) | 25,786 (3.14%) | 30,589 (11.84%) |

On the basis of the particle size and the position from the previous simulation, position 1 and the 7.5 mm particle size of the particles through the waterfall inlet and the 35 mm particle size of the particles through the original feed mouth were selected. By adjusting the feed rate of the waterfall inlet, the influence of the feed rate on the crushing effect was analysed.

In order to prevent excessive sand and dust, current Chinese sand belt conveyors generally run at a low speed. Therefore, the feed rate of the simulated ‘waterfall’ inlet is set to 1 m/s, 2 m/s, 3 m/s, 4 m/s and 5 m/s. After EDEM simulation, the result is as given in Figure 9.

It can be seen from the graph (Figure 9) that when the waterfall inlet feed rate is set to 1–5 m/s, the collision energy between particles drops from 25,260 J at 1 m/s to 24,154.7 J at 5 m/s, a relatively small decrease. While the force on the housing, that is, the wear on the housing fluctuates greatly, the trend is still not obvious. It may be due to the randomness of EDEM simulation, but it can be roughly seen that the overall trend is also decreasing. Although the energy between the particles shows a decreasing trend, the difference is relatively small, so it can be ignored. The emphasis is put on the force on the housing when the particles are crushed. Figure 9 shows the force on the housing. When the feed rate is 1 m/s, the force is the largest, reaching 37,772 N; when the feed rate is 2 m/s, 3 m/s, and 5 m/s, the force is between 32,000 and 33,000 N; and when the feed rate is 4 m/s, the force is the smallest, which is 27,429 N, about 5,000–6,000 N lower than the force in the second case. The energy at 4 m/s is 24,424 J, slightly differing from other cases by 300–800 J. Therefore, in this EDEM software simulation by DEM, when the waterfall inlet feed rate is 4 m/s, the crushing effect reaches the best.

The data growths are also calculated by taking 1 m/s as a comparison, and the calculation results are listed in Table 4.

Data growth compared with that at 1 m/s

1 m/s | 25,260 | 37,772 |

2 m/s | 25,119 (−0.56%) | 31,998 (−15.29%) |

3 m/s | 24,898 (−1.43%) | 333,34.6 (−11.75%) |

4 m/s | 24,424 (−3.31%) | 27,429 (−27.38%) |

5 m/s | 24,154.7 (−4.38%) | 31,862 (−15.65%) |

Through the previous analysis of the simulation data of the feed particle size, the position of the ‘waterfall’ inlet, and the feed rate, the parameters in this EDEM simulation were set (Figure 10). This time, we changed the impeller speed of the crusher to find out a set of speeds for a better crushing effect.

Through the rotating speed parameters provided by the enterprise, the linear speed of its current crusher impeller is generally 50–60 m/s, while the linear speed of the crusher of the same type can be as high as 70 m/s. Therefore, the linear speed of the impeller in this simulation is set to 50 m/s, 55 m/s, 60 m/s, 65 m/s and 70 m/s. Conversely, the speeds to EDEM software counterparts are 795 rpm, 875 rpm, 955 rpm, 1,035 rpm and 1,115 rpm. After EDEM simulation, the result is given in Figure 11.

From Figure 11, it can be found that when the speed is from 795 rpm to 1,115 rpm, the collision energy between particles shows a trend of increasing, and the increase of energy tends to be linear; however, the force on the housing increases slowly at first. When the speed increases to 955 rpm, the force on the housing suddenly increases, which may have something to do with the critical value of the rotating speed of the ‘waterfall’ inlet crusher. Moreover, in the simulation of the rotating speed, when the speed is 795 rpm, the energy between particles is the lowest, and the energy is the highest at 1,115 rpm. Considering the trend mentioned earlier, it can be considered that the collision energy of particles increases linearly with the increase of impeller speed, that is, the crushing effect improves as the rotating speed increases. As to the housing wear, when the rotating speed is between 795 rpm and 955 rpm, the difference of the force on the housing is about 2,000 N. When the rotating speed increases to 1,035 rpm and 1,115 rpm, the difference increases by 5,000–8,000 N, and the force on the housing is increased by about 3–4 times, and the energy between particles is about 2 times higher. Therefore, it is considered that when the speed is 1,035 rpm and 1,115 rpm, the crushing effect may be better, yet the housing wear increases. Therefore, the overall crushing effect at these two speeds is considered as being worse. Compare the crushing conditions at the speeds from 795 rpm to 955 rpm and it can be found that the difference of the force on the housing is smaller, while the increase of the collision energy between particles is more obvious. At 955 rpm, the force on the housing is about 2,000 N more, while the energy between particles is about 3,000–5,000 J more. Therefore, it is considered that in this simulation, when the rotating speed is 955 rpm (i.e., the linear speed of the impeller is 60 m/s), the crushing effect is better.

The growth rates are also calculated to analyse the crushing effect, with 795 rpm (50 m/s) as a comparison. The calculation results are shown in Table 5.

Data compared with 795 rpm (50 m/s)

795 rpm (50 m/s) | 18,248.5 | 23,031.4 |

875 rpm (55 m/s) | 20,529 (12.50%) | 24,377.1 (4.54%) |

955 rpm (60 m/s) | 23,115 (26.07%) | 25,053.4 (8.78%) |

1035 rpm (65 m/s) | 26,611.9 (45.83%) | 31,649.4 (37.42%) |

1115 rpm (70 m/s) | 30,627.5 (67.84%) | 33,809.1 (46.80%) |

The previous analysis shows that the overall crushing effect is better when the ‘waterfall’ inlet is at position 1 (Figure 12). With the size parameters of the counter boards provided by the enterprise, on the basis of position 1, the counter boards are simulated. The three-dimensional model is shown in Figure 12.

In Figure 12, counter boards are added to the ‘waterfall’ crusher. The simulation is carried out by adjusting the angle of the counter boards in order to find a set of angles for the best crushing effect. The range of the counter boards angles is 0°, 5°, 10°, 15°, 20°, 25° and 30°, as shown on the right side of Figure 12. After EDEM simulation, the collision energy (i.e., crushing effect) and the force on the housing (i.e., housing wear) were obtained. In this simulation, an additional set of simulations were carried out to analyse the forces on the same counter board. The counter board which was close to position 1 waterfall inlet was selected and defined as counter board 3. We then evaluate the simulation by considering three kinds of data, and work out a set of counter board angles for the best crushing effect. The specific data are given in Figure 13.

It can be found from the line chart in Figure 13 that when the angle of the counter board is from 0° to 30°, the overall change of the collision energy between particles is relatively small; the maximum difference is about 2,500 J, so the angle of the counter board has little effect on the collision energy between particles. However, as the collision energy reaches the largest when the angle is 0°, if only the collision energy is considered, 0° counter boards is favourable for the crushing effect. On the other hand, when the angle is 20°, the force on the housing is the least, and the wear of the housing is the smallest. Therefore, in this case, 20° counter board is favourable. Finally, the third group data shows the force on the counter board 3. The counter board, which can be easily replaced, wears instead of the housing. In this way, the service life of the crusher is extended. Similarly, if the wear of the counter board decreases, it can last longer. Just as the analysis of the force on the housing shows, the smaller the force on the counter board, the lower the wear of the counter board.

It can be seen from Figure 13 that 20° counter board is the most optimal solution because the force on it is the least and the wear is the lowest. As for the other angles, the energies don’t change much, but the forces on the counter board are lower than that of 0° counter board and much higher than that of 20° counter board. Therefore, the other angles show a relatively poor crushing effect. Given that 0° counter board shows the largest energy, the data of 0° counter board are further analysed.

In summary, from the results of three sets of data, 0° and 20° counter boards are the optimal solutions. Compare the data of the two cases, as shown in Table 6.

Comparison of counter boards angles

0° | 15,078.1 | 23,474.2 | 26,291.4 |

20° | 12,941.7 (−14.17%) | 12,498 (−46.76%) | 16,175.2 (−38.48%) |

Through the previous calculation of growth rate, the calculation is based on the angle of the counter board at 0°. The data in Table 6 show that the energy between particles of 20° counter board is 14.17% less than that of 0° counter board. That is, the crushing effect drops by 14.17%. The force on the housing of 20° counter board is 46.76% less and the force on the counter board is also 38.48% less. That is, the wear of both is reduced by about 40%. In summary, the decrease of the wear of the housing and the counter board with 20° counter board is about 4 times more than the increase of the collision energy between particles with 0° counter board. Therefore, from this EDEM simulation result, for the crusher with additional counter boards, 20° counter boards are favourable to the crushing effect.

With the rotating speed parameters of the crusher provided by the enterprise and the optimal counter boards angle, the EDEM simulation of different rotating speeds was carried out, using the DEM, on the crusher with counter boards, like the previous simulation of the angle. The data of the collision energy between particles, the force on the housing and the force on the counter board were obtained and shown in Figure 14.

It can be seen from the line chart in Figure 14 that the collision energy between particles and the force on the counter board increase with the increase of rotating speed, while the force on the housing increases first, peaks at 955 rpm, and then decreases, and then increases slightly. When the rotating speed is 1,115 rpm, the collision energy between particles reaches the largest, meaning the best crushing effect. When the rotating speed is 795 rpm, the force on the housing reaches the smallest, meaning the lowest wear. This is also true for the counter board. However, when the rotating speed is 795 rpm, the collision energy between particles is also the lowest, that is to say, the crushing effect is the worst, so the rotating speed of 795 rpm requires further analysis. On the other hand, it can be clearly seen from Figure 14 that when the rotating speed is 955 rpm, the force on the housing is the largest, reaching 22,207.5 N, and the wear is the largest. Compared with the results of other rotating speeds, the force on the housing is much larger, and the energy and the force on the counter board are not close to the optimal condition. Therefore, the overall crushing effect is considered to be poor in this case, so it is excluded. Similarly, when the rotating speed is 1,115 rpm, as the force on the counter board is the largest, the wear is the largest too, and the difference is large compared with the results of other rotating speeds. In addition, the force on the housing is only second to that at 955 rpm. Although the collision energy between particles is the largest, in the speed simulation the variation of the energy is smaller than the variations of the force on the housing as well as the force on the counter board. Therefore, from the perspective of the overall effect, the result of 1,115 rpm is not good, so it is excluded too. The remaining cases of 875 rpm and 1,035 rpm are in the middle according to the energy and the forces variations in the figure, so further analysis is needed too. To sum up, the data of speeds of 795 rpm, 875 rpm and 1,035 rpm are further analysed. Based on the data of 795 pm, the growth rate of each data is calculated as given in Table 7.

Data growth compared at 795 rpm

795 rpm (50 m/s) | 10,001.3 | 11,175.3 | 15,532.5 |

875 rpm (55 m/s) | 11,398.4 (13.97%) | 14,622.5 (30.85%) | 19,390.4 (24.84%) |

1,035 rpm (65 m/s) | 14,055.2 (40.53%) | 15,025.6 (34.45%) | 18,624.8 (19.91%) |

From Table 7, it can be seen that the energy at 875 rpm increases by 13.97% and that at 1,035 rpm increases by 40.53%. The energy between particles at this speed is significantly improved, that is, the crushing effect is significantly improved. The force on the housing increases by 30.85% and 34.45% at 875 rpm and 1,035 rpm, respectively, that is, the wear is increased. The housing wear in these two cases is close. From the perspective of the force on the counter board, it also increases by about 20% at these two speeds, and they are also close to each other. The force on the counter board at 1,035 rpm is lower than that at 875 rpm but 19.91% higher than that at 795 rpm. Therefore, from the perspective of crushing energy and machine wear, the crushing energy at 1,035 rpm increases greatly, and the wear of the counter board is lower. Although the wear of the housing is large, it is only about 4% more than that at 875 rpm. Although the housing wear increases by about 30% compared with that at 795 rpm, the crushing energy at this speed is about 40% higher. Therefore, it is considered that the overall crushing effect is the best when the crusher rotating speed is 1,035 (i.e., the linear speed of the impeller is 65 m/s).

In the previous analysis of the impact crusher with counter boards by Sinnott et al. from Australia [2], the distribution of counter boards is continuous. This simulation focuses on the distribution of counter boards. Based on the above counter board angle and rotating speed, the distribution of counter boards is adjusted by changing the number of counter boards. The optimal distribution of counter boards, or the optimal number of the counter boards, is obtained by using the DEM and EDEM simulation. In the previous simulation, the number of counter boards was provided by the enterprise, so in the 3D modelling, the number of counter boards was adjusted for the test. Since the number of counter boards of the enterprise is 14, based on this, it is found that in the modelling when the number of counter boards reached 18, a continuous distribution appears. When it is 10–17, it shows a disjunctive distribution. Therefore, in the modelling, with 14 the intermediate value and 18 the upper limit, the minimum number of counter boards is set to 10. Adjust the number of counter boards among 10, 11, 12, 13, 14, 15, 16, 17 and 18 for EDEM simulation. The distribution model of the counter boards is given in Figure 15.

Through EDEM simulation, the three groups of data are shown in Figure 16.

From the data shown in Figure 16, it can be clearly seen that the collision energy between particles, the forces on the housing and on the counter board generally decrease with the increase of the number of counter boards, but the change of the energy between particles is small, that is, the distribution of counter boards has little impact on the crushing effect, but has a greater impact on the wear of the housing and the counter boards. Although the forces on the housing and on the counter board show a decreasing trend on the whole, there are fluctuations. Some numbers of counter boards result in the forces increasing. From the line chart in Figure 16, as the collision energies between particles are relatively close, from the point of view of housing wear, when the number of counter boards is 18, it is a continuous distribution, and the wear of the housing is low. When the number is 15, 16 and 17, the wear is close and so is the energy between particles. But in terms of the force on the counter board, when the number of counter boards reaches 18, the force is 3,000–6,000 N lower than that of the other three cases. Although the force on the housing is the largest, the excess is no more than 1,000 N, yet the energy between particles reaches the largest value, and the crushing effect is better. Therefore, from the data of these four cases, the overall crushing effect peaks when the number of counter boards is 18. Furthermore, comparing the data of this case with the data of 10–14 counter boards; although the latter shows higher energy between particles, the excess was only about 300 to 2,000 J, while the force on the housing and the force on the counter board were 3,000 to 10,000 N higher, that is, the wear was much greater. Therefore, it is considered that the optimal number of counter boards is 18, contributing to a better crushing effect. In other words, continuous distribution of counter boards is more favourable than disjunctive distribution for the crushing effect.

It is known from the enterprise that the crushing effect and the wear resistance of crushers can be improved by using different materials. At the present, the material used in the enterprise is Cr26, so the material used in the previous simulations is Cr26. In addition, the enterprise has added counter boards in the crusher. However, from the after-sale feedback, although the housing wear can be reduced under the premise of ensuring the crushing effect, the wear of the counter boards is relatively severe. It is hoped that the wear can be reduced by changing the material of the counter boards. The enterprise and other companies in the industry mainly use M17, cemented carbide, 20Cr, high-speed steel, Cr15Mo, etc. as materials for crushers and counter boards. Therefore, this simulation aims to obtain the optimal material for counter boards. Since the choices of materials used in crushers are many, three materials are selected for the counter boards in this simulation and are compared with the material used in the previous simulations. The selected materials are cemented carbide (tungsten and titanium), 20Cr and high-speed steel (steel content 9%).

Through EDEM simulation, the data obtained are shown in Figure 17.

From the data shown in Figure 17, it can be seen that the material has little effect on the collision energy between particles, while the forces on the housing and on the counter board vary greatly with the change in material. For the force on the housing, when the counter boards material is cemented carbide and high-speed steel, the forces are lower than but close to those of the other two materials. The values are 10,619.7 N and 9,698.93 N, respectively. For the force on the counter board, the counter board made of cemented carbide bears lower force, only 17,285.1 N, that is, and the counter board wear is the lowest (Table 8). The force difference from the other three materials is 4,000–8,000 N. Compared with Cr26, cemented carbide shows larger collision energy between particles, meaning better crushing effect, and the lower forces on the housing and on the counter board, meaning lower wear. Therefore, under this simulated condition, when the counter board's material is cemented carbide (tungsten and titanium), the overall crushing effect is the best.

Before and after optimisation

Before optimisation | 30 | 955 | 14 (disjunctive distribution) | Cr26 |

After optimisation | 1,035 | 18 (continuous distribution) | Cemented carbide (tungsten and titanium) | |

Before optimisation | Cr26 | 12,473.2 | 9,359.8 | 19,835 |

After optimisation | Cemented carbide (tungsten and titanium) | 14,130.3 | 17,235.1 | 10,619.7 |

It can be seen from the data comparison results of the above six charts that when large particles hit small particles, the energy generated by the collision between particles is about 5,000 J or below, and the force on the housing is about 8,000 N or below. When small particles hit large particles, the force on the housing is between 15,000 N and 45,000 N, and the energy between particles is between 14,000 J and 30,000 J. It shows that when large particles hit small particles, although the force on the housing is 4 or 5 times less than that of small particles hitting large particles – that is, the wear on the housing is extremely low, the collision energy between particles is 5 or 6 times less, resulting in poor crushing effect. Therefore, it is considered that under the same simulation conditions, for this kind of waterfall inlet crushing, the overall crushing effect of small particles hitting large particles is better than that of large particles hitting small particles.

From the data in Table 8, it can be found that the collision energy between particles peaks at position 3, which was 25,786 J, while at position 1, the force on the housing (i.e., the degree of wear) is the smallest, which is 27,351.2 N. At position 2, the energy was the lowest, an increase of −0.20%. On the contrary, the force on the housing is the largest, an increase of 16.13%. Therefore, it is considered that the crushing effect is the worst at position 2. Comparing the data of positions 1 and 3, the collision energy between particles at position 3 is 784.2 J larger than that at position 1, while the force on the housing at position 3 is 3,237.8 N larger than that at position 1. It can be seen that the collision energy between particles at position 3 increases by 3.137%, compared with position 1, while the force on the housing increases by 11.84%, that is, the crushing effect increases by 3.14%. The crushing effect does not improve significantly, but the housing wear, with an increase of 11.84%, sees a large rise. Therefore, from the perspective of the overall crushing effect, position 1 is considered to be the best waterfall inlet position in this simulation.

By listing the data of the feed rate, the growth rates are calculated and also listed in Table 8. From Table 8, it can be seen that the collision energy between particles and the force on the housing both show negative growths, but the collision energy between particles decreases slightly, with the highest drop of 4.38%. The force on the housing decreases largely, with the lowest drop of 11.75% and the highest drop of 27.38%, that is, the feed rate has no obvious impact on the crushing effect, but its impact on the housing wear is more obvious. According to the growth rate values, when the feed rate is 4 m/s, the housing wear is greatly reduced. Therefore, in this case, the ‘waterfall’ crusher has a better crushing effect.

It can be seen from Table 3 that the maximum increase of the collision energy between particles reaches 67.84% at 1,115 rpm, but the increase of the force on the housing is also the largest, with an increase of 46.80%, that is, the wear of the housing is greater. Seeing the data as a whole, it is found that when the speed increases to 1,035 rpm and 1,115 rpm, the force on the housing suddenly increases, which may have something to do with the critical value of the rotating speed. Therefore, even though the collision energy between particles is greatly increased, in light of wear reduction, cost-saving and utilisation improvement, the above two speeds are not good for the overall crushing effect in this simulation. Perhaps these two speeds can be applied to the crushers of certain materials. With the above two rotating speeds excluded, it can be seen that the collision energy between particles and the force on the housing at the other two speeds also increase. The energy at 955 rpm is 13.57% higher than at 875 rpm, while the wear of the housing only increases by 4.24%. Therefore, when the rotating speed is 955 rpm (i.e., the linear speed of the impeller is 60 m/s), the simulated ‘waterfall’ crusher has a better crushing effect.

Table 8 shows the result of the optimal combination after adding counter boards to the ‘waterfall flow’ inlet crusher and adjusting the angle, the distribution and the number of counter boards, and rotating speed and the material. After optimisation, the crushing energy has been improved to a certain extent. From the point of view of forces, compared with single-mouth crushers, the optimised crusher shows 10% lower wear of the housing and, most importantly, the wear of the counter boards reduces greatly. Therefore, the mechanical performance of the ‘waterfall flow’ inlet crusher is improved, so is the service life of the crusher.

In this paper, the foreign two-flow crusher is analysed, and the traditional Chinese crusher is optimised by a similar crushing mode of ‘waterfall flow’. The traditional Chinese single-mouth crusher is taken as the model, to which a ‘waterfall inlet’ and counter boards are added. The simulation and analysis are carried out on several influencing factors. The crushing effect, the wear of the housing and the counter boards are analysed by using the DEM and EDEM simulation. The simulation results are concluded as follows.

The ‘waterfall flow’ inlet crusher is also called a two-flow crusher. It replaces rock-metal contact mode with rock-rock contact mode, which reduces the wear of the crusher to a certain extent, and more importantly, improves the crushing effect. For the ‘waterfall flow’ inlet crusher, EDEM simulation is carried out on the four factors of ‘waterfall inlet’ position, feed particle size, crusher rotating speed and feed rate. The simulation data are analysed in the aspects of the crushing effect and the housing wear. A group of optimal parameters are obtained: the distance between the ‘waterfall inlet’ and the impeller is 250 mm; the particle size of the small particles through the waterfall inlet is 7.5 mm, the particle size of the large particles through the original feed mouth is 35 mm; the crusher rotating speed is 955 rpm; and the feed rate of ‘waterfall inlet’ is 4 m/s. The ‘waterfall flow’ inlet crusher has a better crushing effect and a lower wear of the housing.

Compared with the traditional single-mouth crusher, although the crushing effect is obviously improved, the wear of the housing is also significantly increased. Therefore, adding counter boards to the ‘waterfall flow’ inlet crusher can obviously reduce the wear of the housing. After the EDEM simulation of the four factors of counter boards angle, the number of counter boards, the rotating speed of the main engine and the material of counter boards, the crushing effect, the wear of the housing and the counter boards are analysed. A group of optimal parameters are obtained: the angle of counter boards is 20°; the number of counter boards is 18 (continuous distribution), the rotating speed is 1,035 rpm; the counter boards material is cemented carbide (tungsten and titanium) and the feed rate of ‘waterfall inlet’ is 4 m/s. Compared with the single-mouth crusher, the crushing effect is improved by about 50%. By adjusting the counter boards, the ‘waterfall flow’ inlet crusher shows 10% lower wear of the housing under the premise of ensuring the crushing effect, so the overall performance is improved.

#### The physical parameters of particles and the inner wall of the crusher

Poisson's ratio | 0.3 | 0.3 |

Shear modulus/GPa | 0.56 | 70 |

Density/kg/m^{3} |
2630 | 7,800 |

#### Growth rate of the data

Position 1 (7.5–35) | 25,001.8 | 27,351.2 |

Position 2 (15–35) | 24,952.6 (−0.20%) | 34,496.7 (16.13%) |

Position 3 (7.5–35) | 25,786 (3.14%) | 30,589 (11.84%) |

#### Data growth compared with that at 1 m/s

1 m/s | 25,260 | 37,772 |

2 m/s | 25,119 (−0.56%) | 31,998 (−15.29%) |

3 m/s | 24,898 (−1.43%) | 333,34.6 (−11.75%) |

4 m/s | 24,424 (−3.31%) | 27,429 (−27.38%) |

5 m/s | 24,154.7 (−4.38%) | 31,862 (−15.65%) |

#### Particle contact parameter settings

The recovery coefficient | 0.2 | 0.25 |

Static friction coefficient | 0.5 | 0.7 |

Rolling friction coefficient | 0.001 | 0.001 |

#### Comparison of counter boards angles

0° | 15,078.1 | 23,474.2 | 26,291.4 |

20° | 12,941.7 (−14.17%) | 12,498 (−46.76%) | 16,175.2 (−38.48%) |

#### Data growth compared at 795 rpm

795 rpm (50 m/s) | 10,001.3 | 11,175.3 | 15,532.5 |

875 rpm (55 m/s) | 11,398.4 (13.97%) | 14,622.5 (30.85%) | 19,390.4 (24.84%) |

1,035 rpm (65 m/s) | 14,055.2 (40.53%) | 15,025.6 (34.45%) | 18,624.8 (19.91%) |

#### Before and after optimisation

Before optimisation | 30 | 955 | 14 (disjunctive distribution) | Cr26 |

After optimisation | 1,035 | 18 (continuous distribution) | Cemented carbide (tungsten and titanium) | |

Before optimisation | Cr26 | 12,473.2 | 9,359.8 | 19,835 |

After optimisation | Cemented carbide (tungsten and titanium) | 14,130.3 | 17,235.1 | 10,619.7 |

#### Data compared with 795 rpm (50 m/s)

795 rpm (50 m/s) | 18,248.5 | 23,031.4 |

875 rpm (55 m/s) | 20,529 (12.50%) | 24,377.1 (4.54%) |

955 rpm (60 m/s) | 23,115 (26.07%) | 25,053.4 (8.78%) |

1035 rpm (65 m/s) | 26,611.9 (45.83%) | 31,649.4 (37.42%) |

1115 rpm (70 m/s) | 30,627.5 (67.84%) | 33,809.1 (46.80%) |

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