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. 2024 Feb 7;9(7):7967–7975. doi: 10.1021/acsomega.3c08017

Collision Energy Analysis within the Vertical Shaft Impact Crusher Based on the Computational Fluid Dynamics-Discrete Element Method

Canhui Wu 1, Limei Zhao 1,*, Zhen Cao 1
PMCID: PMC10882607  PMID: 38405459

Abstract

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Particles in the vertical shaft impact crusher absorb and dissipate collision energy in the impact breakage. The distribution of the collision energy determines the breakage rate of materials and breakage energy consumption of the entire system. In this paper, the gas–solid coupling method is used to explore the regional distribution of collision energy, collision frequency, and collision energy spectrum of the material particle groups. Hence, a theoretical basis is provided for the efficient and energy-saving design of the crusher. First, a coupling mathematical model of the computational fluid dynamics and discrete element method is established to describe the interaction between material and fluid in the crushing chamber. Moreover, the experiment is carried out using a PL8500 VSI crusher and compared with the simulation results to verify the model’s reliability. Finally, the effects of different working conditions on the energy dissipation distribution and energy spectrum are explored. The results show that the collision energy within the crushing chamber can be accurately predicted by using the fluid–solid coupling model. Moreover, increasing the rotational speed can effectively transform low-energy collision events into high-energy collisions and increase the collision frequency with energy dissipation above the threshold energy. Thus, the probability of material breakage is increased. Last, increasing the feed rate minorly affects the material breakage rate, while the specific energy of the entire system is reduced.

1. Introduction

Vertical shaft impact (VSI) crushers are generally used in the third crushing stage. Compared to other tertiary crushers, the VSI crusher consumes less energy and produces a better-shaped grit with a finer product size.1,2 Concrete made of manufactured sand has better physical properties than natural sand concrete. This type of concrete can completely replace natural sand and reduce the damage to water resources caused by excessive exploitation of natural sand.3,4 Furthermore, the concrete made from sand produced by the VSI crusher has higher fluidity, lower porosity, and higher compressive strength than cone crusher-produced sand.5 Using a VSI crusher to crush the material before grinding can reduce the overall energy consumption of the grinding operation by 10–20%.3 Therefore, with an increased demand for energy-saving and consumption reduction in recent years, the application of VSI crushers has become increasingly popular.1 The demand for manufactured sand has increased sharply with the development of the national economy. In addition, an urgent need is presented to develop new, high-efficiency, energy-saving, and environmentally friendly modern VSI crushing equipment.

Investigating the working mechanism of a VSI crush is very important to improve its performance. However, installing the sensor test data is impossible due to the complex working environment in the crushing chamber. Hence, some scholars have started using the DEM (discrete element method) to analyze the material movement within the VSI crusher. According to ref (6), after the material enters the rotor of the VSI crusher, approximately 80% of the particles reach the maximum ejection speed. The collision energy spectrum in the crushing chamber is explored to further explore the crushing equipment specification, circuit design, machine modeling, and process optimization. Djordjevic et al.7 used the DEM to investigate the influence of crusher structure parameters and operating conditions on the collision velocity and energy distribution of particles in the crushing chamber. da Cunha et al.8 conducted simulations to calculate the collision energy spectrum and the residence time distribution of rock particles entering the crushing chamber. Moreover, the maximum collision energy increases with the rotor speed. However, if the rotor speed is too high, then it will cause the particles to move around the inner wall of the crushing chamber, thus increasing the particles’ residence time and reducing the sand output.9

Establishing an appropriate model can be used to accurately predict the performance of the crusher. In recent years, the introduction of collision energy into the breakage model or particle size distribution of crushing products has become a research hotspot. Sinnott and Cleary10 proposed a particle replacement breakage model based on absorbing the threshold energy, i.e., an energy level below in which no material damage occurs. They used it to predict the crusher’s performance. Grunditz et al.11 introduced a genetic algorithm into the particle size prediction model of the VSI crusher based on the collision energy, which improves the accuracy of the predicted particle size distribution. Bwalya and Chimwani12 compared the energy spectrum above the threshold energy in single-rotor and double-rotor impact crushers under different operating conditions. Moreover, the authors concluded that a double-rotor could increase the proportion of high energy, even at low speed, thus improving the breakage efficiency.

The studies mentioned above mostly considered only the movement of particles within the crushing chamber. However, during the operation of a VSI crusher, the material and air turbulence interact to produce a gas–solid two-phase flow movement, and the disturbance of this airflow will have a great impact on the movement of particles.13−15 Sinnott and Cleary’s research has proven that the performance of VSI crushers can be more accurately described if the effect of airflow on the material breakage is fully considered.16 Mayank et al.17,18 used one-way and two-way coupled CFD-DEM (computational fluid dynamics-discrete element method) methods to explore the influence of particles moving in the tumbler mill on mud resistance. A minor error was observed between the two-way coupled model and the experiment. Petit et al.19 used the CFD-DEM model to evaluate the performance of the cross-flow air classifier of the VSI crusher in reducing the dust content of manufactured sand.

The impact and grinding of materials in VSI crushers are accompanied by turbulent air disturbance, resulting in a complex gas–solid two-phase flow motion. Particles mainly break due to the accumulation and dissipation of impact energy absorbed in the complex movement process. However, the distribution pattern of the impact energy absorbed by the particles under multiple impact collisions during breakage is currently unclear. Energy dissipation during breakage has not been fully considered. Therefore, the CFD-DEM is used in this paper to establish a gas–solid coupling model and simulate the flow of particles in a VSI crusher under different operating conditions. Furthermore, relevant information is extracted that reveals the energy dissipation distribution of particles in the crushing chamber and the change law of the collision energy spectrum, providing a theoretical basis for accurate VSI crusher performance prediction.

2. Structure Principle of a VSI Crusher

The rotor is an essential part of the crusher. The PL8500 VSI crusher is investigated in this paper, whose rotor is composed of a rotor body, separating cone, guide plate, and throwing tip, as shown in Figure 1. The schematic diagram of the working principle of the crusher is shown in Figure 2. When the crusher is running, the particles fall vertically from the feed port to the high-speed rotating separating cone. Then, the material is uniformly dispersed to the guide plate. Due to centrifugal force, as well as the extrusion force between materials and other external forces, particles on the guide plate move toward the outer edge of the rotor and are thrown out from the outlet at the end of the guide plate. The material thrown from the guide plate accelerates in a particular direction to the anvil installed within the chamber.20 During the collision, kinetic energy is converted to breakage energy, which breaks the material. Particles that do not fully release the kinetic energy are bounced back and collide with the high-speed moving materials and thrown from the rotor until eventual breakage. This process is continuously repeated.

Figure 1.

Figure 1

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Schematic diagram of the rotor: 1, rotor body; 2, guide plate; 3, separating cone; 4, throwing tip.

Figure 2.

Figure 2

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Structure diagram of a VSI crusher: 1, feed hopper; 2, feed inlet; 3, rotor; 4, anvil; 5, separating cone; 6, crushing chamber; 7, transmission device; 8, product outlet.

During impact breakage, the particles in the crushing chamber are impacted and collide many times by the guide plate, throwing tip, anvil, and other particles. The impact, grinding, and breakage accompany turbulent air disturbance, resulting in a gas–solid two-phase flow movement. Particles have complex movements due to the combined action of the crusher structure and the flow field. The impact energy is absorbed during this process and is dissipated with the breakage of the particles. The particles gradually lose kinetic energy and are discharged through the outlet due to gravity.

According to the impact breakage process of the material particle group within the VSI crusher, the impact energy absorbed by the particles is mainly converted to breakage energy. However, a small part of the energy is consumed by friction between particles. The breakage rate of particles depends on the impact times of particles, their size, and the amount of impact energy absorbed by particles. The breakage efficiency is increased with the impact energy absorbed and converted into helpful breakage energy. Therefore, the denser the collision energy dissipation, the higher the breakage probability of particles and vice versa. Consequently, the collision energy dissipation determines the crusher’s breakage rate of particles and energy consumption.

3. Establishment of a CFD-DEM Simulation Model and Simulation Method of Impact Energy

3.1. Establishing a Simulation Model of the Flow Field in the Crushing Chamber

As fine breakage equipment, the VSI crusher generally processes small particles. When the rotor rotates at high speed in the crushing chamber, it drives the surrounding air to generate a strong airflow whose interference with the material movement status cannot be ignored. Therefore, it is necessary to adequately simulate the effect of the gas on the material. Based on the CFD-DEM (FLUENT17.2 and EDEM2020) and structural parameters of the PL8500 VSI crusher produced by an enterprise, a gas–solid coupling simulation model of particles in the crushing chamber is established in this paper. The model includes fluid and discrete phase simulations, as shown in Figure 3. The movement state of particles in the flow field is obtained via a simulation analysis. The collision location, collision frequency, and energy consumption of the particles are then analyzed.

Figure 3.

Figure 3

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CFD-DEM simulation model: 1, crusher wall; 2, material; 3, fluid inlet; 4, rotor; 5, fluid outlet; 6, fluid.

3.2. CFD-DEM Numerical Simulation Method for the Flow Field in the Crushing Chamber

The fluent is used to determine the flow field movement state in the crushing chamber. The air is regarded as a continuous medium and simulated by solving the RNG k-ε turbulence model. The steady-state simulation is first considered to ensure calculation convergence. Then, the calculated results can be applied to the initial flow field in the transient-state simulation. Once the residual value reaches the predetermined value, the DEM is used to calculate the motion and force of the material system in the crushing chamber. The mass, momentum, and energy are transferred under the gas–solid coupling interface to simulate gas–solid two-phase interaction.21 The two-way coupling can be used to simulate the movement of the gas–solid phase in the crushing chamber more accurately. In other words, the information in the air phase simulation is transferred to the particle phase simulation, and the force of particles relative to air is simultaneously considered to conduct two-way data transmission.22 Although this method improves the accuracy of simulation results, it increases the amount of the simulation calculation.

The air in the crushing chamber can be regarded as a viscous incompressible fluid described by the Navier–Stokes (N-S) equation. The momentum conservation of the N-S equation can be expressed as follows:23

3.2. 1

where ρ is the fluid density, kg/m3; u is the fluid velocity, m/s; t is the time, s; p is the static pressure, Pa; μ is the dynamic viscosity, kg/(m·s); and F represents all external forces, N.

In addition, the law of mass conservation can be expressed as

3.2. 2

The rotor drives the surrounding air to rotate. Hence, the rotation effect in the turbulence changes the fluctuating curl of the turbulence near the wall. Moreover, the turbulence intensity in the circumferential direction is enhanced. Therefore, the flow field in the crushing chamber is characterized by a high strain rate and a large streamline curvature degree. Consequently, the RNG k-ε turbulence model can be used to calculate the flow field.24 The flow problem with a high strain rate and large streamline curvature can be better corrected by modifying the turbulent viscosity coefficient.

When air is incompressible, k can be expressed as

3.2. 3

Parameter ε can be expressed as

3.2. 4

where k is the turbulent kinetic energy, J; ui is the fluid velocity component, m/s; xi is the Cartesian coordinate, m; αk is the invalid Prandtl number of turbulent kinetic energy; μeff is the effective viscosity, kg/(m·s); G is the turbulent kinetic energy generated by the average velocity gradient, J; and ε is the dissipation rate of turbulent flow energy consumption; C1ε = 1.42, and C*2ε are given by the following equation:

3.2. 5

where C2ε = 1.68; η0 = 4.28; β = 0.015; Cμ = 0.085; η = Sk/ε; S is the deflection coefficient of turbulence velocity fluctuation

During simulation, the particle factory injects many particles into the crushing chamber, with the density of particles being significantly higher than the air density. For dense particles, calculating the flow field resistance is important for achieving the interaction between the gas and solid phase flow. In this paper, the Ergun and Wen and Yv drag model is adopted, which is more suitable than other drag models and has a broader application range. Therefore, this model simulates the drag of gas and particles in the crushing chamber.

The calculation formula of the Ergun and Wen and Yv drag model is related to the volume fraction of the solid phase.25 When the volume fraction is higher than 0.2, the influence of the gas phase is relatively small. Therefore, the drag force is independent of the Reynolds number of the gas phase Re. When the volume fraction of a solid phase φ is less than or equal to 0.2, it is necessary to correct the expression by introducing the Reynolds number:

3.2. 6

where Fd is the drag forces, N; dp is the particle diameter, m; φ is the solid volume fraction; and v is the velocity difference between material and gas, m/s. When the volume fraction of a solid phase φ is less than or equal to 0.2, the drag force is affected by the Reynolds number, while the drag coefficient CD is given by the following equation:

3.2. 7

On the other hand, the discrete element method describes the movement state of particles in the crushing chamber. In this study, the particles are brittle materials, the particles are unbreakable spherical particles, and their contact mechanics model conforms to the linear spring damping contact model. Therefore, the contact model is selected to describe the impact and collision between the particles, material, rotor body, and the wall of the crushing chamber.

The normal contact force Fn consists of a linear spring and a damper and can be calculated by the following equation:26

3.2. 8

where kn is the normal spring stiffness, N/m; Δx is the overlap between particles, m; Cn is the normal damping coefficient; and vn is the normal component of the contact velocity, m/s. The spring stiffness kn and the damping coefficient Cn can be expressed as

3.2. 9
3.2. 10

where E* is the equivalent of Young’s modulus, Pa; R* is the equivalent radius, m; m* is the equivalent mass, kg; and Cr is the coefficient of restitution.

The tangential force can be expressed as

3.2. 11

where kt is the tangential spring stiffness, N/m; Ct is the tangential damping coefficient; and vt is the tangential component of contact velocity, m/s. The summation term represents the accumulation of forces used to store the tangential motion energy, i.e., elastic deformation. The damper is used to consume the tangential motion energy, i.e., it represents plastic deformation. Parameter μ1 is the dynamic friction coefficient of the contact surface, and the total tangential force Ft is constrained by Coulomb friction.

Contact parameters must be set within the discrete element software to simulate material flow. Different contact parameters can affect the simulation results.27 The contact parameters of material–material and material–anvil are experimentally measured to improve the accuracy of the simulation results. The coefficients of restitution of material–material and material–anvil are 0.1 and 0.2, respectively. The static friction coefficients of material–material and material–anvil are 0.5 and 0.6, respectively, and the rolling friction coefficients of material–material and material–anvil are 0.01.

3.3. Experimental Validation of the CFD-DEM Numerical Simulation Model

Comparing the specific energy consumed by the crusher in the crushing experiments with the specific energy dissipated by the material in the DEM simulation enables one to validate the accuracy of the simulation calculations, according to the findings of Cleary and Morrison.28 The PL8500 vertical shaft impact crusher is utilized for experimental validation of the simulation model in this work, as shown in Figure 4. Limestone particles extracted from the sand and gravel quarry of the Hongjiadu power station comprised the experimental materials, which were screened into three particle size classes: 10 mm (30%), 14 mm (40%), and 18 mm (30%). The operating parameters of the crusher during operation guided the selection of the parameter ranges for rotor speed and feed rate. The rotor speed was maintained at 1000 and 1600 rpm, while the feed rate was set at 108 t/h. Crushing tests were conducted, and the average power of the crusher operating under two distinct conditions was determined; the average power was then used to calculate the specific energy consumed by the crusher in the experiment. Using the established simulation model, a simulation analysis of material crushing was then conducted under identical operating conditions as the crushing test; the simulation was utilized to derive the specific energy dissipated by the material. As illustrated in Figure 5, the operational specific energy consumptions of the crusher are 0.98 and 1.76 kWh/t, respectively, in Figure 5a and Figure 5b. In contrast, the material under simulation expends specific energies at 0.71 and 1.21 kWh/t, which are 40 and 46% of the energy consumed by the crusher, respectively. This is because not only is the energy dissipated used to crush the particles, but the material also expends energy within the crushing chamber to overcome airflow resistance and friction, resulting in a 40–50% energy loss. This finding is consistent with the results of Unland and Al-Khasawneh’s study.29

Figure 4.

Figure 4

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Working site of a VSI crusher.

Figure 5.

Figure 5

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(a, b) Comparison of specific energy between the experiment and simulation

4. Results and Discussion

4.1. Distribution of Collision Energy

Rotational speed and feed rate were selected via the CFD-DEM simulation model according to the actual operating parameters of the crusher. The rotation speeds were set to 1000, 1300, and 1600 rpm, while the feed rates M for each speed were 30, 40, and 50 kg/s. To enhance the statistical analysis of energy distribution in the crushing chamber, the crushing chamber is partitioned into 80 × 80 × 1 grids utilizing the EDEM postprocessing function. Following the rotor being stabilized, the cumulative energy absorbed and dissipated by the particles throughout a single cycle of operation is computed the resulting data is visually represented using Matlab,30 and the simulation results are shown in Figures 6–8.

Figure 6.

Figure 6

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Energy distribution of rotor speed for 1000 rpm. (a) M = 30 kg/s, (b) M = 40 kg/s, and (c) M = 50 kg/s.

Figure 8.

Figure 8

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Energy distribution of rotor speed for 1600 rpm. (a) M = 30 kg/s, (b) M = 40 kg/s, and (c) M = 50 kg/s.

Figure 7.

Figure 7

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Energy distribution of rotor speed for 1300 rpm. (a) M = 30 kg/s, (b) M = 40 kg/s, and (c) M = 50 kg/s.

Variation of the distribution of the energy dissipation area with the feed rate in the crushing chamber for the same rotational speed is shown in Figures 6–8. In the steady state of the rotor, the cumulative energy loss in each respective region during a single rotation cycle is denoted by a different grid color in the graph. The blank grid indicates no collision in this area, and a logarithmic scale controls the color change to highlight data change. According to Figures 6–8, apparent differences can be observed in the energy dissipation distribution. The accumulated low-energy dissipation mainly occurs inside the rotor. The accumulated high-energy dissipation mainly occurs on the anvil.

According to Figures 6–8, at the same feed rate, with an increase in the rotational speed, the energy distribution in the crushing chamber gradually becomes sparser while the energy dissipation is gradually increased. It is also observed that the collision within the rotor decreases gradually. This shows that the rotational speed affects the residence time of the material in the rotor and directly controls the collision energy gradient. For the constant speed, the energy distribution in the crushing chamber becomes denser with an increased feed rate. In addition, when the rotational speeds are 1000 and 1300 rpm, increasing the feed rate, the maximum accumulated energy dissipations increase from 40 and 60 to 55 and 100 J, respectively.

Furthermore, the collision energy distribution near the anvil is more intensive. Since additional material is thrown out from the rotor during rotation with an increase in the feed rate, a greater amount of material will collide with the anvil. Moreover, increasing the feed rate can improve the rotor’s handling capacity and increase the accumulated collision energy gradient. However, at 1600 rpm, the maximum accumulated energy dissipation decreases from 110 to 95 J and then increases to 105 J with an increase in the feed rate. The rationale behind this phenomenon is that an increase in the feed rate results in a concomitant escalation in both the quantity of material striking the anvil and the quantity of material rebounding from the anvil within the crushing chamber. At a feed rate of 30 kg/s (Figure 8a), the majority of materials undergo direct collisions with the anvil. The material–anvil collisions primarily involve high-energy dissipation with significant maximum cumulative energy dissipation. However, as the feed rate increases to 40 kg/s (Figure 8b), material–material and material–anvil collisions also occur. However, material–material collisions result in a reduction in the impact energy of the material–anvil collision, while material–material collisions diminish the high-energy dissipation of the material–material collision. Nevertheless, the impact energy of the material–anvil collision is diminished by the material–material collision, resulting in a reduction in the level of high-energy dissipation and maximum cumulative energy dissipation. This trend continues as the feed rate is elevated to 50 kg/s (Figure 8c), where the material–material collisions occur with greater frequency and magnitude, and the high-energy collisions between the material and anvil occur with a more pronounced increase, thereby leading to maximum cumulative energy dissipation.

Comparative analysis of the energy dissipation distribution in the crushing chamber shows that different operation parameters influence the energy dissipation distribution. When the rotational speed is 1600 rpm, the crusher performance can be better exerted, improving the rock breakage rate in the crushing chamber.

4.2. Energy Spectrum Analysis under Different Operating Conditions

The effect of rotational speed on the collision energy spectrum when the feed rate is 40 kg/s is shown in Figure 9, while the total energy spectrum of all collisions in a VSI crusher with a change of rotational speed is shown in Figure 9a. A significant amount of extremely low energy dissipation can be found for the three rotational speed cases. The majority of this low-energy dissipation occurs as sound or heat. Hence, these collisions do not damage the particles.29,30

Figure 9.

Figure 9

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Impact of a change in rotational speed on the spectrum of collision energy: (a) total energy, (b) normal energy, and (c) tangential energy.

The collision frequency of lower energy gradually decreases with an increase in rotational speed. In comparison, the collision frequency of higher energy gradually increases. In other words, with an increase in the rotational speed, some low-energy collision events transform into high-energy collision events, while not a single high-energy collision event is observed. Therefore, increasing the rotational speed can improve the energy utilization rate, thus improving the breakage rate of the material.

The maximum energy dissipation increases with the rotational speed since particles obtain more kinetic energy. Maximum energy dissipation generally occurs in the first collision after the material is thrown out of the rotor, thus enhancing the collision energy dissipation. Although the high-energy collision frequency is relatively low, these energies can cause greater damage to particles. The more energy absorbed by the material, the greater the breakage degree. Consequently, increasing the maximum energy dissipation can improve the breakage degree of the material, thus producing finer progeny and effectively improving the breakage rate of the largest particle size.

The total energy consists of normal and tangential components. Generally, the normal component is the leading cause of material breakage, while the tangential component is the leading cause of crusher wear and making a more rounded-shaped product.9 The energy spectrum of a normal component in the collision is shown in Figure 9b. It is very similar to the total energy spectrum in the high-energy range, reflecting that the normal component plays a dominant role in high-energy impact collisions. High-energy collision events of normal components increase with an increase in the rotational speed. In the low-energy range, the fluctuation of the collision frequency of each speed is roughly the same, while the sensitivity of collision frequency to speed is significantly weakened.

According to Figure 9c, the curve of the tangential energy spectrum shifts to the left compared to the total energy spectrum. Moreover, a decreasing trend of high-energy collision frequency smoothens, indicating that its influence on the high-energy range of the total energy spectrum is limited. This curve is very similar to the total energy spectrum in the low-energy range, reflecting that the tangential component is dominant in low-energy collisions. An increase in the rotational speed decreases the tangential low-energy collision frequency and increases the tangential high-energy collision frequency. This indicates that, with an increase in the rotational speed, a part of tangential low-energy collision transfers to tangential high-energy collision, leading to severe crusher wear and a more rounded-shaped product.30

The effect of the feed rate on the collision energy spectrum for the rotational speed of 1300 rpm is shown in Figure 10. Variation of the total energy spectrum with the feed rate in the collision is shown in Figure 10a. The collision frequency of low energy gradually increases with an increase in the feed rate. An increase in the feed rate increases the particle density in the crushing chamber, thus also increasing the collision between the material concerning the rotor and between the materials (this change can also be observed in Figures 6–8). However, energy dissipation caused by these collisions is so weak that it cannot cause material damage. An increase in the feed rate minorly affects high-energy collision frequency, indicating that no obvious relationship exists between the high-energy dissipation and the material density in the crushing chamber. Therefore, modifying the feed rate has a minor effect on the breakage rate and only improves the processing capacity of the crusher.

Figure 10.

Figure 10

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Effect of the feed rate change on the collision energy spectrum: (a) total energy, (b) normal energy, and (c) tangential energy.

A change in the energy spectra of normal and tangential energy dissipation during the collision with the change of feed rate is shown in Figure 10b and Figure 10c, respectively. The high-energy collision frequency change of the normal energy spectrum is similar to that of the total energy spectrum, which once again demonstrates that the normal energy dominates the high-energy range change of the total energy spectrum. The collision frequency of normal and tangential low-energy increases with the feed rate, i.e., increasing the feed rate also increases energy dissipation of irrelevant breakage. Concurrently, the degree of intense contact between the material and the crusher increases, which will increase the crusher’s wear and tear to some degree.

4.3. Threshold Energy Analysis

The threshold energy is the minimum collision energy that leads to material particle damage.31 The threshold energy Ex can be calculated according to the following formula:32

4.3. 12

where Ex is the threshold energy, J, and m is the mass of the material particle, g. Values of a and b can be measured by a single fraction drop weight test. The more samples tested, the more accurate the values of a and b will be.

The threshold energies of particle sizes of 18, 14, and 10 mm were calculated according to eq 12 as 0.720, 0.544, and 0.375 J, respectively. The collision frequency with a collision energy above the threshold energy is then counted. The change in the collision frequency with collision energy above the threshold energy with increasing rotational speed under three different collision types is shown in Figure 11. The material–anvil type and material–material type are characterized by a larger collision frequency in the total energy. These two types of collisions are the main reasons for particle breakage in the crushing chamber. As previously mentioned, the total collision energy consists of normal and tangential components. The collision frequency is the obvious difference between the two energy components. In the normal energy component, the collision frequency of the material–anvil type is the largest. This shows that the anvil is the main location of the high-energy collision after the material is thrown out of the rotor, which can significantly impact material breakage. With the lowest collision frequency, the material–rotor type is utilized. This observation indicates that the rotor primarily induces material acceleration and infrequently contributes to material fracture. On the other hand, in the tangential energy component, the collision frequency of the material–rotor type is the largest, and the collision frequency of the material–anvil type is the least, indicating that the wear of the rotor is more severe than that of the anvil.

Figure 11.

Figure 11

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Impact of rotational velocity on the frequency of collisions when energy dissipation exceeds a certain threshold. (a) Total energy, (b) normal energy, and (c) tangential energy.

Increasing the rotational speed significantly influences the total energy collision frequency of different types. With an increase in the rotational speed, the collision frequency of the three types gradually increases since particles that obtain additional kinetic energy can improve the collision energy dissipation, thus improving the material breakage rate. In addition, with an increase in the rotational speed, the frequency of the material–material type gradually exceeds that of the material–anvil type. This is because the higher the rotational speed, the faster the material. As a result, the velocity of the material escalates significantly, the trajectory within the crusher becomes more intricate, and the frequency of collisions between the particles dramatically increases. For the normal energy component, the occurrence rate of collisions involving energy dissipation surpassing a certain threshold increases progressively as the rotational speed increases. This phenomenon enhances the likelihood that particles will break and is beneficial for material damage. The tangential energy component exhibits a marginal increase in the collision frequency between materials and between anvils as the rotational speed increases. Despite this, the frequency of material–rotor collisions increases dramatically. An increase in rotational speed expedites the material’s egress from the rotor, thereby impeding the development of a material layer within the rotor. As a consequence, both the likelihood of a material–rotor collision and the tangential energy dissipation between the two components are enhanced. Elevating the frequency of material collisions with the rotor will result in an escalation of rotor wear.

5. Conclusions

The energy consumption of the CFD-DEM simulation results is consistent with the experimental results, indicating that the CFD-DEM simulation can effectively describe the energy dissipation of material collision in the crushing chamber.

Energy dissipation distribution reflects the location of the collision and the energy dissipation. With an increase in the rotational speed, the energy distribution became sparser and more converged to the anvil, while the accumulated energy gradually increased. An increase in feed rate increases the energy distribution density in the crushing chamber.

According to the energy spectrum analysis of collisions, some low-energy collisions are transferred to high-energy collisions with increased rotational speed. This is conducive to improving the material breakage rate. On the other hand, the feed rate has a limiting influence on the breakage rate, while the increasing feed rate significantly improves the rotor’s handling capacity. Consequently, the crusher’s overall energy consumption decreases.

For collisions above the threshold energy, with an increase in the rotational speed, the collision frequency of different types can be effectively increased, thus improving the material breakage rate.

In summary, when the working parameters of the VSI crusher were changed, the collision energy dissipation of the material would be changed in the crushing chamber. High-energy collision events increased with the rotational speed of the rotor. Thus, the influence of the breakage activity was effectively increased. The increasing feed rate had a minor effect on the breakage rate. However, at the same time, the intensive degree of contact between the material and the crusher increases, so to a certain extent, it will increase the wear and tear of the crusher.

This work was financially supported by the National Natural Science Foundation of China (no. 52065007).

The authors declare no competing financial interest.

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