# Application of the Discrete Element Method to Study the Effects of Stream Characteristics on Screening Performance

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. DEM

#### 2.1.1. DEM Contact Model Theory

#### 2.1.2. Simulations

^{3}, 2500 kg/m

^{3}, and 2100 kg/m

^{3}. The separation of these particles may represent the essential sorting operation that occurs in a typical screening process. More generally, this model features the main characteristics of many industrial screening applications. Table 2 is a summary of the simulation parameters. The collision properties were calibrated by the method proposed by Quist [19].

#### 2.2. Laboratory Vibrating Screen

#### 2.3. Modeling

_{50}), the aperture size (Ap) and the rate factor (β). The rate factor can be calibrated to specific scenarios to provide more accurate results. The mass passing the aperture would be added to the zone below or added to the total mass passing all decks if there are no decks below the current one.

## 3. Results/Discussion

#### Model Comparison

## 4. Conclusions

- DEM is a powerful tool for calculating the overall efficiency and the product size distribution, while also enabling the analysis of important parameters, such as the size fraction (by sampling from any part of the screen); particle tracking; and the observation of bed material, which helps in stratification analysis. Therefore, DEM can provide a better understanding of different process parameters, such as how various particle densities have an effect on the stratification process and screen efficiency.
- The increase in the passing percentage of small undersized particles mainly occurred at the upper deck, and as a result, the particle bed was thicker at the lower deck, which means that the stratification process mainly affects the screen efficiency in the lower deck.
- In the simulations, the passage rate for the low-density material was lower than for the high-density material, since the low-density material had a lower stratification rate compared to the high-density material.
- In the stratification of materials with various densities, it is easier for the high-density material to move vertically through the particle bed. Thus, the high-density material has a higher probability of passage.

## 5. Future work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Discrete element method (DEM) simulation results for the vibratory screening process with three different feed rates: (

**a**) 4 kg/s, (

**b**) 5 kg/s, and (

**c**) 6 kg/s.

**Figure 9.**Passage rate in different screen sections for different densities and feed rates (LD: Low-density material, BD: Between density material, and HD: High-density material. (

**a**) Low feed rate, 4 kg/s, (

**b**) between feed rate, 5 kg/s, and (

**c**) high feed rate, 6 kg/s.

**Figure 10.**Average particle diameter in overflow material. (

**a**) Upper deck. (

**b**) Lower deck. (LD: Low-density material, BD: Between density material, and HD: High-density material)

**Figure 11.**Average particle velocity for different material densities, (

**a**) upper deck, (

**b**) lower deck. (LD: Low-density material, BD: Between density material, and HD: High-density material)

**Figure 12.**Total number of particles passed through screen deck in different sections with the feed for mixed particle densities. (

**a**) Total number of particles. (

**b**) Partition number.

**Figure 13.**(

**a**) Passage result from model simulation (product model), and DEM simulation (product data). (

**b**) Passage rate in different screen sections by using screen model simulation.

${F}_{n}$ | Normal force, Equation (1), (N) | ${M}_{i,j,{n}_{l}}$ | The mass flow along the screen, Equation (4), (kg) |

${K}_{n}$ | Stiffness of the spring, Equation (1), (-) | ${M}_{down,i,j,{n}_{l}-1}$ | The downward flow, Equation (4), (kg) |

${C}_{n}$ | Viscoelastic damping constant, Equation (1), (m/s) | ${M}_{up,i,j,{n}_{l}}$ | The upward flow, Equation (4), (kg) |

${V}_{n}$ | The relative velocities, Equation (1), (m/s) | ${M}_{BP,i,j}$ | Mass flow of the material in the contact layer, Equation (4), (kg) |

${F}_{t}$ | Tangential force, Equation (2), (N) | ${k}_{j}$ | Passage rate parameter, Equation (4), (-) |

${K}_{t}$ | Stiffness of the spring, Equation (2), (-) | $\Delta t$ | Time step, Equation (4), (s) |

${C}_{t}$ | Viscoelastic damping constant, Equation (2), (-) | $\alpha $ | Slope of the screen deck, Equation (6), (Angle) |

${V}_{t}$ | The relative velocities, Equation (2), (m/s) | $v$ | Transport velocity of the particle along the screen deck, Equation (6), (m/s) |

$f$ | Frequency, Equations (3) and (6), (Hz) | $R$ | Function of stroke, Equation (6), (mm) |

Material Properties | Poisson’s Ratio | Shear Modulus | Density |

Particles (Low density) | 0.3 | 24 MPa | 2100 kg/m^{3} |

Particles (Medium density) | 0.3 | 24 MPa | 2500 kg/m^{3} |

Particles (High density) | 0.3 | 24 MPa | 2900 kg/m^{3} |

Screen (Steel) | 0.2 | 79 GPa | 7800 kg/m^{3} |

Collision Properties | Coefficient of Restitution | Coefficient of Static Friction | Coefficient of Rolling Friction |

Particle-particle | 0.2 | 0.6 | 0.01 |

Particle-screen (Steel) | 0.6 | 0.45 | 0.01 |

Machine Parameters | |||

Screen aperture | 25 mm×25 mm and 10 mm×10 mm | ||

Screen declination | 15° | ||

Screen vibration | Sinusoidal translation, amplitude 6 mm, and frequency 13 Hz | ||

Particle generation rate | For particles at 4 kg/s, 5 kg/s, and 6 kg/s |

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**MDPI and ACS Style**

Davoodi, A.; Asbjörnsson, G.; Hulthén, E.; Evertsson, M.
Application of the Discrete Element Method to Study the Effects of Stream Characteristics on Screening Performance. *Minerals* **2019**, *9*, 788.
https://doi.org/10.3390/min9120788

**AMA Style**

Davoodi A, Asbjörnsson G, Hulthén E, Evertsson M.
Application of the Discrete Element Method to Study the Effects of Stream Characteristics on Screening Performance. *Minerals*. 2019; 9(12):788.
https://doi.org/10.3390/min9120788

**Chicago/Turabian Style**

Davoodi, Ali, Gauti Asbjörnsson, Erik Hulthén, and Magnus Evertsson.
2019. "Application of the Discrete Element Method to Study the Effects of Stream Characteristics on Screening Performance" *Minerals* 9, no. 12: 788.
https://doi.org/10.3390/min9120788