# Investigation of Lateral Confinement, Roller Aspect Ratio and Wear Condition on HPGR Performance Using DEM-MBD-PRM Simulations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{®}Core i7–8700K CPU GHz 3.7. A recently proposed PRM [32] was used, which was implemented as an application programming interface (API) using the Hertz-Mindlin (no-slip) contact model considering a spherical particle replacement [34]. This contact model and particle geometry have the advantage of the ability to track the motion and gross kinetics of a large number of particles with good computational efficiency [25].

#### 2.1. Materials

_{min}) was used in the simulations (Table 3). Finally, in order to replicate the particle bed response when submitted to compressive stresses in a piston-and-die, the authors selected a value of shear modulus of 2 × 10

^{9}Pa and DEM particle density of 3520 kg/m

^{3}, with PRM breakage parameters given in Table 3 [31].

#### 2.2. DEM Equipment Setup

^{2}) and the projected area D × L (mm

^{2}), and the other control as a torque for the rotating movement. A rotating movement with a selected fixed angular velocity and with no motion controller was used in the case of the fixed roll. Being a one-dimensional model, it does not allow for skewing of the rolls. The rolls movement starts only when DEM particles fill the hopper from a particle factory located above the rolls. From this point on in the simulation, new particles were added continuously. Simulations were run until stability was reached for the HPGR performance variables, which typically occurred after about 2 s of operation.

#### 2.3. Base Case

#### 2.4. Confinement Systems

#### 2.5. Aspect Ratio

#### 2.6. Worn Rollers

^{2}and the roll velocity to 0.6 m/s.

#### 2.7. Measurement of Key Variables

^{3}) was also then calculated by [5]:

#### 2.8. Bypass Gap

^{2}and roll velocity of 0.5 m/s was selected to assess this variable. Besides comparing the experimental and simulated performance variables, the bypass flowrate estimated using the empirical model proposed by Campos et al. [22] was taken into consideration in selecting the bypass gap (x

_{bp}) to be used in the pilot-scale HPGR simulations.

## 3. Results and Discussion

#### 3.1. Confinement Systems

#### 3.2. HPGR Aspect Ratio

#### 3.3. Roller Wear Condition

^{2}and the roll velocity to 0.6 m/s and the summary of the results is also shown in Table 8. It shows that increasing the specific force so as to approximately match the power reached by the HPGR with new rollers results in even an increase in product fineness with the worn rolls surface. That led to an even smaller roller gap, reducing HPGR throughout, which was compensated by increasing rolls velocity, resulting in an even higher throughput (Table 8). Although successful, this approach has the limitation of increasing heterogeneity in the product fineness. In addition, the higher pressures demanded can result in working gaps that may reach the minimum safety gap between the rolls.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**CAD images of pilot HPGRs with different confinement systems: (

**a**) Cheek plates, (

**b**) smooth flanges and fixed side plates and (

**c**) studded flanges and fixed side plates.

**Figure 3.**Bottom view of the simulated pilot-scale HPGR with cheek plates representing the mass flow sensors used to measure the total and roll throughput.

**Figure 4.**Top view of the pilot-scale HPGR showing the position of the 60 bins, each one with 100 mm × 5.7 mm, to measure key variables along the rolls.

**Figure 5.**3D rendered DEM simulation image of the pilot-scale HPGR with cheek plates and particles colored by size. HPGR with an aspect ratio of 3.13, operating with specific force of 3.5 N/mm

^{2}, rolls velocity of 0.5 m/s and bypass gap of 11 mm.

**Figure 6.**Comparison of measured and predicted feed and product size distributions from a pilot-scale HPGR with cheek plates. HPGR with an aspect ratio of 3.13, operating with specific force of 3.5 N/mm

^{2}and rolls velocity of 0.5 m/s.

**Figure 7.**Average axial mass flowrate profiles along the rolls with different confinement systems, with an aspect ratio of 3.13, operating with a specific force of 3.5 N/mm

^{2}, rolls velocity of 0.5 m/s and bypass gap of 11 mm. Vertical dotted lines identify the edge of the rolls. * Flanges with reduced bypass gap (6 mm).

**Figure 8.**Axial compressive force profiles along the rolls for the HPGRs in the gap region, with different confinement systems with an aspect ratio of 3.13, operating with a specific force of 3.5 N/mm

^{2}and rolls speeds of 0.5 m/s. Vertical dotted lines identify the edge of the rolls. * Flanges with reduced bypass gap (6 mm).

**Figure 9.**Predicted percentage passing the 45 µm sieve in the product along the rolls with different confinement systems for rolls with aspect ratio of 3.13, operating with a specific force of 3.5 N/mm

^{2}, rolls speed of 0.5 m/s and bypass gap of 11 mm. * Flanges with reduced bypass gap (6 mm).

**Figure 10.**Predicted average axial mass flowrate profiles along the rolls of HPGRs with cheek plates and different aspect ratios, operating at a specific force of 3.5 N/mm

^{2}, rolls velocity of 0.5 m/s and bypass clearance of 11 mm.

**Figure 11.**Axial compressive force profiles along the rolls at the gap region for the pilot-scale HPGRs with cheek plates with different aspect (D/L) ratios, operating at a specific force of 3.5 N/mm

^{2}, rolls at a speed of 0.5 m/s and bypass gap of 11 mm. Vertical dotted lines identify the projection of the rolls length.

**Figure 12.**Predicted percentage passing the 45 µm sieve in the product for the pilot-scale HPGRs with cheek plates with different aspect (D/L) ratios, operating at a specific force of 3.5 N/mm

^{2}, rolls at a speed of 0.5 m/s and cheek plates with bypass gap of 11 mm. Vertical dotted lines identify the projection of the rolls length.

**Figure 13.**Axial compressive force profiles along the rolls at 10 to 20 cm above the gap region of the HPGR with cheek plates with different aspect (D/L) ratios, operating at a specific force of 3.5 N/mm

^{2}and rolls a speed of 0.5 m/s. Vertical dotted lines identify the projection of the rolls lengths.

**Figure 14.**Axial compressive force profiles along the rolls in the gap region for different surface wear conditions operating at specific force of 3.5 N/mm

^{2}and rolls speed of 0.5 m/s. Vertical dotted lines identify the projection of the rolls length.

**Figure 15.**Axial throughput profiles along the rolls for different surface wear conditions for the HPGR operating with cheek plates operating at specific force of 3.5 N/mm

^{2}and rolls speed of 0.5 m/s. Vertical dotted lines identify the projection of the rolls length.

**Figure 16.**Predicted product percent passing 45 µm along the rolls for different surface wear conditions for the HPGR with cheek plates operating at specific force of 3.5 N/mm

^{2}and rolls speed of 0.5 m/s. Vertical dotted lines identify the projection of the rolls length.

Particle Size (mm) | 8.0 | 7.2 | 6.4 | 5.6 |
---|---|---|---|---|

Percentage in volume | 40 | 23 | 22 | 15 |

Contact Type | Coefficient of Restitution | Coefficient of Static Friction | Coefficient of Rolling Friction |
---|---|---|---|

Ore–Steel | 0.15 | 0.49 | 0.47 |

Ore–Ore | 0.20 | 0.55 | 0.51 |

Parameter | ${\mathit{E}}_{\infty}\text{}(\mathbf{J}/\mathbf{kg})$ | ${\mathit{d}}_{\mathit{o}}\text{}\left(\mathbf{mm}\right)$ | $\mathit{\phi}$ | $\mathit{\sigma}$ | $\mathit{\gamma}$ | $\mathit{A}$ | ${\mathit{b}}^{\prime}$ | D_{min} (mm) | E_{max}/E_{50} |
---|---|---|---|---|---|---|---|---|---|

Value | 500 | 75 | 0.35 | 0.8 | 5.0 | 68 | 0.03 | 1.2 | 4 |

Variable | Symbol | Units | Value |
---|---|---|---|

Confinement system | - | - | Cheek plate |

Rolls diameter | D | mm | 1000 |

Rolls length | L | mm | 320 |

Rolls peripheral velocity | U | m/s | 0.5 |

Studs diameter | d_{st} | mm | 15.9 |

Studs protruding height | I_{st} | mm | 5.0 |

Autogenous area fraction | - | - | 0.65 |

Zero gap | x_{0} | mm | 1.0 |

Specific force * | SF | N/mm^{2} | 2.5/3.5 |

**Table 5.**Summary of the results of DEM simulations of pilot-scale HPGR with cheek plates operating with 2.5 N/mm

^{2}, roll velocity of 0.5 m/s, top particle size of 8 mm and for different bypass gaps.

Bypass Gap (mm) | Working Gap (mm) | Throughput | |
---|---|---|---|

Total (t/h) | Bypass (%) | ||

Experiment | 7.5 | 26.7 | 27.8 * |

6 | 6.4 | 27.5 | 14.6 |

11 | 6.8 | 32.2 | 31.3 |

15 | 8.5 | 48.2 | 51.4 |

**Table 6.**Effect of the confinement system on the HPGR performance. Simulations performed with rolls with aspect ratio of 3.13, specific force of 3.5 N/mm

^{2}, roll velocity of 0.5 m/s and bypass gap of 11 mm.

Confinement System | Working Gap (mm) | Throughput (t/h) | Specific Throughput (ts/hm^{3}) | Power (kW) | Ecs (kWh/t) | Product −45 µm (%) | ||
---|---|---|---|---|---|---|---|---|

Rolls | Bypass | Total | ||||||

Cheek plate (Expt.) | 7.4 | - | - | 26.8 | 167.5 | 66.1 | 2.47 | 52.0 |

Cheek plate | 5.5 | 21.2 | 9.7 | 30.9 | 193.1 | 62.4 | 2.02 | 20.9 |

Smooth flanges | 6.3 | 27.4 | 9.3 | 36.7 | 229.4 | 73.2 | 2.00 | 21.4 |

Studded flanges | 11.6 | 33.0 | 6.6 | 39.6 | 247.5 | 71.8 | 1.81 | 19.1 |

Smooth flanges * | 9.6 | 28.6 | 3.5 | 32.1 | 200.5 | 76.4 | 2.38 | 22.5 |

**Table 7.**Effect of aspect ratio on the performance of HPGRs with cheek plates. Simulations performed with a specific force of 3.5 N/mm

^{2}, roll velocity of 0.5 m/s and bypass gap of 11 mm.

Aspect Ratio | Working Gap (mm) | Throughput (t/h) | Specific Throughput (ts/hm^{3}) | Power (kW) | Ecs (kWh/t) | Product −45 µm (%) | ||
---|---|---|---|---|---|---|---|---|

Rolls | Bypass | Total | ||||||

0.83 | 11.8 | 108.4 | 12.6 | 121.0 | 201.7 | 257.6 | 2.13 | 17.2 |

1.22 | 11.7 | 66.7 | 11.0 | 77.3 | 188.5 | 151.6 | 1.96 | 17.5 |

3.13 | 5.5 | 21.2 | 9.7 | 30.9 | 193.1 | 62.4 | 2.02 | 20.1 |

**Table 8.**HPGR performance variables resulting from simulations of the 820 mm long roller (aspect ratio of 1.22) under different wear conditions. Simulations of the HPGR operating at a specific force of 3.5 N/mm

^{2}and rolls velocity of 0.5 m/s.

Roller Wear Condition/Wear Depth | Working Gap (mm) | Throughput (t/h) | Specific Throughput (ts/hm^{3}) | Power (kW) | Ecs (kWh/t) | Product −45 µm (%) |
---|---|---|---|---|---|---|

New/0 mm | 11.7 | 77.3 | 188.5 | 151.6 | 1.96 | 17.5 |

Parabolic/2.5 mm | 9.8 | 80.4 | 196.1 | 162.2 | 2.02 | 15.2 |

Trapezoidal/2.5 mm | 4.7 | 78.8 | 192.2 | 117.0 | 1.49 | 17.1 |

Trapezoidal/5.0 mm | 6.7 | 82.6 | 201.5 | 104.7 | 1.27 | 15.6 |

Trapezoidal/2.5 mm * | 3.8 | 85.0 | 207.4 | 155.2 | 1.82 | 18.3 |

^{2}and roll tangential velocity of 0.6 m/s.

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**MDPI and ACS Style**

Rodriguez, V.A.; Barrios, G.K.P.; Bueno, G.; Tavares, L.M. Investigation of Lateral Confinement, Roller Aspect Ratio and Wear Condition on HPGR Performance Using DEM-MBD-PRM Simulations. *Minerals* **2021**, *11*, 801.
https://doi.org/10.3390/min11080801

**AMA Style**

Rodriguez VA, Barrios GKP, Bueno G, Tavares LM. Investigation of Lateral Confinement, Roller Aspect Ratio and Wear Condition on HPGR Performance Using DEM-MBD-PRM Simulations. *Minerals*. 2021; 11(8):801.
https://doi.org/10.3390/min11080801

**Chicago/Turabian Style**

Rodriguez, Victor Alfonso, Gabriel K. P. Barrios, Gilvandro Bueno, and Luís Marcelo Tavares. 2021. "Investigation of Lateral Confinement, Roller Aspect Ratio and Wear Condition on HPGR Performance Using DEM-MBD-PRM Simulations" *Minerals* 11, no. 8: 801.
https://doi.org/10.3390/min11080801