# Variability Study of Bond Work Index and Grindability Index on Various Critical Metal Ores

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## Abstract

**:**

_{i}) for a given ore varies along with the grinding size. In this study, a variability bysis is carried out with the Bond standard grindability tests on different critical metal ores (W, Ta), ranging from coarse grinding (rod mills) to fine grinding (ball mills). The relationship between w

_{i}and grinding size did not show a clear correlation, while the grindability index (gpr) and the grinding size showed a robust correlation, fitting in all cases to a quadratic curve with a very high regression coefficient. This result suggests that, when performing correlation studies among ore grindability and rock mechanics parameters, it is advised to use the grindability index instead of the Bond work index.

## 1. Introduction

_{R}is the proportionality coefficient and P and F are the particle sizes of the product and feed, respectively [µm].

_{K}is a different proportionality coefficient.

_{B}= 10·w

_{i}, and w

_{i}is expressed in kWh/t.

_{i}in the case of crushing, rod milling and ball milling [13,15]. The practical interest of w

_{i}is unquestionable. From a technical perspective, it constitutes the most reliable method of characterizing ore grindability when designing the necessary tumbling mills to process that ore. Bearman et al. (1997) showed that other mechanical characterization tests are insufficient when predicting the grinding ore behavior.

_{i}as the characteristic parameter of ore grinding behavior, it is not fully understood at the industrial level, even being handled as a constant value. Bond himself usually reported in his papers separately the grindability values for the Bond rod mill test (BRM) and the Bond ball mill test (BBM), but no study could be found analyzing the information from BRM and BBM test values and deepening them to explain the variability obtained.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Bond Ball Mill (BBM) Standard Test

^{3}, and this volume’s weight is fixed as the mill charge in all subsequent cycles. Additionally, fresh feed particle size distribution (PSD) is obtained to calculate the 80% passing size (F

_{80}) and undersize weight already present in the feed.

_{100}) selected according to the industrial grinding size target, always between 28 and 325 Tyler mesh (40–600 microns).

^{3}weight. The second cycle number of revolutions is calculated considering the predefined circulating load value (250%), according to Equation (4),

_{i}is the number of mill revolutions at run i; P

_{S}is the expected product weight once it reaches the steady state (g), calculated by dividing the initial 700 cm

^{3}weight by 3.5; F

_{f,i}is the weight of fines already in the feed (g), which can be calculated from the feed PSD and the total fresh feed weight added in the run i (which equals the total undersize product in the run i−1) and gpr

_{i−1}is the net grams produced in the previous run, i−1.

_{80,}and the BBM work index can be calculated using Equation (5),

_{i}, is expressed in kWh/sht; P

_{100}, F

_{80}and P

_{80}are expressed in microns and gpr is expressed in g/rev. Bond named gpr as the grindability index.

_{i}should conform with the motor output power to an average overflow ball mill of 8 ft inner diameter grinding wet in a closed circuit. This value should be multiplied by correcting factors to conform with other situations, such as dry grinding (at least 1.30) or different inner mill diameters. A complete and updated description of correction factors was written by Rowland [40].

#### 2.3. Bond Rod Mill (BRM) Standard Test

^{3}. Dry grinding cycles are performed with 100% circulating load in a laboratory rod mill 12” × 24” with a wave-type lining, running at 46 rpm. The grinding charge consists of six 1.25” diameter and two 1.75” diameter steel rods 21” long, weighing 33.380 kg. In this case, P

_{100}values can range from 4 to 65 Tyler mesh (4.7 mm to 200 microns).

_{80}are calculated, and the BRM work index is calculated from Equation (6).

_{i}should conform with the motor output power to an average overflow rod mill of 8 ft inner diameter grinding wet in an open circuit.

#### 2.4. Grindability Tests

_{100}for every ore. Then, the values of gbp and w

_{i}were obtained for each ore, and an attempt to model their variation with P

_{100}was performed in each case. Full details of the performed tests and results are available in the supplementary material.

## 3. Results and Discussion

_{i}versus P

_{100}is plotted in Figure 2, for both BBM and BRM tests. The obtained values show a lack of continuity, and a clear trend function could hardly be defined. Nonetheless, when observing Figure 3, which depicts the variation of gpr versus P

_{100}in both BBM and BRM tests, a fairly clear trend can be seen; according to this, Figure 3 also shows the quadratic fit of gpr consolidated values versus P

_{100}, with a determination coefficient of 99.76%.

_{i}versus P

_{100}plot revealing a lack of continuity again (Figure 4), plotting gpr versus P

_{100}(Figure 5) showed a similar trend to the previous ore. Moreover, the quadratic fit was almost perfect in this case, with a coefficient of determination of 100.00%.

_{i}values with P

_{100}shows a better continuity than in previous cases (Figure 7), so the determination coefficient reached again a very high value, 99.89%.

_{i}values versus P

_{100}in the case of Panasqueira ore yeilded a clear trend in the case of BBM w

_{i}values, but a with a roller-coaster type shape in the case of BRM w

_{i}values (Figure 8). Unexpectedly, when plotting gpr values versus P

_{100}(Figure 9), again a quadratic fit yielded a very high value of the determination coefficient, 99.10%.

_{i}versus P

_{100}plot (Figure 10), a clear quadratic trend was obtained when plotting gpr values versus P

_{100}(Figure 11), with a very high value of the determination coefficient, 99.95%.

_{i}values with grinding size, both in BBM and BRM grindability tests. While w

_{i}versus P

_{100}plots show no continuity in general (being erratic in the case of Panasqueira ore, BRM w

_{i}values) when plotting gpr versus P

_{100,}a parabolic shape is clearly depicted with all ores. Furthermore, the quadratic fitting determination coefficients overcame 99.7% in all cases.

_{i}with mechanical parameters (geotechnical) or operational parameters (drilling, blasting) should be revised considering gpr values instead of w

_{i}values, which probably would yield a better determination coefficient.

_{i}is worldwide known as the Bond index, and without the intention of subtracting an iota of importance from the broad contribution of Fred Bond (w

_{i}is the most practical tool in rod and ball mill calculation), it seems fair to propose the naming of gpr as the Maxson index. This so-called Maxson index should be meaningful, not only for being the critical parameter to obtain the Bond work index but also for characterizing the ore breakage behavior.

## 4. Conclusions

- According to the obtained results, BBM and BRM grindability tests showed no continuity or clear correlation when considering w
_{i}values versus P_{100}, but a clear tendency was obtained in all cases when plotting gpr versus P_{100}. - It is advised that energy consumption modelling based on correlations involving w
_{i}and other mechanical or operational parameters would yield a better determination coefficient using gpr values instead. - The re-signifying of gpr evidenced to characterize the ore breakage behavior and its origin justify the proposal of naming gpr as the Maxson grindability index.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Ball Size | Balls | ||
---|---|---|---|

Inch | cm | Number | Weight (g) |

1.45 | 3.683 | 43 | 8803 |

1.17 | 2.972 | 67 | 7206 |

1.00 | 2.540 | 10 | 672 |

0.75 | 1.905 | 71 | 2011 |

0.61 | 1.549 | 94 | 1433 |

Total: | 285 | 20,125 |

Ball Size | Balls | ||
---|---|---|---|

Inch | cm | Number | Weight (g) |

1.500 | 3.810 | 25 | 5690 |

1.25 | 3.175 | 39 | 5137 |

1.000 | 2.540 | 60 | 4046 |

0.875 | 2.223 | 68 | 3072 |

0.750 | 1.905 | 93 | 2646 |

Total: | 285 | 20,592 |

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**MDPI and ACS Style**

García, G.G.; Oliva, J.; Guasch, E.; Anticoi, H.; Coello-Velázquez, A.L.; Menéndez-Aguado, J.M.
Variability Study of Bond Work Index and Grindability Index on Various Critical Metal Ores. *Metals* **2021**, *11*, 970.
https://doi.org/10.3390/met11060970

**AMA Style**

García GG, Oliva J, Guasch E, Anticoi H, Coello-Velázquez AL, Menéndez-Aguado JM.
Variability Study of Bond Work Index and Grindability Index on Various Critical Metal Ores. *Metals*. 2021; 11(6):970.
https://doi.org/10.3390/met11060970

**Chicago/Turabian Style**

García, Gloria G., Josep Oliva, Eduard Guasch, Hernán Anticoi, Alfredo L. Coello-Velázquez, and Juan M. Menéndez-Aguado.
2021. "Variability Study of Bond Work Index and Grindability Index on Various Critical Metal Ores" *Metals* 11, no. 6: 970.
https://doi.org/10.3390/met11060970