4.1.3. Particle Spectrum

The collision frequency distribution of particle specific energy was plotted for normal and tangential particle contact in Figure 13. This represents the collisions statistics for specific energy that are applied to particles per time unit. The x axis indicates the specific energy of contact, which means the amount of energy that is transferred per mass of grinding media. The y axis indicates the number of contacts per unit of time, at each specific energy level.

**Figure 13.** Particle collision spectra for normal (left) and shear (right) contact at different operational velocities.

The wider specific energy distribution is observed for normal contact, in comparison to the shear contact distribution. This means that normal contacts can have a higher specific energy value than shear contacts. In relation to the agitator rotational velocity, higher velocities are associated with a small increase in both collisions' frequency and specific energy range. This can be observed for both normal and tangential contacts.

By looking at the relationship between energy levels and collision frequency, it is also possible to correlate with breakage behavior. In this sense, contacts with greater values of specific energy have a higher tendency to overcome the minimum specific energy required for a certain particle to break. This means that contacts of higher specific energy values have a higher probability of causing breakage in a single or fewer contacts. However, this can also lead to a non-energy efficient behavior once this increases the chance to apply more energy than necessary to cause particle breakage. In contrast, smaller values of specific energy might initially lead to particle weakness, instead of direct breakage. Because of that, it can be necessary for a larger amount of low specific energy collisions cause breakage. At the same time, by applying a greater amount of small specific energy contacts increases the chance to apply the minimum amount of energy that is required for particle breakage.

#### *4.2. Wear Simulation*

The wear simulation started after at least three revolutions at steady-state conditions, thus, allowing the wear simulation to be performed under stable conditions.

#### 4.2.1. Particle Trajectory and Velocity

Figure 14 shows the streaming lines associated with particle absolute translational velocity.

A red box surrounds the grinding media trajectory for the new liner condition, shown in the left side of the image. Comparing the left and right side of the picture, it can be noted that red boxes on the right side miss the streaming lines both at the top and bottom parts of the mill. This indicates that media motion is negligible in those regions. In the bottom part of the mill, it is noted that the dead zone effect is emphasized by liner wear.

**Figure 14.** Particle trajectory and absolute translational velocity for new (left) and worn liner (right) conditions, at different mill velocities.

Figure 15 shows the relationship between particle absolute translational velocity and the base liner wear. It is possible to note that particle velocity reduces with wear, due to the reduction in the liner surface area. This reduction is more aggressive for higher agitator velocities. This means that a more representative decrease in particle velocity is obtained when operating at higher agitator velocity. Based on the extrapolated data, it can be expected that particle velocity will be independent on agitator velocity when the base liner is approximately 40% to 50% worn.

**Figure 15.** The relationship between average particle velocity and the base liner wear intensity.

#### 4.2.2. Power

Figure 16 shows the relationship between base liner volume and simulation power. It is possible to note that power reduction is intensified at higher rotational velocities. In the operational context, the power is kept constant during the liner lifecycle by increasing mill filling.

**Figure 16.** The relationship between simulation power and base liner volume.

#### 4.2.3. Particle Spectrum

Figure 17 shows normal and shear energy spectrums for the three operational velocities, at different wear stages. By comparing shear (right) and normal (left) collision spectra, it is possible to note that normal contacts are more affected by wear. In this sense, a greater reduction in the collision frequency was observed for normal contacts, in comparison to shear. This reduction is emphasized at greater specific energies, especially above 1 × <sup>10</sup>−<sup>1</sup> J/kg. Based on the idea that collisions of greater specific energies can lead to an inefficient

use of energy, it can be suggested that wear scenarios can be related to a better energy use behavior. This indicates that the agitator wear pattern affects mostly high energy contact, while maintaining low energy contacts that present a better energy efficiency behavior. However, it is important to emphasize that the collision frequency and energy reduction will probably generate a coarser product, and thus, the better energy use behavior will be mainly caused by the overall power consumption reduction. Recently, Oliveira [31] applied a mechanistical model to predict product size distribution by using the particle contact spectra obtained with DEM simulations. The simulation considered grinding media as the mill charge, in the absence of ore and slurry. By taking into consideration different proportions of shear power involved in inter particle collision, the model successfully predicted product size distribution of laboratory-scale experiment, for different solids concentration ratios. In this sense, this model can be applied to quantify the wear effect on product size distribution.

**Figure 17.** Particle collision spectra at different liner conditions and rotational velocities.

In the operational context, it is important to evaluate the effect on the target product size, such as mineral liberation, to prevent mineral losses in further beneficiation processes. In this sense, a wider evaluation is necessary to guarantee the overall process efficiency, which includes a proper understanding of the effect on the downstream process. As an alternative, various operational conditions can be approached to guarantee the obtaining of the target mineral product size, while maximizing energy efficiency. In the specific case of the Mins-Rio project, the product requirement is in relation to fines generation, for pipeline transport requirements. In this sense, it is necessary to evaluate the effect on fines generation to guarantee the product adequacy.

Comparing the collision spectra behavior at different mill rotational velocities it can be noted that higher rotational velocities intensified the overall collision frequency reduction, such as reduced the maximum value of specific energy (J/kg). This explains the greater power reduction observed for this rotational velocity.

#### 4.2.4. Wear Volume

The relationship between the liner volume and simulation time is shown in Figure 18 for the base and intermediate liner parts. It can be noted that wear is more intensive in the base liner, resulting in a more representative volume reduction. The increase in the agitator velocity also intensifies wear. This effect is more representative of the intermediate liner part. This is a consequence of a wider distribution of particle trajectory when operating at higher rotational velocity, as shown in Figure 18.

**Figure 18.** Base and intermediate liner volume during simulation time.

#### *4.3. VTM-1500 Wear Measurement*

Based on the three-dimensional scanning of VTM-1500 liner parts, [30] presented the relationship between operational hours and liner mass, separately for the base and intermediate liner parts.

The absolute mass value was converted as liner volume percentage, and are presented in Figure 19, in relation to the operational time. The wear ratio is defined as the relationship between wear percentage and operational time.

The liner volume comparison between the two liner parts reinforces that wear is more aggressive in the base liner. In this sense, at the end of the lifecycle, or 3000 h, the intermediate liner reached approximately 67% of the initial volume, while the base liner reached 35.5% of its initial volume. Because of that, the base liner requires sooner and more frequent replacement. Moreover, the base liner wear ratio significantly increases after 2000 h.

**Figure 19.** Base and intermediate liner volume reduction during liner operational time (in hours).

#### *4.4. DEM Wear Modeling*

Figure 20 compares the simulated geometry and industrial liner designs under several wear conditions. The visual comparison between wear patterns shows that DEM provided a remarkably similar wear design. The next stage would be to quantify the wear relation. For that, a time relation was established in order to obtain a scale-up factor that correlates simulation seconds and operational hours. The scale-up factors were calculated for the base and intermediate liners, at each operational velocity. The final scale-up factor, per velocity, was obtained as an average value in between the liner and intermediate factors.

**Figure 20.** Comparison between 3D worn screw after DEM simulation and industrial worn liner.

Figure 21 shows the predicted liner volume, based on the obtained DEM model. By comparing the intermediate and base liner predictions, a better agreement was achieved when using the 87 rpm as agitator velocity. In relation to the base liner, the results compared favorably during most of the operational time, except for the last liner measurement, which corresponds to approximately 3000 h. This is probably because the last liner measurement presents an aggressive behavior, which representatively differs from the trend.

**Figure 21.** Model predicted and measured values of base and intermediate liner volume during operational time (h).

For the intermediate liner, the behavior was well predicted up to approximately 1500 h. This is probably due to the fact of filling increases during the liner lifetime. The filling increasing is performed during the liner lifetime with the aim to keep constant power by activating upper parts of the mill. Because of that, added grinding media gets in contact with upper parts of the intermediate liner, thus resulting in additional wear. In contrast, the liner volume predictions for 130 rpm and 190 rpm did not fit very well when evaluating base and intermediate liner parts.

To summarize, it was noted that the wear prediction presented a relative agreement with industrial measurements in the first half of the liner lifecycle. Differently, the agreement was not very effective for the second half of the lifecycle, especially for the intermediate liner part. In relation to the liner part, the disagreement can be explained by the wear compensation in the industrial context. In order to keep constant power consumption, additional grinding media is added to the mill, thus activating the upper parts of the intermediate and generating extra wear. This filling compensation was not taken into account by the DEM simulation, and then it can be expected a lower wear rate and the end of the lifecycle for the intermediate liner part. In relation to the base liner, the differences after 3000 h can be explained by a possible variation in the material properties after several wears, which should be confirmed by liner material properties evaluation. In this sense, the intensive wear could substantially affect liner material resistance properties, thus reducing wear resistance for very worn conditions. This effect was not taken into account by the DEM simulations, resulting in a large difference for the base liner prediction after 3000 h.

#### **5. Conclusions**

Once the vertical stirred mill screw liner is responsible for media movement, and consequently, grinding, it is very important to perform accurate monitoring of wear progress. However, it is not possible to directly install a sensor for wear measurement. The paper addressed this issue by performing DEM simulations, with the aim to provide a better understanding of screw liner wear behavior and effects. The simulation was performed for a 1:10 reduced scale geometry from the Metso Vertimill VTM-1500 model, to reduce simulation effort.

The simulations applied different scale-up methodologies for agitator rotational velocity. In this sense, three different mill velocities were simulated. Firstly, a reduced velocity was obtained based on a dataset model. This consists of a more recent approach for velocity scale-up in laboratory-scale equipment. Moreover, a direct scale-up factor based on the

geometry reduction was applied, thus resulting in a higher operational velocity of 190 rpm. Finally, an intermediary velocity was tested to provide a better understanding of the effects of operating in between the lower and maximum mill velocities.

The wear simulation results qualitatively showed that the wear profile obtained using DEM presents a relative similarity to the wear design observed in the full-scale equipment at the beginning of the liner lifecycle. The worn agitator geometries were exported, at different simulation times, to provide a volume quantification of wear. By comparing worn geometries obtained from DEM simulations and industrial measurement, a time correlation was proposed. In this sense, a scale-up factor was obtained to correlate simulation time, in seconds, and operational time, in hours. This scale-up factor was then applied to simulation results to predict wear in the operational context, for the base and intermediate liner parts. By comparing the obtained wear prediction and industrial measurement, a better agreement was encountered for the 87 rpm mill velocity. Based on that, the recommendation would be to apply the developed model under different operational conditions, to evaluate different strategies for wear compensation, such as changing mill speed and grinding media filling.

Additionally, DEM outputs were evaluated to provide a better understanding of wear effects. From that, it was noted that wear introduced a significant decrease in simulation power and particle average translational velocity. In relation to particle trajectory, the particle velocity reduction was intensified in the top and bottom parts of the mill, thus resulting in null particle motion in those areas. In the bottom part of the mill, this is known as the dead zone effect. The particle collision spectra indicated that wear affects more intensively normal contacts of greater specific energy. Although this might cause a decrease in fines generation, this can lead to an improvement in energy usage. This is because the predominance of low energy contacts is related to an increase in energy efficiency, once this reduces the occurrence of high-intensity contacts, which apply greater energy than required for particle breakage.

To summarize, the obtained results indicate that liner wear affects particle breakage and energy consumption. A better understanding and proper quantification about its effects can play a key role in the development of strategies for optimizing operational procedures to keep grinding efficiency and to reduce wear rates. In this sense, the recommendations would be to evaluate the relationship between operational conditions and liner wear, in the industrial context.

The model did not consider particle breakage, as ore particles itself are not included in the simulation. Grinding media wear also not considered. Finally, the current work did not consider the slurry (fluid), so as there would be a recommendation to apply CFD (computational fluid dynamics) or SPH (smoothed particle hydrodynamics) to describe the mill charge with more details.

**Author Contributions:** P.M.E. wrote the paper and carried out all the experimentation, D.B.M. planned the experimental part and reviewed the paper, R.G. reviewed the paper and L.C.R.M. provided the technical support on the site of Minas-Rio operation. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors thank CAPES and Anglo American for the financial support.

**Acknowledgments:** The authors acknowledge the license of ROCKY Software provided by ESSS and its technical support during the simulations performed. Thanks to Anglo American for the support and permission to publish the results from Vertimill™ laser wear measurement. Thanks to peer reviewers for the comments that significantly contributed to the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

