**1. Introduction**

The reduction of mineral deposits created the necessity for extracting more complex minerals with reduced ore grades and grindability [1]. Consequently, there is an arising need for processing reduced particle size that can propitiate the liberation of valuable minerals for post concentration stages. In this context, additional power is required to achieve a finer grain size. Therefore, grinding and regrinding applications are increasing in importance.

At the same time, grinding is energy inefficient, and this is the main reason why it is pointed as responsible for around 34% to 44% of the energy required in a mineral processing plant [2,3]. The numbers are even more alarming if we consider the situation in a global context. In the 1980s, grinding was responsible for around 3% to 4% of total world electrical energy consumption [2], and more recently, this number was indicated as close to 1.8% [4]. In fact, Napier-Munn went beyond and argued that real energy consumption in grinding is even greater than those numbers, once consumption of liners and grinding media represents a large amount of extra energy. Regardless of which is the correct number, it is conclusive that the grinding process is responsible for a significant portion of the world's power consumption.

Given the rising importance of the representative energy consumption of grinding equipment, it is very important to develop the process of improved energy efficiency. In relation to this issue, Shi (2009) [5] demonstrated that the application of vertical stirred mills presents the energy saving around 30% when compared to tumbling ball mills used for coarse grinding. By applying various methodologies, other researches confirmed the obtained results and reinforced this better energy efficiency behavior for fine-grinding and ultra-fine grinding applications. This behavior is the main reason why vertical stirred mills are pointing as trend equipment for fine-grinding and ultra-fine-grinding applications.

Several approaches for vertical stirred mills modeling can be found in literature, among which stand out the mechanistic approach, Discrete Element Method (DEM), empirical models, and finally, the Population Balance Model (PBM). However, the understanding of the screw liner wear is not well developed yet.

As indicated by Esteves et al. [6], operational costs of vertical stirred mills are divided into electrical energy (50%), balls (40%), and liners (10%). Liner wear intensifies grinding media consumption, increases mill filling, and consequently, affects electrical power consumption. Consequently, liner wear affects all operational costs components, such as maintenance practices and equipment reliability. As highlighted by Allen and Noriega [7], the understanding of liner wear life can also provide information that allows best practices for maintenance schedules that can minimize spare parts and labor costs. Consequently, a better understanding of wear behavior, such as monitoring methods can precisely provide its measurement and/or prediction is a topic of great need in the mineral processing industry. In this paper, DEM simulations are used to predict the screw liner wear behavior of a vertical stirred mill.

Computational simulations based on DEM made many contributions to the science of comminution since its first application by Mishra and Rajamani [8], for the simulation and modeling of tumbling ball mills. According to Weerasekara et al. [9], since the last two decades, the DEM became an essential tool to help design, optimization, and modeling of comminution devices. More recently, there is also an increasing interest in applying the method for the prediction of liners and lifters wear, such as its effects on load behavior.

As there is no available information about how to determine and quantify wear for vertical stirred mills, the approach is based on what is presented for other grinding equipment. The understanding of liner and lifters wear, especially in tumbling mills, is not a new subject in the area, and several papers are found addressing this issue.

In the specific case of wear evaluation, Cleary [10] proposed a method that used DEM to predict liner wear rates and distribution in a 5.0 m diameter ball mill. With a similar approach, Cleary and Owen [11] evaluated wear in a 3D slice of a SAG mill, and finally, Cleary, Sinnott, and Morrison [12] performed an evaluation and comparison between wear in tower and pin mills. Kalala and Moys [13] used DEM to estimate adhesion, abrasion, and impact wear in dry ball mills with further validation with industrial wear measurement. Later, Kalala, Bwalya, and Moys [14] validated the use of DEM for wear prediction in mill liners by comparing normal and tangential forces between experimental data and DEM simulations. More recently, Cleary and Owen [15] simulated liner wear evolution in a Hicom Mill and was able to convert DEM abrasion measurements in a wear rate measurement that was calibrated with experimental data. Boemer and Ponthot [16] established a generic wear prediction procedure applying DEM to a 3D ball mill and validated the results with experimental data obtained in a 5.8 m diameter industrial cement ball. Finally, Xu et al. [17] obtained a numerical prediction of wear in SAG mills using DEM simulations that were quantitatively validated by experiment data available in other researches. In fact, the use of DEM for wear prediction in SAG mills reached such a high level that has recently been used to evaluate operational strategies to account for liner wear.

For the specific case of vertical stirred mills, DEM was first applied by Cleary, Sinnott, and Morrison [12] to investigate the relative performance of stirred mills with two different agitator designs. The paper analysis media flow, energy absorption, flow structures, wear, mixing, and transport efficiency, and allows a good and wide understanding of the performance of vertical stirred mills. For the case of the screw agitator, it can be seen that media motion is a simultaneously lifting and circulating movement inside the equipment. The simulations indicate that the collisional energy associated with media motion is mostly dominated by shear. In relation to media-media and media-liner interactions, shear energy represents more than three times the impact energy. Based on shear energy absorptions, the author infers that the equipment wear is dominated by abrasion and is more intensive on the outer radial edge of the screw. In a slightly different approach, Morrison, Cleary, and Sinnott [18] used DEM to compare the energy efficiency between the ball and vertical stirred

mills in pilot-scale and proposed that the higher efficiency associated with the stirred mill can be explained by analyzing energy spectra associated with collisions frequencies inside the mill. Therefore, the higher energy efficiency of the vertical mill can be explained by the presence of a great number of contacts of low energy. Sinott, Cleary, and Morrison [19] applied DEM to understand how flow and energy are affected by media shape in stirred mills, concluding that grinding performance tends to significantly deteriorate when using non-spherical media. By analyzing rates of shear power absorption, the author also proposes that the increase in non-sphericity of the media can significantly intensify the screws' wear.

In a different approach, Sinott, Cleary, and Morrison [20] evaluated slurry transport inside the mill using the SPH (Smoothed Particle Hydrodynamics) method and based on DEM simulations. Allen and Noriega [7] applied DEM with SPH to understand the screw liner wear. The results demonstrate that shear power is more intensive at the screw outside edges and at the bottom of the mill. This explains why the screw wears from the outside to inside and from the bottom to the top, such as have been seen in the industry. In addition, results indicate that shear power is exponentially related to screw diameter, and consequently, worn screws tend to wear slower as they present smaller diameters. Based on this description, it is possible to note that although DEM is widely applied in the understanding and evaluation of vertical stirred mills performance, the liner wear topic is still superficially approached.

To summarize, the use of DEM to evaluate liner wear in tumbling mills came from a quantitative evaluation and evolved another level. Nowadays, DEM can predict and quantify the wear in SAG and Ball mills, being used in the optimization of materials and operational parameters. Unfortunately, for the case of the vertical stirred mills, the studies are still preliminary and qualitative. Solving this issue requires more in-depth studies and validation with experimental data.

In this paper, the simulation results were compared with industrial measurements performed in Minas Rio Project, an iron ore beneficiation plant of Anglo American, which is in Minas Gerais State, in Brazil. An empirical evaluation of wear is an important tool for validation and calibration of modeling techniques, such as performed by some researches [13,15–17,21,22] for several types of grinding equipment. However, there are few available information about how to determine and quantify wear for vertical stirred mills. Based on that, the approach is based on what is presented for other mills.

The understanding of liner and lifters wear in tumbling mills is not a new subject in the area, and several papers are found addressing this topic. In the case of tumbling mills, the wear profile is commonly estimated in two-dimensional methods, taking the assumption that wear has a uniform profile. More recently, with the advent of new technologies, it is easier to perform three-dimensional measurements, and there are also highly sophisticated devices available [16]. Three-dimensional measurements are being widely used to calculate wear on the surface of liners in grinding equipment, and the technique was successfully used for SAG mills [17,23], and also for a Hicom Mill [15].

#### **2. Gravity Induced Stirred Mill**

Vertical stirred mills are grinding equipment applied for comminution, especially for fine grinding in regrinding applications where feed material is under 1mm. The main parts of the equipment are the grinding chamber, internal liner, screw impeller, screw liner, motor engine, ball feeder, slurry feeder, and the discharge, as shown in Figure 1.

**Figure 1.** Vertical stirred mill components [24].

Figure 2 emphasizes the screw impeller, such as its liner parts. As the screw impeller is responsible for media motion and is currently in contact with media and slurry, it suffers intensive wear. Due to the wear, liner parts required periodic replacement. The liner is divided into several parts, allowing the substitution to be performed differently, according to the wear pattern. The number of parts depends on the equipment supplier and on the equipment size. The liner parts are attached to the screw and protect it from wear.

**Figure 2.** Vertical stirred mill screw liner parts [24].

Figure 3 shows the expected wear shape of the base liner part. From that, it is possible to note that the liner does not suffer homogeneous wear. In this sense, it is expected that the bottom part of the liner suffers more intensive wear at the edges.

**Figure 3.** Wear pattern for the bottom liner [25].

As the liner wears, the total surface area decreases, and consequently, both media motion and power draw decrease. In the operational context, the liner wear compensation is performed by adding additional grinding media to keep constant power draw. In this sense, the liner wear measurement can be estimated and accomplished by measuring mill filling. Although this provides an idea about wear conditions, visual inspections of the liner are necessary. For this inspection, it is necessary to completely empty the mill, in a very effort and time-consuming inspection.

Figure 4 shows the screw liner after completely emptying the mill. It can be seen the difference between a new and an old liner of the VTM-1500. The figure on the left side shows a liner with intensive wear, and the right side shows the replaced liner. From the figure, it can be inferred that wear predominates at the bottom and edges of the screw, causing a great decrease in the screw area.

**Figure 4.** Left: Screw liner with intensive wear at the bottom. Right: New screw liner [6].

Based on what was presented, the aim of this paper is to gather what has already been discussed on the subject and also to propose the use of DEM for evaluating the liner wear during a complete liner lifecycle.

#### **3. Methodology**

#### *3.1. Dem Model Setup*

DEM simulations were performed using the Rocky 4.2.2 software (ESSS, Florianópolis, Brazil). A 1:10 scale version of the Metso Vertimill VTM-1500 (Metso, Helsinki, Finland) was simulated. Table 1 and Figure 5 shows geometry dimensions and screw design.

**Table 1.** Dimensions and operation parameters of VTM-1500 and its scaled-down version considered in the discrete element method (DEM) simulations.


**Figure 5.** Vertimill 1:10 scale of the VTM-1500.

The contact models used in the simulations were Linear Hysteresis for normal forces and Elastic Coulomb for tangential forces [26]. Table 2 summarizes the contact model parameters and materials properties setup used for the simulation.


The simulation was performed only considering grinding media in the grinding environments, in the absence of slurry and ore particles. This can be acceptable for the process where the ore contributions for breakage are negligible, such as in the vertical stirred mills, where the breakage mechanisms are mainly created by the energy involved in grinding media collisions. However, it is also known that grinding media interaction is affected by ore and slurry properties. Consequently, both solids concentration and particle size distribution can affect power consumption and grinding performance. To approximate the slurry effect in the grinding environment, the shear modulus was reduced, thus making contact between balls softer, in comparison to steel-steel contact (Steel: 200 Gpa). This approximates to the ore and slurry interactions behavior.

In relation to the mill rotational speed, three different velocities were simulated: 87 rpm, 130 rpm, and 190 rpm. The 87 rpm was obtained based on a model for velocity scale-up, as proposed by Mazzinghy et al. [27] and adapted by Esteves et al. [28]. The model is based on an equipment dataset and consists of a more recent approach for velocity scale-up. The 190 rpm is obtained considering a fixed tip speed of 3.5 m/s for the mill agitator. This is the usual method for velocity scale-up and was widely applied for reduced scale equipment test work and simulation. The 130 rpm was obtained as an intermediary velocity in between the two scale-up approaches.

#### *3.2. Dem Outputs*

During the simulation, the interaction between particles and geometry is individually described by first physical principles, according to the contact model defined. This information is saved during each simulation step and is further used to generate the simulation outputs, such as: particle energy spectra, particle trajectory, particle absolute translational velocity, power consumption, and wear design.

#### *3.3. Wear Model*

The Archard's wear law, together with the DEM outputs, were used to quantify liner boundary wear. The wear quantification is realized step by step, and this information is used to currently update the liner shape during the simulation. The Archard's wear law is presented by Equation (1) [26]:

$$A. \, dh = \mathbb{K}. \, dw \, \tag{1}$$

where A is the surface area of a boundary element (m2), h is the loss in depth (m), w is the shear work (J), and K is the wear rate (m3/J).

The incremental loss in depth consists of the amount of wear generated in the liner surface. This information is used to currently update the liner shape and volume. The shear work consists of the DEM shear outputs. In this sense, the DEM shear stress results for the interaction between the liner and grinding media are used to continuously quantify the boundary wear. The wear factor is defined as the relationship between the contact energy and the amount of lost surface. A wear factor of 1 × <sup>10</sup>−<sup>6</sup> m3/J was established for the simulation. This indicated the amount of volume that is lost according to the energy amount involved at each contact between grinding media and liner. The increase of these parameters can extremely accelerate the wear ratio. Although the use of greater values can accelerate the obtaining of a wear surface, it can also generate unwanted damages on the surface that are not in accordance with reality. Whereas the use of very small factors can bring the need for a very long simulation to obtain representatives wear information. In the present case, several values were tested, until the obtaining of a feasible shape for the wear. As a result, it is necessary to adapt to the simulation and real time.
