*3.4. Boundary Definition*

The boundary definition of the geometrical mesh directly affects the computational cost to run the wear simulation, such as the wear results. Figure 6 shows the effect of triangle size in mesh refinement.

**Figure 6.** Boundary definition for the geometrical mesh of the wear parts [29]

The defining of greater triangle sizes decreases the total number of triangles and creates a bad refinement for the mesh, decreasing the computational simulation cost. Contrastingly, the existence of smaller triangle sizes highly increases the number of triangles, refining the

geometrical mesh and causing a representative increase in the computational simulation cost. Figure 7 shows the effect of mesh refinement in the wear simulation results.

**Figure 7.** Effect of boundary definition and mesh refinement in the obtained wear pattern [29].

It is possible to note the final wear shape is affected by a refinement degree. In this sense, the existence of a more refined mesh brings a better wear resolution in the final geometry of the object. However, as finer meshes representatively increase computational cost, it is very important to investigate the sensitivity of mesh refinement degree, to obtain a reasonable balance between wear resolution and feasibility of computational cost [26].

#### *3.5. Industrial Wear Measurement*

The industrial measurements presented were obtained by Silva [30] from the regrinding circuit of the Minas-Rio project, which is an iron ore plant from Anglo American located in the southeast region of Brazil. The regrinding circuit is composed of two parallel lines, each one with eight VTM-1500. The regrinding product is specified with a P80 of 36 μm, mill capacity as 190 t/h per mill, and finally, specific energy is established as 5.9 kWh/t.

The process flowsheet is indicated in Figure 8 and shows that the regrinding circuit is located downstream of the flotation plant [27]. Thus, the regrinding plant is fed with concentrate material, which tends to present greater stability in relation to density and solids concentrate. This creates the perfect space to use this data as input for simulation validation.

**Figure 8.** Minas-Rio process flowsheet [27].

The wear measurements were performed for the base and intermediate liner parts at three different liner lifetimes: 0 h, 1000 h, 2000 h and 3000 h. The measurement was performed using a three-dimensional laser scanning technique. Performing the measurement required to complete stop and unload the mill, as shown in Figure 9.

**Figure 9.** Scanning procedure to obtain a three-dimensional measurement of liner parts [30].

After unloading the mill, a laser device and a reception sensor are used to capture data that is used to generate a three-dimensional geometry of the worn parts. The generated geometry is then compared with the new liner model, in a coordinate system.

The gaps associated with geometrical positions are used to generate a dimensional report and a deviation map, which are later converted into wear quantification. The wear measurements obtained on the VTM-1500 will be presented and used for the comparison to DEM wear simulations.

#### *3.6. Wear Model*

The industrial wear measurements were compared with the DEM simulation results. For that, three-dimensional geometries of the agitator screw were exported at different simulation times. Each geometry was sliced in different liner parts, such as the industrial VTM-1500 design. The Meshlab software was used to calculate the volume of base and intermediate worn liners, thus generating a relationship between liner volume and simulation time.

This result was then compared with industrial wear measurement of the full scale VTM-1500. A liner fitting was established to correlate DEM simulation time (in seconds) and operational time (in hours). This scale-up factor was obtained for each simulation, at different agitator velocities. Finally, the scale-up factor and wear simulation are combined, to predict base and intermediate liners wear. The prediction can then be compared with industrial measurement. The explained process is shown in Figure 10.

**Figure 10.** A flowchart explaining the wear model development based on the DEM model and VTM-1500 equipment.

#### **4. Results**

Results are divided into four sections: Steady-state simulation results, wear simulation results, VTM-1500 wear measurements, and finally, the DEM wear model prediction. The steady-state simulation results are shown in the initial section, as well as the present results that were obtained at the beginning of the simulation, after a minimum of three mill revolutions and before the beginning of the wear simulation. This is defined as steady-state simulation and aims to understand the mill behavior before wear. The second section presents results obtained during the wear simulation, after wear parameters were settled. This comprises of evaluating the simulation outputs, such as wear quantification. The VTM-1500 wear measurement consists of the next stage and is focused on presenting and adapting industrial wear measurements presented by Silva [30]. Finally, the last section comprises the correlation between industrial and simulated wear patterns, such as the presentation of the wear model prediction. This is performed for the three different mill agitator velocities.

#### *4.1. Steady-State Simulation*

#### 4.1.1. Particle Trajectory

Figure 11 shows the particle trajectory colored as a function of particle absolute translational velocity, for the three agitator velocities. A red box was constructed in the surrounding area of the particle trajectory, for the 190 rpm condition. By placing the same box over the particle trajectory of the mills operating at 130 rpm and 87 rpm, it noticeable that the top part of the box is not filled with trajectory streaming lines. This means that the media motion height range is reduced when reducing mill velocity. In other words, it indicates that by increasing mill velocity, the upper parts of the mill were activated.

**Figure 11.** Particle trajectory at different mill rotational velocities.

A dashed red line is placed at the bottom part of the mill. It is visible that streaming lines are also reduced in this bottom area. Because of the reduced motion, this area is identified as "dead zone". The velocity reduction, and thus, the dead zone effect is intensified for reduced mill velocities. This is in accordance with the velocity behavior at the mill top zone. Based on that, it was verified that agitator rotational velocity has a direct effect on the particle trajectory distribution, over the complete height of the mill.

#### 4.1.2. Particle Velocity and Power

Figure 12 shows the particle average translational velocity and simulation power as a function of mill rotational speed. It is conclusive that both particle velocity and power increases with mill speed. This demonstrates that the agitator rotational velocity influences the overall mill power and grinding media kinetic energy, thus having a direct relation in the energy that can be transferred into breakage mechanisms.

**Figure 12.** Left: The relationship between agitator speed and particle average translational velocity (m/s). Right: The relationship between agitator speed and simulation power (W).
