*3.2. DEM Simulations of the Laboratory Jaw Crusher*

Figure 8a is a snapshot of the DEM simulation of particles being crushed in the virtual jaw crusher. In this perspective, a view of the breakage of particles, modeled using the Particle Replacement Model, may be observed. On the other hand, Figure 8b shows qualitative results on the velocity profile of the particles along the crushing chamber. In this figure, the higher velocities of the particles appear closer to the discharge, given the greater freedom of the fragments to move downwards in the chamber as they become progressively finer. Such a result shows the capabilities of the DEM model to represent the dynamics of the particles that are expected to appear in real jaw crushers.

**Figure 8.** Perspective view of DEM simulation of the laboratory jaw crusher (**a**) and particle velocities profile through the crushing chamber (**b**).

Figure 9 shows a comparison between the experimental and simulated breakage of a single particle contained in the 63/53 mm range inside the jaw crusher chamber. The DEM simulation coupled to the PRM is capable to provide a valid qualitative representation of fragmentation observed in the experiment.

Experimental

0.00 s 0.06 s 0.58 s

**Figure 9.** *Cont*.

**Figure 9.** Comparison of experimental and simulated breakage of a single 63/52-mm particle in the jaw crusher chamber.

Simulation results are shown in Figure 10 for different feed particle sizes, showing the qualitative results of the particle bed compression within the crushing chamber. The compressive force on the particles is represented by the colored lateral bar. Particle visualization shows the plate zone where the particles are broken according to their sizes and the differences in the stress field exerted on the plates according to particle size. As expected, given the V-shape of the jaw plates, high stresses are experienced at the highest positions along the plate when coarser particles are fed and immediately get in contact with them. However, in order to simulate more precisely the behavior of the ore and conclude about the real stress patterns on the plates, it is necessary to take into account the decompression features of the PRM in the instant in time immediately after particle breakage. Such an improved description could be reached by an improved calibration of the relaxation parameter of the Particle Replacement Model, as presented by Barrios et al. [19].

**Figure 10.** Particle bed compression inside the crushing chamber for different particle size classes fed to the crusher.

An equivalent analysis of the forces exerted on the plates can be seen from direct evaluation of the stress intensity on the plate geometry mesh (Figure 11). The figure is a snapshot of the DEM simulation that shows qualitatively the variation of the compressive force on the geometry of the swing and fixed plates. From the simulation it is observed that the area that is subjected to the highest stresses is located closest to the discharge opening, for all feed sizes. This is consistent with observations by Lindqvist and Evertsson [24], who studied the wear of the plates of a jaw crusher from both experiments and analytical models on the basis of measurement of pressure and forces exerted on the fixed and swing jaws. Figure 11 also shows that, when the crusher was fed with the coarser particles (63/52 mm), the plates were subjected to higher compressive forces.

Validation of the DEM simulation was carried out by comparing it to the experimentally measured values of throughput, power, and product size distribution. For instance, the mean net power demanded in experiments in which the crusher was fed with 63/52 mm material was 0.34 kW, whereas simulations yielded a mean value of 0.32 kW, thus demonstrating the very good agreement.

Figure 12 shows the variation of measured and the predicted net power of the jaw crusher, with good agreement between simulations and experiments. In the experiments, the highest powers were obtained when crushing the coarsest feed particles (63/52 mm). The fluctuation in the values were also found to be smaller for finer feeds. The peaks in power intensity represent the instants in which the machine squeezes and fractures either individual particles or assemblies of particles as they move down the crushing chamber, whereas the low values represent lack of particles being compressed by the crusher plates in those moments in time.

**Figure 11.** Snapshot of the compressive force on the geometries (fixed and swing jaws) for different feed particle sizes.

**Figure 12.** Measured (**a**) and comparison of measured and simulated (**b**) net power of the laboratory jaw crusher.

Figure 13 shows the variation of the throughput during the tests, which demonstrates that an increase in feed size resulted in a reduction in crusher throughput. The figure also shows the good agreement between the DEM simulation results and the measurements using the integrating load cell.

**Figure 13.** Experimental (**a**) and DEM simulations and experiment (**b**) of the laboratory jaw crusher throughput.

A more detailed comparison between experiments and simulation results is presented in Figure 14. The results show the good agreement between the experiments and the DEM simulations, in which the simulations captured very well the trends observed in the experiments regarding the effect of feed particle size on throughput and net power. Indeed, the reduction in throughput as particle size increased was well described by the DEM simulation (Figure 14a), as well as the increase in power required to crush the coarser feed particles (Figure 14b). In addition, Figure 14c compares measured and predicted product size distributions for the case in which the crusher was fed with a particle size distribution (Table 5). It shows very good agreement with the experimental results. Nevertheless, these are limited to the minimum sphere size simulated of 2.36 mm, given the additional computational cost associated to simulating finer particles.

Figure 14d shows the simulated compressive force for different feed particle sizes. The model shows that forces increase with feed particle size. This trend agrees with results from single particle experiments, as demonstrated by Tavares and King [25], as well as results from the present work (Figure 6). Unfortunately, it was not possible to validate this in the present work due to lack of proper instrumentation in the jaw crusher, such as load cells or others sensors, installed on the plates to register the changes in force, as carried out in earlier studies [24,26].

**Figure 14.** Comparison between experiments and DEM simulations for the jaw crusher throughput (**a**), power (**b**) and product size distribution (**c**); simulated trend on the compressive force (**d**). Figures a, b and d presented as a function of mean feed particle size.

#### *3.3. Sensitivity Analysis of the Jaw Crusher DEM Model*

Figure 15 shows the product particle size distributions for different stroke frequencies (Figure 15a) and closed side settings (Figure 15b) from the laboratory jaw crusher DEM simulations. Figure 15a shows a finer product for higher stroke frequencies for the same CCS, whereas Figure 15b shows a finer product for smaller CSS for a fixed value of frequency. A similar behavior of the product size distribution with frequency and closed side setting was found in earlier studies [6,14].

Time series showing the variation of the crusher throughput in the simulations as a function of frequency are presented in Figure 16. These data were extracted from the "particle mass flow sensor" of EDEM and filtered using a statistical moving mean (continuous line). The non-filtered data correspond to the markers. These data were extracted from the virtual experiments that considered a feed composed of multiple sizes operating in partially choke and non-choke feed condition during 7.5 s.

Results show the dynamics of the jaw crusher DEM model and the throughput response to the disturbances given by the stroke frequency of the swing plate. As observed in Figure 16, the DEM simulations respond to the changes in frequency. Additionally, more stable behavior with less scattered results from operation at the frequency of 9.0 Hz.

**Figure 15.** Product particle size distributions for different stroke frequencies and a constant CSS of 7.5 mm (**a**) and for different closed side settings for a fixed frequency of 6 Hz (**b**) in DEM simulations of the laboratory jaw crusher for a feed particle size distribution (Table 5).

**Figure 16.** DEM jaw crusher simulation results showing raw throughput data for different stroke frequencies. Crusher fed with a range of sizes (63–13 mm) and CSS constant at 7.5 mm.

Figure 17 presents results on the sensitivity analyzes of the jaw crusher DEM model with the embedded Particle Replacement Model. It shows the variation of crusher capacity, compressive force, power and reduction ratio as a function of stroke frequency and closed side setting.

From Figure 17a, it is evident that throughput increases with closed side setting. This has been observed in several studies in the literature [6]. Regarding frequency, capacity initially increases, reaches a maximum value and then drops at higher frequencies. This trend is less pronounced for intermediate values of CSS, whereas it disappears at the largest values of CSS, in which throughput increases monotonically with frequency. As such, it is possible to conclude that high values of CSS combined with high frequencies apparently allow reaching the highest throughputs. The variation of throughput as a function of frequency was also described by Rose and English [10] using an analytical model, whereas the relationship among these variables has already been object of simulations by Johansson et al. [14] who found similar trends.

The effect of CSS and frequency on crusher power is shown in Figure 17b. It allows to conclude that power demanded by the jaw crusher increases significantly with frequency as well as with a reduction in closed side setting. A similar general trend was found elsewhere [14].

A further examination on the effectiveness of the crusher can be extracted from analyzing the reduction ratio (*R*80). It expresses the ratio between the feed (*F*80) and the product (*P*80) 80% passing sizes of an operation [27]. Experimentally, it is typically desirable to reach the maximum values of reduction ratio for a given specific energy consumption. From the DEM model (Figure 17c) it is possible to conclude that the highest values of *R*<sup>80</sup> are reached both with the smallest CSS as well as the highest frequency. The same trend was also experimentally found by Fladvad and Onnela [6].

Figure 17d presents the resulting compressive force on the plates as a function of frequency and CSS. The highest compressive forces are achieved with smaller values of CSS. The results also show a modest increase in compressive forces with frequency.

**Figure 17.** Response surface analysis of the jaw crusher DEM simulations showing throughput (**a**), power (**b**), reduction ratio (**c**) and compressive force (**d**) as a function of closed side setting (CSS) and stroke frequency.

#### **4. Discussion**

The DEM simulations results demonstrate the validity of properly calibrated simulations of the jaw crusher performance as a tool for improved design and optimization of industrial equipment. The approach of running simulations at a small (laboratory) scale allows the concept to be proved and the technology to be validated. The following step could be its application in the design of a customized jaw crusher with the aim of improving crusher performance. This could represent, for instance, setting the crusher frequency and stroke amplitude to values that maximize the machine performance for a given feed ore. Other potential applications include analyzes of jaw crusher operational response to fluctuations in particle size distribution in the feed, ore competence, as well as feed segregation. On the other hand, such a tool could be used by equipment manufacturers to customize the machine design in terms of jaw wear surface and crusher chamber geometry.

In particular, the use of PRM is an efficient solution to represent, in a realistic way, the performance of the jaw crusher in terms of throughput, specific energy consumption, compressive force, and product particle size distribution. This model offers some computational benefits in comparison with other DEM breakage methods, such as the Bonded-Particle Model [17]. Among its greatest advantages is its reduced computational effort, ability to describe different loading conditions, ease in model parameter estimation and calibration, besides reasonably good resolution in describing the product size down to relatively fine sizes.

#### **5. Conclusions**

Simulations of a laboratory jaw crusher with a Particle Replacement Model embedded in DEM were able to reproduce the experimental performance of a laboratory jaw crusher in size reduction of a gold ore from the department of Huila–Colombia, in terms of power, throughput, and product size distribution. Very good agreement was observed between measured and predicted results obtained for different feed sizes.

The DEM model demonstrated high sensitivity to changes in CSS and swing jaw frequency, allowing to show some trends in throughput, power, reduction ratio, and compressive force. The trends observed were generally in good agreement with the literature.

Simulations of the jaw crusher incorporating a description of particle breakage can be a useful tool in design and optimization of the machine, since DEM may be an excellent tool to predict machine performance, including assessing measures that are hard to obtain experimentally, such as the stress gradient on the jaw plates.

**Author Contributions:** Conceptualization, G.K.B. and N.J.-H.; methodology, G.K.B.; software, G.K.B.; validation, G.B., N.J.-H. and S.N.F.-T.; formal analysis, G.K.B. and N.J.-H.; investigation, G.K.B. and N.J.-H.; resources, G.K.B., N.J.-H. and L.M.T.; data curation, G.K.B.; writing—original draft preparation, G.K.B., N.J.-H., S.N.F.-T. and L.M.T.; writing—review and editing, G.K.B., N.J.-H. and L.M.T.; visualization, G.K.B. and N.J.-H.; supervision, G.K.B. and N.J.-H.; project administration, G.K.B. and L.M.T.; funding acquisition, G.K.B., N.J.-H., S.N.F.-T. and L.M.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** One of the authors (L.M.T.) would also like to thank funding from the Brazilian Agencies CNPq (grant number 310293/2017-0) and FAPERJ (grant number E-26/202.574/2019).

**Acknowledgments:** The authors wish to thank the Servicio Geológico Colombiano, based on Cali for the support by means of its infrastructure, equipment and laboratories. The authors also thank the EDEM Company for providing the EDEM software by means of "Take EDEM with you" program.

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

#### **References**


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