**Gabriel Kamilo Barrios 1,\*, Narcés Jiménez-Herrera 1,\*, Silvia Natalia Fuentes-Torres 1 and Luís Marcelo Tavares 2**

Received: 10 July 2020; Accepted: 12 August 2020; Published: 14 August 2020

**Abstract:** The Discrete Element Method (DEM) is a numerical method that is able to simulate the mechanical behavior of bulk solids flow using spheres or polyhedral elements, offering a powerful tool for equipment design and optimization through modeling and simulation. The present work uses a Particle Replacement Model (PRM) embedded in the software EDEM® to model and simulate operation of a laboratory-scale jaw crusher. The PRM was calibrated using data from single particle slow compression tests, whereas simulations of the jaw crusher were validated on the basis of experiments, with very good agreement. DEM simulations described the performance of the crusher in terms of throughput, product size distribution, compressive force on the jaws surface, reduction ratio, and energy consumption as a function of closed side setting and frequency.

**Keywords:** crushing; jaw crusher; Discrete Element Method; Particle Replacement Model; comminution; simulation; modeling; primary crushing; particle breakage

#### **1. Introduction**

Jaw crushers are widely used in the primary crushing stage and, sometimes, even in the secondary for many applications, including the processing of metallic, non-metallic, energetic, and industrial minerals, as well as in the processing of construction and demolition waste.

Despite the technology being over a century old [1], the original designs of the jaw crushers have been maintained nearly unchanged, taking advantage of the simplicity of their structure and mechanical operation. These features result in ease in manufacturing, repairing, dissembling and low capital cost in comparison to other types of crushers [2].

This machine is composed of two metallic plates forming a V-shape. One of them is fixed while the other swings, moving due to action of an eccentric shaft connected to a motor. When in operation, the ore is fed to the top opening and travels down along the chamber. On its path, the ore is crushed in successive cycles of application of stress, primarily compression, which are applied when the moving plate approaches the fixed plate. In the return movement of the moving plate, the ore particles slip down the chamber until they are stressed once again in the following cycle. The process continues until particles reach a size that is finer than the bottom opening so, in that moment, the ore particles drop out of the crushing chamber [3].

Jaw crushers are robust, being an attractive option in operations where the feed has a coarse top size and a moderate reduction ratio without fines is required [2]. Their performance, in terms of capacity or throughput, power and energy consumption, depends on material properties, equipment design and operating parameters. On one hand, the material characteristics are given by density, hardness, bulk density, particle size distribution, particle top size and particle strength (toughness) and crushability of the feed material [4]. The design parameters of the crusher include the size of the top opening, the set, the volume of the crushing chamber, and the type of jaw surface, which may be smooth or corrugated [5]. The equipment operational parameters include the frequency and amplitude of the movable jaw stroke, the feed rate, the closed side setting (CSS) of the discharge opening, among others [6,7]. It is worth mentioning that the material that is used to line the jaws must be hard and tough in order to endure impact and wear during operation. Some aspects of the crusher materials and a failure analysis of a jaw crusher have been investigated by Olawale and Ibitoye [8].

Different mathematical models have been developed to describe the performance of the jaw crusher. The first generation models were based on empirical expressions to predict capacity [9,10] and energy consumption [10–12]. Later, more robust mathematical models were proposed, based on the population balance model, to represent more details of the machine performance, including the full product size distribution [13]. More recently, a model that describes the kinematics of the equipment to predict flow, capacity, power, among others, has been proposed [14].

Over the last few decades mechanistic approaches that rely on the Discrete Element Method have shown great value in the description of the performance of different types of crushers. Fusheng et al. [15] and Legendre and Zevenhoven [16] performed DEM simulations of size reduction of a single particle in a jaw crusher, in which the bonded particle model (BPM) was used to describe particle breakage. Particle breakage models in DEM usually require significant computational effort and their application in systems with multiple particles, such as those found in crushers operating in industry, may be complex [17]. Among the particle breakage model approaches compared in a recent review by Jimenez-Herrera et al. [16], PRM using spheres was identified as the one with the lowest computational cost, making it attractive to simulate the machine operation in which the feed is constituted by a stream of particles. Indeed, a successful application of PRM has been demonstrated to selected compression crushers, including a jaw crusher [18].

The present work describes the modeling and simulation of a laboratory-scale jaw crusher using DEM with the particle replacement model embedded to describe product size distribution, throughput and crusher power. The PRM has been implemented as a modification of the Hertz-Mindlin contact model, through which each spherical mother particle is replaced by a distribution of daughter spherical particles every time the mother particle is subjected to a force that surpasses a maximum set value. A comprehensive description of the model used is presented elsewhere [19]. DEM simulations were validated on the basis of experiments in a laboratory jaw crusher in the size reduction of a gold ore. Additionally, a sensitive analysis of the simulation model was carried out to investigate the effects of the closed side setting (CSS) and frequency on capacity, power, compressive force and reduction ratio.

### **2. Materials and Methods**

#### *2.1. Materials*

The material used in this study is a gold-bearing ore from the San José mine in Íquira, Huila region, in Colombia. The ore is an intrusive igneous rock from the Ibagué batholith, with phaneritic texture, coarse-to-medium grain sizes, intermediate felsic composition, being predominantly composed of granodiorites. Table 1 presents the mineralogical composition of the Íquira gold ore determined by optical microscopy, which shows that it is composed mainly of quartz and feldspar as main gangue minerals, pyrite, carbonates with a smaller percentage of other metallic minerals such as galena, hematite and arsenopyrite [20].

**Table 1.** Mineral composition of the gold ore from Íquira-Huila

Figure 1 shows a snapshot of the Run of Mine sample collected for testing. The particles were classified into three narrow sizes for testing: 63/53, 31.5/26.5 and 16.0/13.2 mm.

**Figure 1.** Run of Mine sample of the Íquira-Huila gold ore (**a**) and particles classified in narrow sizes (**b**).

#### *2.2. Laboratory-Scale Jaw Crushing Tests*

Figure 2 shows a snapshot of the Otsuka Iron Works Ltd. laboratory-scale jaw crusher used in the present study, which has the universal design [2]. Table 2 summarizes the main operational parameters of the machine, used in the experimental tests. Each batch crushing test was conducted using about 6 kg of sample with particles contained either in narrow sizes or with a distribution of sizes.

The jaw crusher throughput for each experimental test was measured using an integrating load cell coupled to an Arduino UNO data acquisition device. The net power was calculated from measurements with an amperage multimeter, whereas the product particle size distributions were measured using a √ 2 series of sieves in a laboratory sieve shaker.

**Table 2.** Operational parameters used in the laboratory-scale jaw crushing experimental tests

**Figure 2.** Laboratory-scale jaw crusher at the Colombian Geological survey, with the insert showing the top view of the crushing chamber.

Figure 3 shows the jaw crusher scheme indicating the main components of the machine and the operating variables such as the discharge opening and the displacement of the swing jaw.

**Figure 3.** Scheme of the jaw crusher showing the main components of the machine.