Rock crushers usually hold the rocks to be crushed in between two solid surfaces and apply a force that forces the molecule of the materials to separate or change alignment. Rock crushers are extensively applied in the mining sector where rocks containing the ore are crushed before the mineral is extracted.

In most cases, mining operations may have more than one crusher depending on the desired outcome of the crushing process. The primary crusher handles course rocks while the secondary, tertiary and sometimes the quaternary works on finer gradations that can allow for effective extraction of minerals.

Unlike the alluvial gold found in river beds, most of the gold mined underground is found in hard rocks that contain a lot of other materials. To get pure gold from these gold-bearing rocks has to be processed. The first stage is to crush the rocks to smaller fine gravels that will allow for gold molecules to be extracted.

The crushing of gold-bearing rocks is not as easy as it may seem. This is because the rocks have to be crushed to very fine gravels that can allow for gold molecules to be dissolved in mercury or any other chemical used to extract gold from the ore. What this means is that in large scale mining the mines may have more than one crusher (primary, secondary and tertiary crushers) in order to achieve the desired crushing levels.

This type of rock crusher employs the compressive force to break up larger rocks into smaller pieces. The crusher has two vertical jaws; a fixed jaw and a swing jaw. The rocks to be crushed are filled into the crushing chamber (the gap between the two jaws) and then a weighted flywheel is used to create an eccentric motion in the swing jaw to provide the required inertia to crush the rocks.

Jew crushers are designed to be heavy duty machines used as the primary crushers in many mining operations. Because of this, the crushers are robustly constructed. The outer shell of the crusher is made from strong steel or cast iron while the jaws are fashioned from hardened cast iron with a Ni-hard or manganese steel removable lining.

Dodge crushers are designed with the swing jaw fixed at the lower end enabling material to be crushed progressively as they move down the crushing chamber. Dodge crusher as more effective in crushing tough and abrasive rocks.

The gyratory crusher works on the same principle as the jaw crusher but has a conical head and a concave surface. The crushing chamber is lined with a hardened manganese steel material. The rock crushing is caused by a circular movement in the crushing surface and the materials are progressively crushed until they are of a smaller size that can fall off the narrow end of the chamber. The gyratory crusher is often used as either primary or secondary crusher in many mining operations as it delivers sufficient force to crush large ore bearing rocks.

The cone crusher is the most widely used crusher in mining operation across the world. The crusher is designed in a similar fashion as the gyratory crusher but the crushing chamber is less steep with the sides near parallel.

Crushing is done by a gyrating spindle as the rocks move from the wider upper section until they are small enough to fall off the lower narrow opening. Cone crushers are perfect for hard to mid hard ore bearing rocks and are highly productive making it perfect for use in crushing intensive mines. There four major types of Cone Crushers

The Symons cone crusher is widely used to crush medium harness to very hard rocks. Its size allows it to be used as a secondary or tertiary crusher in mining operations and as a mobile crusher in building and construction and chemical industries.

As the name suggests a single cylinder hydraulic cone is made up of a single crushing cone, a hydraulic control system, an eccentric shaft, bowl liner, adjusting sleeve and a hydraulic safety system. It is perfect as a secondary or a tertiary crusher in mining.

Impact crushers do not use pressure to crush rocks but rather employ impact. The material is placed in a cage where an impact is used to crush them. The cage has narrow openings to allow crushed rocks of the right size to escape. There are two major types of impact crushers:

Small scale mining continues to contribute significantly to the growth of Ghana's economy. However, the sector poses serious dangers to human health and the environment. Ground failures resulting from poorly supported stopes have led to injuries and fatalities in recent times. Dust and fumes from drilling and blasting of ore present health threats due to poor ventilation. Four prominent small scale underground mines were studied to identify the safety issues associated with small scale underground mining in Ghana. It is recognized that small scale underground mining in Ghana is inundated with unsafe acts and conditions including stope collapse, improper choice of working tools, absence of personal protective equipment and land degradation. Inadequate monitoring of the operations and lack of regulatory enforcement by the Minerals Commission of Ghana are major contributing factors to the environmental, safety and national security issues of the operations.

A DEM model of a toothed double-roll crusher was established based on bonded particle model.Validation in terms of product size distribution was conducted for three groups of tests.The effects of rotation speed and structure of rolls on the crushing process were investigated.The breakage mechanism of the particle was discussed based on fracture dynamics.

A discrete element method (DEM) model of the crushing process of a toothed double-roll crusher (TDRC) is established using the bonded particle model. DEM results and experimental data are compared quantitatively and a relatively good agreement is observed. The effects of rotation speed and structure of crushing rolls on the performance of TDRC are investigated numerically. The results show that when the rolls' speed is relatively high, the nipping condition would be improved, and more cracks could be created to release the increasing strain energy, generating more fractions of small sizes in the products. But, when rolls' speed exceeds 150rpm, the crushing performance would not be significantly improved. A reasonable working gap and better nipping behaviour are obtained using the spiral-tooth-roll or the staggered-tooth-roll. The validated DEM model could be applied to gain a fundamental understanding of the crushing mechanisms of TDRC.

Guoguang Li, Boqiang Shi, Ruiyue Liu, "Dynamic Modeling and Analysis of a Novel 6-DOF Robotic Crusher Based on Movement Characteristics", Mathematical Problems in Engineering, vol. 2019, Article ID 2847029, 11 pages, 2019. https://doi.org/10.1155/2019/2847029

This paper proposes a novel 6-DOF robotic crusher that combines the performance characteristics of the cone crusher and parallel robot, such as interparticle breakage and high flexibility. Kinematics and dynamics are derived from the no-load and crushing parts in order to clearly describe the whole crushing process. For the no-load case, the kinematic and dynamic equations are established by using analytical geometry and Lagrange equation. Analytical geometry is mainly used to solve the inverse kinematics and then establish the velocity relationship between generalized coordinates and actuators. Lagrange equation which takes into account the weight of the mantle and actuators is used to solve driving forces of actuators. For the crushing case, crushing pressure is related to the compression ratio and particle size distribution, but the selection and breakage functions should be established first. Because the trajectory model of the mantle is difficult to be established by using analytical method, it can be obtained by an eccentric simulation. The results of input velocities and driving forces of actuators are distinctive due to the eccentric angle and selection of the initial position. Finally, the proposed approach is verified by a numerical example and then the energy consumption is calculated.

Crushers are commonly used in the mining, construction, and recycling industries to crush a variety of raw materials [1]. Many different types of crushers have been developed over the years, which play a vital role in reducing the particle size of granular solids [2]. As one of the typical crushers, cone crusher is an indispensable piece of equipment [3]. It is typically used in secondary and tertiary crushing stages in minerals processing plants [4, 5]. The mantle and concave are the two main crushing parts. The main shaft of the mantle is suspended on a spherical radial bearing at the top and in an eccentric at the bottom [6]. The crushing action of the mantle around the pivot point is an oscillating motion which can be described with a cyclic function of the eccentric angle. Previous research of scholars has made the performance experience a significant improvement, but cone crusher is inevitably accompanied by high power consumption and low flexibility due to its own structural characteristics. Meanwhile, the parallel robot has received a great concern from many researchers. Compared with serial robot, the parallel robot is a closed-loop mechanism presenting very good potential in terms of high stiffness, large payload, and high speed capability [710]. It has been widely used in many fields, such as medical equipment, entertainment, and factory automation [11]. The forward kinematic solution is more complicated than inverse kinematic solution because of the coupling among actuators. The mantle motion of cone crusher is usually set in advance and then the motors are adjusted, which is similar to the inverse kinematic solution. Contemporary crushers are developing towards intelligence. This paper proposes a novel 6-DOF robotic crusher which has their respective advantages through combining the performance characteristics of the cone crusher and parallel robot.

A novel 6-DOF robotic crusher has achieved both interparticle breakage of a cone crusher and high flexibility of a parallel robot. In order to systematically describe the performance characteristics of the whole crushing process, modeling and analysis would be performed from the no-load and crushing parts. Kinematics and dynamics are essential research issues in evaluating the performance. For the no-load case, the inverse kinematic solution which describes the velocity relationship between generalized coordinates and actuators is established. It plays a vital role in the design and component selection [12]. The dynamics of a 6-DOF robotic crusher are complicated by the existence of multiple closed-loop chains, which have several effects caused by inertia, centripetal, and gravity forces [13]. Dynamic modeling can be used for computer simulation without the need of a real system to test various specified tasks, and it plays an important part in system control [14, 15]. Dynamic equations accounting for the parallel configuration of a 6-DOF robotic crusher can be derived in the task-space through the modeling approach of Lagrange equation which provides a well analytical and orderly structure. For the crushing case, the crushing process can be described by a number of crushing zones. The output from the previous crushing zone is the input for the next crushing zone. Crushing pressure is generated on the surfaces of the mantle and concave, and it is related to the compression ratio and particle size distribution.

The trajectory model of the mantle is an essential element for establishing the kinematic and dynamic equations. But it is very difficult to be established by using analytical method. Taking into account the motion characteristics of cone crusher, a small-scale cone crusher is created and the model is obtained by an eccentric simulation. Then, the mathematical calculation tools, MATLAB and Maple, can be employed to solve the input velocities and driving forces of the actuators.

3D geometric model of a novel 6-DOF robotic crusher is shown in Figure 1, which consists of a fixed unit (CFU) and a drive unit (CDU). The CDU has six actuators. Each actuator is made up of a cylinder and a piston which are connected together by a prismatic joint. The upper and lower ends of each actuator are both spherical joint. A coordinate frame O(X,Y,Z) is attached to the fixed base and the other coordinate frame O1(X1,Y1,Z1) is attached to the mantle.

Particles are squeezed and crushed between the mantle and concave. The transition of the closed side setting (CSS) and open side setting (OSS) is achieved by the extension and contraction of six actuators. The motion of the mantle can be described by a cyclic function of the eccentric angle which represents the angle between the eccentric axis and vertical axis. The final crushed material is excluded from the OSS due to gravity.

A generalized coordinate vector which describes the position and orientation of a 6-DOF robotic crusher is defined as . In Figure 2, the matrix denotes the translation vector of the mantle frame O1,X1,Y1,Z1 with respect to the reference frame . defines an Euler angles system representing orientation of the mantle frame O1,X1,Y1,Z1 in regard to the reference frame O,X,Y,Z [16].

Inverse kinematic is to solve the lengths and velocities of six actuators through the trajectory model of the mantle. The rotation matrix of frame O1,X1,Y1,Z1 relative to the reference frame O,X,Y,Z is given by [14]where

From the geometric model of the 6-DOF robotic crusher, vector can be expressed as [1618]where (i=1,2,,6) denotes the length vector of each actuator, which is Bi to Ai in O-XYZ. (i=1,2,,6) represents the coordinates of Ai(i=1,2,,6) in O1-X1Y1Z1. (i=1,2,,6) denotes the coordinates of Bi(i=1,2,,6) in O-XYZ.

According the principle of virtual work, the generalized force which is projected along the variation of the generalized coordinates can be derived as follows [14, 20]:where F denotes the matrix of six driving forces. Equation (13) has been employed, and then (16) can be rewritten as

The kinetic energy of the mantle includes its translational kinetic energy and rotational kinetic energy with respect to its center of mass, which can be written aswhere Mu denotes the mass of the mantle, is the angular velocity vector of the mantle with respect to the mantle frame, and is the rotational inertia matrix in regard to mass center of the mantle.

In Figure 3, li denotes the length of the ith actuator; gi represents the length between the lower spherical joint and the center of mass. S1 is the length between the lower spherical joint and the center of mass of a cylinder. S2 is the length between the upper spherical joint and the center of mass of a piston [19]. Then, the length gi can be denoted aswhere

As shown in Figure 4, the crushing process can be described by a number of different crushing zones. The feed material is crushed by the interparticle breakage and flows through each crushing zone in the crushing chamber. The material is transformed to the product by a repeated crushing process and crushed once in each crushing zone between the mantle and concave.

In Figure 5, crushing pressure p is generated on the surfaces of the mantle and concave [21]. It is related to the compression ratio and particle size distribution . Compression ratio represents the proportional relationship between compression length and height of crushing zone. Particle size distribution describes the uniformity of the particle size distribution. The compressive ratio is the largest value when the material moves to the closed side. Meantime, the corresponding pressure p is also the largest value of the same horizontal cross section. Crushing pressure p can be represented as

A process model of consecutive crushing events is presented, as shown in Figure 6. The selection function Si describes particles of all sizes which enter a crushing process have some probability of being broken, and the probability is constantly changing as the particle size changes. A certain proportion of particles in each size range are selected for breakage and the remainder passes through the process unbroken during the crushing events. The breakage function Bi reflects the particle size distribution of each size range after particles are broken into smaller fragments.

The process model uses the output from the previous crushing event as input for the next crushing event. Each crushing zone corresponds to a crushing event, and the size-reduction process can be described aswhere P represents the product size distribution and F is the feed size distribution. The total number of crushing events is denoted as n.

Selection and breakage functions can be established by the compression ratio and particle size distribution through the analysis of the experimental results. Thus, S and B can be established aswherewhere ai are fitted constants. xmin represents the minimum particle size of different crushing zones, and xmax denotes the maximum particle size. xi is the particle size distribution of each size range.

In this section, a trajectory model of the mantle is established by an eccentric simulation. The main purpose is to solve the input velocities and driving forces of a 6-DOF robotic crusher. At the same time, it demonstrates the suggested approach can solve the dynamic problem effectively. Furthermore, the power of six actuators and energy consumption are calculated.

The parameters of a 6-DOF robotic crusher are presented in Table 1. The trajectory model of the mantle is an essential element for establishing the kinematic and dynamic equations for the 6-DOF robotic crusher. But it is very difficult to be established by using analytical method.

A small-scale cone crusher is created in a virtual environment by using ADAMS in order to obtain the trajectory model of the mantle, which can be shown in Figure 7. The oscillating motion of the mantle is accomplished by the eccentric simulation. Position and orientation of point O1 relative to the fixed point can be extracted and shown in Table 2.

The movement simulation based on ADAMS is carried out to establish the trajectory model of the mantle for the 6-DOF robotic crusher. Then, the model of the mantle frame O1,X1,Y1,Z1 relative to the reference frame O,X,Y,Z can be described aswhere =1.483rad/s.

The proposed approach is used to solve the kinematic and dynamic equations. Input velocities and driving forces of six actuators have the same time period, as shown in Figures 9 and 10. Input velocities of actuators 4 and 5 are greater than others. Negative value indicates that the actuator is contracting. The values of driving forces are in the interval , and the maximum value is found on actuators 3 and 6. They can be used as a basis for the design and component selection. The difference of the peak value is related to the eccentric angle and selection of the initial position.

Settings of connectors and motions of 3D model in ADAMS are shown in Figure 8 [22]. In order to validate the proposed approach, driving forces of six actuators are simulated by using ADAMS, which are represented in Figure 11. Figures 10 and 11 are obtained by executing the simulation for 20s. It can be observed that the calculated and simulated outputs have good agreements, which indicates the suggested approach of dynamic modeling is suitably selected.

Power of six actuators can be described with a cyclic function of the time, as shown in Figure 12. Power is only related to the payload consumption when six actuators are all expanding, and it has nothing to do with the structure. The energy consumption of the 6-DOF robotic crusher can be mainly divided into two parts: energy consumption during breakage E1 and no-load mechanical energy E0. E1 is obtained by integrating the pressure p over the stroke s and multiplying the cross-sectional surface area A perpendicular to the compressed volume. Similarly, E0 can be calculated by integrating the power of six actuators over the time. Therefore, the energy consumption E of the 6-DOF robotic crusher can be expressed aswhere T represents the crushing period of particles.

A novel 6-DOF robotic crusher was proposed which could achieve both interparticle breakage of a cone crusher and high flexibility of a parallel robot. The kinematic and dynamic models were derived from the no-load and crushing parts in order to systematically describe the performance characteristics. For the no-load case, the kinematic model was established by analytical geometry and Jacobian matrix was conducted. The dynamic model which takes into account the weight of the mantle and actuators was derived based on the Lagrange equation. For the crushing case, the crushing process could be described by a number of different crushing zones. The crushing pressure was related to the compression ratio and particle size distribution, and the closed side was the largest location of the same horizontal cross section. In order to establish the trajectory model of the mantle, a small-scale cone crusher was created and the model was obtained by an eccentric simulation. The result showed that the position and orientation functions changed periodically. Then the mathematical calculation tools, MATLAB and Maple, were employed to solve the input velocities and driving forces of actuators. The suggested approach had been verified by using ADAMS. Input velocity and driving force of each actuator were different due to the eccentric angle and selection of the initial position. Finally, the power of six actuators and energy consumption were given.

Copyright 2019 Guoguang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A prototype DEM cone crusher has been successfully modelled using the PRM approach.The effect of CSS and eccentric speed was compared favourably with literature data.PRM is useful to predict cone crusher performance on product size distribution.

The feasibility of the discrete element method to model the performance of a cone crusher comminution machine has been explored using the particle replacement method (PRM) to represent the size reduction of rocks experienced within a crusher chamber. In the application of PRM, the achievement of a critical octahedral shear stress induced in a particle was used to define the breakage criterion. The breakage criterion and the number and size of the post breakage progeny particles on the predicted failure of the parent particles were determined from the results of an analysis of the experimental data obtained from diametrical compression tests conducted on a series of granite ballast particles. The effects of the closed size setting (CSS) and eccentric speed settings on the predicted product size distribution compare favourably with the available data in the literature.

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