Study on the technical parameters model of the functional components of cone crushers

2.1 Working principle of the cone crusher

When a cone crusher operates, its moving cone surface repeatedly moves towards and away from its fixed cone surface. When the moving cone approaches the fixed cone, the particles between the two cones are crushed under high stress in the extrusion cavity. When particles collide with the moving cone, they are located in between the moving and fixed cones. These particles then fall freely due to gravity. After one cycle, the moving cone contacts the particles again and extrudes them. After several cycles, larger particles are broken down into smaller particles before passing through the discharge mouth. As shown in Figure 1, particulate materials fall and are discharged during most of the cycle; compression only occurs over a short time period. During most of the cycle, the crusher discharges the crushed particles, so it has a large capacity. Particles can be discharged quickly, greatly improving productivity of the crusher.

Figure 1

Diagram of a working cone crusher.

2.2 Kinematic analysis of the cone crusher

If we hold one end of a string, make a ball and fasten it to the other end of the string, and move the ball in a circle, the ball moves in a conical motion. The friction between the cone and ore makes the cone rotate around the axis. However, the rotational speed of the moving cone spinning around the axis is typically 15–20 rad/min, which is too slow to affect the materials. Thus, such conical motion can be described as a periodic oscillatory motion.

The kinetic characteristics of the cone can be determined by analyzing the motion law of any point on the moving cone. As shown in Figure 2, an arbitrary moving point “A” is considered and the cone generates spatial and cyclical vibrations around the suspension point. In direction C (i.e., the operational direction), the largest diameter of the circular route of the moving cone, including the moving cone at the smallest edge of the closed side, is at the open side. Point “B” is on the fixed cone relative to point “O.” Point “A” is at the azimuth angle that the plane makes as it moves through an arc around the suspension point. The arbitrary point “A” on the moving cone goes in and out of the fixed cone along the arc track, changing the shape of the cavity and crushing and discharging the particles.

Figure 2

Arbitrary point on the surface of the moving cone.

Let the angular velocity of the eccentric sleeve be ω, which is also called the implicated angular velocity for convenience. The rotational angular velocity is ω ₁, and the absolute angular velocity is ω ₀. The two are the velocity of the moving cone relative to the eccentric sleeve and the fixed cone, respectively, and the precession Angle is set as γ _0. α is the angle between absolute angular velocity and rotational angular velocity.

The projection relation of ω, ω ₁, and ω ₀ on the ordinate is as follows:

2.3 Preparation of partical simulation

EDEM is the world’s first universal simulation and analysis software based on advanced DEM, which can quickly and easily build parametric models of particle systems. When modeling the shape of iron ore pellets, Barrios et al. [21] proposed two modes: sphere and overlapping sphere, the latter of which has been used by many people in discrete element model simulation for industrial applications involving irregularly shaped particles. Metzger and Glasser [22] used 27 particles to form aggregates with uniform voidage in EDEM software and calculated the size of aggregates by calculating the number of primary particles bonded together at any given time. It is used to simulate the breaking of bonded aggregate in ball mill. In this article, an overlapping sphere model is created in EDEM software for simulation.

Obtain the coordinate information of small particles. First, import the pressure ball model established in the first step (Figure 5a) to make the opening of the two pressure ball models opposite. Then, a particle factory is set up in which the size and number of filling small particles are generated. After the small particles are stabilized, one ball model is pressed on top of another, and the filled particles are compacted into the shape of the particle model we need. After buckle takes shape, the coordinate value information of all small particles is derived by using the final data export function in the post-processing. The coordinate information data in the generated file is transposed in Word and Excel, and then the data is copied and pasted into TXT files (Figure 5b). In the process of data processing, we should pay attention to the following points:

1. All the small particles should be around the origin of coordinates;

2. In the material property setting, small impact recovery coefficient, static friction coefficient, and rolling friction coefficient should be used, which can all be 0.01, so as to eliminate the strain stress after forming as soon as possible;

3. When processing the exported data, the length unit of the coordinate information must be converted to m.

In the process of material property setting, small collision recovery coefficient, static friction coefficient, and rolling friction coefficient should be taken as far as possible. Here we take 0.01 for all of them. As shown in Figure 3c, this is beneficial to eliminate stress and strain as soon as possible after forming.

Figure 3

Simulation of the ball model. (a) The built model. (b) TXT document, and (c) The simulated ball model.

At the beginning of the calculation, the minimum particle radius entering the calculation domain is 10 mm, and the Rayleigh time step adopts this minimum half. After particle replacement, the actual minimum particle size is 3 mm, and Rayleigh becomes smaller and bonding occurs. The contact model itself requires a smaller time step to accurately capture the changes in interparticle bonding forces. So, 5% was used. The time step of proportion is calculated. The properties of particle and equipment plate are shown in Table 1.

The principle of bonding is that small particles are connected into large particles through bond, and the particle breakage is reflected by the fracture of bond. The properties of bonding parameters are shown in Table 2. The crushing simulation process is shown in Figure 4.

Figure 4

Simulation picture of particle breakage. (a) Pre-particle replacement, (b) after particle replacement, (c) before particle crushing and (d) after particle crushing.

3.1 Factors influencing the working performance of the crusher

3.2 Design of the orthogonal test

During experimentation, we set the rotational speed of the moving cone to 250, 350, and 450 rpm, and the base angle of the moving cone to 40°, 45°, and 50°. The precession angle was set to 1°, 1.5°, and 2°. These data are shown in Table 3 to create an orthogonal array.

As shown in Figure 5, the optimization of the key components of the crushing chamber of a cone crusher is mainly analyzed and optimized for the bottom angle of the moving cone, the swing speed of the moving cone, and the precession angle and length of the parallel zone at the lower end of the fixed cone.

Figure 5

Diagram of moving cone combination.

4.1 Test data processing

In this article, orthogonal test is carried out on the experimental scheme [24]. The different parameters in different test groups had different results. We selected “crushing time” and “maximum value of maximum crushing force” as two indicators to analyze the work efficiency and crushing effect of the crusher. By analyzing the data, we described how the various factors affected crushing efficiency and crushing effect. By analyzing the corresponding trends of the different factors, the combination of optimal crushing efficiency and crushing effect was obtained. According to the simulation results, we determined the crushing time and the maximum value of the maximum crushing force from the test groups, as shown in Tables 4 and 5.

The factors that affect the crushing time from most influential to least are C (shape of moving cone), D (rotational speed of moving cone), B (base angle of moving cone), and A (precession angle). Determined by the optimal plan: the optimal plan refers to the optimal level combination of factors within the allowable range of the test. The determination of the optimal level of each factor is related to the test index. If the larger the index is, the better, the higher the index should be, that is, the level corresponding to the maximum value in each column or K _i (i = 1,2,3). Instead, choose a level that makes the index small. In this simulation experiment, time is the index to consider the efficiency of crusher. The shorter the time, the higher the efficiency, so the smaller the index, the better. It is necessary to select the corresponding level of the minimum value in each column or K _i (i = 1, 2, 3).

Therefore, the parameter set that contributes to the best crushing effect is C2D3B3A3, in which the precession angle is 1.5°, the base angle of the moving cone is 50°, the shape is half-cylinder, and the rotational speed is 450 rad/min. Increased maximum crushing force indicates better crushing effect; thus, when analyzing the maximum crushing force, we applied the series in which the factors’ influence and the indicator are directly proportional. The best combination of the levels is A3B3C2D1, in which the precession angle is 2°, the base angle of the moving cone is 50°, the shape is cuboid, and the rotational speed is 250 rad/min.

4.2 Test data verification

The best combination of factors and levels cannot be determined only by indicators. If factors and levels are not appropriate, the optimal scheme will not achieve the test goal. Thus, we must analyze the selected factors and levels to find a new optimal solution that can be verified by drawing tendency charts.

Using the crushing time charts shown in Figure 6, the optimal combination can be determined to have a precession angle of 1.5°, a moving-cone base angle of 50°, a half-cylinder-shaped moving cone, and a rotational speed of 450 rad/min. This optimal scheme is C2D3B3A3 and yields the shortest time for breaking all particle bonds (i.e., the highest level of productivity).

Figure 6

Line charts of crushing time.

Using the charts of maximum value of maximum crushing force shown in Figure 7, the combination of factor levels that yield the best crusher parameters can be determined to be a precession angle of 2°, a moving-cone base angle of 50°, a cuboid moving cone, and a moving-cone rotational speed of 250 rad/min. This design yields the largest maximum crushing force on the particles, which helps achieve the best crushing effect. Thus, the optimal scheme is A3B3C2D1.

Figure 7

Line charts of the maximum value of maximum crushing force.

From these results, we know that these factors have different effects on the indicators; thus, we cannot rank them only by their influences because each indicator has its own optimal scheme. For this reason, we identified an optimized model for the main working parameters of the Y51 cone crusher using the GA-SVW method and artificial intelligence learning (Figure 8). Figure 9 shows the diagram of iterative adaptive, illustrating the adaptability of the optimization model.

Figure 8

Encapsulated module of the optimization model.

Figure 9

Iterative adaptive graph of the model.

4.3 Verification of the cavity after optimization

The selected optimal combination was used as the test group and was tested and analyzed using DEM. The results of the indicators are shown in Figures 10 and 11. The number of bond breakages in the same time indicates that the more the bond breakage, the higher the crushing efficiency.

Figure 10

Crushing time comparison chart. (a) Before optimization and (b) after optimization.

Figure 11

Maximum crushing force comparison chart. (a) Before optimization and (b) after optimization.

As shown in Table 6, after optimization, the time required to break the same number of particle bonds decreased (i.e., productivity improved). The maximum value of maximum crushing force increases compared to that before analysis. During the whole crushing process, the maximum crushing force fluctuates markedly compared with the origin, decreasing the performance after a long operational period due to uneven loading. After analysis, the main moving cone experiences even loading, improving mechanical durability; the working life of the crusher also increases due to even loading.