Research on the Wear Behavior of the Fixed Cone Liner of a Cone Crusher Based on the Discrete Element Method.

Taking reducing the wear of the fixed cone liner of a cone crusher as the starting point, the movement and geometry parameters of the cone crusher are studied using the discrete element method. To improve the service life and working efficiency of the whole cone crusher. The UG model and discrete element Yade model of the cone crusher are established, and the different shapes of the tin ore are represented using Yade's preprocessor through eight different ways of particle combination and superposition. The static friction coefficient between the manganese ore and the cone crusher is studied and calibrated using the slope method. The relative error between the Yade and test results is 1.58%, and the calibration result is 0.44. The repose angle of the manganese ore is studied using the collapse method. The repose angle increases with the increase of the static friction coefficient and the dynamic friction coefficient, but the change trend is different. The effect of the dynamic friction coefficient on the repose angle is obviously greater than that of the static friction coefficient. The dynamic friction coefficient obtained by Yade is 0.042. Taking the swing distance, rotating speed, and bottom angle of the fixed cone as the orthogonal experimental factors of Yade, the regression equation of the fixed cone liner was obtained through the nonlinear processing of SPSS 25.0. According to Matlab R2017b, the influences of the swinging distance, rotating speed, and bottom angle of the fixed cone on the fixed cone liner are obtained. According to Yade's research results, the order of the influence degree of liner wear is: the rotating speed of moving cone, the swinging distance of the fixed cone, and the base angle of fixed rotation. When the swinging distance of the fixed cone is 146 mm, the rotating speed of the moving cone is 198 rpm, the fixed rotation bottom angle is 28°, and the minimum value of the liner wear is 23 mm. Yade's results are consistent with the change trend of the wear amount of the bushing obtained from the test. The research results show the correctness of using the Yade method to study the wear of the fixed cone liner of a cone crusher, which provides a theoretical basis for reducing the wear of the fixed cone liner of a cone crusher, and puts forward a new method to study the wear of relevant parts of a fixed cone crusher. At the same time, the research results are of great significance for achieving energy-saving in mining enterprises.

Introduction

It is estimated that in the past five years, the crushers in the China’s mining industry have consumed more than 2.2 million tons of lining materials.[1−3] As the main crushing machine of metal ores, a cone crusher is composed of a fixed cone, a moving cone, an upper and lower frame, an eccentric sleeve, a hydraulic cylinder, etc. In the working process of a cone crusher, the cone crusher constantly impacts the ore with the change of the distance between the moving cone liner and the fixed cone liner to achieve the purpose of crushing. However, because of the rapid wear of the fixed cone liner, the fixed cone liner needs to be replaced frequently.[4−7] The frequent replacement of the fixed cone liner not only affects the working efficiency of the cone crusher, but also costs a lot of money. Therefore, it is very necessary to reduce the wear of the fixed cone liner and improve the service life of the cone crusher. At the same time, reducing the wear of the fixed cone liner is of great significance for achieving high efficiency and energy saving in mining enterprises.

For cone crushers and other mining crushers, the existing research methods are mainly theoretical calculations, finite element analysis, tests, and other methods, to study the wear of key components.[8,9] Martha et al. studied the relationship between the total number of ore fracture keys and the working time in a two-stage crusher using a theoretical calculation method, so as to obtain the optimal crushing time and reduce the energy consumption of the mining machinery.[10] Liang et al. analyzed the influence of the hammer head installation angle on the resultant force of a crusher through a theoretical calculation method, and obtained the growth rate of the resultant force of the crusher.[11] Carradó analyzed the different failure modes of the broken teeth of a double rod crusher in a work through the finite element method, and put forward prevention suggestions for various failure modes.[12] Limanskiy and Vasilyeva observed the movement track of a crusher in the feed port of the gyratory crusher through the finite element method, so as to improve the geometry of the feed port, change the movement track of the crusher, and improve the impact speed between the crushers.[13] Ming et al. analyzed the relationship between the transmissivity of stress wave and the punch impact rate, and the coal rock joint area and the relative density through the finite element software ANSYS. The result shows that when the relative density of the joint contact surface was fixed, the transmissivity of stress wave increased linearly with the increase of the joint contact area, and the transmissivity of stress wave increased nonlinearly with the increase of the punch impact rate. In addition, compared with the coal rock with a small contact area but a discrete distribution, the attenuation of stress wave through the joints with a large contact area and compact distribution is more obvious.[14] Guo et al. analyzed the relationship between the installation angle, length, and biting capacity of the lining plate of a mobile crusher through the test, and finally analyzed the heat-treatment process of the lining plate with the finite element method.[15]

The purpose of this manuscript is to analyze the influence of the swinging stroke of the fixed cone, the rotating speed of the moving cone, and the bottom angle of the fixed cone on the wear of the fixed cone liner using the discrete element method (DEM), and to study the best numerical combination of the minimum wear of the fixed cone liner. In the end, this manuscript provides a theoretical basis for reducing the wear of the fixed cone liner of a cone crusher, and provides a new research method for the optimization of the cone crushers in the future. This manuscript has a practical significance for reducing the production cost and safety risks of an enterprise, improving the service life of the cone crushers and the economic benefits of the enterprise.

At the same time, the contact between a cone crusher and an ore is discontinuous. The traditional finite element method based on the continuous force cannot analyze the crushing mechanism of the ore and the wear of the fixed cone liner. However, in the physical prototype of the tin ore crushing test in the cone crusher, the analysis of the wear characteristics of the fixed cone liner shows a great deviation in the data, it is difficult to extract accurately the relevant data, and the data collection is difficult. The DEM is a numerical method to solve the problem of a discontinuous medium. It has a wide application prospect in geotechnical engineering and environmental engineering.[16−18] From the test results, the research on the wear of the fixed cone liner of the cone crusher using the DEM is still blank, and the DEM in other application fields defines the particle as a rigid body, so it cannot be used to investigate the effect of crushing. In addition, the existing DEM applied in other areas focuses on the feasibility study, but an in-depth analysis of the influence law of the target’s influencing factors was not achieved.

Methods and Materials

Methods

The numerical method used in this study is the DEM. The basic principle of the DEM is to divide the research object into several independent elements, to iteratively calculate the force and motion state between the elements, and finally obtain the motion state and position of the element in each time step. The core of the principle of the DEM is the contact model and Newton’s second law. The contact force between the elements is mainly calculated using the contact model, and the motion state of the elements is mainly calculated by Newton’s second law.[19−21] The soft sphere model is selected based on the DEM,[22] and the internal contact deformation is shown in Figure .

Figure 1

Particle contact deformation.

Particle i contacts with the matched particle j at point C under external action, and finally moves to C′, in this model, the contact force is obtained by calculating the normal overlap α and the tangential displacement δ. When the environment is a soft sphere model and two particles collide, in order to quantify the spring force in the model, each part of the action is split and calculated, as shown in Figure .

Figure 2

Mechanics model of contact force between particles.

The contact model is very important for the simulation results of the DEM. Because there is no adhesion force in the silicon ore, Hertz Mindlin (no slip) built-in in the soft ball model is used as the model between the silicon ore and the silicon ore and the external.[23]

The elastic coefficient in the Hertz Mindlin (no slip) built-in model belongs to the physical characteristic parameter of the particle itself,[24] which is generally calculated using the following formulawhere R is the particle radius; subscripts i and j represent the particle i and particle j in contact with it; E is the particle elastic modulus; v is the particle Poisson’s ratio.

When particle i and particle j are the same material and have the same diameter, then kn can be simplified as

The tangential elastic coefficient kt is obtained from Mindlin contact theorywhere G is the particle shear modulus.

When particle i and particle j are the same material and have the same diameter, then kt can be simplified as

Tin Ore Particle Model of the DEM

As an important industrial mineral, the tin ore is mainly distributed in South China and southwest China.[25] In this study, the tin ores (Figure ) are analyzed. Yade’s preprocessor represents the different shapes of the tin ore by eight different particle combinations (Figure ), and is used to obtain the maximum values of different particles in a three-dimensional coordinate system (Table ).[26]

Figure 3

Tin ore.

Figure 4

Measurement of the repose angle in simulations. (a) Combination mode 1. (b) Combination mode 2. (c) Combination mode 3. (d) Combination mode 4. (e) Combination mode 5. (f) Combination mode 6. (g) Combination mode 7. (h) Combination mode 8.

Table 1

Coordinate Values of Different Particles

combination mode	maximum value in X direction (mm)	maximum value in Y direction (mm)	maximum value in Z direction (mm)
1	150	250	500
2	200	150	400
3	250	200	150
4	450	200	100
5	200	250	150
6	250	400	150
7	200	200	150
8	250	250	150

It can be seen from Figure and Table that the shape and size of particles formed by the eight combined stacking methods are different. Therefore, the virtual particle generator is added to the factories in the Yade preprocessor to generate a fixed number of eight combined particles in a certain period of time.[27]

Dynamic Friction Coefficient of the Tin Ore

Minerals, seeds, and other materials have the properties of particles. The repose angle of a single material particle is affected by its own physical properties and the mechanical coefficient between particles.[28−30] Therefore, this study analyzes the repose angle of the tin ore particles by combining experiments with the DEM. In the laboratory, the repose angle of tin ore particles was measured using a collapsing bucket (Figure ).

Figure 5

Collapsing bucket.

The average value of the values is taken as the measurement result of the repose angle in the test. The repose angle of the tin ore obtained in the test is 23.6°.

A cuboid container with a certain volume is built in Yade, and the particle factory is ordered to generate tin ore particles in the cuboid container. Making one side of the cuboid container rise vertically at a speed of 0.05 m/s, the tin ore starts to move, and flows out of the cuboid container. After all tin ore particles become stable, the rest angle of the tin ore is measured.

Taking and coding the static friction coefficient (X1) and the dynamic friction coefficient (X2) (Table ), the rest angle of the tin ore discrete element model in each case was measured (Figure S1).

Table 2

Factor Level Coding

	factor
code	X1	X2
1.414	0.8	0.08
1	0.7	0.07
0	0.5	0.05
–1	0.3	0.03
–1.414	0.2	0.02

Digimizer was used to measure the simulation results of the orthogonal calibration test. This software can use different scale tools to accurately measure the information in the picture. The measured image is imported into digimizer in the format of the tag image file format, and the orthogonal calibration simulation diagram is drawn using the angle measurement tool in the software (Figure S2). Finally, the rest angle of the tin ore under different values of μ1 and μ2 in this study is obtained (Table S1).

The regression equation model of the repose angle obtained using SPSS 25.0 is as follows

In order to obtain the relationship between the static friction coefficient, the dynamic friction coefficient, and the rest angle more intuitively, the response surface graph is drawn with Matlab R2017b software as shown in Figure .

Figure 6

Angle of the repose response surface.

According to the regression equation and Figure , the rest angle increases with the increase of the static friction coefficient and the dynamic friction coefficient, but the change trend is different. Fixing the dynamic friction coefficient at the zero water level, when the static friction coefficient is at the low water level, the angle of repose increases to a certain extent, when the static friction coefficient is at a high level, the angle of repose increases slightly, but the increase is not obvious; fixing the static friction coefficient at the zero water level, the angle of repose increases with the increase of the dynamic friction coefficient, and the effect is significant. The effect of the dynamic friction coefficient on the repose angle is greater than that of the static friction coefficient.

Fixing the dynamic friction coefficient at the zero water level, when the static friction coefficient is at a low water level, the angle of repose increases to a certain extent. When the static friction coefficient is at a high level, the angle of repose increases slightly, but the increase is not obvious. Setting the static friction coefficient as 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 respectively, and the dynamic friction coefficient as 0.02, 0.04, 0.06, and 0.8, respectively, for the simulation calibration test, finally, the rest angle of tin ore discrete element particles was calculated (Figure ).

Figure 7

Repose angle of tin ore discrete element particles.

From Figure , when the static friction coefficient is 0.1–0.5, the angle of repose increases, and then the value of the angle of repose becomes stable and basically unchanged. When the dynamic friction coefficient is 0.02, the static friction coefficient is in the range of 0.5–1.0, and the rest angle is about 23–24°, which is close to the actual measured rest angle of 23.6°. Therefore, the static friction coefficient is selected as 0.5, and the result is brought into eq to get the dynamic friction coefficient of 0.042.

Figure 10

Calibration result fitting.

The rest angle of Yade is 23.4° and the relative error of Yade is 0.85%. The actual deviation is small, so the calibration test is over.

Static Friction Coefficient of the Tin Ore

Using the inclined plane method as the research method, a plate with a length, a width, and thickness of 420, 310, and 10 mm, respectively, was built in Pro/E and introduced into Yade’s preprocessor. Steel was set as the plate material. As a single particle is easy to roll on the contact material, when establishing the particle model in Yade, it is set that the tin ore group particles are composed of nine tin ore group particle simulation models, so as to ensure that the tin ore group particles do not roll on the contact material, only produce sliding, and the tin ore group particle discrete element model is shown in Figure .[31−33]

Figure 8

Discrete element model of manganese ore group particles.

During the simulations, the particle factory and the upper plane of the plate were set to coincide. The total simulation time is 12 s. Within the first 0.01 s, a tin ore group particle is generated in the particle factory. After 0.01 s, the plate was set to rotate around the fixed axis at a speed of 0.2 rpm (Figure ).[34,35] When the movement of the tin ore occurs, the rotation angle of the plate represents the friction angle.

Figure 9

Schematic diagram of the simulation principle.

In Yade software, the static friction coefficients between tin ore and the contact model are set as 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 respectively.

Yade software was set to save the simulation data at an interval of 0.01 s during the simulations, and then through the post-processing module, the instantaneous sliding time of the tin ore group particles can be obtained, and then the sliding friction angle of the tin ore group particles can be obtained.[36−38] In order to get a more accurate regression model of the sliding friction angle, the test results were processed by SPSS 25.0 software, as follows

Finally, the calibration results of the static friction coefficient of the cassiterite and the steel plate are analyzed and fitted (Figure ).

The measured value of 25.2° of the sliding friction angle from the test is substituted into the regression eq , and the higher-order regression equation is solved by Matlab R2017b, and the static friction coefficient is obtained to be 0.44.

The static friction coefficient is input into Yade, and the simulation verification test is carried out. The virtual test is repeated three times, and the average value of the sliding friction angle is 24.8°. The relative error between the measured value and the real environment is 1.58%. The actual deviation is small, and the calibration test is finished. The final calibration result is 0.44.

Model of Cone Crusher

The geometry of the cone crusher was obtained by field investigation. In order to ensure the accuracy of the calculation results of the DEM as much as possible, in line with the actual situation, based on the size of the three view drawing of the cone crusher, the main dynamic cone part (Figure ) is modeled by UG first, and then the whole cone crusher is modeled based on it (Figure ).

Figure 11

Broken parts of the main dynamic cone.

Figure 12

UG model of the cone crusher.

The UG model is added to Yade through the sub module of geometry, and the internal and external models of the cone crusher in Yade are shown in Figure .

Figure 13

Internal and external models in Yade. (a) Internal model. (b) External model.

In dynamics, the command dynamic cone is linear rotation, rotating speed is 1200 rad/s, start and end time is 2 and 12 s (corresponding to the starting time of the cone crusher).[39−42]

Results and Discussion

Simulation Results of Yade

Other parameters of the tin ore have been set up through the particle factory and existing research.[43−46] The swinging distance, rotating speed, and bottom angle of the fixed cone have been taken as the orthogonal test factors of Yade (Table ). The discrete element calculation simulation has been carried out for the wear amount of the lining plate (Table ), in which the Yade of each serial number has been simulated 10 times.

Table 3

Factor Values

	factor
code	fixed cone swing distance X1/mm	moving cone speed X2/r/min	moving cone bottom angle X3/°
1.682	200	230	30
1	170	200	25
0	150	180	22
–1	130	160	19
–1.682	100	130	14

Table 4

Test Scheme and Results

serial number	fixed cone swing distance X1/mm	moving cone speed X2/rpm	moving cone bottom angle X3/°	wear of fixed cone liner L/(mm)
1	1	1	1	90.09
2	1	1	–1	81.27
3	1	–1	1	62.79
4	1	–1	–1	69.72
5	–1	1	1	30.87
6	–1	1	–1	37.38
7	–1	–1	1	34.65
8	–1	–1	–1	32.76
9	1.682	0	0	89.67
10	–1.682	0	0	35.28
11	0	1.682	0	81.27
12	0	–1.682	0	46.41
13	0	0	1.682	24.78
14	0	0	–1.682	26.25
15	0	0	0	26.46
16	0	0	0	24.78
17	0	0	0	26.25
18	0	0	0	26.46
19	0	0	0	24.78
20	0	0	0	26.67
21	0	0	0	26.67
22	0	0	0	26.04
23	0	0	0	24.15

Analysis and Optimization of Wear

The data in Table were processed and regressed by SPSS 25.0. The regression equation of the wear of the fixed cone liner was obtained as follows

According to the calculation using Matlab R2017b, the influence rule of the fixed cone swing distance, the rotating speed of the moving cone, and the fixed rotation base angle on the fixed cone liner plate are obtained (Figure ).

Figure 14

Response surface. (a)Fixed rotation bottom angle at the zero level. (b) Swinging distance of the fixed cone at the zero level. (c) Rotating speed of the dynamic cone at the zero level.

Figure a–c show the interaction between the fixed cone swing distance and the rotating cone speed on the wear of the fixed cone liner; the interaction between the rotating speed and the fixed rotation base angle on the wear of the fixed cone liner; the interaction between the cone swing distance and fixed rotation base angle on liner wear of the fixed cone liner.

When the swing distance of the fixed cone is at the zero level, the wear decreases first and then increases with the increase of the rotating speed of the dynamic cone, and the wear of the fixed cone liner has a nonlinear relationship with the rotating speed of the dynamic cone; when the rotating speed of the moving cone is at the zero water level, with the increase of the swinging distance of the fixed cone, the wear amount decreases first and then increases. The wear amount of the fixed cone liner plate also has a nonlinear relationship with the swinging distance of the fixed cone.

When the rotating speed of the moving cone is at the zero water level, the wear amount of the fixed cone liner shows a downward trend with the increase of the fixed rotation base angle; when the fixed rotation base angle is at the zero water level, the wear amount of the fixed cone liner shows an upward trend with the increase of the rotating speed of the moving cone.

When the swing distance of the fixed cone is at the zero water level, the wear amount of the fixed cone liner decreases slightly with the increase of the fixed rotation base angle, which shows that the change of the fixed rotation base angle has little effect on the wear amount of the fixed cone liner; when the fixed rotation base angle is at the zero water level, the wear amount of the fixed cone liner decreases with the increase of the fixed cone swing distance.

It can be seen from the quadratic regression equation model of the wear amount and the response surface of wear amount that within the range of orthogonal test factors, the significant influence order of three factors on the wear amount is as follows: the rotating speed of the moving cone has the largest influence on the wear amount, the swinging distance of the fixed cone is the second, and the fixed rotation base angle has the smallest influence on the wear amount. The results show the relationship between some geometric parameters, motion parameters, and the wear amount of the fixed cone liner. It provides a new method and idea for the research and reduction of the wear amount of the fixed cone liner. It also provides a theoretical reference and basis for optimizing the cone crusher, improving the service life of the cone crusher, and reducing the production cost of the enterprise and potential safety hazards.

Let F(min) = L, its constraint range is constructed using the data given in Table

According to eq , the equation of the wear of the fixed cone liner plate is solved in Matlab R2017b, and the final result is: when the swing distance of the fixed cone is 146 mm, the rotating speed of the moving cone is 198 rpm, the fixed rotation bottom angle is 28°, the wear amount is the smallest, and the result is 23 mm.

Test Verification

In order to ensure the smooth development of the test, the fixed rotation base angle is set at 25°. Through Yade’s postprocessor, the wear of the liner plate was obtained when the swinging distance of the fixed cone was 100, 130, 150, 170, and 200 mm, and the rotating speed of the moving cone was 130, 160, 180, 200, and 230 rpm. The corresponding test values are obtained using a laser measuring instrument, and the comparison results are as follows (Figure ).

Figure 15

Comparison of the results of wear.

By analyzing the wear of Yade and the test, it is found that when the swinging distances of the fixed cone are 100, 130, 150, 170, and 200 mm, with the increase of the rotating speed of the dynamic cone from 130 to 230 rpm, there are some deviations in the wear of the test and simulations under different swinging distances of the fixed cone, but the change trend of the test and simulation results is basically the same. The results of simulations are slightly less than those of experiments. The main reasons for this phenomenon are: in the simulation of Yade, the cone crusher and the tin ore are in the ideal state, and the surfaces of the fixed cone liner and the tin ore are clean enough. In the process of the test, the fixed cone liner and tin ore will inevitably be mixed in the extra impurities. The change of the distance between the moving cone liner and the fixed cone liner is essential to crush the tin ore and impurities. At the same time, the extra impurities increase the surface roughness of the fixed cone liner and the tin ore, which further aggravates the wear of the fixed cone liner in the test, resulting in the wear of the test is greater than that of the simulations.

Under the same cone swing distance, when the rotating speed of the dynamic cone is lower than 180 rpm, the wear amount of the simulations and the test decreases gradually with the increase of the rotating speed of the dynamic cone. When the rotating speed is greater than 180 rpm, the wear of the simulations and the test increases with the increasing rotating speed of the dynamic cone. The maximum difference between the test results and the simulation results is 6.01 mm. In conclusion, it can be seen from the analysis that there is a certain deviation between the test and the wear amount of the cone-shaped liner obtained from Yade simulations, but the trend of the change of the test and the wear amount obtained from Yade simulations is consistent, which proves the correctness of the study on wear of the cone liner of the cone crusher by Yade.

Conclusion

This study analyzes the relationship between the geometric parameters, motion parameters, and the wear of the fixed cone liner in the working process of a cone crusher, which not only plays an important role in the service life and working efficiency of the whole machine, but also provides a preliminary research basis for achieving high efficiency and energy saving in the mining industry. Based on the soft sphere model of the DEM, the different shapes of the tin ore are represented by Yade’s preprocessor through eight different particle combinations. In this paper, the static friction coefficient between the cassiterite and the cone crusher is studied and calibrated using the slope method. The relative error between the Yade and test results is 1.58%, and the calibration result is 0.44. The repose angle of the tin ore is studied using the collapse method. The repose angle increases with the increase of the static friction coefficient and the dynamic friction coefficient, but the change trend is different. The influence of the dynamic friction coefficient on the repose angle is obviously greater than that of the static friction coefficient. The dynamic friction coefficient obtained by Yade is 0.042. The discrete element model of the cone crusher is established by UG 23.0 and Yade. The simulation using the DEM provides a new idea and method for the study of the wear of the fixed cone liner, which has important theoretical significance and a strong engineering application value. In addition, based on Yade’s three factor five level quadratic orthogonal rotation-combined simulation experiments, the regression equation of the wear amount of the fixed cone liner was established using SPSS 25.0 and variance analysis was carried out. The corresponding response surface was obtained using Matlab R2017b. The results show that the relationship between the wear of the fixed cone liner and the swing distance of the fixed cone, the rotating speed of the moving cone, and the base angle of the fixed rotation is nonlinear. The influence rule of the factors studied on the wear of the fixed cone liner is determined: the rotating speed of the moving cone has the greatest influence on the wear of the fixed cone liner, the swing distance of the fixed cone takes the second place, and the fixed rotation base angle has the least influence on the wear of the fixed cone liner. Using Matlab R2017b, the equation of the wear amount of the fixed cone liner was solved. Finally, when the swing distance of the fixed cone was 146 mm, the rotating speed of the moving cone was 198 rpm, the fixed rotation bottom angle was 28°, the wear amount was the smallest, and the result was 23 mm. According to the comparison between the bench test and Yade virtual simulation test results, there is a certain deviation in the value of the wear of the cone liner obtained from the simulation and test results, but the change trend and the relationship between them are consistent. Therefore, it is feasible to use the DEM to analyze the wear of the fixed cone liner of the cone crusher, and the research results will play an important role in improving the service life and working efficiency of the whole cone crusher in the future. At the same time, the research results are of great significance for achieving high efficiency and energy saving in the mining industry.