Method for determining optimal grinding medium in grinding process based on discrete element simulation

Abstract

The invention discloses a discrete element simulation-based method for determining an optimal grinding medium in a grinding process, which comprises the following steps of: (1) firstly, determining geometrical characteristics of a ball mill, constructing a ball mill model, and importing the ball mill model into discrete element software; (2) defining material particle parameters and grinding medium parameters respectively; wherein the material particle parameters comprise density, Young modulus, Poisson's ratio and material particle size; (3) grinding medium parameters comprise density, Young modulus, Poisson's ratio, particle size and quantity; (4) carrying out periodic boundary modeling on the ball mill, and setting a material particle cut-off particle size of the discrete element numerical simulation model; (5) based on different grinding medium parameters, respectively researching to obtain a grinding machine torque power curve graph reaching the cut-off particle size of the material particles under different parameter conditions; (6) performing linear fitting on the obtained mill torque power curve graph to obtain an optimal grinding medium; and based on different material particle parameters, the step (4) and the step (5) are repeated, and the optimal grinding medium is obtained. According to the method, the grinding medium under different parameter conditions is simulated and analyzed to correspondingly obtain the torque power curve of the grinding machine, linear fitting is carried out to obtain the optimal grinding medium, and a favorable reference basis is provided for actual industrial production.

Description

Technical Field

[0001] The invention relates to the technical field of ball mill grinding medium selection simulation, and in particular to a method for determining an optimal grinding medium in a grinding process based on discrete element simulation. Background Art

[0002] Ball mill is the most widely used grinding equipment in industry, mainly used in building materials, metallurgy, mining, chemical industry, electric power and other industries. Ball mill lifts the grinding medium to a certain height through the liner to grind mineral particles and abrasives. The proportion of balls of different sizes is called ball grading. When determining the ball grading, the particle size of the material entering the mill should be taken into consideration. When the particle size of the material entering the mill is small, the particle size of the grinding medium needs to be smaller; conversely, when the particle size of the material entering the mill is large, the particle size of the grinding medium needs to be larger.

[0003] The inside of the ball mill is the collision between the material and the grinding medium. The grinding efficiency of the mineral particles depends on the movement of the grinding medium, which in turn depends to a large extent on the working parameters of the ball mill, the structure of the ball mill and the characteristics of the grinding medium itself. The main working parameters of the ball mill that are currently being studied the most are the rotation rate and the filling rate. In addition, the density parameter selection of the grinding medium and the gradation of the grinding medium also play a key role in the grinding effect and energy consumption of the ball mill.

[0004] Existing technologies focus on fine-tuning based on existing working conditions, mainly by changing the ball grading to improve the grinding effect and by selecting ceramic balls to reduce energy consumption. This method does not focus on the interaction between the grinding media and the material particles as a whole in the ball mill, and ignores the impact of this interaction on the grinding effect, which can lead to limited or unstable optimization effects. In addition, when selecting grinding media, grinding media with specific densities are not selected for different materials. Ceramic balls are uniformly selected as grinding media to reduce energy consumption, which results in a reduction in output and specific surface area. In addition, since no comprehensive simulation has been performed, the optimization effect needs to be verified through experiments, which not only requires more time and resources, but the results are also affected by the experimental conditions, resulting in uncertainty in the optimization effect. Summary of the invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a method for determining the best grinding medium in the grinding process based on discrete element simulation, so as to provide a favorable reference basis for actual industrial production.

[0006] Technical solution: The method for determining the best grinding medium in the grinding process based on discrete element simulation of the present invention comprises the following steps:

[0007] (1) Determine the geometric characteristics of the ball mill, build a ball mill model, and import it into discrete element software;

[0008] (2) defining material particle parameters and grinding medium parameters respectively; wherein the material particle parameters include density, Young's modulus, Poisson's ratio, and material particle size; the grinding medium parameters include density, Young's modulus, Poisson's ratio, particle size, and quantity;

[0009] (3) Perform periodic boundary modeling on the ball mill and set the material particle cutoff size of the discrete element numerical simulation model;

[0010] (4) Based on different grinding media parameters, the torque-power curves of the mill that achieve the material particle cutoff size under different parameter conditions are studied separately;

[0011] (5) performing linear fitting on the obtained mill torque power curve to obtain the best grinding medium;

[0012] (6) Study different material particle parameters and repeat the above steps (4) and (5) to obtain the best grinding media.

[0013] Furthermore, in step (3) of the determination method of the present invention, the periodic boundary modeling is that particles escaping from the ball mill from the y+ direction will return to the ball mill from the y- direction, and particles escaping from the ball mill from the y- direction will return to the ball mill from the y+ direction.

[0014] Furthermore, in step (4) of the determination method of the present invention, the mill torque-power curve diagram includes a density-mill torque-power curve diagram, a Young's modulus-mill torque-power curve diagram, a Poisson's ratio-mill torque-power curve diagram, a particle size-mill torque-power curve diagram, and a quantity-mill torque-power curve diagram.

[0015] Furthermore, the density-mill torque power curve diagram of the determination method of the present invention is a mill torque power curve diagram constructed by achieving the material particle cutoff particle size under different density parameters.

[0016] Furthermore, the Young's modulus-mill torque power curve diagram of the determination method of the present invention is a mill torque power curve diagram constructed by respectively achieving the material particle cutoff particle size under different Young's modulus parameters.

[0017] Furthermore, the Poisson's ratio modulus-mill torque power curve diagram of the determination method of the present invention is a mill torque power curve diagram constructed by achieving the material particle cutoff particle size under different Poisson's ratio parameters.

[0018] Furthermore, the particle size-mill torque power curve of the determination method of the present invention is a mill torque power curve constructed by achieving the material particle cutoff particle size under different particle size parameters.

[0019] Furthermore, the quantity-mill torque power curve diagram of the determination method of the present invention is a mill torque power curve diagram constructed by achieving the material particle cutoff particle size under different quantity parameters.

[0020] Further, the linear fitting of the determination method of the present invention is to obtain the optimal grinding medium under the intersection conditions obtained by fitting the density-mill torque power curve, Young's modulus-mill torque power curve, Poisson's ratio-mill torque power curve, particle size-mill torque power curve and number-mill torque power curve.

[0021] Beneficial effects: Compared with the prior art, the significant advantages of the present invention are: the present invention uses discrete element simulation to simulate and analyze the movement and interaction of grinding media with different parameters during the grinding process, and through simulation analysis, determines the optimal grinding media to most effectively transfer energy, reduce invalid collisions and energy waste, and thus reduce energy consumption; for industrial processes that require long-term, large-scale grinding operations, the optimal grinding media can ensure that the particles are subjected to uniform force during the grinding process, thereby reducing over-grinding or insufficient grinding and improving the quality and consistency of the final product. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A front sectional view of a model diagram of a ball mill established by the present invention;

[0023] Figure 2 A side elevational sectional view of a model of a ball mill established in the present invention;

[0024] Figure 3 Schematic diagram of particle flow in a ball mill under grinding media simulated in the present invention. DETAILED DESCRIPTION

[0025] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0026] The models used in the determination method of the present invention include the Hertz-Mindlin (no sliding) and Bonding V2 models.

[0027] The method for determining the best grinding medium in the grinding process based on discrete element simulation of the present invention comprises the following steps:

[0028] (1) Determine the geometric characteristics of the ball mill, build a ball mill model, and import it into discrete element software;

[0029] (2) defining material particle parameters and grinding medium parameters respectively; wherein the material particle parameters include density, Young's modulus, Poisson's ratio, and material particle size; the grinding medium parameters include density, Young's modulus, Poisson's ratio, particle size, and quantity;

[0030] (3) Perform periodic boundary modeling on the ball mill and set the material particle cutoff size of the discrete element numerical simulation model;

[0031] (4) Based on different grinding media parameters, the torque-power curves of the mill that achieve the material particle cutoff size under different parameter conditions are studied separately;

[0032] (5) performing linear fitting on the obtained mill torque power curve to obtain the best grinding medium;

[0033] (6) Based on different material particle parameters, repeat the above steps (4) and (5) to obtain the best grinding media.

[0034] Specifically, the method for determining the best grinding medium in the grinding process based on discrete element simulation includes the following steps:

[0035] (1) Determine the geometric features of the ball mill, determine the coordinate system to construct the ball mill model, and import it into the discrete element software; the coordinate system is constructed with the center of the ball mill body as the coordinate origin, the center direction of the circular side of the ball mill body is the positive direction of the y-axis, the opposite direction of gravity is the positive direction of the z-axis, and the positive direction of the x-axis is determined according to the right-hand rule.

[0036] (2) Define the material particle parameters and grinding medium parameters respectively; wherein the material particle parameters include density, Young's modulus, Poisson's ratio, and material particle size; the grinding medium parameters include density, Young's modulus, Poisson's ratio, particle size, and quantity.

[0037] (3) The ball mill is modeled with periodic boundaries. The periodic boundary conditions allow particles that escape from the computational domain on one side of the boundary to return to the computational domain from the other side. For example, for this ball mill model, particles that escape from the ball mill in the y+ direction will return to the ball mill in the y- direction, and particles that escape from the ball mill in the y- direction will return to the ball mill in the y+ direction. The material particle cutoff size of the discrete element numerical simulation model is set.

[0038] (4) With the density of grinding media as the variable, Young's modulus, Poisson's ratio, particle size and number as the quantitative factors, the mill torque power curve is constructed when the material particle cutoff size is reached by limiting different grinding media densities.

[0039] (5) Taking the Young's modulus of the grinding medium as the variable, and the density, Poisson's ratio, particle size and number as the quantitative values, the mill torque power curve is constructed by limiting the Young's modulus of different grinding media to achieve the material particle cutoff particle size.

[0040] (6) Taking the Poisson's ratio of the grinding medium as the variable, and the density, Young's modulus, particle size and number as the quantitative factors, the mill torque power curve is constructed when the material particle cutoff particle size is reached by limiting the Poisson's ratio of the grinding medium.

[0041] (7) With the particle size of the grinding medium as the variable, and the density, Young's modulus, Poisson's ratio and number as the quantitative factors, the mill torque power curve is constructed when the material particle cutoff particle size is reached by limiting different grinding medium particle sizes.

[0042] (8) With the number of grinding media as the variable, density, Young's modulus, Poisson's ratio and particle size as the quantitative factors, the torque-power curve of the mill is constructed when the cutoff particle size of the material particles is reached by limiting the number of grinding media.

[0043] (9) Linearly fit the mill torque power curve obtained in steps (4) to (8), and use the parameters corresponding to the intersection conditions as the optimal grinding media for the specific material particles.

[0044] (10) Study different material particle parameters and repeat the above steps (4) to (9) to obtain the best grinding media.

[0045] Example 1

[0046] The method for determining the best grinding medium in the grinding process based on discrete element simulation in this embodiment includes the following steps:

[0047] (1) Use 3D modeling software to build a ball mill model and import it into discrete element software; perform numerical simulation modeling on the geometric features of the ball mill, such as Figure 1 and Figure 2 shown.

[0048] (2) Material particles formed by bonding small particles are established according to materials with different grindability. The particle parameters are shown in Table 1 below. The particle sizes of the material particles are 10 mm, 5 mm, 2.5 mm, 2 mm, and 1 mm.

[0049] Table 1 Material particle parameters

[0050] Material Grindability Coefficient <![CDATA[Density / (g / cm 3 )]]> Young's modulus / Gpa Poisson's ratio X1 3.2-6.0 200-400 0.2-0.3 X2 2.3-2.8 5-25 0.1-0.4 X3 3.2-3.6 30-100 0.2-0.5

[0051] (3) Grinding media with different density parameters are selected for materials with different grindability. The parameters are shown in the following table. The number of grinding media is determined to be 40 mm (25 pieces), 30 mm (39 pieces), 25 mm (57 pieces), and 20 mm (159 pieces).

[0052] Table 2 Grinding media parameters

[0053] Grinding media selected according to the material's grindability coefficient <![CDATA[Density / (g / cm 3 )]]> Young's modulus / Gpa Poisson's ratio <![CDATA[X1]]> 5.8-6.8 100-400 0.2-0.3 <![CDATA[X2]]> 3.8-5.8 100-400 0.1-0.4 <![CDATA[X3]]> 3.8-7.8 100-400 0.2-0.5

[0054] (4) The ball mill is modeled with periodic boundaries. The periodic boundary conditions allow particles that escape from the computational domain on one side of the boundary to return to the computational domain from the other side. For example, for this ball mill model, particles that escape from the ball mill in the y+ direction will return to the ball mill in the y- direction, and particles that escape from the ball mill in the y- direction will return to the ball mill in the y+ direction. The material particle cutoff size of the discrete element numerical simulation model is set.

[0055] (5) With the density of grinding media as the variable, Young's modulus, Poisson's ratio, particle size and number as the quantitative factors, the mill torque power curve is constructed when the material particle cutoff size is reached by limiting different grinding media densities.

[0056] (6) Taking the Young's modulus of the grinding medium as the variable, and the density, Poisson's ratio, particle size and number as the quantitative values, the mill torque power curve is constructed by limiting the Young's modulus of different grinding media to achieve the material particle cutoff particle size.

[0057] (7) Taking the Poisson's ratio of the grinding medium as the variable, and the density, Young's modulus, particle size and number as the quantitative factors, the mill torque power curve is constructed when the material particle cutoff particle size is reached by limiting the Poisson's ratio of the grinding medium.

[0058] (8) Taking the particle size of the grinding medium as the variable, density, Young's modulus, Poisson's ratio and number as the quantitative factors, the mill torque power curve is constructed when the material particle cutoff particle size is reached by limiting different grinding medium particle sizes.

[0059] (9) With the number of grinding media as the variable, density, Young's modulus, Poisson's ratio and particle size as the quantitative factors, the torque-power curve of the mill is constructed when the cutoff particle size of the material particles is reached by limiting the number of grinding media.

[0060] (10) Linearly fit the mill torque power curve obtained in steps (4) to (8), and take the parameters corresponding to the intersection condition as the optimal grinding medium for the specific material particles. The model is as follows: Figure 3 shown.

[0061] (11) Study different material particle parameters and repeat the above steps (5) to (10) to obtain the best grinding media.

Claims

1. A method for determining the best grinding medium in a grinding process based on discrete element simulation, characterized in that: The steps include: (1) Determine the geometric characteristics of the ball mill, build a ball mill model, and import it into discrete element software; (2) defining material particle parameters and grinding medium parameters respectively; wherein the material particle parameters include density, Young's modulus, Poisson's ratio, and material particle size; the grinding medium parameters include density, Young's modulus, Poisson's ratio, particle size, and quantity; (3) Perform periodic boundary modeling on the ball mill and set the material particle cutoff size of the discrete element numerical simulation model; (4) Based on different grinding media parameters, the torque-power curves of the mill that achieve the material particle cutoff size under different parameter conditions are studied separately; (5) performing linear fitting on the obtained mill torque power curve to obtain the best grinding medium; (6) Study different material particle parameters and repeat the above steps (4) and (5) to obtain the best grinding media.

2. The method for determining the best grinding medium in the grinding process based on discrete element simulation according to claim 1 is characterized in that: In step (3), the periodic boundary modeling is that particles that leave the ball mill from the y+ direction will return to the ball mill from the y- direction, and particles that leave the ball mill from the y- direction will return to the ball mill from the y+ direction.

3. The method for determining the best grinding medium in the grinding process based on discrete element simulation according to claim 1 is characterized in that: In step (4), the mill torque power curve diagram includes a density-mill torque power curve diagram, a Young's modulus-mill torque power curve diagram, a Poisson's ratio-mill torque power curve diagram, a particle size-mill torque power curve diagram, and a quantity-mill torque power curve diagram.

4. The method for determining the best grinding medium in a grinding process based on discrete element simulation according to claim 3 is characterized in that: The density-mill torque power curve is a mill torque power curve constructed by achieving the material particle cutoff diameter under different density parameters.

5. The method for determining the best grinding medium in the grinding process based on discrete element simulation according to claim 3 is characterized in that: The Young's modulus-mill torque power curve is a mill torque power curve constructed by respectively achieving the material particle cutoff particle size under different Young's modulus parameters.

6. The method for determining the best grinding medium in a grinding process based on discrete element simulation according to claim 3 is characterized in that: The Poisson's ratio modulus-mill torque power curve is a mill torque power curve constructed by achieving the material particle cutoff particle size under different Poisson's ratio parameters.

7. The method for determining the best grinding medium in a grinding process based on discrete element simulation according to claim 3 is characterized in that: The particle size-mill torque power curve is a mill torque power curve constructed by respectively achieving the material particle cutoff particle size under different particle size parameters.

8. The method for determining the best grinding medium in a grinding process based on discrete element simulation according to claim 3 is characterized in that: The quantity-mill torque power curve is a mill torque power curve constructed by achieving the material particle cutoff particle size under different quantity parameters.

9. The method for determining the best grinding medium in a grinding process based on discrete element simulation according to claim 1, characterized in that: The linear fitting is to obtain the optimal grinding medium under the intersection conditions obtained by fitting the density-mill torque power curve, Young's modulus-mill torque power curve, Poisson's ratio-mill torque power curve, particle size-mill torque power curve and number-mill torque power curve.

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