Particle packing theory-based method for grinding medium gradation simulation of ball mill

Abstract

The present invention relates to the field of grinding medium gradation simulation of ball mills. Disclosed is a particle packing theory-based method for grinding medium gradation simulation of a ball mill. The method comprises the following steps: establishing a numerical simulation coordinate system of a ball mill; performing discrete element numerical simulation and modeling on grinding media and material particles; performing periodic boundary modeling on the ball mill, and setting cut-off particle sizes of the material particles; adjusting the cut-off particle sizes of the material particles on the basis of a particle amount in the discrete element numerical simulation model; comparing simulation results of the different cut-off particle sizes to determine a cut-off particle size interval; performing coarse-grained modeling on the material particles in the ball mill, and correspondingly adjusting the width of a periodic boundary; and calculating the grinding effect of the material particles under different grinding medium gradations; and adjusting a particle size gradation of the material particles to obtain an optimal grinding medium gradation design. The optimal grinding medium gradation scheme and the adjusting method under different working conditions obtained according to the present invention can reduce the cement production cost.

Description

A simulation method for ball mill grinding media gradation based on particle packing theory Technical Field

[0001] The invention relates to the field of ball mill grinding medium gradation simulation, and in particular to a ball mill grinding medium gradation simulation method based on particle accumulation theory. Background Art

[0002] Ball mills are the most widely used industrial equipment for re-grinding crushed materials, primarily in the building materials, metallurgy, mining, chemical, and power industries. Ball mills use lining plates to elevate grinding media (primarily steel or ceramic balls) to a certain height, where they perform dry or wet crushing and grinding of mineral particles and abrasives. The ratio of grinding media of varying particle sizes is called the grinding media gradation. This gradation is determined based on the particle size of the feed material. Smaller feed materials require smaller grinding media; larger feed materials require larger grinding media.

[0003] Inside a ball mill, particles collide with each other. The grinding efficiency of mineral particles depends on the movement of the grinding media, which in turn is largely determined by the mill's operating parameters, structure, and the characteristics of the grinding media. The most studied operating parameters of a ball mill are rotation rate and fill rate. In addition, the grinding media material and gradation also play a key role in the mill's grinding performance and energy consumption.

[0004] Existing technologies focus on fine-tuning existing operating conditions, primarily by changing the grinding media gradation to improve the grinding effect. This approach ignores the interaction between the grinding media and the material particles within the ball mill, neglecting the impact of this interaction on the grinding effect, resulting in limited or unstable optimization results. Furthermore, without comprehensive simulation, the optimization results must be verified through experiments, which not only requires more time and resources, but also results are affected by experimental conditions, resulting in uncertainty in the optimization results. Summary of the Invention

[0005] The present invention provides a ball mill grinding media gradation simulation method based on particle accumulation theory. The purpose is to obtain the interaction relationship between grinding media and cement particles under different grinding media gradations and cement particle size distributions through discrete element numerical simulation methods and coarse granulation models, thereby realizing the optimization of grinding media gradation in the ball mill.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A ball mill grinding media gradation simulation method based on particle accumulation theory includes the following steps:

[0008] Step 1: Create a ball mill geometric model and establish a numerical simulation coordinate system for the ball mill;

[0009] Step 2: Based on the numerical simulation coordinate system, discrete element numerical simulation modeling is performed on the grinding media and material particles in the ball mill to obtain a grinding media and material particle model;

[0010] Step 3: Perform periodic boundary modeling on the ball mill, set the material particle cutoff size of the discrete element numerical simulation model, and obtain a periodic boundary model;

[0011] Step 4: Adjust the cutoff particle size of the material particles according to the particle amount in the discrete element numerical simulation model;

[0012] Step 5: Compare the simulation results of different cut-off particle sizes to determine the feasible cut-off range of the material particle size;

[0013] Step 6: Coarse-grained modeling is performed on the material particles in the ball mill to obtain a particle coarse-grained model, and the width of the periodic boundary is adjusted;

[0014] Step 7: numerically simulate the grinding effect of material particles under different grinding media gradations;

[0015] Step eight, adjust the particle size distribution of the material particles to obtain the grinding medium distribution design.

[0016] Furthermore, the numerical simulation coordinate system in step 1 is:

[0017] The center of the circular side of the ball mill body is taken as the coordinate origin, the direction pointing to the center of the circular side of the other 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 of the coordinate system.

[0018] Furthermore, the discrete element numerical simulation model in step 2 depends on the parameters of the total mass, density and particle size of the grinding media and the material particles.

[0019] Furthermore, in step three, the periodic boundary model supports that particles in the computational domain that escape from the ball mill in the positive direction of the y-axis will return to the ball mill in the negative direction of the y-axis, and particles that escape from the ball mill in the negative direction of the y-axis will return to the ball mill in the positive direction of the y-axis.

[0020] Furthermore, in step three, the maximum particle size of the grinding media and material particles in the ball mill is less than 0.4 times the width of the periodic boundary.

[0021] Furthermore, in step 4, the cutoff particle size of the material particles in the discrete element simulation model is increased so that the number of particles in the calculation domain of the periodic boundary model is less than a predetermined value.

[0022] Furthermore, in step six, when calculating the interaction on the coarse-grained model, the speed-up factor of the calculation speed is the cube of the magnification factor of the cutoff particle size of the material particles in the discrete element simulation model.

[0023] Furthermore, step seven is to conduct a numerical simulation study on the grinding effect of material particles in the ball mill under different grinding media gradations based on the ball mill geometry model, grinding media and material particle model, periodic boundary model, material particle cutoff particle size, and particle coarsening model.

[0024] Furthermore, in step eight, based on the output of cement grinding products per unit time and the energy consumption per unit cement product, different particle size gradations of the material particles are used to obtain the respective optimal grinding media gradations.

[0025] Compared with the prior art, the beneficial technical effects of the present invention are:

[0026] This application uses numerical simulation to model the interaction between the grinding media and the material particles within the ball mill. This fully considers the impact of this interaction on the sanding effect, allowing for more precise optimization of the grinding media gradation and ball mill operating conditions, resulting in better sanding results. Furthermore, using numerical simulation for optimization design allows for the acquisition of optimization results on a computer without the need for experimental verification, saving time and resources while also preventing the impact of experimental conditions on the results, increasing the certainty of the optimization effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG1 is a schematic diagram of a ball mill device provided in an embodiment of the present invention;

[0028] FIG2 is a front cross-sectional view of a ball mill body provided by an embodiment of the present invention;

[0029] FIG3 is a side sectional view of a ball mill body provided by an embodiment of the present invention;

[0030] FIG4 is a schematic diagram of concentrated particle flow in a ball mill under different grinding media gradations provided by an embodiment of the present invention.

[0031] In the figure: 1. Ball mill body; 2. Periodic boundary modeling area. Modes for Carrying Out the Invention

[0032] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. Before describing in detail the technical solutions of each embodiment of the present invention, the nouns and terms involved are explained. In this specification, components with the same name or the same number represent similar or identical structures and are for illustrative purposes only.

[0033] Explanation of terms

[0034] Particle gradation, also known as particle size gradation, refers to the number of particles of each size in a bulk material composed of different particle sizes. It is usually expressed as a percentage of the total amount.

[0035] A preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0036] A ball mill grinding media gradation simulation method based on particle accumulation theory in the present invention comprises the following steps:

[0037] Step 1: Create a ball mill geometric model and establish a numerical simulation coordinate system for the ball mill.

[0038] To perform numerical simulation modeling of the ball mill's geometric features, the coordinate system must first be determined. Refer to Figures 1, 2, and 3. The coordinate origin is the center of the circular side of the ball mill body 1. The direction pointing toward the center of the other circular side of the ball mill body is the positive y-axis direction. The direction opposite to gravity is the positive z-axis direction. The positive x-axis direction is determined using the right-hand rule.

[0039] Step 2: Perform discrete element numerical simulation modeling on the steel balls and material particles in the ball mill to obtain the grinding medium and material particle models.

[0040] The modeling properties of the steel balls and material particles are set as follows:

[0041] Steel ball: Density: 7850kg / m 3 , particle size: 20mm, 17mm, 15mm, 13mm, 10mm (adjustable)

[0042] Material particles: density: 3100kg / m 3 , particle size: 10mm, 5mm, 2mm, 1mm, 0.5mm, 0.2mm, 0.08mm, 0.045mm (of which material particles of 0.2mm and below account for more than 50%)

[0043] The mass of steel balls in the ball mill is 400 kg, and the mass of material particles in the ball mill is 80 kg.

[0044] Step three: perform periodic boundary modeling on the ball mill, set the material particle cutoff size of the discrete element numerical simulation model, and obtain a periodic boundary model.

[0045] Periodic boundary conditions are a common method for simplifying simulation models and improving computational speed while ensuring numerical simulation accuracy. Periodic boundary conditions allow particles that escape the computational domain from 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 y- direction will return to the ball mill in the y+ direction. Calculations under periodic boundary conditions generally require that the maximum particle size of the steel balls and material particles in the model be less than 0.4 times the width of the periodic boundary. As shown in Figure 2, a section of at least 50 mm in length is intercepted at the y-center of the ball mill body 1 for periodic boundary simulation, serving as periodic boundary modeling region 2.

[0046] By cutting off a 50mm length of ball mill for periodic boundary simulation, the mass of the steel balls in the periodic domain is 20kg, and the mass of the material particles is 4kg. This can reduce the original particle amount to 1 / 20 of the initial conditions, which can significantly reduce the amount of calculation. 0.2mm is set as the cutoff particle size of the material particles (the cutoff particle size is defined as the minimum particle size of the material particles in the numerical simulation model, and particles smaller than this particle size are represented as particles of this particle size). The number of particles in the periodic domain is calculated to be approximately 1.18×10 8 indivual.

[0047] Step 4: According to the particle amount in the discrete element numerical simulation model, the cut-off particle size of the material particles in the ball mill is adjusted.

[0048] When the number of particles in the discrete element simulation exceeds 10 million, the computational efficiency will be greatly reduced. The cutoff particle size of the material particle simulation is adjusted to avoid the number of particles exceeding 100 million. By adjusting the cutoff particle size to 0.5 mm, the number of particles in the periodic calculation domain is about 1.18×10 7 The cut-off particle size is adjusted to 1 mm, and the number of particles in the periodic calculation domain is approximately 1.72 million.

[0049] Step 5: Compare the simulation results of different cut-off particle sizes to determine the feasible cut-off range of the material particle cut-off particle size, that is, verify the adjustment of the material particle cut-off particle size in the ball mill.

[0050] In a ball mill, large steel balls crush large particles, while small steel balls grind small particles. If the particle cutoff size is too large, the final optimization simulation result may be to use as many large steel balls as possible. Therefore, we compared the simulation results for different cutoff sizes and determined the feasible cutoff range through a cutoff size independence experiment.

[0051] Step 6: Coarse-grained modeling is performed on the material particles in the ball mill to obtain a particle coarse-grained model, and the width of the periodic boundary is adjusted.

[0052] Coarse-grained modeling is a method for reducing the total number of particles in a simulation by using larger particles to represent the original (smaller) particle group. Contact, adhesion, and other models must be modified to account for interactions on this scaled-up system, making the dynamics of the scaled-up system similar to those of the original system. Proper coarse-grained modeling can significantly improve computational efficiency while maintaining accuracy. Because the maximum particle size should be less than 0.4 times the width of the periodic boundary, the width of the periodic boundary should be increased by a corresponding factor when coarse-grained modeling is used.

[0053] After calculation, the number of particles and calculation speed before and after amplification are as follows:

[0054] After the particle size is enlarged, the increase in calculation speed is linearly related to the reduction in the number of particles on the one hand, and linearly related to the enlargement of the particle size on the other hand. Therefore, the speed increase after enlargement is the cube of the enlargement factor.

[0055] Table 1 Comparison of cut-off particle size magnification and calculation speed increase

[0056]

[0057] The simulation results of different magnification factors are compared, and the feasible range of magnification is determined through the magnification independence experiment.

[0058] Step seven, perform numerical simulation calculation on the grinding effect of material particles under different grinding media gradations.

[0059] As shown in FIG4 , based on the ball mill geometric model, steel ball and material particle model, periodic boundary model, material particle cutoff size, and particle coarsening model established in steps one to six, a numerical simulation study is conducted on the grinding effect of material particles in the ball mill under different steel ball gradations.

[0060] Step 8: Adjust the particle size distribution of the material particles according to the working conditions and select the optimal design of the grinding medium distribution.

[0061] The ball mill steel ball gradation demand design is carried out according to the needs. The cement grinding product output per unit time and the energy consumption per unit cement product are used as the evaluation response targets. The particle size gradation of the feed material particles is adjusted to obtain the optimal steel ball gradation design and the influence of steel balls of different sizes on the ball mill grinding output and grinding energy consumption, and further obtain the optimal coordination of the steel ball gradation-feed material particle gradation combined system.

[0062] The above-described embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A ball mill grinding media gradation simulation method based on particle stacking theory, characterized in that: The following steps are involved: Step 1: Create a ball mill geometric model and establish a numerical simulation coordinate system for the ball mill; Step 2: Based on the numerical simulation coordinate system, discrete element numerical simulation modeling is performed on the grinding media and material particles in the ball mill to obtain a grinding media and material particle model; Step 3, performing periodic boundary modeling on the ball mill, setting the material particle cutoff size of the discrete element numerical simulation model, and obtaining a periodic boundary model; Step 4: adjusting the cut-off particle size of the material particles according to the particle amount in the discrete element numerical simulation model; Step 5, comparing the simulation results of different cut-off particle sizes, and determining the feasible cut-off interval of the material particle cut-off particle size; Step 6, coarse-graining modeling is performed on the material particles in the ball mill to obtain a particle coarse-graining model, and the width of the periodic boundary is adjusted; Step 7, performing numerical simulation calculation on the grinding effect of material particles under different grinding medium gradations; Step eight, adjust the particle size distribution of the material particles to obtain the grinding medium distribution design.

2. A ball mill grinding media gradation simulation method based on particle accumulation theory according to claim 1, characterized in that: The numerical simulation coordinate system in step 1 is: The center of the circular side of the ball mill body is taken as the coordinate origin, the direction pointing to the center of the circular side of the other 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 of the coordinate system.

3. According to the method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory as claimed in claim 1, it is characterized in that: The discrete element numerical simulation model in step 2 depends on the parameters of the total mass, density and particle size of the grinding media and material particles.

4. The method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory according to claim 1, characterized in that: In step 3, the periodic boundary model supports that particles in the computational domain that leave the ball mill from the positive direction of the y-axis will return to the ball mill from the negative direction of the y-axis, and particles that leave the ball mill from the negative direction of the y-axis will return to the ball mill from the positive direction of the y-axis.

5. The method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory according to claim 1, characterized in that: In step 3, the maximum particle size of the material particles in the ball mill is less than 0.4 times the width of the periodic boundary.

6. The method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory according to claim 1, characterized in that: In step 4, the cutoff particle size of the material particles in the discrete element simulation model is increased so that the number of particles in the calculation domain of the periodic boundary model is less than a predetermined value.

7. The method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory according to claim 1, characterized in that: In step six, when calculating the interaction on the coarse-grained model, the speed-up factor of the calculation speed is the cube of the magnification factor of the cutoff particle size of the material particles in the discrete element simulation model.

8. The method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory according to claim 1, characterized in that: Step seven is to conduct numerical simulation research on the grinding effect of material particles in the ball mill under different grinding media gradations based on the ball mill geometry model, grinding media and material particle model, periodic boundary model, material particle cutoff particle size, and particle coarsening model.

9. The method for simulating the gradation of grinding media in a ball mill based on particle accumulation theory according to claim 1, characterized in that: In step eight, based on the output of cement grinding products per unit time and the energy consumption per unit cement product, different particle size gradations of material particles are used to obtain the optimal grinding media gradations for each.

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