Simulation method for grading the grinding medium of a ball mill based on particle packing theory

Abstract

The present invention relates to the field of simulating the particle size distribution of grinding media in ball mills, and discloses a method for simulating the particle size distribution of the grinding media of a ball mill based on particle packing theory. It comprises the following steps: establishing a numerical simulation coordinate system for the ball mill; performing a discrete element numerical simulation model of the grinding media and material particles; performing a periodic model of the ball mill boundaries and defining the particle cut-off diameter; based on the number of particles in the discrete element numerical simulation model, adjusting the particle cut-off diameter; and comparing the simulation results for different particle cut-off diameters to determine the particle cut-off diameter range.Perform coarse particle modeling of the ball mill particles and corresponding adjustments to the periodic boundary width; calculate the grinding effect of the material particles under different grinding media particle sizes; adjust the particle size distribution of the material particles to obtain the optimal grinding media particle size design. The optimized grinding media particle size distribution scheme and the adjustment method for different working conditions obtained by the present invention can reduce the cost of cement production. Fig. 1;

Description

Title of the invention: Method for simulating the graduation of the grinding medium of a ball mill on the theory of particle stacking Technical field

[0001] The present invention relates to the field of simulation of the particle size of grinding media in ball mills, and more particularly to a method of simulating the particle size of grinding media in a ball mill based on the particle stacking theory. State of the art

[0002] Ball mill is the most widely used equipment in industry for regrinding crushed materials, mainly used in building materials, metallurgy, mining, chemical industry, electric power and other industries. Ball mill uses a liner plate to lift the grinding elements (mainly steel balls or ceramic balls) to a certain height for dry or wet crushing and grinding of mineral particles and abrasives.The corresponding proportions of steel balls of different sizes are called the particle size of steel balls. When determining the particle size of steel balls, the particle size of the grinding materials should be combined. When the particle size of the grinding materials is small, the particle size of the grinding medium should be smaller; conversely, when the particle size of the grinding material is large, the particle size of the grinding medium should be larger.

[0003] What happens inside the ball mill is the collision interaction of particles, the grinding efficiency of mineral particles depends on the movement of the grinding medium, the movement of the grinding medium largely depends on the working parameters of the ball mill, the structure of the ball mill, the characteristics of the grinding medium itself. Currently, the most studied main operating parameters of the ball mill are the rotation speed and the filling ratio, in addition, the material and particle size of the grinding medium also play a key role in the grinding effect and energy consumption of the ball mill.

[0004] The existing technology focuses on fine-tuning based on the existing working conditions, mainly by changing the particle size of the steel balls to improve the grinding effect. This method does not pay attention to the overall interaction between the steel balls and the material particles in the ball mill, and ignores the impact of this interaction on the grinding effect, which will lead to limited or unstable optimization effects. In addition, since no full simulation is performed, the optimization effect must be verified by experiments, which not only requires more time and resources, but the results are also affected by the experimental conditions, resulting in uncertainty about the optimization effect.

[0005] Content of the invention

[0006] The present invention relates to a method for simulating the graduation of grinding media of a ball mill based on the particle stacking theory, the objective is to obtain the relationship between steel balls and cement particles under different steel ball particle sizes and cement particle size distributions by means of a discrete element numerical simulation method and a coarse-grained model, in order to obtain an optimization of the particle size of the steel balls in the ball mill.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A method for simulating the graduation of grinding media of a ball mill based on particle stacking theory, comprising the following steps:

[0009] Step 1: To create a geometric model of the ball mill, establish a numerical simulation coordinate system of the ball mill;

[0010] Step 2: Based on the numerical simulation coordinate system, performing discrete element numerical simulation modeling of the grinding medium and material particles in the ball mill to obtain grinding medium and material particle models;

[0011] Step 3: Perform periodic boundary modeling of the ball mill, define the cutting diameter of the material particles in the discrete element numerical simulation model, and obtain the periodic boundary model;

[0012] Step 4: Adjust the particle cut-off diameter of the material according to the particle quantity in the discrete element numerical simulation model;

[0013] Step 5: Compare the simulation results of different particle cutoff diameters to determine the achievable cutoff range for the material particle cutoff diameters;

[0014] Step 6: Perform coarse-grained modeling of the ball mill particles to obtain a coarse-grained model of the particles and adjust the width of the periodic boundary;

[0015] Step 7: Perform a numerical simulation calculation of the grinding effect of material particles under different grinding medium particle sizes;

[0016] Step 8: Adjust the particle size of the material particles to achieve the gradation design of the grinding medium.

[0017] In addition, the numerical simulation coordinate system of step 1 is:

[0018] Taking the center of the circle of the circular side of one side of the ball mill body as the coordinate origin, the direction of the center of the circle pointing to the other circular side of the ball mill body is the positive direction of the y-axis, and 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.

[0019] Furthermore, the discrete element numerical simulation model in step 2 depends on the parameters of the total mass, density and respective particle diameter of the grinding medium and material particles.

[0020] Furthermore, in step 3, the periodic boundary model supports particles in the calculation domain that leave the ball mill in the positive y-axis direction will return to the ball mill in the negative y-axis direction, and particles that leave the ball mill in the negative y-axis direction will return to the ball mill in the positive y-axis direction.

[0021] Furthermore, in step 3, the maximum particle diameter in the ball mill is less than 0.4 times the width of the periodic boundary.

[0022] Further, in step 4, the cutoff diameter of the material particles in the discrete element simulation model is increased so that the number of particles in the computational domain of the periodic boundary modeling is less than a predetermined value.

[0023] Furthermore, in step 6, when calculating the interaction on the coarse-grained model, the acceleration multiple of the calculated velocity is the cubic of the amplification factor of the cutoff diameter of the material particles in the discrete element simulation model.

[0024] In addition, step 7 is to carry out numerical simulation research of the grinding effect of material particles in the ball mill under different grinding medium particle sizes based on the geometric model of the ball mill, the grinding medium and material particle models, the periodic boundary model, the cutting diameter of the material particles, the coarse particle model.

[0025] Further, in step 8, different particle sizes of material particles are used based on the yield of cement grinding product per unit time and the energy consumption per unit of cement product, to obtain the optimum particle size of each grinding medium.

[0026] Compared to the prior art, the beneficial technical effects of the present invention are:

[0027] This application models the overall interaction between the grinding medium and the material particles in the ball mill by numerical simulation, which makes it possible to take into account the effect of this interaction on the grinding effect, and thus to more accurately optimize the particle size of the grinding medium and the operating conditions of the ball mill, and to obtain a better grinding effect. At the same time, the use of numerical simulation to optimize the design makes it possible to obtain the optimization results on the computer without the need for experimental verification, this not only saves time and resources, but also avoids the influence of experimental conditions on the results and improves the certainty of the optimization effect. Description of the drawings

[0028] [Fig. 1] is a schematic diagram of a ball mill device proposed by an embodiment of the present invention;

[0029] [Fig.2] is a front sectional view of the main body of the ball mill proposed by the embodiment of the present invention;

[0030] [Fig.3] is a side sectional view of the main body of the ball mill proposed by an embodiment of the present invention;

[0031] [Fig.4] is a schematic diagram of the flow of concentrated particles from a ball mill under different granulometry of grinding media provided by the embodiment of the present invention.

[0032] In the figure: 1. the main body of the ball mill; 2. the modeling domain of the periodic boundaries.

[0033] Specific embodiments

[0034] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, before describing in detail the technical solutions of each embodiment of the present invention, the terms and terminology used are explained and illustrated, in this specification, parts with the same name or labeling represent a similar or identical structure and are used for illustration purposes only.

[0035] Explanation of terms

[0036] 1) The particle size is also called the granulometry (granularity). The amount of each particle size in bulk materials composed of different particle sizes. Often expressed as a percentage of the total.

[0037] A preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0038] In the present invention, a method for simulating the graduation of grinding media of a ball mill based on the particle stacking theory, comprising the following steps:

[0039] Step 1: Carry out a numerical simulation modeling of the geometric characteristics of the ball mill. First, a coordinate system must be determined.

[0040] Referring to Figures 2 and 3, taking the center of the circle of the circular side of one side of the ball mill body as the coordinate origin, the direction of the center of the circle pointing to the other circular side of the ball mill body is the positive direction of the y-axis, and 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.

[0041] Step 2: Model the steel balls and material particles in the ball mill.

[0042] The properties of steel balls and material particles are:

[0043] steel ball: density: 7850 kg / m3, particle size: 20 mm, 17 mm, 15 mm, 13 mm, 10 mm (adjustable)

[0044] material particles: density: 3100 kg / m3, particle diameter: 10 mm, 5 mm, 2 mm, 1 mm, 0.5 mm, 0.2 mm, 0.08 mm, 0.045 mm (of which material particles of 0.2 mm and below account for more than 50%)

[0045] The mass of steel balls in the ball mill: 400 kg, the mass of material particles in the ball mill: 80 kg.

[0046] Step 3: Perform periodic boundary modeling of the ball mill.

[0047] Periodic boundary conditions are a common method to simplify the simulation model to improve the calculation speed while ensuring the accuracy of the numerical simulation. The periodic boundary condition allows particles leaving the calculation domain on one side of the boundary to be returned to the calculation domain on the other side, for example, for this ball mill model, particles leaving the ball mill in the y+ direction will be returned to the ball mill in the y- direction, and particles leaving the ball mill in the y- direction will be returned to the ball mill in the y+ direction, and the calculation of the periodic boundary condition generally requires that the maximum particle diameter be less than 0.4 times the width of the periodic boundary. As shown in [Fig.2], a length of at least 50 mm is cut from the center of the ball mill in the y direction for periodic boundary simulation.

[0048] By cutting the ball mill with a length of 50 mm and carrying out periodic boundary simulation, the mass of the steel ball in the periodic domain is 20 kg and the mass of the material particles is 4 kg, the original particle quantity can be reduced to 1 / 20 of the initial state, the calculation quantity can be reduced significantly. Set 0.2 mm as the cut-off diameter of the material particles (the particle cut-off diameter is defined as the minimum diameter of the material particles in the numerical simulation model, and particles smaller than this particle diameter are represented by particles of this size), after calculation, the number of particles in the periodicity domain is about 1.18x108.

[0049] Step 4: Adjust the limit particle diameter of the ball mill.

[0050] When the number of particles in the discrete element simulation exceeds 10 million, its calculation efficiency will be greatly reduced. Adjust the particle diameter limit of the material particle simulation to avoid hundreds of millions of particles. By adjusting the particle diameter limit to 0.5 mm, the number of particles in the periodic calculation domain is about 1.18 x 107; by adjusting the particle diameter limit to 1 mm, the number of particles in the periodic calculation domain is about 1.72 million.

[0051] Step 5: Check the adjustment of the limiting particle diameter of the ball mill.

[0052] In the ball mill, the large steel balls crush the large material particles and the small steel balls grind the small material particles, if the cutting diameter of the material particles is too large, the final optimization result of the simulation may be the more large steel balls, the better. Therefore, the simulation results of different particle cutting diameters are compared, and the achievable cutting range of the particle cutting diameters is determined by the experiment of independence of the particle cutting diameters.

[0053] Step 6: Perform coarse-grained modeling of the ball mill particles.

[0054] 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. Modifications to contact, adhesion, and other models are required to calculate the interactions on this large-scale system so that the dynamics of the large-scale system are similar to those of the original system. Through reasonable coarse-grained modeling, computational efficiency can be significantly improved while ensuring computational accuracy. Since the maximum particle diameter must be less than 0.4 times the width of the periodic boundary, after coarse-grained modeling of the particles, the width of the periodic boundary must also be enlarged by a corresponding multiple.

[0055] After calculation, the number of particles and the calculation speed before and after amplification are as follows:

[0056] Note: Once the particle diameter is enlarged, the increase in the calculation speed is on the one hand linearly linked to the reduction in the number of particles, and on the other hand linearly linked to the amplification of the particle diameter, therefore the increased speed after amplification is the third power of the amplification factor.

[0057] Table 1: Comparison between the enlargement factor of the cutting diameter and the acceleration factor of the calculation speed

[0058] [Tables 1] Magnification factor Number of particles at different particle cut-off diameters Acceleration factor of 1 to speed 0.2 mm 0.5 mm 1 mm 2 mm 5 mm 10 mm 1 11796X104 1186X104 172X104 24xl04 l,7xl04 2464 1 2 2949xl04 296xl04 43xl04 5,9xl04 4371 616 8 3 1311X104 132xl04 19xl04 2,6xl04 1942 273 27 4 737xl04 74xl04 llxl04 l,5xl04 1092 154 64 5 472X104 47xl04 6.8xl04 9556 698 98 125

[0059] Compare the simulation results of different magnification factors and determine the achievable magnification range through magnification-independent experiments.

[0060] Step 7: Perform a simulation calculation on the grain size of the steel ball.

[0061] As shown in [Fig.4], based on the geometric model of the crusher balls, steel ball and material particle model, periodic boundary model, material particle cut-off diameter and coarse particle model established in steps 1 to 6, carry out numerical simulation research on the grinding effect of material particles in ball mill under different size of steel balls.

[0062] Step 8: Select the optimal design based on the requirements of the working conditions.

[0063] Designing the particle size requirements of the steel balls of the ball mill according to needs, taking the yield of the cement grinding product by unit time and energy consumption per unit of cement product as the evaluation response objectives, adjust the particle size of the incoming material particles to obtain the optimal design of the particle size of the steel balls, the influence of the steel balls of different diameters on the grinding efficiency and grinding energy consumption of the ball mill, and further obtain the optimal coordination of the combined system of particle size of steel balls and particle size of feed material.

[0064] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention; without departing from the spirit of the design of the present invention, various distortions and improvements made by persons of ordinary skill in the art of the technical scheme of the present invention will fall within the scope of protection determined by the claims of the present invention.

Claims

Claims

1. A method for simulating the grinding medium particle size of a ball mill based on particle stacking theory, characterized in that it comprises the following steps: Step 1: To create a geometric model of the ball mill, establish a numerical simulation coordinate system of the ball mill; Step 2: Based on the numerical simulation coordinate system, perform discrete element numerical simulation modeling of the grinding medium and material particles in the ball mill to obtain grinding medium and material particle models; Step 3: perform periodic boundary modeling of the ball mill, set the cut-off diameter of the material particles in the discrete element numerical simulation model, and obtain the periodic boundary model;Step 4: Adjust the material particle cut-off diameter according to the particle quantity in the discrete element numerical simulation model; Step 5: Compare the simulation results of different particle cut-off diameters to determine the achievable cut-off range for the material particle cut-off diameters; Step 6: Carry out coarse-grained modeling of the ball mill particles to obtain a coarse-grained model of the particles and adjust the width of the periodic boundary; Step 7: Carry out numerical simulation calculation of the grinding effect of the material particles under different grinding medium particle sizes; Step 8: Adjust the material particle size to obtain the gradation design of the grinding medium.;

2. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that the numerical simulation coordinate system in step 1 is: Taking the center of the circle of the circular side of one side of the ball mill body as the coordinate origin, the direction from the center of the circle pointing to the other circular side of the ball mill body is the positive direction of the y-axis, and 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. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that the discrete element numerical simulation model in step 2 depends on the parameters of the total mass, density and respective particle diameter of the grinding medium and material particles.

4. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that, in step 3, the periodic boundary model supports the particles in the calculation domain which leave 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 the particles which leave 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.

5. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that in step 3, the maximum particle diameter in the ball mill is less than 0.4 times the width of the periodic boundary.

6. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that in step 4, the cut-off diameter 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 modeling is less than a predetermined value.

7. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that in step 6, when calculating the interaction on the coarse grain model, the acceleration multiple of the calculated speed is the cubic of the factor amplification of the cut-off diameter of material particles in the discrete element simulation model.

8. The method for simulating the grinding medium particle size of a ball mill on the particle stacking theory according to claim 1, characterized in that step 7 is to carry out a numerical simulation research on the grinding effect of the material particles in the ball mill under different grinding medium particle sizes on the basis of the geometric model of the ball mill, the grinding medium and material particle models, the periodic boundary model, the material particle cut-off diameter, the coarse particle model.

9. The method for simulating the grinding medium particle size of a ball mill based on the particle stacking theory according to claim 1, characterized in that in step 8, different particle sizes of material particles are used based on the yield of the cement grinding product per unit time and the energy consumption per unit of cement product, to obtain the optimum particle size of each grinding medium.

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