A method for evaluating ball mill crushing efficiency based on relative regional energy

Abstract

A ball mill crushing efficiency evaluation method based on relative regional energy is proposed. The method divides the ball mill motion simulation area into several areas along the radial and axial directions, and respectively counts the number of collisions and the energy loss of a single collision at different times in the divided areas, calculates the total energy loss of each collision area, and divides the total regional energy by the total number of objects to obtain the relative regional energy of each group, thereby evaluating the overall crushing efficiency of the ball mill during the motion process. The calculation of relative regional energy can not only avoid the drawback of inaccurate evaluation caused by ball mill segregation and stratification, but also can be used for the horizontal comparison of the crushing performance of ball mills under different working conditions in each group. This method can accurately reflect the working efficiency in each area of ​​the ball mill, thereby providing a theoretical basis for the study of the axial segregation characteristics of particles and the overall crushing efficiency, and is helpful to provide new ideas and methods for the subsequent optimization of ball mill production efficiency, which has high theoretical value and engineering significance.

Description

Technical Field

[0001] The invention relates to the technical field of ball mill crushing efficiency evaluation, and in particular to a ball mill crushing efficiency evaluation method based on relative regional energy. Background Art

[0002] Ball mills are widely used in particle mixing, such as pharmaceutical, metallurgy, chemical, silicate and other industries.

[0003] Since its introduction, there has been no major breakthrough in the working efficiency of ball mills. How to improve crushing and grinding efficiency to reduce energy consumption has been a hot topic of research.

[0004] With the rapid development of various particle simulation technologies, there have been many studies on ball mill crushing efficiency in recent years, mainly including the influence of power and torque, particle velocity field and impact energy, drum size and speed, steel ball size and liner structure and other parameters on ball mill crushing efficiency.

[0005] Many studies have shown that axial mixing and segregation of particulate matter occur during ball mill crushing, but almost all crushing studies are based on the assumption of uniform particles, that is, the distribution of media and other particulate materials in the drum is uniform, and ignore the movement behavior of different types of particles along the axial direction.

[0006] However, when there is axial segregation during particle movement, the axial distribution of media and particles in the rotating drum is not uniform, which means that the number of particles with the same particle size will fluctuate along the axial direction of the drum, and particles of different sizes will gradually gather and produce alternating segregation bands. Therefore, the assumption that the crushing effect in each area of ​​the drum is uniform is not completely suitable for the crushing of longer drums.

[0007] Particle flows in rotary drums often present complex phenomena, especially mixing and segregation behaviors, which have a great impact on product quality and production efficiency of mixing equipment such as ball mills.

[0008] The axial mixing-segregation phenomenon refers to the segregation and stratification of particles along the axial direction of the drum during the mixing process, forming a state in which large and small particles are alternately arranged and distributed along the axial direction.

[0009] Although the research on particle mixing and segregation phenomena has received extensive attention, previous studies have only investigated the radial mixing and segregation behavior of particles in two-dimensional planes or sliced ​​thin rollers, and usually ignored the mixing-segregation phenomena in longer rollers.

[0010] Although the understanding of the axial segregation behavior of particles in the rotary drum is increasing, most studies have only qualitatively analyzed the influencing factors and segregation characteristic patterns of axial segregation, and have not substantially introduced quantitative analysis into the overall crushing research. There is still a lack of research on evaluating the relationship between axial segregation characteristics and crushing efficiency.

[0011] Among many studies, the amount of calculation required for large-scale particle crushing is difficult to bear, so current research focuses on short drum crushing with a small number of particles. Most of the research results are based on the understanding that particles are evenly distributed along the axial direction, and there are relatively few studies on the factors affecting the crushing efficiency of longer drums.

[0012] In the patent application with application publication number CN109359364A and patent application name: A method for evaluating crushing energy of a ball mill, the calculation domain of the ball mill is only divided into regions, and only the total regional energy is counted, without making a detailed study on the superposition of the regional total energy along the axial direction of the drum to the radial section and along the radial direction of the drum to the axial section. Therefore, it is not suitable for regional energy analysis on the axial and radial surfaces, and therefore cannot be applied to the lateral evaluation of multi-operating condition mills. Summary of the invention

[0013] Technical problem to be solved by the present invention: The purpose of the present invention is to solve the deficiencies in the prior art and provide a method for evaluating the crushing efficiency of a ball mill based on relative regional energy.

[0014] The technical solution of the present invention includes dividing the motion simulation area of ​​a ball mill into several sub-areas along the radial and axial directions, counting the number of collisions and the energy loss of a single collision in the sub-areas at different times, calculating the total collision energy loss of each sub-area, and dividing the total collision energy loss of the sub-area by the total number of related objects in the sub-area to obtain the relative regional energy of each sub-area, and making a relative regional energy diagram of each sub-area based on the relative regional energy of each sub-area to evaluate the overall crushing efficiency of the ball mill during the motion process.

[0015] Further, the total number of related objects is the sum of the number of media and the number of abrasives, and the relative regional energy of each sub-region is the total energy of the sub-region divided by the total number of related objects;

[0016] The relative area energy includes radial relative area energy and axial relative area energy;

[0017] The total regional energy of the collision of each region is superimposed on the radial section along the axial direction of the roller to obtain the radial relative regional energy;

[0018] The axial relative regional energy can be obtained by superimposing the total regional energy of collisions in each region on the axial section along the radial direction of the roller.

[0019] Furthermore, the efficiency evaluation method specifically includes the following process:

[0020] Step 1: construct a ball mill crushing model based on discrete element method and perform simulation;

[0021] Firstly, the geometric model, material parameters and contact parameters of the ball mill's rotary drum, steel ball medium and abrasive particles are set;

[0022] Secondly, based on the discrete element method, an axial segregation model of a ball mill is constructed, and medium and abrasive particles of different particle sizes are generated in the rotary drum; the medium and abrasive particles are subjected to equal volume random distribution to represent the uniform distribution characteristics of internal particles before the ball mill is operated; after the generated abrasive particles are stably distributed, the rotary drum of the ball mill is rotated until the internal abrasive particles of the rotary drum move stably and obvious axial segregation and stratification phenomena appear;

[0023] Finally, add a particle bonding model, replace the original abrasive particles with breakable bonded particle clusters, build a new ball mill crushing model and simulate the crushing behavior; when the abrasive particles are basically crushed, proceed to the next step;

[0024] Step 2: evenly divide the grids along the axial and radial directions of the rotary drum along the calculation domain;

[0025] The entire simulation area is meshed evenly. The number of meshes in the two dimensions of the radial section is N, and the number of meshes in the axial section is N'.

[0026] Step 3, calculating the total regional energy of collision in each region;

[0027] Count the number of collisions and energy losses in each grid area respectively, and calculate the total collision energy loss in each sub-area, that is, the total regional energy of collisions in each sub-area;

[0028] Step 4: Count the relative regional energies of radial and axial sections;

[0029] Step 5: Make a relative regional energy diagram and analyze the relationship between axial segregation characteristics and overall crushing efficiency;

[0030] According to the statistical relative regional energy information, the corresponding radial and axial relative regional energy pictures are drawn and compared with the particle distribution characteristics in the ball mill drum to evaluate the crushing efficiency of the ball mill.

[0031] Furthermore, the size and number of the grids in step 2 depend on the size of the medium particles, and the grid size is 1.5-2 times the size of the larger medium particle size; the relationship between N and N' is:

[0032] Among them, the inner diameter and length of the ball mill drum are D and L respectively.

[0033] Furthermore, the total energy of the collision of each sub-region in step 3

[0034] Among them, E i,j,z Reflects the total energy loss caused by collision in the region (i, j, z); e k Sampling is done according to the distribution;

[0035] At any time, for the ball mill drum area (i, j, z), the number of collision states S and the single collision energy loss e in the grid area are counted to satisfy the following relationship:

[0036] e~Θ(E min ,E max )

[0037] Among them, E min is the minimum loss energy in the collision of the grid area, E max is the maximum energy loss in the collision in this area, Θ is the distribution function, and the distribution function is related to parameters such as the number of particles and rotation speed in this area.

[0038] Furthermore, the relative area total energy of the radial section

[0039] Relative area total energy of axial section

[0040] Where N Δt is the total number of time steps in the collected crushing process, N t is the total number of related objects in each group.

[0041] Further, the material parameters include density, Poisson's ratio and shear modulus;

[0042] The contact parameters include rolling friction coefficient, sliding friction coefficient and restitution coefficient.

[0043] The beneficial effects of the present invention compared with the prior art are as follows: the present invention divides the ball mill motion simulation area into several areas along the radial and axial directions, and respectively counts the number of collisions and the energy loss of a single collision at different times in the divided areas, calculates the total energy loss of each collision area, and divides the total regional energy by the total number of objects to obtain the relative regional energy of each group, thereby evaluating the overall crushing efficiency of the ball mill during the motion process; the calculation of the relative regional energy can not only avoid the inaccurate evaluation caused by the segregation and stratification of the ball mill, but also can be used for the lateral comparison of the crushing performance of ball mills under different working conditions in each group, which is helpful to study the relationship between the axial segregation characteristics of the particles and the overall crushing efficiency, and provide new ideas and methods for the subsequent optimization of the production efficiency of the ball mill. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart of the method for evaluating the crushing efficiency of a ball mill in the present invention;

[0045] Figure 2 It is a schematic diagram of the replacement and crushing of abrasive particles in the ball mill of the present invention;

[0046] Figure 3 is a modeling side view of radial meshing in the present invention;

[0047] Figure 4 It is a modeling front view of axial mesh division in the present invention;

[0048] Figure 5 It is the radial segregation characteristics and relative regional energy diagram of the ball mill;

[0049] Figure 6 It is the axial segregation characteristics and relative regional energy diagram of the ball mill;

[0050] Figure 7 is a diagram of the relative area energies of different types of particles;

[0051] Figure 8 It is the relationship diagram between overall crushing efficiency and axial segregation characteristics. DETAILED DESCRIPTION

[0052] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings. The embodiments are only used to explain the present invention and do not constitute a limitation on the protection scope of the present invention.

[0053] like Figure 1-8 As shown, the present invention provides a ball mill crushing efficiency evaluation method based on relative regional energy. When axial segregation occurs in the ball mill, a ball mill crushing efficiency evaluation method that can be used for comparison of multiple working conditions is provided based on the relative regional energy index, thereby accurately evaluating the working efficiency in each area of ​​the ball mill to reflect the overall crushing efficiency.

[0054] like Figure 1 As shown, the specific steps of the present invention are as follows:

[0055] Step 1: Build a ball mill crushing model and simulate it;

[0056] Firstly, the geometric model, material parameters and contact parameters of the ball mill rotary drum, steel ball medium and abrasive particles are set. The material parameters in the model include density, Poisson's ratio and shear modulus; the contact parameters include rolling friction coefficient, sliding friction coefficient and restitution coefficient; the bonding bond parameters in the crushing link include critical normal stress, critical tangential stress, etc.

[0057] Secondly, the axial segregation model of the ball mill is constructed based on the discrete element method, and the collision between particles is described by the hard ball model. The medium and abrasive particles of different particle sizes are generated in the rotating drum, where the grinding ball particles are steel balls with diameters of 60mm and 20mm respectively; the abrasive particles are pyrite with a diameter of 40mm. The three types of particles are randomly mixed in the drum with equal volumes to represent the uniform distribution characteristics of the particles before the ball mill works; until the particle movement inside the drum is stable and obvious axial segregation and stratification phenomena appear;

[0058] Then, during the ball mill crushing process, the particle bonding model was used to simulate the crushing behavior, such as Figure 2 As shown. The critical tangential stress and critical normal stress of the bonding model are added to the new model. When the force between the element particles is greater than the critical stress, the bond breaks. Then, the abrasive particles are replaced with 30 breakable bonded particle clusters with a diameter of 10 mm at 0.01 s. The crushing behavior of several groups of new models is simulated for 5 s respectively. When the abrasive particles are basically crushed, the next step is entered.

[0059] Step 2: Divide the drum area into grids along the computational domain;

[0060] In the discrete element model of the ball mill rotary drum, the entire simulation area is divided into N×N×N' grids, such as Figure 3 and Figure 4 As shown, a more detailed grid area division method is used to adapt to the two angles of radial and axial sections. The grid size and number depend on the size of the medium particles, which is usually 1.5-2 times the larger medium particle size. Usually, the inner diameter and length of the ball mill drum are D and L respectively. The number of divisions in the two dimensions of the radial section is N, and the number of grid divisions in the axial section is N'. Then there is in, Figure 3 This is a schematic diagram of radial mesh division observed from the side view. Figure 4 This is a schematic diagram of the axial mesh division observed from the front view.

[0061] Step 3: Calculate the total regional energy of collision in each region;

[0062] against Figure 3 and Figure 4 For the grid area in , at any time, the number of collisions and energy loss in each grid area are counted, and the total collision energy loss in each area is calculated, that is, the total regional energy of collisions in each area. For the ball mill drum area (i, j, z), the number of collisions in the time t is S, and the energy loss of a single collision is e, then the following relationship is satisfied:

[0063] e~Θ(E min ,E max )

[0064] Among them, E min is the minimum loss energy in the collision of the grid area, E max is the maximum energy loss in the collision in this area, Θ is the distribution function, which is related to the number of particles in this area, the rotation speed and other parameters.

[0065] Therefore, the total regional energy of the sample region (i, j, z) is

[0066]

[0067] In the formula, e k Sampling is done according to the distribution. i,j,z It reflects the total energy loss caused by collisions in the region (i, j, z).

[0068] Step 4: Calculate the relative regional energy of radial and axial sections;

[0069] When comparing the crushing performance of ball mills under different working conditions, there are often different amounts of media and materials. The absolute total regional energy cannot reflect the energy loss relative to a single particle under each working condition and cannot be used for horizontal comparison of each group. Therefore, relative regional energy is used.

[0070] When evaluating the total regional energy of the radial section, in order to simplify the calculation, the Monte Carlo method is used to sample the energy loss of each collision, calculate the total number of collisions and their energy distribution in each area, and sample the energy distribution. On the basis of statistically analyzing the total regional energy of each sample grid, the collected total regional energy is superimposed on the radial section along the drum axis, and the total number of related objects in each group, that is, the sum of the number of media and the number of abrasives, is calculated. The total regional energy is divided by the total number of related objects to obtain the relative regional energy of each group.

[0071]

[0072] Where N Δt is the total number of time steps in the collected crushing process, N t is the total number of related objects in each group.

[0073] Similarly, when evaluating the relative regional total energy of the axial section, the energy of each region is superimposed on the axial section along the radial direction, and the calculation process is similar.

[0074] Step 5: Make a relative regional energy diagram and analyze the relationship between axial segregation characteristics and overall crushing efficiency;

[0075] First, draw the corresponding radial relative area energy picture, such as Figure 5 shown.

[0076] From the radial cross-section observation, it is not difficult to find that the statistical relative regional energy of the medium steel ball-abrasive particles is mainly concentrated in the core part. However, considering that the ball mill drum is actually very long, the segregation characteristics of different radial shaft sections are different. Therefore, it is difficult to characterize the overall crushing efficiency only by the relative regional energy of the radial cross-section.

[0077] Similarly, the collision loss energy of the two diameter steel ball media is added in each area, such as Figure 6 As shown, this represents the relative regional energy distribution characteristics of the axial section.

[0078] In general, the axial segregation characteristics of the dielectric strip are consistent with the relative regional energy distribution of the axial cross section.

[0079] Next, taking the segregation-crushing model at steady state as an example, the collision times and single collision loss energies of steel ball media-abrasive particles with different diameters were counted respectively. According to the definition of relative regional energy index, the total collision loss energy distribution of steel ball media-particles with two diameters along with crushing time was calculated and expressed in grayscale, as shown in Figure 7 As shown,

[0080] Among them, the left side of the picture shows the axial segregation distribution of steel ball media with different diameters in the initial crushing stage, and the right side of the picture shows the relative area total energy distribution of the axial section of the corresponding medium-abrasive.

[0081] from Figure 7 As can be seen from the left pictures (a) to (b), the two sides of the end cover and the middle of the drum are large white medium bands, which are alternately distributed with the small gray medium bands along the axial direction; from the axial relative area energy diagram of the medium-abrasive on the right, it can be seen that the collision loss energy of the 60mm diameter steel ball medium and the abrasive particles also occurs in the end covers on both sides and the middle area of ​​the drum, which is almost consistent with the axial segregation characteristics of the large white medium band. However, since the abrasive particles are agglomerated together due to adhesion at the beginning of crushing, the number of collisions with the medium is relatively small, so the energy loss shown in the relative area energy grayscale diagram is not obvious, that is, the crushing efficiency of the 60mm diameter steel ball medium is not high in the initial stage.

[0082] On the other hand, during the crushing process, the 20mm diameter steel ball medium belt is almost evenly mixed with the abrasive particles in the remaining areas along the axial direction of the drum except for the end cover areas on both sides, so that the energy loss distribution of the 20mm diameter steel ball medium-abrasive collision is concentrated and evenly distributed in the remaining areas except for the end covers on both sides, which is basically consistent with the axial segregation distribution characteristics of the blue-green small medium belt.

[0083] In addition, the collision loss energy of the two diameter steel ball media is added in each area, such as Figure 7(c) shows the total energy loss during the collision between the abrasive particles and the steel ball medium. In general, the axial segregation characteristics of the medium belt are directly related to the total energy distribution in each area.

[0084] Furthermore, the same method was used to calculate the relative regional collision loss energy of four groups of different axial segregation characteristics, and the relative regional total energy grayscale diagram (axial section) within 0.1s after the start of crushing was drawn to study the relationship between the four groups of different axial segregation characteristics and crushing efficiency.

[0085] like Figure 8 Through comparative analysis, it can be seen that there is a direct relationship between the axial segregation characteristics, the relative area loss energy of the axial section, and the overall crushing efficiency.

[0086] For example, in Figure 8 In group A at the initial stage of mixing and segregation shown in (a), the two steel ball media are almost evenly distributed along the axial direction of the drum, and there is no axial segregation feature. At this time, the collision loss energy in the relative regional energy grayscale image is basically consistent along the axial direction and has the highest brightness, so the overall crushing efficiency is the highest;

[0087] exist Figure 8 In group B shown in (b), preliminary axial segregation characteristics are generated, and the corresponding relative regional energy grayscale image also reflects some axial segregation characteristic trends, and the color brightness is reduced. At this time, the overall crushing efficiency is reduced compared with group A;

[0088] As the particle mixing proceeds, Figure 8 As shown in (b-c), the axial segregation characteristics of the media and particles in groups C and D also tend to be stable, the relative regional energy loss of the two groups of axial regions, and the overall crushing efficiency decreases with the increase of the axial segregation degree.

[0089] According to this method, after evaluating the crushing efficiency of the ball mill, in general, the axial segregation characteristics directly affect the relative regional energy distribution of the medium-particles and determine the overall crushing efficiency.

[0090] The more obvious the axial segregation characteristics of the ball mill are, the more the total regional energy of the medium-particles will produce axial segregation characteristics, and the lower the overall crushing efficiency of the ball mill will be.

[0091] Therefore, after using this method to evaluate the crushing efficiency of the ball mill, it can be seen that during the operation of the ball mill, the influence of the axial segregation characteristics of the medium on the overall crushing effect should be fully considered, and the axial segregation characteristics of the ball mill should be avoided as much as possible during the crushing process.

[0092] The above specific implementation methods are only for illustrating the technical concept and structural features of the present invention, and the purpose is to enable relevant persons familiar with this technology to implement it. However, the above content does not limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for evaluating ball mill crushing efficiency based on relative regional energy, characterized in that : It includes dividing the motion simulation area of ​​the ball mill into several sub-areas along the radial and axial directions, respectively counting the number of collisions and the single collision energy loss in the sub-areas at different times, calculating the total collision energy loss of each sub-area, and dividing the total collision energy loss of the sub-area by the total number of related objects in the sub-area to obtain the relative regional energy of each sub-area, and making a relative regional energy diagram of each sub-area based on the relative regional energy of each sub-area to evaluate the overall crushing efficiency of the ball mill during the motion process; The process includes the following: Step 1: construct a ball mill crushing model based on discrete element method and perform simulation; Firstly, the geometric model, material parameters and contact parameters of the ball mill's rotary drum, steel ball medium and abrasive particles are set; Secondly, based on the discrete element method, an axial segregation model of a ball mill is constructed, and medium and abrasive particles of different particle sizes are generated in the rotary drum; the medium and abrasive particles are subjected to equal volume random distribution to represent the uniform distribution characteristics of internal particles before the ball mill is operated; after the generated abrasive particles are stably distributed, the rotary drum of the ball mill is rotated until the internal abrasive particles of the rotary drum move stably and obvious axial segregation and stratification phenomena appear; Finally, add a particle bonding model, replace the original abrasive particles with breakable bonded particle clusters, build a new ball mill crushing model and simulate the crushing behavior; when the abrasive particles are basically crushed, proceed to the next step; Step 2: evenly divide the grids along the axial and radial directions of the rotary drum along the calculation domain; The entire simulation area is meshed evenly. The number of meshes in the two dimensions of the radial section is N, and the number of meshes in the axial section is N'. Step 3, calculating the total regional energy of collision in each region; Count the number of collisions and energy losses in each grid area respectively, and calculate the total collision energy loss in each sub-area, that is, the total regional energy of collisions in each sub-area; Step 4: Count the relative regional energies of radial and axial sections; Step 5: Make a relative regional energy diagram and analyze the relationship between the axial segregation characteristics and the overall crushing efficiency. Based on the statistical relative regional energy information, draw the corresponding radial and axial relative regional energy pictures, compare them with the particle distribution characteristics in the ball mill drum, and evaluate the ball mill crushing efficiency.

2. The method for evaluating ball mill crushing efficiency based on relative regional energy according to claim 1, characterized in that: The total number of related objects is the sum of the number of media and the number of abrasives, and the relative area energy of each sub-area is the total energy of the sub-area divided by the total number of related objects; The relative area energy includes radial relative area energy and axial relative area energy; The total regional energy of the collision of each region is superimposed on the radial section along the axial direction of the roller to obtain the radial relative regional energy; The axial relative regional energy can be obtained by superimposing the total regional energy of collisions in each region on the axial section along the radial direction of the roller.

3. The method for evaluating ball mill crushing efficiency based on relative regional energy according to claim 1, characterized in that: The size and number of the grids in step 2 depend on the size of the medium particles. The size of the grid is 1.5-2 times the size of the larger medium particle. The relationship between N and N' is: Among them, the inner diameter and length of the ball mill drum are D and L respectively.

4. The method for evaluating ball mill crushing efficiency based on relative regional energy according to claim 1, characterized in that: The total regional energy of the collision of each sub-region in step 3 Among them, E i,j,z Reflects the total energy loss caused by collision in the region (i, j, z); e k Sampling is done according to the distribution; At any time, for the ball mill drum area (i, j, z), the number of collision states S and the single collision energy loss e in the grid area are counted to satisfy the following relationship: e~Θ(E min ,AND max ) Among them, E min is the minimum loss energy in the collision of the grid area, E max is the maximum energy loss in the collision in this area, Θ is the distribution function, and the distribution function is related to parameters such as the number of particles and rotation speed in this area.

5. The method for evaluating ball mill crushing efficiency based on relative regional energy according to claim 1, characterized in that: Relative area total energy of radial section Relative area total energy of axial section Where N Δt is the total number of time steps in the collected crushing process, N t is the total number of related objects in each group.

6. The method for evaluating ball mill crushing efficiency based on relative regional energy according to claim 1, characterized in that: The material parameters include density, Poisson's ratio and shear modulus; The contact parameters include rolling friction coefficient, sliding friction coefficient and restitution coefficient.

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