Ball mill product particle size distribution prediction method based on discrete element simulation and overall balance model

Abstract

The invention provides a ball mill product particle size distribution prediction method based on discrete element simulation and an overall balance model, and the method comprises the steps: obtaining feed particle size distribution and product particle size distribution data through a ball mill grinding test; calibrating exclusive crushing characteristic information through a material impact crushing test; discrete element simulation is carried out, and a steel ball collision energy distribution characteristic value is extracted; constructing a mathematical mapping model of steel ball collision energy distribution and an ore grinding rate function; generating a distribution function of an overall balance model in combination with the crushing characteristic information and the collision energy distribution characteristic value; with the purpose of minimizing the error between a product particle size distribution measured value and a predicted value, an ore grinding rate function is inversely optimized, and a mapping relation among energy distribution, feeding particle size distribution and the ore grinding rate function is established; discrete element simulation is carried out on a to-be-predicted scene, and a grinding rate function is dynamically generated through the mapping model; and inputting the feeding particle size distribution, the ore grinding rate function and the distribution function into the overall balance model, and outputting a product particle size distribution predicted value.

Description

Technical Field

[0001] This invention belongs to the technical field of computer-aided engineering (CAE) applications in industrial process optimization, and specifically relates to a method for predicting the particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model. Background Technology

[0002] Ball mills are key grinding equipment in process industries such as mining, cement plants, power plants, and powder material preparation. The particle size distribution of their products directly affects the efficiency and quality of downstream processes. However, the operation of ball mills exhibits significant nonlinear and time-varying characteristics, involving complex particle crushing dynamics, fluid-particle interactions, and mechanical motion coupling effects. This complexity of multi-physics coupling makes it extremely difficult to establish accurate mechanistic models.

[0003] Currently, the "Plan-Body Balance Model" (PBM) is widely used in industry and academia to simulate the grinding behavior of ball mills. This model describes the grinding process through two core functions: a grinding rate function and a distribution function. The grinding rate function quantifies the probability of different particle sizes breaking down per unit time, while the distribution function characterizes the sub-particle size distribution after the breaking down of a specific particle size. The traditional method for implementing PBM is to first determine the distribution function through laboratory crushing tests, then calculate the grinding rate function based on the feed and product particle size distribution data of the industrial ball mill, and finally substitute the obtained function into the PBM equation to predict particle size distribution. Although PBM can match actual data well under certain steady-state conditions, it has inherent limitations. The grinding rate function is extremely sensitive to changes in operating parameters; when the liner wears, steel balls are replenished, or the throughput fluctuates, the original function becomes inapplicable. Existing models cannot respond to changes in feed properties in real time and require recalibration through experiments. Furthermore, the distribution function calibrated in the laboratory is insufficient to reflect the collective particle interaction effects within an industrial-scale ball mill.

[0004] To address these issues, recent research has attempted to introduce the Discrete Element Method (DEM) to simulate particle motion within ball mills. DEMs are used to obtain the trajectory of steel balls and the distribution of collision energy, and a breakage probability model is established by combining this with particle crushing mechanics. However, existing DEM-PPM coupling studies also have significant limitations: they only use average collision energy to predict the breakage rate, ignoring the non-uniformity of energy distribution; they have not established the mathematical transfer relationship between operating parameters, collision energy spectrum, and grinding rate; and full-scale DEM simulation is not feasible for industrial-grade ball mills. These shortcomings prevent current technologies from effectively solving the dynamic prediction problem of ball mill particle size distribution, severely restricting the optimization control potential of process industries. Therefore, there is an urgent need to develop new prediction methods that can adapt to changes in operating conditions and balance accuracy and efficiency. Summary of the Invention

[0005] To address the shortcomings and deficiencies of existing technologies, this invention provides a method for predicting ball mill grinding behavior based on the synergy of discrete element simulation and machine learning. Its core innovation lies in constructing a dynamically adjustable grinding rate mapping mechanism to achieve accurate particle size prediction under varying operating parameters. Specifically, it solves industry pain points through the following technological breakthroughs:

[0006] 1. Co-modeling of material properties and energy spectrum

[0007] Impact crushing tests are used to calibrate the specific crushing characteristics of materials (such as Et). 10 Relationship and t 10 - t n By combining discrete element method (DEM) simulations with family curves to extract characteristic values ​​of the energy distribution in steel ball collisions, a quantitative correlation between the distribution function and collision energy is established for the first time. This design breaks through the limitation of traditional global equilibrium models that rely on fixed parameters, enabling the distribution function to respond to changes in collision energy in real time.

[0008] 2. Dynamic mapping mechanism of energy-rate

[0009] Based on the normal distribution, the collision energy spectrum is characterized, and the Rosin-Rammler distribution describes the feed particle size characteristics.

[0010] An innovative mathematical mapping model of the energy distribution of steel ball collisions and the grinding rate function was constructed.

[0011] This mechanism enables the grinding rate function to adapt to fluctuations in operating conditions such as ball loading rate and rotational speed, significantly reducing prediction bias compared to traditional models.

[0012] 3. Efficient collision statistics and granularity calculation

[0013] The design incorporates a time-step collision deduplication algorithm (collision is determined when the distance between the centers of the spheres is less than or equal to the sum of their radii), which significantly improves the accuracy of energy feature extraction. Simultaneously, the lower triangular matrix is ​​used to express the particle size distribution function, clarifying the particle size fragmentation path and providing high-fidelity input parameters for the overall equilibrium model.

[0014] 4. End-to-end closed-loop prediction system

[0015] The dynamically generated grinding rate function and distribution function are input into the overall equilibrium model, forming a closed-loop technology of "material characterization → energy extraction → dynamic mapping → particle size prediction". In laboratory validation, the system achieved a high degree of agreement between the predicted and measured particle size distribution values, with computation time kept within industrially feasible limits.

[0016] This solution fundamentally addresses the shortcomings of the overall equilibrium model in adapting to changes in operating parameters, and for the first time achieves accurate prediction of ball mill particle size distribution under varying operating conditions, providing core technical support for energy conservation and emission reduction in the process industry.

[0017] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0018] A method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model includes:

[0019] Through multiple ball mill grinding tests under different operating conditions, data on feed particle size distribution and product particle size distribution were obtained.

[0020] Specific crushing characteristics are determined through material impact crushing tests;

[0021] With the goal of minimizing the error between the measured and predicted values ​​of product particle size distribution, the grinding rate function is inverted and optimized.

[0022] Discrete element simulation was performed based on the operating conditions of the grinding test to extract the characteristic values ​​of the energy distribution of steel ball collisions.

[0023] A mathematical mapping model is constructed between the energy distribution of steel ball collisions and the grinding rate function, including:

[0024] a: Combining crushing characteristic information with collision energy distribution feature values, generate the distribution function of the overall balance model of the ball mill;

[0025] b: Establish a predictive mapping relationship between energy distribution, feed particle size distribution, and grinding rate;

[0026] Discrete element simulation is performed on the scenario to be predicted, and the grinding rate function is dynamically generated through a mapping model.

[0027] The grinding rate function and distribution function are input into the overall equilibrium model, and the predicted value of product particle size distribution is output.

[0028] Furthermore, the specific pulverization characteristic information is Et 10 Relationship or t 10 - t n Family curves.

[0029] Furthermore, the particle size distribution function is a lower triangular matrix, where the elements represent the mass percentage of a specific particle size that enters a finer particle size after crushing.

[0030] Furthermore, the error minimization is achieved by minimizing the sum of squared relative errors between the measured and predicted values, and by optimizing the grinding rate function parameters through an iterative algorithm.

[0031] Furthermore, in the mathematical mapping model, the energy distribution of the steel ball collision conforms to a normal distribution, and the particle size distribution of the feed conforms to a Rosin-Rammler distribution.

[0032] Furthermore, the discrete element simulation employs a time-step collision deduplication algorithm, determining a collision when the distance between the centers of the two steel balls is less than or equal to the sum of their radii.

[0033] Furthermore, the discrete element simulation uses the Hertz-Mindlin contact model to calculate the interaction force between the steel balls.

[0034] Furthermore, the predicted mapping relationship is generated by driving the grinding rate function through the spectral characteristic value of the steel ball collision energy and the feed particle size distribution parameter.

[0035] And, a ball mill particle size distribution prediction system based on discrete element simulation and overall equilibrium model, comprising:

[0036] Material property calibration unit: configured to calibrate specific crushing characteristic information through material impact crushing tests;

[0037] Experimental data acquisition unit: configured to acquire feed particle size distribution and product particle size distribution data through multiple sets of ball mill grinding tests under different operating conditions, with the goal of minimizing the sum of squared relative errors between the measured and predicted product particle size distribution values, and inverting the grinding rate function through an iterative algorithm;

[0038] Discrete Element Simulation Engine: Configured to perform DEM simulation based on grinding test operating conditions, execute time-step collision deduplication algorithm, and extract the energy distribution feature value of steel ball collision;

[0039] Distribution function generator: Combines crushing characteristic information and collision energy eigenvalues ​​to generate the overall equilibrium model distribution function of the lower triangular matrix;

[0040] Grinding rate prediction unit: Establishes a predictive mapping relationship between the grinding rate function, collision energy spectrum, and feed particle size distribution;

[0041] Prediction Execution Unit: Configured to perform DEM simulation of the scenario to be predicted, dynamically generate grinding rate function through mapping model, and input it together with distribution function and feed particle size distribution into overall equilibrium model to output predicted value of ball mill product particle size distribution.

[0042] A ball mill operating parameter intelligent optimization system includes:

[0043] The particle size distribution prediction system described above;

[0044] Real-time monitoring unit: configured to collect mill current, vibration spectrum and sound signals;

[0045] Parameter tuning engine: Based on predicted particle size distribution and real-time monitoring data, it dynamically optimizes ball loading rate, rotation speed and feeding rate through reinforcement learning algorithm;

[0046] Digital twin interface: Generates a 3D visualization model of the mill's motion state.

[0047] And a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method described above.

[0048] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0049] Compared with the prior art, the present invention and its preferred embodiments have at least the following beneficial effects:

[0050] 1. Overcoming the bottleneck of dynamic adaptation of operating parameters

[0051] By constructing a mathematical mapping model between collision energy distribution and grinding rate function, this study achieves for the first time adaptive correction of the grinding rate function based on key parameters such as ball loading rate and rotational speed. This mechanism fundamentally solves the failure problem of traditional overall equilibrium models under varying operating conditions, freeing particle size prediction capabilities from being limited by fixed parameter conditions. The prediction results highly match the actual particle size distribution, significantly reducing prediction bias caused by parameter fluctuations.

[0052] 2. Improve the accuracy of material property characterization

[0053] Employs proprietary grinding characteristics information (such as Et) 10 Relationship and t 10 - t n The distribution function (DFC) quantifies material crushing behavior using a family curve and precisely expresses the particle size transformation path using a lower triangular matrix, enabling it to accurately respond to changes in ore hardness. Compared to traditional laboratory calibration methods, this significantly reduces material adaptability maintenance costs.

[0054] 3. Optimize the performance of discrete element simulation.

[0055] An innovative time-step collision deduplication algorithm (judgment criterion: distance between ball centers ≤ sum of radii) significantly improves the accuracy of collision energy statistics and avoids energy feature distortion caused by repeated counting. This design, while ensuring accuracy, elevates the simulation efficiency of industrial-grade ball mills to an engineering-feasible level.

[0056] 4. Construct a closed-loop prediction system for the entire process.

[0057] This system establishes an adaptive technology chain encompassing "material property calibration → dynamic energy extraction → rate function generation → particle size distribution prediction." By employing an overall equilibrium model, the system achieves macroscopic particle size prediction while maintaining the interpretability of the microscopic pulverization mechanism, providing a solution for industrial optimization that combines accuracy and practicality. Attached Figure Description

[0058] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0059] Figure 1 For t 10 - t n Family curve diagram;

[0060] Figure 2 Diagram of the discrete element interaction model;

[0061] Figure 3 This is a diagram illustrating a collision detection method according to an embodiment of the present invention;

[0062] Figure 4 t in a test instance of the present invention 10 - t n Family curve graph;

[0063] Figure 5 This is a cross-sectional view of the discrete element grinding process in an embodiment of the present invention;

[0064] Figure 6 This is a frequency diagram of the collision energy of a steel ball according to an embodiment of the present invention;

[0065] Figure 7 This is a comparison chart of the actual and predicted particle size distribution values ​​of the ball mill products according to an embodiment of the present invention;

[0066] Figure 8 This is a flowchart illustrating the overall process of an embodiment of the present invention. Detailed Implementation

[0067] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0068] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0069] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0070] To overcome the shortcomings and deficiencies of existing technologies, this invention proposes a method for predicting ball mill grinding behavior that combines discrete element method (DEM) simulation and machine learning. This method assumes that the grinding rate of particles of different sizes within the ball mill is mainly determined by the feed particle size distribution and the collision energy spectrum of the steel balls. Figure 8 As shown, its basic implementation process is as follows:

[0071] First, for the specific ball mill under study, grinding tests were conducted under different operating conditions to measure and record the feed particle size distribution and product particle size distribution of the ball mill.

[0072] Then, the pulverization characteristics of the given material are characterized in the laboratory through experiments;

[0073] Based on the ball mill operating conditions corresponding to the grinding test, discrete element simulation was performed to derive the collision energy spectrum of the steel balls and extract the characteristic values ​​of the steel ball collision energy.

[0074] Based on the crushing characteristics of the material and the characteristic value of the collision energy of the steel ball, the distribution function of particles of different sizes is calculated;

[0075] Under each operating condition of the grinding test, the corresponding grinding rate function is calculated based on the feed particle size distribution, product particle size distribution, and distribution function of the ball mill, and an overall equilibrium model of the ball mill under that operating condition is established.

[0076] For ball mill feed particle size distribution, steel ball collision energy spectrum and grinding rate function under different operating conditions, a predictive mapping model of the relationship between the three is established (hereinafter referred to as grinding rate prediction model).

[0077] For the ball mill operation scenario to be predicted, discrete element simulation is performed based on its operating conditions to derive the corresponding steel ball collision energy spectrum.

[0078] The energy spectrum of steel ball collisions in the ball mill operating scenario to be predicted is substituted into the grinding rate prediction model to predict the corresponding grinding rate function. Simultaneously, the eigenvalues ​​of the steel ball collision energy spectrum are extracted, and its distribution function is calculated based on the material properties.

[0079] By substituting the grinding rate function and distribution function of the ball mill operating scenario to be predicted into the overall equilibrium model, the particle size distribution of the grinding product of the ball mill operating scenario to be predicted is calculated.

[0080] The following is a detailed description of the steps in the embodiments of the present invention:

[0081] (1) For the ball mill to be studied, keep the feed type unchanged, change its feed particle size distribution, throughput, ball loading rate, steel ball diameter distribution, mill speed, grinding concentration, liner shape and other operating conditions, and measure and record the feed particle size distribution and product particle size distribution of the ball mill under each operating condition.

[0082] (2) The crushing behavior of the material is characterized using an impact crushing tester or other types of ore crushing characteristic testing instruments. The impact crushing tester can be one of various impact crushing test instruments such as a falling hammer tester, a double pendulum tester, and a rotary crushing tester. Other types of ore crushing characteristic testing instruments can also be used, but the instrument must be able to provide input energy data to allow for the expression of the crushing behavior of the material. The crushing behavior of the material refers to the relationship between the particle size distribution of the crushed product of particles with a certain initial particle size and the unit crushing energy.

[0083] Mathematical models of particle crushing behavior can describe the crushing behavior of particles. There are various forms of mathematical models of particle crushing behavior, and their general formula can be expressed as:

[0084] (1)

[0085] The meanings of each parameter in the formula are as follows:

[0086] X: Fineness index of crushed product, usually expressed as the percentage content of crushed product that is finer than a certain absolute or relative particle size. For example, "the mass percentage of particles smaller than 75μm in the crushed product" or "the mass percentage of particles smaller than 1 / 10 of the initial feed particle size in the crushed product", etc.

[0087] C1,…,C n The parameters of the mathematical model f for particle crushing behavior can represent the crushing properties of the ore. The number of parameters in different forms of mathematical models for particle crushing behavior is mostly 1-3.

[0088] x f : Particle size of ore before crushing (feed particle size).

[0089] E: Unit crushing energy, which is equal to the ratio of impact crushing energy to the mass of the ore being tested.

[0090] In each test, the ore particles are crushed m×n times at m particle size levels and n energy levels. The value of m is typically 4 or 5, and the value of n is typically 3. The feed for each level combination of crushing processes consists of dozens of representative narrow-sized ore particles obtained through screening and random sorting. The fineness index X of the crushed product at each level combination can be obtained through screening.

[0091] A complete ore impact crushing test can yield m×n sets of X and x.f And E value. The mathematical model f of particle crushing behavior is used to analyze the X and x values ​​of this m×n set. f By performing curve fitting with the E value, C1,…,C can be determined. n The value of x can then be used to predict any x within the effective range of the mathematical model of particle crushing behavior. f And the X value corresponding to the E value.

[0092] The particle size distribution of the feed ore after crushing can be predicted using a particle size distribution function. However, for simplification, interpolation is typically used to calculate the particle size distribution of the crushed products. 10 -t n Family curves are one of the most commonly used interpolation methods for calculating the specific particle size distribution of crushed products, such as... Figure 1 As shown.

[0093] Figure 1 t in n This indicates that the particle size in the crushed product is smaller than the initial particle size x. f The percentage of particles that are 1 / n. Where, t 10 It can be used as an indicator of the fineness of crushed products. It is generally considered that t... 10 -t n The shape of the family of curves does not change with x f Changes occur as they change. Therefore, based on a set of t2, t4, t... 10 t 25 t 50 t 75 and x f The value of can be interpolated to obtain the cumulative particle size distribution curve of the crushed ore products.

[0094] For a specific type of material, the model parameters C1,…,C n The value of and its specific t 10 - t n The family curves represent its pulverizing characteristics.

[0095] (3) Adjust the parameters, such as mill speed, material filling amount and steel ball ratio, according to the ball mill operating conditions corresponding to the grinding test, and perform discrete element simulation.

[0096] Establish a scaled model of the three-dimensional ball mill, import the model into DEM software, and set the material properties of the ball mill cylinder and particles, including: size, density, Poisson's ratio, coefficient of restitution, Young's modulus, and the dynamic and static friction coefficients between steel balls.

[0097] When setting up a discrete element contact model, the Hertz-Mindlin model is a preferred choice for calculating forces. The contact model can be set up in the software, such as... Figure 2 As shown, normal contact force ( ) is the amount of overlap Functions:

[0098] (2)

[0099] in It is the normal spring stiffness constant. It is the damping coefficient in the normal direction. It is the normal component of the relative velocity;

[0100] Tangential contact force ( ):

[0101] (3)

[0102] in It is the normal spring stiffness constant. It is the tangential overlap. It is the damping coefficient in the normal direction. It is the normal component of the relative velocity. It is the static friction coefficient.

[0103] Based on the corresponding operating conditions of the ball mill grinding test, the simulated rotation speed, the number of particles in each size, and parameters such as Poisson's ratio, Young's modulus, and coefficient of restitution are set to ensure that the simulation is in a stable state during the simulated operation time.

[0104] The main function of discrete element simulation (DEM) is to generate collision data between steel balls and count the number of contacts between the balls in each time step. To avoid detecting more than one collision in a single time step for two stationary contacting static systems, this invention re-examines the previous collision data within each collision detection time step, stores the previous data, optimizes the data for each collision time step, and excludes repeated collisions within a single time step. Figure 3 As shown. The criterion for judging the collision of two steel balls is... This means that the distance between the centers of the two steel balls is less than or equal to the sum of their radii. In the first time step, steel balls P1-P7 did not collide; in the second time step, 4 collisions were recorded, and there were no duplicate collisions compared to the first time step; in the third time step, 3 collisions were recorded, but there were two duplicate collisions compared to the second time step, so the number of collisions counted in this time step was 1.

[0105] Substitute the simulated velocity data into the kinetic energy formula. Calculations are performed, and then the impact energy of the colliding steel ball is statistically analyzed, based on which... This refers to the relative normal velocity of the two steel balls during their collision, while This refers to the average mass of the two colliding steel balls;

[0106] Export the corresponding collision energy spectrum and extract the feature values ​​of the collision energy at each time step.

[0107] (4) Substitute the average collision energy of the steel balls in each grinding test into equation (1) to calculate the fineness index t of the crushed product for a specific feed particle size. 10 Combined with t 10 - t n The cumulative particle size distribution curve of the crushed product is obtained by family curve calculation, and the cumulative particle size distribution curve is converted into the mass distribution frequency of each particle size.

[0108] For each grinding test, the above operation was repeated for different particle sizes of the ball mill feed to obtain the mass distribution frequency of all particle sizes, which is expressed in the form of a lower triangular matrix as the distribution function A. j As shown in equation (4):

[0109]

[0110] In equation (4), This represents the mass percentage of feed particles of size j that, after being crushed, enter size i.

[0111] (5) The overall equilibrium model of the grinding behavior of the ball mill can be expressed as follows:

[0112]

[0113] Right now:

[0114]

[0115] The meanings of each parameter in the formula are as follows:

[0116] This refers to the product particle size distribution column matrix;

[0117] , refers to the column matrix of feed particle size distribution;

[0118] , refers to the column matrix of grinding rate functions.

[0119] Under each operating condition of the grinding test, the corresponding feed particle size distribution and distribution function of the ball mill were substituted into equation (5), and then the product particle size distribution P was calculated using the following formula. j The experimental value P je Its predicted value P jp The weighted sum of squares (SSQ) of the differences:

[0120] (7)

[0121] The grinding rate function S is determined by iterative calculations aimed at minimizing SSQ. j The value of .

[0122] (6) For the ball collision energy spectrum and grinding rate function of the ball mill under different operating conditions, establish a mathematical model of the relationship between the two (hereinafter referred to as the grinding rate prediction model). );

[0123] Grinding rate prediction model = f(a function of the energy spectrum of steel ball collisions, feed particle size distribution)

[0124]

[0125] in, The probability density function representing the energy of a steel ball collision generally follows a normal distribution, and is as follows:

[0126]

[0127] In the formula, and Represents the mean and standard deviation of the collision energy;

[0128] The feed particle size distribution function can be the Rosin-Rammler distribution or other distributions. The Rosin-Rammler distribution function is as follows:

[0129]

[0130] In the formula: Indicates characteristic particle size, The distribution index reflects the uniformity of particle size distribution.

[0131] (7) For the ball mill operation scenario to be predicted, establish a proportional model of the ball mill, import it into the discrete element software, adjust the corresponding parameters in the discrete element simulation, such as Young's modulus, coefficient of restitution, Poisson's ratio, etc., set the Hertz-Mindlin contact model, adjust the time step, generally 1e-5s, count the collision frequency in the simulation time according to the new statistical frequency method, and then calculate the corresponding impact energy according to the statistical collision particles, and derive the energy spectrum of the steel ball collision.

[0132] (8) Substitute the steel ball collision energy spectrum of the ball mill operation scenario to be predicted into the grinding rate prediction model to predict its corresponding grinding rate function. At the same time, extract the characteristic values ​​of its steel ball collision energy and calculate its distribution function according to the material properties;

[0133] (9) Substitute the grinding rate function and distribution function of the ball mill operation scenario into the overall equilibrium model to calculate the grinding product particle size distribution of the ball mill operation scenario to be predicted.

[0134] The grinding mathematical model currently used in this embodiment of the invention for ball mill grinding behavior is the "overall equilibrium model," which to some extent describes the crushing speed of different particle sizes of ball mill feed inside the mill and the particle size distribution of the product. However, the motion inside the ball mill is complex and variable, and the grinding rate also varies with operating conditions, making it difficult to predict the impact of changes in operating conditions on the ball mill grinding rate.

[0135] The discrete element method (DEM) is a numerical simulation method that can calculate particle motion and collisions, but current computing power cannot be applied to large-scale ball mills in industrial applications. There is a lack of publicly available or licensed research on the impact of changes in ball mill operating conditions on grinding rates. This invention combines a global equilibrium model and discrete element simulation to address the problem of insufficient predictive power in the global equilibrium model.

[0136] The following provides a specific application example to further demonstrate and introduce the solution of the embodiment of the present invention:

[0137] I. Preparation before the test: Taking a small laboratory ball mill as an example, a grinding test was conducted at a speed of 54 rpm, and the cumulative particle size distribution curves of the feed and the product were recorded.

[0138] II. The crushing behavior of materials was characterized by a falling hammer tester. Five different narrow-sized ore particles were selected and subjected to impact crushing at three different energies, resulting in a total of 15 particle size-energy combinations, as shown in Table 1.

[0139] Table 1. Required particle size, quantity, and energy level for the pulverization test.

[0140]

[0141] t of the pulverized product 10 -t n Family curves such as Figure 4 As shown.

[0142] 3. Create a full-scale ball mill simulation model in Solidworks, import it into DEM software, and set the material properties of the ball mill liner and steel balls in DEM, including particle size, density, Young's modulus, Poisson's ratio, etc., as shown in Table 2.

[0143] Table 2 DEM parameter settings

[0144] <![CDATA[Density (kg / m 3 ).]]> 7800 Young's modulus (GPa) 0.1 Poisson's ratio 0.3 coefficient of recovery 0.7 static friction coefficient 0.2 rolling friction coefficient 0.01

[0145] Based on the ball mill operating conditions, adjustments were made in the discrete element method (DEM) software to set simulation parameters such as time step and statistical frequency to ensure the stability of the simulation run time. The DEM simulation cross-section of the grinding process is shown below. Figure 5 As shown. Generate an executable data file. Based on the coordinates and diameter information of the steel balls in the file, calculate the collision frequency, and simultaneously detect non-repeating collisions between adjacent steel balls, saving the calculated collisions. Calculate the impact energy of the saved collisions, such as... Figure 6 As shown, the system is basically in a stable state, and the feature values ​​of the steel ball collisions have been extracted.

[0146] Substitute the collision energy characteristic value and the feed particle size into equation (1) to calculate the fineness index of the crushed product.

[0147] Substitute the known data into the overall equilibrium equation to minimize the weighted sum of squares (SSQ) of the model, obtain the grinding rate function, and then solve for it. .have:

[0148] Feed particle size distribution function ;

[0149] Grinding rate function ;

[0150] Distribution matrix of crushed products ;

[0151] Therefore, we have:

[0152] =

[0153]

[0154] And the error between the predicted value and the actual value is as follows: Figure 7 As shown, it achieves good predictive results.

[0155] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0156] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0157] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0158] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0159] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other various forms of methods for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model. All equivalent changes and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model, characterized in that, include: Through multiple sets of ball mill grinding tests under different operating conditions, data on feed particle size distribution and product particle size distribution were obtained. Specific crushing characteristics are determined through material impact crushing tests; With the goal of minimizing the error between the measured and predicted values ​​of product particle size distribution, the grinding rate function is inverted and optimized. Discrete element simulation was performed based on the operating conditions of the grinding test to extract the characteristic values ​​of the energy distribution of steel ball collisions. A grinding rate prediction model based on steel ball collision energy distribution and feed particle size distribution is constructed, including: a: Combining crushing characteristic information with collision energy distribution feature values, generate the distribution function of the overall balance model of the ball mill; b: Establish a predictive mapping relationship between energy distribution, feed particle size distribution, and grinding rate; Discrete element simulation is performed on the scenario to be predicted, and the grinding rate function is dynamically generated through the grinding rate prediction model. The grinding rate function and distribution function are input into the overall equilibrium model, and the predicted value of product particle size distribution is output.

2. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: The specific pulverization characteristic information is Et. 10 Relationship or t 10 - t n Family curves.

3. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: The particle size distribution function is a lower triangular matrix, where the elements represent the mass percentage of a specific particle size that enters a finer particle size after crushing.

4. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: The error minimization is achieved by minimizing the sum of squared relative errors between the measured and predicted values, and by optimizing the grinding rate function parameters through an iterative algorithm.

5. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: In the mathematical mapping model, the energy distribution of the steel ball collision follows a normal distribution, and the particle size distribution of the feed follows a Rosin-Rammler distribution.

6. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: The discrete element simulation uses a time-step collision deduplication algorithm, which determines a collision when the distance between the centers of two steel balls is less than or equal to the sum of their radii.

7. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: The discrete element simulation uses the Hertz-Mindlin contact model to calculate the interaction force between the steel balls.

8. The method for predicting particle size distribution of ball mill products based on discrete element simulation and overall equilibrium model according to claim 1, characterized in that: The predicted mapping relationship is generated by driving the grinding rate function with the spectral characteristic value of the steel ball collision energy and the feed particle size distribution parameter.

9. A ball mill particle size distribution prediction system based on discrete element simulation and overall equilibrium model, characterized in that, include: Material property calibration unit: configured to calibrate specific crushing characteristic information through material impact crushing tests; Experimental data acquisition unit: configured to acquire feed particle size distribution and product particle size distribution data through multiple sets of ball mill grinding tests under different operating conditions, with the goal of minimizing the sum of squared relative errors between the measured and predicted product particle size distribution values, and inverting the grinding rate function through an iterative algorithm; Discrete Element Simulation Engine: Configured to perform DEM simulation based on grinding test operating conditions, execute time-step collision deduplication algorithm, and extract the energy distribution feature value of steel ball collision; Distribution function generator: Combines crushing characteristic information and collision energy eigenvalues ​​to generate the overall equilibrium model distribution function of the lower triangular matrix; Grinding rate prediction unit: Establishes a predictive mapping relationship between the grinding rate function, collision energy spectrum, and feed particle size distribution; Prediction Execution Unit: Configured to perform DEM simulation of the scenario to be predicted, dynamically generate grinding rate function through mapping model, and input it together with distribution function and feed particle size distribution into overall equilibrium model to output predicted value of ball mill product particle size distribution.

10. A ball mill operating parameter intelligent optimization system, characterized in that, include: The particle size distribution prediction system as described in claim 9; Real-time monitoring unit: configured to collect mill current, vibration spectrum and sound signals; Parameter tuning engine: Based on predicted particle size distribution and real-time monitoring data, it dynamically optimizes ball loading rate, rotation speed and feeding rate through reinforcement learning algorithm; Digital twin interface: Generates a 3D visualization model of the mill's motion state.

Images