Method and system for predicting grinding particle size of sand mill

Abstract

The invention relates to the technical field of grinding, in particular to a sand mill grinding particle size prediction method and system.The method comprises the steps that a particle group balance model for grinding materials is established, and the particle group balance model comprises a selection distribution function and a smashing distribution function of the materials; performing gradient correction on the selection distribution function and the crushing distribution function to obtain a nonlinear function, and establishing a distribution proportion function of each particle size changing along with the grinding time based on the nonlinear function; obtaining a simulation value obtained through calculation of the distribution proportion function, determining each adjustment coefficient in the distribution proportion function based on the simulation value and the corresponding experiment value, and obtaining the distribution proportion function with the minimum distribution proportion difference; based on the distribution proportion function with the minimum distribution proportion difference, the grinding particle size is predicted; according to the method, gradient disappearance and gradient explosion in the parameter optimization fitting process can be inhibited, and the fitting precision is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of grinding, in particular to a sand mill grinding particle size prediction method and system. BACKGROUND

[0002] With the development of new energy battery technology, it is particularly important to predict the particle size and production capacity of ground battery materials. Accurately predicting the particle size distribution of grinding through parameters such as the filling amount of grinding medium, grinding time, and size of grinding medium is very important for the design of grinding equipment itself and related supporting grinding production lines.

[0003] In related technologies, using a matrix population balance model to perform parameter optimization fitting may easily lead to gradient disappearance or gradient explosion, which in turn causes the data to deviate from the measured data and reduces the fitting accuracy. SUMMARY

[0004] The present application aims to provide a sand mill grinding particle size prediction method and system, which aims to suppress gradient disappearance and gradient explosion during parameter optimization fitting and improve fitting accuracy.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical solutions: In a first aspect, the present application provides a sand mill grinding particle size prediction method, which includes the following steps: S100, a population balance model for grinding material is established, which includes a selection distribution function of the material and a crushing distribution function; S200, the selection distribution function and the crushing distribution function are gradient corrected to obtain a nonlinear function, and a distribution ratio function of each particle size changing with grinding time is established based on the nonlinear function; S300, a simulation value calculated by the distribution ratio function is obtained, and each adjustment coefficient in the distribution ratio function is determined based on the simulation value and the corresponding experimental value to obtain a distribution ratio function with the smallest distribution ratio difference; S400, the grinding particle size is predicted based on the distribution ratio function with the smallest distribution ratio difference.

[0006] Optionally, the selection distribution function and the crushing distribution function are gradient corrected to obtain a nonlinear function, and a distribution ratio function of each particle size changing with grinding time is established based on the nonlinear function, which includes: S210, the porosity and initial particle size of the material are obtained, and the adjustment index of the population balance model is corrected based on the porosity and initial particle size to obtain a nonlinear function; wherein the adjustment index of the population balance model is related to the crushing distribution function, the selection distribution function, and the particle size distribution at the time of feeding; S220, a time influence function is established, for each particle size, the rotor linear speed related to the particle size and the material itself characteristics are set as preset coefficients, and a product of the nonlinear function and the time influence function is taken as a distribution proportion function of the particle size.

[0007] Optionally, an expression of the nonlinear function is as follows: ; wherein, θ is an adjustment index of the particle population balance model, B is a breakage distribution function, and S is a selection distribution function, is an initial particle size distribution, u is a number of breakage events, represents porosity, represents a particle size value, and b represents an adjustment coefficient.

[0008] Optionally, an expression of the time influence function is as follows: wherein, represents a grinding time, , is an adjustment coefficient.

[0009] Optionally, a simulation value calculated through the distribution proportion function is obtained, each adjustment coefficient in the distribution proportion function is determined based on the simulation value and a corresponding experimental value, and a distribution proportion function with minimum distribution proportion difference is obtained. S310, a distribution proportion of each particle size interval under a plurality of corresponding grinding times is calculated based on the distribution proportion function, and a simulation value is obtained ; S320, a grinding experiment is performed on the material, a distribution proportion of each particle size interval under a plurality of grinding times is obtained, and a corresponding experimental value is obtained to the simulation value ; S330, a target function of an error between the simulation value and the experimental value is established, the target function is minimized to be solved, an optimal value of each adjustment coefficient in the distribution proportion function is determined, and a distribution proportion function with minimum distribution proportion difference is obtained.

[0010] Optionally, an expression of the target function is as follows: ; wherein, represents a target function, is a simulation value, is an experimental value. t represents a grinding time, i represents a particle size interval, m represents a total number of grinding times, and n represents a total number of particle size intervals.

[0011] In a second aspect, the embodiment of the present application provides a sand mill grinding particle size prediction system, the system comprises: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method of any one of the above.

[0012] The present application has the beneficial effects that: the present application discloses a sand mill grinding particle size prediction method and system, by introducing a nonlinear term function, the gradient correction of the selection distribution function and the crushing distribution function can inhibit the gradient disappearance and gradient explosion in the parameter optimization fitting process, effectively improve the fitting precision, and solve the problem that in the prior art, due to the lack of control of the nonlinear term, the gradient disappearance or gradient explosion is easily caused, and then the data deviates from the measured data. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0014] Figure 1 is a flowchart of the sand mill grinding particle size prediction method in the embodiment of the present application;

[0015] Figure 2 is a fitting curve diagram using the group balance model in the related art for fitting;

[0016] Figure 3 is a fitting curve diagram using the group balance model in the embodiment of the present application for fitting;

[0017] Figure 4 is a structure diagram of the sand mill grinding particle size prediction system in the embodiment of the present application. DETAILED DESCRIPTION

[0018] The concept, specific structure and generated technical effects of the present application will be described clearly and completely in the following embodiments and drawings, so as to fully understand the purpose, scheme and effect of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0019] In related technologies, dynamic models based on material crushing mechanisms, which incorporate the physical processes in mill grinding, are of great significance and value for optimizing the grinding process, improving grinding energy efficiency, and controlling output particle size. Matrix models treat the entire crushing process as an accumulation of repeated crushing events; population balance models (PBMs) view the crushing process as a continuous process in time and can examine the influence of material properties and mill operating conditions (grind media size, shaft speed, etc.) on material crushing.

[0020] The expression for the particle swarm balance model is as follows: ; ; ; ; ; ; ; ; ; ; in, It is the particle size distribution function of the material after u crushing events, where G represents the particle group. Represents the crushing distribution function. Indicates the choice of distribution function. This indicates the grinding time experienced in each "primitive" step. Represents the identity matrix. This refers to the "prime" shattering incident. This indicates the particle size distribution at the time of feeding. express The segment selection distribution function, This represents the cumulative crushing distribution function. θ and γ are the adjustment coefficient and adjustment exponent of the particle swarm balance model, respectively, and γ is the model parameter of the crushing distribution function. , as well as These parameters relate to the inherent properties of the material and the operating conditions of the equipment.

[0021] Matrix population balance model is to regard the comminution as a series of linked comminution events, the feed of each "elementary" comminution event is the discharge of the previous "elementary" comminution event, the longer the comminution time, the more the number of repeated "elementary" comminution. The size distribution of the feed and the discharge is represented by n discrete size intervals defined by n screen sizes in equal proportion, the size of the particles in the ith size interval is represented by the top size of the interval, i.e. the ith screen size. The comminution probability of the particles in each size interval is represented by the selection function , the physical meaning of which is the proportion of the particles in the ith size interval that is comminuted in one "elementary" comminution event, which may be different for different particle sizes. The distribution of the daughter particles of the particles in each size interval to other size intervals is represented by the breakage function , such as , which represents the proportion of the particles in the first size interval that is comminuted and falls into the second size interval. The breakage function is usually represented by the cumulative breakage function , such as , which represents the proportion of the particles in the first size interval that is comminuted and falls into the third size interval and below.

[0022] Assuming that a comminution process is composed of n "elementary" comminution events, the relationship between the feed and the discharge of the final comminution process can be described by the formula , i.e. the change of the particle population is obtained by subtracting the comminuted particle population from the newly born particle population, and then adding the initial particle population and multiplying the size distribution of the feed. Wherein, , represents the breakage distribution function, represents the selection distribution function, represents the grinding time experienced by each "elementary" step, represents the unit matrix, represents the "elementary" comminution event, represents the size distribution of the feed, represents the size distribution of the discharge.

[0023] But from the formula , it can be observed that the values of the selection distribution function and the breakage distribution function are continuously less than 1 or greater than 1. Therefore, in the formula , due to the lack of control of the nonlinear term, the value of after multiplication is easy to cause gradient disappearance or gradient explosion, and then cause the data to deviate from the measured data.

[0024] In order to solve the problem existing in the prior art that the value of The value is easy to cause gradient disappearance or gradient explosion, and further cause the problem that data deviates from measured data.

[0025] Referring to Figure 1 , Figure 1 The application provides a sand mill grinding particle size prediction method. S100, a particle group balance model for material grinding is established, and the particle group balance model comprises a selection distribution function of the material and a crushing distribution function; S200, the selection distribution function and the crushing distribution function are gradient corrected to obtain a nonlinear function, and a distribution proportion function of each particle size changing with grinding time is established based on the nonlinear function; S300, a simulation value calculated by the distribution proportion function is obtained, each adjustment coefficient in the distribution proportion function is determined based on the simulation value and a corresponding experimental value, and a distribution proportion function with minimum distribution proportion difference is obtained; S400, grinding particle size prediction is performed based on the distribution proportion function with the minimum distribution proportion difference.

[0026] After the initial particle size distribution of the material is obtained, the particle size distribution of the material in the grinding process can be predicted by the distribution proportion function with the minimum distribution proportion difference.

[0027] In the embodiments provided by the application, the selection distribution function and the crushing distribution function are gradient corrected by introducing a nonlinear term function, so that gradient disappearance and gradient explosion in the parameter optimization fitting process are inhibited, fitting precision is effectively improved, and the problem that the value after multiplication is easy to cause gradient disappearance or gradient explosion and further cause data to deviate from measured data is solved due to lack of control of the nonlinear term in the prior art.

[0028] In some embodiments, in S200, the selection distribution function and the crushing distribution function are gradient corrected to obtain a nonlinear function, and a distribution proportion function of each particle size changing with grinding time is established based on the nonlinear function, which comprises the following steps. S210, the porosity and the initial particle size of the material are obtained, and an adjustment index of the particle group balance model is corrected based on the porosity and the initial particle size to obtain a nonlinear function; wherein the adjustment index of the particle group balance model is related to the crushing distribution function, the selection distribution function and the particle size distribution at the time of feeding; S220, a time influence function is established, for each particle size, the rotor linear speed related to the particle size and the material itself characteristics are all set as preset coefficients, and the product of the nonlinear function and the time influence function is taken as the distribution proportion function of the particle size.

[0029] ​In some embodiments, the expression of the nonlinear function is: wherein θ is the adjustment index of the population balance model, B is the breakage distribution function, S is the selection distribution function, is the initial particle size distribution, i.e., the particle size distribution at the time of feeding, u is the number of breakage events, represents the porosity, represents the particle size value, and b represents the adjustment coefficient. b is related to the material parameters and the rotor structure related coefficient, and needs to be fitted by experimental data.

[0030] In some embodiments, the expression of the time influence function is: wherein, represents the grinding time, , is the adjustment coefficient.

[0031] Specifically, the rotor linear speed related to the distribution ratio function of a certain particle size and the material itself characteristics are all set to a preset coefficient to obtain the distribution ratio function of a certain particle size; the expression of the distribution ratio function is: wherein, represents a function varying with the porosity and the initial particle size, represents a function varying with time, , represents the porosity, represents the grinding time, represents the particle size value.

[0032] In the present embodiment, starting from the idea of population balance, a nonlinear function is introduced to gradient correct the selection distribution function and the breakage distribution function, and the particle size distribution of the material is separated by the separation variable method into a function varying with time and a function varying with the porosity and the initial particle size, and the specific principle is: The distribution ratio function of a certain particle size is related to the grinding medium or the porosity , the rotor linear speed , the material itself characteristics , the grinding time , and the particle size value . In the present embodiment, the particle size distribution of the lithium iron phosphate electrode material after the production process is stable, so the rotor linear speed and the material itself characteristics are not discussed, and are all set to a preset coefficient. In particular, the rotor linear speed and material itself characteristics is set to 1. In later stage, according to different material itself characteristics and rotor linear velocity , the preset coefficient is adjusted accordingly.

[0033] According to the principle of separation of variables, the distribution ratio function can be expressed as The function of particle size distribution of material changing with time is a linear function, which shows that time has a positive correlation with the grinding system, , is an adjustment coefficient; , is a parameter related to the system itself, which needs to be fitted by experimental data.

[0034] The function of particle size distribution of material changing with time adopts a linear term function fitting, which can simplify the calculation process and reduce the dependence on the selection of time element. According to the principle of separation of variables, the time term, particle size, porosity and other parameters in the distribution ratio function are separated, which can achieve time-space decoupling.

[0035] It should be noted that in the present application, the nonlinear term used for gradient correction of the selected distribution function and the crushing distribution function includes but is not limited to the nonlinear function In the present embodiment, by introducing the nonlinear term, the distribution ratio function of a certain particle size has lower requirements for the initial particle size distribution and the element selection of grinding time, and the selection of initial value causes less disturbance to the final result.

[0036] In some embodiments, in S300, the simulation value calculated by the distribution ratio function is obtained, and each adjustment coefficient in the distribution ratio function is determined based on the simulation value and the corresponding experimental value, so as to obtain the distribution ratio function with the smallest distribution ratio difference; In S310, the distribution ratio of each particle size interval under a plurality of grinding times is calculated based on the distribution ratio function to obtain simulation values . In S320, a grinding experiment is performed on the material to obtain the distribution ratio of each particle size interval under a plurality of grinding times, and corresponding experimental values are obtained. ; In S330, the calculation simulation values and the experimental values The target function of the error between the simulation value and the experimental value is minimized to determine the optimal value of each adjustment coefficient in the distribution ratio function, and the distribution ratio function with the minimum distribution ratio difference is obtained.

[0037] Specifically, by minimizing the target function, the adjustment coefficient in the distribution ratio function when the distribution ratio difference is minimum is calculated as the optimal value of the adjustment coefficient b, , in the distribution ratio function, and the distribution ratio function with the minimum distribution ratio difference is obtained. The grinding particle size prediction is performed based on the distribution ratio function with the minimum distribution ratio difference.

[0038] In some embodiments, the expression of the target function is: ; Wherein, represents the target function, is the simulation value, is the experimental value. t represents the grinding time, i represents the particle size interval, m represents the total number of grinding times, and n represents the total number of particle size intervals.

[0039] Specifically, the target function can be optimized by means of the fmincon function in Matlab, and by finding the optimal adjustment parameter, the error between the experimental value and the simulation value is minimized. The fmincon function is a function in Matlab for solving nonlinear programming problems, and is particularly suitable for solving the minimum value problem of a multivariate function with nonlinear constraints.

[0040] In an embodiment, the algorithm of the group balance model in the related art and the improved group balance model algorithm are compared respectively, a grinding machine with a model of KDP400 is selected as the grinding equipment, the same 0.1mm zirconium beads are used as the grinding material, the filling rate is 80%, the grinding time is 90 minutes, the same rotor structure and speed are used, and the same batch is used as the control group to compare the difference between the two calculation methods, and the results are shown in Figure 2 Using the group balance model in the field of ultra-fine grinding particle size estimation will cause gradient explosion, resulting in poor fitting of the data pieces, and gradually increasing over time.

[0041] Using the improved group balance model, the specific fitting curve is shown in Figure 3 It can be seen that the fitting degree is higher than that of the group balance model, and the fitting curve follows well over time, and is not sensitive to the initial value of the parameter optimization, and does not produce under-fitting.

[0042] Corresponding to the method of Figure 1 , reference is made to Figure 4The embodiment of the present application provides a sand mill grinding particle size prediction system, comprising: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the above method.

[0043] It can be seen that the contents in the above method embodiments are all applicable to the system embodiment, the system embodiment specifically implements the same functions as the above method embodiments, and achieves the same beneficial effects as the above method embodiments.

[0044] Those skilled in the art can understand that all or some of the above disclosed methods and systems can be implemented as software, firmware, hardware and appropriate combinations thereof. Some or all physical components can be implemented as software executed by a processor, such as a central processing unit, a digital signal processor or a microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software can be distributed on a computer readable medium, which can include computer storage media (or non-transitory media) and communication media (or transitory media). As known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information such as computer readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. In addition, as known to those skilled in the art, communication media generally includes computer readable instructions, data structures, program modules or other data in modulated data signals such as carrier waves or other transmission mechanisms, and can include any information delivery medium.

[0045] The above is a specific description of the preferred embodiment of the present disclosure, but the present disclosure is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the present disclosure, and these equivalent modifications or replacements are all included in the scope defined by the claims of the present disclosure.

Claims

1. A method of predicting the grind size of a sand mill, characterized by, The method comprises the following steps: S100, establishing a particle group balance model for grinding the material, the particle group balance model comprising a selection distribution function and a crushing distribution function of the material; S200, performing gradient correction on the selection distribution function and the crushing distribution function to obtain a nonlinear function, and establishing a distribution ratio function of each particle size changing with grinding time based on the nonlinear function; S300, obtaining a simulation value calculated by the distribution ratio function, determining each adjustment coefficient in the distribution ratio function based on the simulation value and a corresponding experimental value, and obtaining a distribution ratio function with minimum distribution ratio difference; S400, performing grinding particle size prediction based on the distribution ratio function with minimum distribution ratio difference.

2. The method of claim 1, wherein, The gradient correction on the selection distribution function and the crushing distribution function to obtain a nonlinear function, and the establishment of a distribution ratio function of each particle size changing with grinding time based on the nonlinear function, comprise: S210, obtaining porosity and initial particle size of the material, and correcting an adjustment index of the particle group balance model based on the porosity and the initial particle size to obtain a nonlinear function; wherein the adjustment index of the particle group balance model is related to the crushing distribution function, the selection distribution function and the particle size distribution at the time of feeding; S220, establishing a time influence function, for each particle size, setting a rotor linear speed related to the particle size and a material itself characteristic as a preset coefficient, and taking a product of the nonlinear function and the time influence function as a distribution ratio function of the particle size.

3. The method of claim 2, wherein the step of determining the particle size distribution of the sand is performed by a method selected from the group consisting of sieve analysis, laser diffraction, image analysis, and a combination thereof. An expression of the nonlinear function is: ； where θ is the adjustment index of the population balance model, B is the breakage distribution function, S is the selection distribution function, is the initial particle size distribution, u is the number of breakage events, denotes the porosity, denotes the particle size value, b denotes the adjustment factor.

4. The method of claim 2, wherein the method is characterized by: The expression of the time influence function is: wherein, denotes the grinding time, , is an adjustment factor.

5. The method of claim 1, wherein, The simulation value calculated by the distribution ratio function, the determination of each adjustment coefficient in the distribution ratio function based on the simulation value and a corresponding experimental value, and the obtaining of a distribution ratio function with minimum distribution ratio difference; S310, calculating the distribution proportion of each particle size interval under the corresponding plurality of grinding times based on the distribution proportion function, to obtain a simulation value ; S320, performing a grinding experiment on the material to obtain a distribution proportion of each particle size interval under a plurality of grinding times, and obtain the experimental value corresponding to the simulation value corresponding experimental value ; S330, establishing a calculation simulation value and an experimental value between the error of the target function, the target function is minimized to determine the optimal value of each adjustment coefficient in the distribution ratio function, and the distribution ratio function with the smallest distribution ratio difference is obtained.

6. The method of claim 5, wherein, An expression of the objective function is: ； wherein denotes the objective function, is the simulation value, is the experimental value, t denotes the grinding time, i denotes the particle size interval, m denotes the total number of grinding times, and n denotes the total number of particle size intervals.

7. A sand mill grind size prediction system characterized by, The system comprises: at least one processor; at least one memory for storing at least one program; when the at least one program is executed by the at least one processor, the at least one processor implements the method in any one of claims 1 to 6.

Images