Lithium ion battery positive and negative electrode active material discrete element contact parameter calibration method
By combining physical experiments on the angle of repose with multi-stage simulation optimization, and employing Plackett-Burman experiments to screen significant parameters and response surface methodology to optimize parameter combinations, the problem of low accuracy and efficiency in the calibration of contact parameters for positive and negative electrode active materials in lithium-ion batteries was solved. This resulted in efficient and accurate parameter calibration, meeting the requirements of electrode manufacturing and performance simulation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-23
- Publication Date
- 2026-03-13
AI Technical Summary
Existing technologies struggle to efficiently and accurately calibrate the discrete element contact parameters of positive and negative electrode active materials in lithium-ion batteries, resulting in low accuracy and efficiency of DEM simulations, high costs, and an inability to meet the needs of electrode manufacturing and performance simulation.
By combining physical experiments on the angle of repose with multi-stage simulation optimization, significant parameters were screened through Plackett-Burman experiments, a quadratic regression model was established using the response surface methodology, the optimal parameter combination was optimized, and the discrete element model was validated.
This improves the accuracy and efficiency of contact parameter calibration for positive and negative electrode active materials in lithium-ion batteries, reduces costs, and provides reliable electrode manufacturing and performance simulation results.
Smart Images
Figure CN121662230A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electrode material parameter calibration technology, and in particular to a discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries. Background Technology
[0002] The mechanical properties and contact behavior of active material particles in lithium-ion batteries' positive and negative electrodes are key factors affecting the compaction density, interfacial mechanical stability, and long-term cycle life of battery electrodes. The discrete element method (DEM) can effectively simulate the microscopic mechanical response of battery materials during manufacturing and cycling; however, its simulation reliability highly depends on the accuracy of contact parameters, including elastic modulus, static / dynamic friction coefficients, coefficient of restitution, and surface energy. Currently, these parameters are mainly measured using macroscopic mechanical testing equipment, but due to size effects, it is difficult to directly and accurately obtain the contact characteristics of micron-sized particles. Although micro-nano measurement equipment such as nanoindenters and atomic force microscopes can be used, their high cost, complex processes, and stringent operational requirements result in low parameter acquisition efficiency and high costs, severely hindering the widespread application of DEM technology.
[0003] Existing technologies include methods for parameter calibration that combine experiments and simulations, such as iteratively fitting the axial force-displacement response using uniaxial compression experiments and DEM simulations. However, these methods remain complex, and both accuracy and efficiency need improvement. Furthermore, while similar experiment-simulation calibration methods exist in fields like agricultural engineering, the mechanical properties, microstructure, deformation mechanisms, and accuracy requirements of battery electrode materials differ fundamentally from those of biomass materials. Their models, response indices, and validation standards are designed for biomass molding processes and cannot be directly applied to the field of battery electrode material fabrication, where high precision, reliability, and process relevance are crucial. Therefore, establishing a solution that can efficiently and accurately calibrate the discrete element contact parameters of lithium-ion battery positive and negative electrode active materials while effectively balancing accuracy, efficiency, and cost is essential for obtaining reliable electrode manufacturing and performance simulation results.
[0004] There is still a lack of a contact parameter calibration method in the current technology that is specifically designed for the characteristics of lithium-ion battery electrode materials and can balance calibration accuracy, efficiency and cost-effectiveness. Summary of the Invention
[0005] Therefore, it is necessary to provide a discrete element method for calibrating the contact parameters of positive and negative electrode active materials of lithium-ion batteries, addressing the aforementioned technical problems in the existing technology. By combining physical experiments on the angle of repose with multi-stage simulation optimization, the method can systematically and accurately obtain key contact parameters, taking into account calibration accuracy, efficiency, and cost-effectiveness.
[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows: A discrete element method for calibrating the contact parameters of positive and negative electrode active materials in lithium-ion batteries includes the following steps: S1. Obtain the macroscopic mechanical response of the electrode active material through the angle of repose test, and establish the corresponding discrete element model; S2. Obtain the parameters to be calibrated and their value ranges by combining the database and pre-experiment. Use the Plackett-Burman experiment to screen out the significant parameters that have a significant impact on the target response value. And use the steepest climbing experiment to initially approximate the optimal parameter range. S3. Based on the response surface methodology, establish a quadratic regression model of the angle of repose and significant parameters, and perform multi-parameter collaborative optimization with the goal of minimizing the relative error to determine the optimal parameter combination; S4. Substitute the optimal parameter combination into the discrete element model in step S1 for simulation verification.
[0007] Preferably, step S1 includes: Step S11: Measure the angle of repose of the electrode active material and use it as the response value of the parameter calibration experiment; Step S12: Determine the particle size distribution of the electrode active material and establish a discrete element model.
[0008] Preferably, in step S11, the funnel method is used to determine the angle of repose of the electrode active material, and the experimental device is an angle of repose tester; The specific operation of step S12 is as follows: use a scanning electron microscope to observe the electrode active material under a microscope, select at least 3-5 images with different fields of view, perform binarization processing on them, obtain the particle size distribution, obtain the values of D10, D50, and D90, calculate the median particle size and the main distribution range of the particle size, then set the normal distribution parameters consistent with the statistical results in the discrete element software, generate particles that conform to the statistical characteristics of real materials, debug and determine the total number of particles generated and the generation rate and mode in the model through simulation pre-experiment, and complete the construction of a discrete element model that can replace real materials for simulation.
[0009] Preferably, in step S1, a simplified three-dimensional model is geometrically scaled and established. The three-dimensional model includes the funnel and base model of the angle of repose tester. In the simulation environment, by setting the parameters of the pellet plant, a group of particles with specific physical property parameters is generated, and the physical process of them falling from the funnel and naturally accumulating on the base platform to form a material pile is simulated.
[0010] Preferably, the formed stable stockpile is post-processed using an image processing algorithm. By identifying the stockpile outline and performing multiple sampling measurements along different directions and positions of the stockpile, the average value is finally calculated as the angle of repose of the batch of material.
[0011] Preferably, the parameters to be calibrated in step S2 include intrinsic parameters, basic contact parameters, and contact model parameters. The intrinsic parameters include the density, Young's modulus, and Poisson's ratio of the positive and negative electrode active materials. The basic contact parameters include the collision recovery coefficient and the static / rolling friction coefficient. The contact model parameters include surface energy.
[0012] Preferably, in step S2, after the Plackett-Burman test screens out significant parameters, the steepest climbing experiment selects the top three factors in terms of influence to conduct the steepest climbing experiment. The factor with the highest significance is used as the climbing direction unit, and the average of the difference between its high and low levels is used as the step size. The remaining non-significant factors are fixed at the intermediate level, and the experimental plan is arranged accordingly.
[0013] Preferably, step S3 includes: S31. Box spectroscopy for experimental variables that have a significant impact in the Plackett-Burman experiment. Behnken test; S32. Perform variance analysis on the Box-Behnken test results, further analyze the significance of each experimental variable, interaction term, and quadratic term on the target response value, and obtain the second-order regression equation of the rest angle through regression fitting analysis of the experimental results using the Box-Behnken test, and analyze the interaction effect of the regression model. S33. Using Design-Expert software, with the rest angle value obtained from physical experiments as the target value, solve the optimized second-order regression equation to obtain the result.
[0014] Preferably, Box In the Behnken experiment, based on the results of the steepest climb experiment, the set of data with the smallest relative error of the angle of repose was selected as the intermediate level. The two sets of data above and below the intermediate level were selected as the low level and high level for experimental design. The angle of repose was simulated and calculated for each set of experimental data. The influence factor was taken at three levels from low to high and coded as -1, 0 and 1 respectively for analysis.
[0015] Preferably, the specific operation of step S4 is as follows: substitute the optimal parameters into the discrete element model in step S1 and repeat the experiment multiple times to obtain the angle of repose through simulation. The relative error between the simulated experiment and the actual experiment's angle of repose is used to prove that the calibration parameters can effectively represent the stacking characteristics of the electrode active material, wherein the relative error is controlled within 2%.
[0016] Due to the adoption of the above technical solutions, the present invention has the following advantages compared with the prior art: This invention is specifically designed for the characteristics of positive and negative electrode active materials for lithium-ion batteries. It fully considers their mechanical behavior during the manufacturing process and effectively overcomes the problems of size limitations, equipment dependence, and low calibration efficiency in traditional measurement methods. This method not only significantly improves the reliability and accuracy of electrode material contact parameter calibration, but also simplifies the experimental process. The obtained parameters are more consistent with the actual working conditions of battery electrode preparation, thus providing accurate and reliable discrete element model parameter inputs for electrode manufacturing process optimization and battery performance simulation. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the angle of repose measurement according to the present invention; Figure 2 This is a particle size distribution diagram of Mn3O4 in this invention; Figure 3 This is a simulation model diagram of the stacking experiment of the present invention; Figure 4 This is a schematic diagram of the repose angle measurement in the simulation model of the present invention; Figure 5 This is a Pareto diagram of the present invention; Figure 6 This is a schematic diagram of the interaction term between the rolling friction coefficient E and the surface energy J of Mn3O4-Mn3O4 according to the present invention; Figure 7 This is a schematic diagram of the interaction term between the collision recovery coefficient F and the surface energy J of the active material and device of the present invention; Figure 8 The figure shows the simulation results of this invention. Detailed Implementation
[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
[0020] Existing technologies include methods for parameter calibration that combine experiments and simulations, such as iteratively fitting the axial force-displacement response using uniaxial compression experiments and DEM simulations. However, these methods remain complex, and both accuracy and efficiency need improvement. Furthermore, while similar experiment-simulation calibration methods exist in fields like agricultural engineering, the mechanical properties, microstructure, deformation mechanisms, and accuracy requirements of battery electrode materials differ fundamentally from those of biomass materials. Their models, response indices, and validation standards are designed for biomass molding processes and cannot be directly applied to the field of battery electrode material fabrication, where high precision, reliability, and process relevance are crucial. Therefore, establishing a solution that can efficiently and accurately calibrate the discrete element contact parameters of lithium-ion battery positive and negative electrode active materials while effectively balancing accuracy, efficiency, and cost is essential for obtaining reliable electrode manufacturing and performance simulation results.
[0021] Based on this, the present invention provides a discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries, comprising the following steps: S1. Obtain the macroscopic mechanical response of the electrode active material through the angle of repose test, and establish the corresponding discrete element model; S2. Obtain the parameters to be calibrated and their value ranges by combining the database and pre-experiment. Use the Plackett-Burman experiment to screen out the significant parameters that have a significant impact on the target response value. And use the steepest climbing experiment to initially approximate the optimal parameter range. S3. Based on the response surface methodology, establish a quadratic regression model of the angle of repose and significant parameters, and perform multi-parameter collaborative optimization with the goal of minimizing the relative error to determine the optimal parameter combination; S4. Substitute the optimal parameter combination into the discrete element model in step S1 for simulation verification.
[0022] The calibration method of this invention systematically achieves accurate acquisition of key contact parameters by combining physical experiments on the angle of repose with multi-stage simulation optimization, taking into account calibration accuracy, efficiency and cost-effectiveness.
[0023] In a specific embodiment, step S1 includes: Step S11: Measure the angle of repose of the electrode active material and use it as the response value of the parameter calibration experiment; Step S12: Determine the particle size distribution of the electrode active material and establish a discrete element model.
[0024] In a specific embodiment, step S11 uses the funnel method to determine the angle of repose of the electrode active material, and the experimental apparatus is an angle of repose measuring instrument. The specific operation of the angle of repose determination is as follows: the angle of repose of the electrode active material is measured using the angle of repose measuring instrument. During the test, the material is slowly added to the funnel with a spatula, and it falls along the funnel onto the cylindrical platform to form an accumulation state. Once the electrode active material powder has filled the entire cylindrical platform and the accumulation height remains stable, the addition of electrode active material is stopped. This measurement is repeated 3 to 5 times, and the average value is calculated. In a specific embodiment, step S12 involves the following steps: The target powder material of the electrode active material is observed using a scanning electron microscope (SEM). At least 3-5 images from different fields of view are selected to ensure the representativeness of the statistical results and avoid local bias. The acquired SEM images are binarized to accurately identify and statistically analyze the particle outline size, thereby obtaining the cumulative particle size distribution data of the powder material and obtaining the values of D10, D50, and D90. Based on the measured particle size distribution data, the median particle size and the main distribution interval of the particle size are calculated. Then, based on this, normal distribution parameters consistent with the statistical results are set in the discrete element method (EDEM) software to generate particles that conform to the statistical characteristics of real materials. Furthermore, to define the contact mechanical behavior between particles, based on the macroscopic adhesion characteristics exhibited by the positive and negative electrode powder materials, the appropriate "Hertz-Mindlin with JKR" algorithm is selected to simulate the adhesion system. The "Cohesion" contact model was used. Finally, the total number of particles generated and their generation rate and mode in the model were determined through simulation pre-experimentation to ensure the stability of numerical calculation, thereby completing the construction of a discrete element model that can replace real materials for simulation.
[0025] In a specific embodiment, to improve computational efficiency, the actual instrument can be geometrically scaled proportionally to create a simplified 3D model. Specifically, in step S1, a simplified 3D model is created by geometrically scaling proportionally. This 3D model typically only needs to include models of core components such as the funnel and base of the angle of repose tester. Subsequently, in the simulation environment, by setting the parameters of the particle factory, a particle group with specific physical properties is generated, and the physical process of its falling from the funnel and naturally accumulating on the base platform to form a stockpile is simulated. The parameters set here refer to the parameters to be calibrated, including intrinsic parameters, basic contact parameters, and contact model parameters. Intrinsic parameters include the density, Young's modulus, and Poisson's ratio of the positive and negative electrode active materials; basic contact parameters include the collision recovery coefficient and the static / rolling friction coefficient; and contact model parameters include surface energy.
[0026] In a specific embodiment, to obtain high-precision angle of repose data, after simulation, an image processing algorithm (such as a Python script) is used to post-process the formed stable stockpile. This program identifies the stockpile outline and performs multiple sampling measurements along different directions and positions of the stockpile, finally calculating the average value as the angle of repose result for that batch of material, effectively avoiding random errors that may be caused by a single measurement. This scaling step can be flexibly adjusted according to computing resources and accuracy requirements; the post-processing algorithm is not limited to Python scripts, but can also be other programs with image recognition and calculation functions.
[0027] In a specific embodiment, the parameters to be calibrated in step S2 include intrinsic parameters, basic contact parameters, and contact model parameters. Intrinsic parameters include the density, Young's modulus, and Poisson's ratio of the positive and negative electrode active materials. Basic contact parameters include the collision recovery coefficient and the static / rolling friction coefficient. Contact model parameters include surface energy (JKR surface energy). First, preliminary values are assigned to the parameters using the EDEM's built-in material database (GEMM). For key simulation parameters such as JKR surface energy, which are difficult to obtain directly and are sensitive to particle size and moisture content, their value range can be preliminarily determined through simulation pre-experiments.
[0028] In a specific embodiment, Plackett's design software was used to design the repose angle of the electrode active material. The Burman experiment was used to determine the significance of each parameter's influence on the angle of repose; analysis of variance was performed on the results to obtain the parameter significance analysis results. This invention does not restrict the specific selection of experimental design software; any software tool capable of performing statistical analysis and optimization functions such as Plackett-Burman experimental design, analysis of variance, and response surface optimization can be applied to the parameter calibration method described in this patent.
[0029] In a specific embodiment, after the Plackett-Burman experiment screens out significant parameters in step S2, the steepest climb experiment selects the top three factors in terms of influence for the steepest climb experiment. The factor with the highest significance is used as the unit of climb direction, and the average of the difference between its high and low levels is used as the step size. All other non-significant factors are fixed at the intermediate level. The experimental plan is arranged accordingly. Discrete element simulation is used to obtain the results of each set of rest angles, and the relative error is calculated by comparing them with the measured values. The parameter combination with the smallest error is then determined.
[0030] In a specific embodiment, step S3 includes: S31. Box spectroscopy for experimental variables that have a significant impact in the Plackett-Burman experiment. Behnken test; S32. Perform variance analysis on the Box-Behnken test results, further analyze the significance of each experimental variable, interaction term, and quadratic term on the target response value, and obtain the second-order regression equation of the rest angle through regression fitting analysis of the experimental results using the Box-Behnken test, and analyze the interaction effect of the regression model. S33. Using Design-Expert software, with the rest angle value obtained from physical experiments as the target value, solve the optimized second-order regression equation to obtain the result.
[0031] In a specific embodiment, Box In the Behnken experiment, based on the results of the steepest climb experiment, the set of data with the smallest relative error of the angle of repose was selected as the intermediate level. The two sets of data above and below the intermediate level were selected as the low level and high level for experimental design, and the angle of repose was simulated and calculated for each set of experimental data. The influence factor was taken at three levels from low to high and coded as -1, 0, and 1 respectively for analysis. Based on the results of the steepest climb experiment, the parameter combination with the smallest relative error of the angle of repose was selected as the center point (level 0), and the two sets of parameters above and below it were selected as the low level (-1) and high level (1) respectively. Response surface methodology was designed accordingly, and the angle of repose of each set of experiments was calculated by discrete element method simulation.
[0032] In a specific embodiment, step S4 is specifically performed as follows: the obtained optimal parameters are substituted into the discrete element model in step S1 and the experiment is repeated multiple times to simulate the angle of repose and the actual experimental stacking morphology. The relative error between the simulated experiment and the actual experiment's angle of repose is used to prove that the calibration parameters can effectively represent the stacking characteristics of the electrode active material, wherein the relative error is controlled within 2%.
[0033] The following is in conjunction with the appendix Figure 1 To be continued Figure 8 Specific embodiments of the present invention will be described in detail below.
[0034] This invention uses Mn3O4, a positive and negative electrode active material, as an example. The discrete element method for calibrating the contact parameters of Mn3O4 includes the following steps: S1. Obtain the macroscopic mechanical response of the electrode active material through repose angle testing and establish the corresponding discrete element model. Specifically, this includes: Step S11: Measure the angle of repose of the electrode active material Mn3O4 and use it as the response value of the parameter calibration experiment.
[0035] The angle of repose of the active material Mn3O4 was determined using the funnel method, with an angle of repose measuring instrument as the experimental setup. This apparatus mainly consists of an iron stand, a funnel, and a cylindrical platform. During the experiment, the active material was slowly added to the funnel using a spatula, falling down the funnel onto the cylindrical platform and accumulating. Once the powder had completely covered the cylindrical platform and the accumulation height remained stable, the addition of active material was stopped. This process should be repeated 3-5 times, and the average value should be calculated. A schematic diagram of the measurement is attached. Figure 1 As shown. Based on the above method, the average repose angle was obtained as 41.75° after multiple experiments.
[0036] Step S12: Determine the particle size distribution of the active material Mn3O4 and establish a discrete element model.
[0037] Scanning electron microscopy was used to observe the target powder material of active material Mn3O4. At least 3-5 different fields of view were selected to avoid local bias and obtain high-quality images. These images were then binarized to obtain the particle size distribution of the Mn3O4 material (D10=4.4 μm, D50=7.25 μm, D90=11.93 μm), as shown in the attached image. Figure 2 As shown, the median particle size of Mn3O4 and the main range of particle size are calculated, which can represent the entire particle system in the calculation.
[0038] Then, spherical Mn3O4 particles were created in the Discrete Element Method (EDEM) software according to the normal distribution method consistent with the statistical results. At the same time, the generation time and total number of Mn3O4 were determined by combining simulation pre-experiments.
[0039] Since the angle of repose of Mn3O4 is independent of the size of the measuring instrument and the mass of the material being measured, to simplify the calculation, the angle of repose measuring instrument was scaled down to a ratio of 1:5, and then a 3D model was created. Only the funnel and base models of the angle of repose measuring instrument were imported into the simulation software. The specific simulation model is shown in the attached figure. Figure 3 As shown.
[0040] To more accurately measure the angle of repose of the stockpiled material, an image processing algorithm (based on a Python script) was used to post-process the simulation results. Multiple sampling measurements were performed along different directions and positions of the stockpile, and the average value was calculated as the angle of repose for that batch of material. This effectively avoided random errors that might arise from a single measurement. A schematic diagram of multiple angle of repose measurements is attached. Figure 4 As shown.
[0041] S2. Using a comprehensive database and preliminary experiments, the parameters to be calibrated and their value ranges are obtained. The Plackett-Burman experiment is used to screen for significant parameters that have a significant impact on the target response value. Finally, the steepest ramp experiment is used to initially approximate the optimal parameter range. Specifically, this includes: Obtain the parameters to be calibrated and their value ranges: Based on the simulation pre-experiment, set the parameters required for the simulation of Mn3O4 material, as shown in Table 1.
[0042] Table 1. Parameter table of the simulation model to be calibrated Plackett-Burman test results and analysis: The upper and lower limits of the test parameters are represented by +1 and -1 respectively, and the test parameters are AJ coded as shown in Table 2.
[0043] Table 2 List of Plackett-Burman test parameters A Plackett-Burman experiment was designed to measure the angle of repose of Mn3O4 using experimental design software. Twelve groups of experiments were designed, and the results are shown in Table 3. Analysis of variance was performed on the results, and the final results of the parameter significance analysis are shown in Table 4. A Pareto diagram is attached. Figure 5 As shown.
[0044] Table 3 Plackett Burman's experimental protocol and results table Table 4 Plackett Burman's test significance analysis table As shown in the Pareto diagram and Table 4, the P values of the rolling friction coefficient E, JKR surface energy J, and collision recovery coefficient F of the active material Mn3O4 are all less than 0.05, indicating that they have the most significant impact on the repose angle of the response value; the other parameters have a relatively small impact on the simulation results.
[0045] The steepest ramp experiment was used to approximate the region of maximum response value: After the Plackett-Burman experiment, based on the selected significance parameters, the top three factors (E, J, F) were selected for the steepest ramp experiment. The most significant factor was used as the ramp unit, and the step size was the average difference between the high and low levels of the factor. The remaining parameters were selected using intermediate values. The angle of repose for each group of data was calculated using a discrete element model and compared with the measured angle of repose to calculate the relative error. Since the most significant parameter is the rolling friction coefficient E between active materials, E was used as the ramp unit. The experimental scheme and results are shown in Table 5. Table 5 shows that as the experimental factor values increase, the angle of repose gradually increases, and the relative error first decreases and then increases, with factor 3 showing the smallest error.
[0046] The steepest climb experiment in this invention is an experimental method used to determine the significant factors affecting experimental results and to find the optimal response region.
[0047] Table 5 Analysis of the results of the steepest climb test S3. Based on the response surface methodology, establish a quadratic regression model for the angle of repose and significance parameters. Perform multi-parameter collaborative optimization with the objective of minimizing relative error to determine the optimal parameter combination. Specifically, this includes: S31. Box spectroscopy for experimental variables that have a significant impact in the Plackett-Burman experiment. Behnken test.
[0048] Based on the results of the steepest climb experiment, the data set with the smallest relative error in the angle of repose (data set 3) was selected as the intermediate level. The two data sets above and below this intermediate level (data sets 4 and 5) were selected as the low and high levels for experimental design, and the angle of repose was simulated and calculated for each data set. Influence factors were selected at three levels from low to high, and coded as -1, 0, and 1 respectively for analysis. Response surface methodology was then designed, and the angle of repose for each experimental set was calculated using discrete element method (DEM) simulation. The experimental scheme and results are shown in Table 6.
[0049] Table 6 Box Behnken test protocol and results table S32. Perform variance analysis on the Box-Behnken test results to further analyze the significance of each experimental variable, interaction term, and quadratic term on the target response value. Use the Box-Behnken test to perform regression fitting analysis on the experimental results to obtain the second-order regression equation of the rest angle and analyze the interaction effect of the regression model.
[0050] By performing an analysis of variance on the Box-Behnken experiment results in Table 6, we can further analyze the significance of each experimental variable, interaction term, and quadratic term on the target response value, as shown in Table 7.
[0051] Table 7. Analysis of Variance Table for the Quadratic Regression Model The second-order regression equation for the rest angle was obtained by regression fitting analysis of the experimental results through the Box-Behnken experiment, as shown in Table 8.
[0052] Table 8. Quadratic Regression Equations for the Mathematical Regression Model As shown in the table above, the P-value of the fitted model is <0.001, and the P-value of the missing-fit term is >0.05, indicating that the model is highly significant and the regression equation has a good fit. The model's coefficient of determination is 0.994, and the corrected coefficient of determination is 0.982, indicating that the model's prediction of actual values is highly reliable and can accurately reflect the relationship between experimental factors and the relative error of the angle of repose. It can be used for the prediction and analysis of the angle of repose with small error.
[0053] Through Box-Behnken experiments, while ensuring model significance and fit, insignificant terms can be ignored, and the quadratic regression equation can be simplified to: Analysis of the interaction effects of the regression model: Appendix Figure 6 A schematic diagram of the interaction term between the rolling friction coefficient E and the surface energy J of Mn3O4-Mn3O4 is attached. Figure 7 This is a schematic diagram of the interaction term between the collision recovery coefficient F of the active material and the device and the surface energy J.
[0054] From the appendix Figure 6 and attached Figure 7 It can be intuitively observed that when the value of parameter F is fixed, within a unit range, the effect curves of parameters E and J are steeper, indicating a more significant impact on the angle of repose, and both parameters E and J have a positive effect on the angle of repose. When the value of parameter E is fixed, the effects of parameters F and J on the angle of repose are relatively gentler, with the effect curve of parameter J being steeper than that of parameter F within a unit range, indicating a more significant impact, and both parameters have a positive effect on the angle of repose. Furthermore, the response surface methodology shows that the order of significance of the factors' effects on the angle of repose is: E > J > F, which is consistent with the results shown in the significance analysis table.
[0055] S33. Using Design-Expert software, with the rest angle obtained from physical experiments as the target value, solve the optimized second-order regression equation to obtain the optimal parameter combination.
[0056] Using Design-Expert software, with the repose angle obtained from physical experiments as the target value, the optimal solution was found for the optimized second-order regression equation. The obtained parameter values were: rolling friction coefficient between Mn3O4 and Mn3O4 active particles E=0.163, static friction coefficient between Mn3O4 and equipment F=0.213, and JKR surface energy J=0.108 J / m. 2 .
[0057] S4. Substitute the optimal parameter combination into the discrete element model in step S1 for simulation verification.
[0058] The parameters obtained above were substituted into the EDEM software for three simulation experiments for verification. The simulated angle of repose was 41.77°, while the measured angle of repose obtained in step S1 was 41.75°. The relative error between the simulated and measured angle of repose was calculated to be 0.048%. (Appendix) Figure 8 The simulation results are shown in the attached figure. Figure 1 Comparing the measured images, the two outlines are very similar, indicating that the selected parameters can well represent the stacking characteristics of active Mn3O4 particles.
[0059] When implementing the parameter calibration method described in this invention, any experimental design software with Plackett-Burman experimental design, analysis of variance, and response surface optimization functions can be used. It is not limited to specific commercial or open-source tools. Any software that can achieve the above-mentioned significance screening, model building, and multi-parameter collaborative optimization analysis is applicable to the method of this invention.
[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0061] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.
Claims
1. A method for calibrating discrete element contact parameters of positive and negative electrode active materials for lithium-ion batteries, characterized in that, Includes the following steps: S1. Obtain the macroscopic mechanical response of the electrode active material through the angle of repose test, and establish the corresponding discrete element model; S2. Obtain the parameters to be calibrated and their value ranges by combining the database and preliminary experiments. Use the Plackett-Burman experiment to screen out the significant parameters that have a significant impact on the target response value, and use the steepest climbing experiment to initially approximate the optimal parameter range. S3. Based on the response surface methodology, establish a quadratic regression model of the angle of repose and significant parameters, and perform multi-parameter collaborative optimization with the goal of minimizing the relative error to determine the optimal parameter combination; S4. Substitute the optimal parameter combination into the discrete element model in step S1 for simulation verification.
2. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 1, characterized in that, Step S1 includes: Step S11: Measure the angle of repose of the electrode active material and use it as the response value of the parameter calibration experiment; Step S12: Determine the particle size distribution of the electrode active material and establish a discrete element model.
3. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 2, characterized in that, In step S11, the funnel method is used to determine the angle of repose of the electrode active material, and the experimental device is an angle of repose tester. The specific operation of step S12 is as follows: a scanning electron microscope is used to observe the electrode active material under a microscope. At least 3-5 images with different fields of view are selected and binarized to obtain the particle size distribution. The values of D10, D50, and D90 are obtained. The median particle size and the main distribution range of the particle size are calculated. Then, in the discrete element software, the normal distribution parameters consistent with the statistical results are set to generate particles that conform to the statistical characteristics of real materials. The total number of particles generated and the generation rate and mode in the model are determined through simulation pre-experiment. The construction of a discrete element model that can replace real materials for simulation is completed.
4. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 3, characterized in that, In step S1, a simplified three-dimensional model is geometrically scaled and established. The three-dimensional model includes the funnel and base model of the angle of repose tester. In the simulation environment, by setting the parameters of the pellet plant, a group of particles with specific physical property parameters is generated, and the physical process of them falling from the funnel and naturally accumulating on the base platform to form a material pile is simulated.
5. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 4, characterized in that, The formed stable stockpile is post-processed using an image processing algorithm. By identifying the stockpile outline and taking multiple sampling measurements along different directions and positions of the stockpile, the average value is finally calculated as the angle of repose of the batch of material.
6. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 1, characterized in that, The parameters to be calibrated in step S2 include intrinsic parameters, basic contact parameters, and contact model parameters. The intrinsic parameters include the density, Young's modulus, and Poisson's ratio of the positive and negative electrode active materials. The basic contact parameters include the collision recovery coefficient and the static / rolling friction coefficient. The contact model parameters include surface energy.
7. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 1, characterized in that, In step S2, after the Plackett-Burman test screened out significant parameters, the steepest climbing experiment selected the three factors with the highest degree of influence to conduct the steepest climbing experiment. Among them, the factor with the highest significance is used as the climbing direction unit, and the average value of the difference between its high and low levels is used as the step size. The remaining non-significant factors are fixed at the middle level, and the experimental plan is arranged accordingly.
8. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 1, characterized in that, Step S3 includes: S31. Box spectroscopy for experimental variables that have a significant impact in the Plackett-Burman experiment. Behnken test; S32. Perform variance analysis on the Box-Behnken test results, further analyze the significance of each experimental variable, interaction term, and quadratic term on the target response value, and obtain the second-order regression equation of the rest angle through regression fitting analysis of the experimental results using the Box-Behnken test, and analyze the interaction effect of the regression model. S33. Using Design-Expert software, with the rest angle value obtained from physical experiments as the target value, solve the optimized second-order regression equation to obtain the result.
9. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 8, characterized in that, The Box In the Behnken experiment, based on the results of the steepest climb experiment, the set of data with the smallest relative error of the angle of repose was selected as the intermediate level. The two sets of data above and below the intermediate level were selected as the low level and high level for experimental design. The angle of repose was simulated and calculated for each set of experimental data. The influence factor was taken at three levels from low to high and coded as -1, 0 and 1 respectively for analysis.
10. The discrete element contact parameter calibration method for positive and negative electrode active materials of lithium-ion batteries according to claim 1, characterized in that, The specific operation of step S4 is as follows: Substitute the optimal parameters into the discrete element model in step S1 and repeat the experiment multiple times to obtain the angle of repose through simulation. The relative error between the simulated experiment and the actual experiment's angle of repose is used to prove that the calibration parameters can effectively represent the stacking characteristics of the electrode active material. The relative error is controlled within 2%.