Lithium battery cyclic expansion force simulation method and system and readable storage medium
By constructing a multiphysics coupling model for lithium batteries, the expansion and volume change of electrode active particles are accurately calculated, solving the problem of inaccurate expansion force prediction in existing technologies. This achieves efficient and accurate prediction of lithium battery cycle expansion force, supporting optimized design of battery modules.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI GUOXUAN HIGH TECH POWER ENERGY
- Filing Date
- 2025-12-04
- Publication Date
- 2026-04-14
AI Technical Summary
Existing technologies cannot effectively cover the interaction of multiple physical fields and aging effects during long-term charging and discharging of lithium batteries, resulting in inaccurate prediction of expansion force and slow research and development iteration due to reliance on long-cycle experiments.
An equivalent structural model of a lithium battery is constructed, and a two-way coupling mechanism of electrochemical, thermal, mechanical, and aging models is established. By calculating the expansion strain, thermal expansion strain, and irreversible volume increment of electrode active particles, and combining the gas generation pressure to calculate the cyclic expansion force, a fully coupled simulation method is formed.
It achieves accurate prediction of the expansion force of lithium batteries throughout their entire life cycle, solves the problems of disconnection in cross-scale parameter transfer and lack of interaction between multiple physical fields, improves prediction accuracy, replaces high-cost physical testing, and supports the optimized design of battery modules.
Smart Images
Figure CN121859528A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of lithium-ion battery simulation technology, and in particular to a method, system, and readable storage medium for simulating the cyclic expansion force of lithium batteries. Background Technology
[0002] During long-term charge-discharge cycles, lithium-ion batteries inevitably experience volume expansion due to the lithium insertion / extraction mechanism of electrode materials, the growth of the solid electrolyte interphase (SEI) film, and the generation of by-reaction gases. This continuous accumulation of expansion force is a key factor leading to relaxation of the battery module preload, deformation of the battery pack structure, and even failure. With the widespread application of high-energy-density batteries, accurate prediction of the cell's expansion force throughout its entire lifecycle has become a core requirement for safe battery structural design.
[0003] Existing methods for predicting expansion force typically rely solely on static stress-strain constitutive relationships for simulation, neglecting the volume change sources driven by electrochemical reaction kinetics and failing to effectively encompass the cumulative impact of aging on battery volume. While some existing technologies involve physical field simulations, they often suffer from issues of multi-physics decoupling or missing interactions. For example, considering only a single electrochemical force or thermo-mechanical coupling fails to accurately reflect the deep bidirectional coupling mechanism between the four physical fields of electrochemistry, heat, mechanics, and aging, particularly lacking a quantitative description of irreversible volume increases and dynamic pressure changes caused by aging. Furthermore, relying on traditional long-cycle charge-discharge experiments to obtain full-lifecycle expansion force data is not only time-consuming and costly but also severely restricts the speed of product development and iteration.
[0004] Therefore, how to establish a simulation method that can comprehensively consider the interaction of multiple physical fields and aging effects in order to accurately predict the cyclic expansion force of lithium batteries has become an urgent technical problem to be solved. Summary of the Invention
[0005] The main objective of this invention is to provide a method, system, and readable storage medium for simulating the cyclic expansion force of lithium batteries. The aim is to establish a simulation method that can comprehensively consider the interaction of multiple physical fields and aging effects, so as to achieve accurate prediction of the cyclic expansion force of lithium batteries.
[0006] To achieve the above objectives, this invention proposes a method for simulating the cyclic expansion force of lithium batteries, comprising the following steps: Construct an equivalent structural model of lithium batteries and establish a two-way coupling mechanism between electrochemical, thermal, mechanical and aging models; Based on the electrochemical model and the thermal model, the expansion strain of the electrode active particles and the thermal expansion strain of the material are calculated. Based on the aging model, the SEI thickening and lithium plating are calculated and converted into irreversible volume increments; the expansion strain, thermal expansion strain, and irreversible volume increments are used as expansion inputs and applied to the mechanical model to solve the displacement field and update the volume of the core in the equivalent structural model according to the displacement field. The gas production rate is calculated based on the aging model, and the gas production pressure is calculated based on the gas production rate, the current temperature, and the updated volume of the core. The gas generation pressure is applied as a load to the inner surface of the battery casing in the equivalent structural model, and the cyclic expansion force of the lithium battery is calculated.
[0007] Preferably, the equivalent structural model includes a core model and a battery casing model that encapsulates the core model; The core model is a multi-layer structure, including alternating layers of negative electrode, separator and positive electrode, wherein the negative electrode and the positive electrode respectively include a current collector layer and an active material layer coated on the surface of the current collector layer.
[0008] Preferably, the following formula is used when calculating the gas production pressure:
[0009] in, For gas production pressure, The gas production rate, Let be the ideal gas constant. The current temperature. This refers to the updated volume of the core.
[0010] Preferably, the method further includes a feedback step of correcting the electrochemical model based on the volume change output by the mechanical model, wherein the feedback step includes updating the volume fractions of the solid and liquid phases; the update of the liquid phase volume fraction satisfies:
[0011] The update of the solid volume fraction satisfies:
[0012] in, This is the updated liquid volume fraction. This represents the initial liquid phase volume fraction. It is the change in volume. For the initial volume, This is the updated solid volume fraction.
[0013] Preferably, the feedback step further includes correcting the diffusion coefficient, solid-phase conductivity, and liquid-phase conductivity in the electrochemical model based on the updated volume fraction of the solid or liquid phase; the correction satisfies the Bruggeman equation form:
[0014] Where X represents the corrected diffusion coefficient, solid-phase conductivity, or liquid-phase conductivity. Represents the corresponding initial value. The updated solid volume fraction or liquid volume fraction is given, and m is the correction index.
[0015] Preferably, when calculating the irreversible volume increment, the SEI thickening amount Based on calculations of the solvent composition and the physical parameters of lithium ions in the electrolyte, the following relationship is satisfied:
[0016] in, Specific surface area; and This indicates the concentration of the SEI component; and Indicates the molar mass of the SEI component; and Indicates the density of the SEI component; Indicates lithium concentration; Indicates the molar mass of lithium; This indicates the lithium density.
[0017] Preferably, when calculating the irreversible volume increment, the condition for determining lithium plating is: when the negative electrode potential is less than 0V, the lithium plating volume calculation is triggered; the lithium plating volume calculation is based on the lithium plating amount determined by the Baker-Verbrugge equation.
[0018] Preferably, the reaction rate constant, diffusion coefficient, and ionic conductivity parameters in the electrochemical model are temperature-dependent and satisfy the Arrhenius equation:
[0019] Where Y represents the current reaction rate constant, diffusion coefficient, or ionic conductivity. This represents the initial value of the corresponding parameter. R is the activation energy, R is the gas constant, and T is the cell temperature.
[0020] Preferably, the electrochemical model is based on the Baker-Verbrugge equation and Fick's law.
[0021] Preferably, the method further includes a battery module preload design step: using the simulation method to obtain the expansion force curve of the lithium battery throughout its entire life cycle, and determining the peak expansion force. Set the module preload according to the peak expansion force. ,in, The range of values is times .
[0022] This application also discloses a lithium battery cycle expansion force simulation system, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any of the preceding claims.
[0023] This application also discloses a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method described in any of the preceding claims.
[0024] The above technical solution has the following advantages: This invention constructs an equivalent structural model of a lithium battery and establishes a two-way coupling mechanism between electrochemical, thermal, mechanical, and aging models. This enables precise calculation of the reversible expansion of electrode active particles, material thermal expansion, and irreversible volume increments caused by SEI thickening and lithium plating. Specifically, this invention introduces a dynamic coupling calculation of gas pressure and volume. Based on the gas generation output from the aging model and the real-time updated core volume, the gas generation pressure is calculated and applied as a dynamic load to the battery casing, thus realistically simulating the internal physical and mechanical responses of the battery. This fully coupled simulation method effectively solves the problems of disconnected cross-scale parameter transfer and lack of multi-physics interaction in existing technologies, significantly improving the prediction accuracy of the cyclic expansion force throughout the entire life cycle of lithium batteries. It can replace high-cost, long-cycle physical testing and provides scientific and efficient data support for the pre-tightening force optimization design of battery modules. Attached Figure Description
[0025] The present invention will now be described in detail with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a schematic diagram of the thickness equivalent structure of the core model provided in an embodiment of the present invention.
[0026] Figure 2 This is a three-dimensional structural diagram of a complete battery provided in an embodiment of the present invention.
[0027] Figure 3 The graph showing the relationship between the expansion rate of graphite anode particles and SOC is provided for an embodiment of the present invention.
[0028] Figure 4 A schematic diagram of the bidirectional coupling mechanism of electrochemical-thermal-mechanical-aging multiphysics fields provided in the embodiments of the present invention. Detailed Implementation
[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the following specific embodiments are only used to explain the invention and do not constitute a limitation thereof.
[0030] This invention provides a simulation method for the cyclic expansion force of lithium batteries based on a fully coupled electrochemical-thermal-mechanical-aging approach. This method aims to address the problems of disconnected cross-scale transmission, lack of bidirectional interaction among multi-physics fields, and difficulty in quantifying irreversible expansion in existing technologies. By constructing a refined equivalent structural model and introducing a dynamic coupling mechanism between gas pressure and volume, it achieves accurate prediction of battery expansion force throughout its entire lifespan.
[0031] like Figure 1 and Figure 2 As shown, this embodiment first constructs an equivalent structural model of a lithium battery. Considering the balance between computational efficiency and accuracy, the model adopts a multi-layer thickness equivalent three-dimensional modeling method. Specifically, the model includes a core 1 and a battery casing 2 encapsulating the core 1. To accurately capture the mechanical response inside the cell, the core 1 is constructed as a multi-layered, alternating structure, sequentially arranged from the outside to the inside as a negative electrode foil 11, a negative electrode material region 12, a separator 13, a positive electrode material region 14, a positive electrode foil 15, a positive electrode material region 14, a separator 13, a negative electrode material region 12, and a negative electrode foil 11. This refined layered modeling not only realistically reproduces the physical structure of the cell but also provides a precise geometric carrier for the subsequent coupling of various physical fields at the microscopic level.
[0032] The battery casing 2 encapsulates the core 1 according to the design dimensions, forming a complete three-dimensional model of the entire battery. Based on this geometric model, this embodiment establishes a two-way coupling mechanism of electrochemistry-thermal-mechanical-aging.
[0033] like Figure 4 As shown, the physical fields do not simply transfer in one direction, but rather interact closely. First, the electrochemical model, as the core driving force, is responsible for calculating the expansion strain of the electrode active particles. This electrochemical model, based on the Baker-Verbrugge equation and Fick's law, can accurately describe the diffusion and intercalation process of lithium ions within the active particles. For the graphite anode, its expansion degree has a non-linear relationship with the battery's state of charge (SOC), such as... Figure 3 As shown, and satisfying the relation:
[0034] in and These represent the average and maximum concentrations of the negative electrode particles in the electrochemical model, respectively. For the lithium iron phosphate (LFP) cathode, the volume change during charge and discharge follows a specific molar volume relationship, specifically satisfying the formula:
[0035] in The partial molar volume of the material is typically 3.6 for LFP materials. ,
[0036] This is the difference between the average and maximum lithium-ion concentration in the cathode particles in the electrochemical model. The expansion of both cathode and anode particles mainly stems from the concentration gradient change, which is a reversible process. Secondly, the thermal model calculates the internal temperature field of the battery based on the heat generated by the electrochemical reaction. Temperature changes not only affect the chemical reaction rate but also directly drive the thermal expansion and strain of the materials.
[0037] In this embodiment, the thermal expansion strain of the material Through the coefficient of thermal expansion With temperature change The product is used to calculate, which satisfies:
[0038] It is worth noting that this embodiment fully considers the temperature sensitivity of the parameters. Key parameters in the electrochemical model, such as the positive and negative electrode reaction rate constants, diffusion coefficients, and ionic conductivity, are all set to be temperature-dependent and strictly follow the Arrhenius equation. Its form satisfies:
[0039] in These represent the positive and negative electrode reaction rate constants, diffusion coefficients, and ionic conductivity, respectively. This represents the corresponding initial value; It is the activation energy; It is the ideal gas constant; This refers to temperature. This means that as the battery temperature rises or falls, the internal reaction kinetics are dynamically adjusted, which in turn affects heat generation and expansion, achieving a deep coupling between heat and electrochemistry.
[0040] Secondly, the aging model is used to quantify the irreversible volume increase during cycling. This is a key difference between this embodiment and existing static mechanical simulations. The aging model outputs the solid electrolyte interphase (SEI) film thickness, lithium deposition, and gas production in real time. The SEI film thickness is primarily determined by considering the effects of additive components (such as EC and DMC) and changes in lithium deposition reaction concentration. SEI thickness is... It is calculated based on the physical parameters of the solvent components and lithium ions in the electrolyte. The specific calculation formula is as follows:
[0041] In the formula, Specific surface area; , , These represent the concentrations of the SEI component and lithium, respectively. , , These represent the molar masses of the corresponding components; , , These represent the densities of the corresponding components.
[0042] For lithium plating, this embodiment sets clear judgment conditions: when the negative electrode potential is less than 0V, it is considered that lithium plating is triggered, and the volume increase caused by lithium plating is calculated based on the amount of lithium plating determined by the Baker-Verbrugge equation.
[0043] The volume increase caused by lithium plating at the negative electrode during cycling satisfies:
[0044] in This refers to the amount of lithium coating. This represents the molar volume of lithium. These volume changes caused by aging mechanisms are summarized as irreversible volume increments. Together with the aforementioned reversible expansion strain and thermal expansion strain, the total expansion input of the mechanical model is constituted, and the total expansion input satisfies:
[0045] The mechanical model receives the total expansion input mentioned above, including positive electrode expansion, negative electrode expansion, thermal expansion, and irreversible expansion, and solves for the displacement field of each part. This process simulates the macroscopic deformation of core 1 during charge-discharge cycles. Based on the solved displacement field, the model updates the current volume of core 1 in real time. Of particular importance is the introduction of a dynamic coupling calculation of gas generation pressure and structural volume in this embodiment. The aging model calculates the amount of gas generated along with SEI growth and lithium plating.
[0046] This embodiment does not simply assume a constant gas pressure, but calculates the current gas production pressure based on the real-time updated volume of core 1, combined with the current temperature and gas production rate, using the ideal gas law. Specifically, the gas production pressure... The calculation formula is:
[0047] in, The gas production rate (the change is small under normal cyclic decay and can be approximated as no change; the pressure change caused by the volume change of each component of the core is mainly considered). Let be the ideal gas constant. The current temperature. This is the updated core volume.
[0048] This step is crucial because it connects the gases produced by chemical aging with the geometric space resulting from mechanical deformation. The calculated gas generation pressure is applied directly to the inner surface of the battery casing 2 as a distributed load. This approach realistically simulates the "expansion" effect on the casing caused by gas generation and volume constraints inside the battery, thus enabling the calculation of more accurate cyclic expansion forces.
[0049] To create a closed-loop feedback loop, this embodiment also feeds back the volume change output from the mechanical model to the electrochemical model. This feedback is not merely a numerical transfer, but a correction of microscopic parameters. Specifically, based on the volume change, the model updates the volume fractions of the solid and liquid phases. The liquid phase volume fraction... The update satisfies:
[0050] in This is the initial volume fraction. It is the change in volume. The initial volume; the solid phase volume fraction The update satisfies:
[0051] As volume expands, the liquid phase volume fraction decreases accordingly, while the solid phase volume fraction increases. Based on the updated volume fractions, this embodiment uses the Bruggeman equation to correct the key transport parameters in the electrochemical model—diffusion coefficient, solid-phase conductivity, and liquid-phase conductivity. The corrected parameters satisfy the following form:
[0052] in This represents the corrected diffusion coefficient or solid-liquid phase conductivity. Represents the corresponding initial value. The solid volume fraction is required according to the parameters. or liquid volume fraction , To correct the exponent, this embodiment takes... .
[0053] The corrected parameters will participate in the electrochemical calculations of the next time step, thus forming a truly fully coupled closed loop of "electrochemistry-thermal-mechanical-aging".
[0054] At the system implementation level, this embodiment can use multiphysics simulation platforms such as COMSOL Multiphysics for solving the problem. Users configure the cell's geometry and material properties through the parameter input module, such as particle size, open-circuit voltage (OCV), areal density, compacted density, Poisson's ratio, elastic modulus, and operating parameters. The multiphysics solver simultaneously calculates the aforementioned governing equations. The aging assessment module monitors the SEI thickness, lithium plating area, and capacity decay in real time.
[0055] Finally, the results output module generates a curve showing the change in expansion force with the number of cycles, as well as a three-dimensional stress cloud map. The expansion force data obtained based on the above simulation method has extremely high engineering application value, especially in the design of preload for battery modules.
[0056] This embodiment also provides a battery module preload design method. The method involves obtaining the expansion force evolution curve of the lithium battery throughout its entire life cycle through simulation, and identifying the peak expansion force. When designing the module press-fitting process, the preload of the module should be considered. Set to 1.2 to 1.5 times the peak expansion force, that is .
[0057] This design principle ensures that the battery structure will not be damaged by excessive expansion force throughout its entire life cycle, and also prevents cell loosening or poor contact due to insufficient pre-tightening force, thereby significantly improving the structural safety and service life of the battery pack.
[0058] In summary, this embodiment achieves high-precision prediction of the cyclic expansion force of lithium batteries by constructing a refined geometric model and establishing a four-field bidirectional coupling model, including a pressure-volume dynamic coupling mechanism. This method not only reveals the complex interaction mechanism of multiphysics fields at the microscopic and macroscopic scales but also provides an efficient and low-cost auxiliary means for battery structure design, effectively replacing long-cycle physical testing and accelerating product development iteration.
[0059] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.
Claims
1. A method for simulating the cyclic expansion force of a lithium battery, characterized in that, Includes the following steps: Construct an equivalent structural model of lithium batteries and establish a two-way coupling mechanism between electrochemical, thermal, mechanical and aging models; Based on the electrochemical model and the thermal model, the expansion strain of the electrode active particles and the thermal expansion strain of the material are calculated. Based on the aging model, the SEI thickening and lithium plating are calculated and converted into irreversible volume increments; the expansion strain, thermal expansion strain, and irreversible volume increments are used as expansion inputs and applied to the mechanical model to solve the displacement field and update the volume of the core in the equivalent structural model according to the displacement field. The gas production rate is calculated based on the aging model, and the gas production pressure is calculated based on the gas production rate, the current temperature, and the updated volume of the core. The gas generation pressure is applied as a load to the inner surface of the battery casing in the equivalent structural model, and the cyclic expansion force of the lithium battery is calculated.
2. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, The equivalent structural model includes a core model and a battery casing model that encapsulates the core model; The core model is a multi-layer structure, including alternating layers of negative electrode, separator and positive electrode, wherein the negative electrode and the positive electrode respectively include a current collector layer and an active material layer coated on the surface of the current collector layer.
3. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, The following formula is used to calculate the gas production pressure: in, For gas production pressure, The gas production rate, Let be the ideal gas constant. The current temperature. The volume of the updated core.
4. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, The method further includes a feedback step of correcting the electrochemical model based on the volume change output by the mechanical model, wherein the feedback step includes updating the volume fractions of the solid and liquid phases; the update of the liquid phase volume fraction satisfies: The update of the solid volume fraction satisfies: in, This is the updated liquid volume fraction. This represents the initial liquid phase volume fraction. It is the change in volume. For the initial volume, This is the updated solid volume fraction.
5. The lithium battery cycle expansion force simulation method according to claim 4, characterized in that, The feedback step further includes correcting the diffusion coefficient, solid-phase conductivity, and liquid-phase conductivity in the electrochemical model based on the updated volume fraction of the solid or liquid phase; the correction satisfies the Bruggeman equation form: Where X represents the corrected diffusion coefficient, solid-phase conductivity, or liquid-phase conductivity. Represents the corresponding initial value. The updated solid volume fraction or liquid volume fraction is given, and m is the correction index.
6. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, When calculating the irreversible volume increment, the SEI thickening amount Based on calculations of the solvent composition and the physical parameters of lithium ions in the electrolyte, the following relationship is satisfied: in, Specific surface area; and This indicates the concentration of the SEI component; and Indicates the molar mass of the SEI component; and Indicates the density of the SEI component; Indicates lithium concentration; Indicates the molar mass of lithium; This indicates the lithium density.
7. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, When calculating the irreversible volume increment, the condition for determining lithium plating is: when the negative electrode potential is less than 0V, the lithium plating volume calculation is triggered; the lithium plating volume calculation is based on the lithium plating amount determined by the Baker-Verbrugge equation.
8. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, The reaction rate constant, diffusion coefficient, and ionic conductivity parameters in the electrochemical model are temperature-dependent and satisfy the Arrhenius equation: Where Y represents the current reaction rate constant, diffusion coefficient, or ionic conductivity. This represents the initial value of the corresponding parameter. R is the activation energy, R is the gas constant, and T is the cell temperature.
9. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, The electrochemical model is based on the Baker-Verbrugge equation and Fick's law.
10. The lithium battery cycle expansion force simulation method according to claim 1, characterized in that, The method also includes a battery module preload design step: using the simulation method to obtain the expansion force curve of the lithium battery throughout its entire life cycle, and determining the peak expansion force. ; Set the module preload according to the peak expansion force. ,in, The range of values is times .
11. A lithium battery cycle expansion force simulation system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 10.
12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 10.