Battery dynamic equivalent stiffness calculation method based on multi-physical field coupling characteristics

Abstract

This invention discloses a method for calculating the dynamic equivalent stiffness of a battery based on the coupling characteristics of multiple physics fields. The method includes: acquiring the expansion force and surface temperature of the battery under different states of charge during charging in a constant displacement mode; converting the expansion force into stress; and performing thermal correction of the stress based on the temperature rise change and the coefficient of thermal expansion to obtain the actual stress of the battery throughout the full state of charge (SOC) range during charging. In a constant pressure mode, acquiring the displacement change of the battery under different states of charge during charging and converting it into strain; and performing strain correction based on the initial displacement related to the initial pressure and the sensor deformation to obtain the actual strain of the battery throughout the full SOC range during charging. Based on the intrinsic properties of the battery's solid / liquid phase materials and Hooke's law, and according to the actual stress and actual strain, calculating the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress, and temperature. This invention effectively reflects the mechanical behavior of the battery under real service conditions and overcomes the limitations of single mechanical loading experiments.

Description

Technical Field

[0001] This invention relates to the field of battery technology, and in particular to a method for calculating the dynamic equivalent stiffness of a battery based on the coupling characteristics of multiple physics fields. Background Technology

[0002] In the design and application of lithium-ion batteries, their mechanical behavior, especially expansion and contraction, has a significant impact on their electrochemical performance, safety, and lifespan. Lithium-ion batteries exhibit dynamic mechanical characteristics related to state of charge (SOC), temperature, and applied preload during charging and discharging, such as expansion force, constrained stress, and expansion displacement. Therefore, accurately describing and predicting the expansion behavior of lithium-ion batteries under actual operating conditions is crucial for battery safety, lifespan, and performance optimization.

[0003] Equivalent stiffness measures the ability of a lithium-ion battery to resist elastic deformation and is a key indicator of how easily a lithium-ion battery deforms under external forces. As an important parameter characterizing the mechanical response characteristics of a lithium-ion battery under multi-physics coupling conditions, equivalent stiffness can provide quantitative indicators of the mechanical performance of lithium-ion batteries under different operating conditions.

[0004] In current research, the equivalent stiffness of lithium-ion batteries is generally obtained through static stress-strain testing. However, research on the dynamic equivalent stiffness of lithium-ion batteries under different state of charge (SOC), preload, and temperature variations is relatively scarce. Therefore, calculating the dynamic equivalent stiffness of lithium-ion batteries during actual operation based on factors such as temperature, pressure, and SOC is of great significance for battery performance research. Accurately describing and predicting the expansion behavior of lithium-ion batteries under actual operating conditions is crucial for battery safety, lifespan, and performance optimization. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings and defects of the prior art and provide a method for calculating the dynamic equivalent stiffness of a battery based on the multi-physics coupling characteristics.

[0006] This invention is achieved through the following technical solution:

[0007] A method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics includes:

[0008] In constant displacement mode, the expansion force and surface temperature of the battery under different charging states are collected. The expansion force is converted into stress. The stress is thermally corrected based on the temperature rise change and thermal expansion coefficient to eliminate the influence of thermal expansion and obtain the actual stress of the battery in the full SOC range during charging.

[0009] In constant pressure mode, the displacement change of the battery under different states of charge during the charging process is collected and converted into strain. The strain is corrected based on the initial displacement related to the initial pressure and the sensor deformation to obtain the actual strain of the battery in the full SOC range during the charging process.

[0010] Based on the intrinsic properties of the battery solid / liquid phase materials and Hooke's law, the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress and temperature is calculated according to the actual stress and actual strain.

[0011] Preferably, the stress is obtained by dividing the expansion force by the area of ​​the battery subjected to the force.

[0012] Preferably, the coefficient of thermal expansion is the relative rate of change of a unit length of material with temperature.

[0013] Preferably, the actual stress is obtained by subtracting the product of the temperature rise change and the coefficient of thermal expansion from the stress.

[0014] Preferably, the actual strain is obtained by dividing the corrected displacement change by the initial displacement related to the initial pressure, wherein the corrected displacement change is equal to the actual displacement of the battery during the charging process minus the initial displacement related to the initial pressure.

[0015] Preferably, the actual displacement of the battery is the displacement after removing the sensor deformation, which is obtained by subtracting the sensor deformation from the directly measured battery displacement data.

[0016] Preferably, the formula for calculating the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress, and temperature is as follows:

[0017] ;

[0018] in, Indicates dynamic equivalent stiffness. This represents the actual displacement of the battery during the charging process after removing sensor deformation. Indicates stress, Indicates the coefficient of thermal expansion. This represents the change in temperature. This represents the initial displacement related to the initial pressure.

[0019] Preferably, the full SOC range refers to the 0%–100% SOC range.

[0020] Preferably, the acquisition of battery expansion force under different charging states during the charging process in constant displacement mode is achieved by using a mechanical clamp of a constant displacement device to apply a constant displacement constraint to the battery, directly converting the volume expansion change during battery charging into a measurable mechanical signal, namely expansion force.

[0021] Preferably, the method of collecting the displacement change of the battery under different charging states during the charging process in constant pressure mode is to apply constant pressure to the battery using a mechanical clamp of a constant pressure device, so as to directly convert the volume expansion change of the battery during the charging process into a measurable displacement change.

[0022] This application achieves coupled testing of multiple physical fields (thermal, electrical, and mechanical) by simultaneously measuring the force, temperature, and displacement of the battery within the same experimental system. This effectively reflects the mechanical behavior of the battery under real-world service conditions and overcomes the limitations of traditional single mechanical loading experiments. Furthermore, this application proposes a stress correction based on the coefficient of thermal expansion, improving the accuracy of stress calculation. It also considers the influence of initial pressure on initial displacement and the sensor compression displacement problem, thus correcting for strain. This improves the accuracy of strain calculations. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method for calculating the dynamic equivalent stiffness of a battery based on the multi-physics coupling characteristics of the present invention.

[0024] Figure 2 This is a schematic diagram of the constant displacement device of the present invention.

[0025] Figure 3 This is a schematic diagram of the constant pressure device of the present invention.

[0026] Figure 4 This is a schematic diagram of a spring model for analyzing the multi-mode mechanical characteristics of battery electromechanical coupling.

[0027] Figure 5 It is a bar chart showing the difference in elastic modulus under different pressures and SOC when considering thermal correction.

[0028] Figure 6 It is a bar chart showing the difference in elastic modulus under different pressures and SOC when considering sensor strain correction.

[0029] Figure 7 It is a bar chart showing the difference in elastic modulus under different pressures and SOCs when considering stress and strain corrections. Detailed Implementation

[0030] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0031] The method of this invention utilizes data on the expansion force and displacement changes of lithium-ion batteries during charging under different mechanical boundary conditions. Based on the intrinsic properties of the battery's solid / liquid phase materials and the definition of Hooke's Law, and taking into account the effects of battery temperature rise, thermal expansion coefficient, initial pressure on initial displacement, and pressure sensor displacement correction, the dynamic equivalent stiffness of the battery under actual working conditions is calculated. This enables quantitative analysis of the battery's mechanical behavior and provides key parameters for accurately describing and predicting the battery's expansion behavior under multi-physics fields.

[0032] In the calculation of the battery equivalent stiffness in this invention, the battery is not considered as a simple, homogeneous solid block. Instead, the mechanical properties of the battery are considered to be jointly determined by the "solid" and "pore" phases. Therefore, based on the concept of equivalent stiffness derived from linear elasticity theory and Hooke's law, this invention distinguishes the complex porous composite structure of the battery into a solid phase and a liquid phase, such as... Figure 4 As shown, the battery is modeled as a series spring consisting of a solid phase and a liquid phase, and mechanical analysis is performed using external sensors. The symbols in the figure are defined as follows: The total equivalent stiffness of the battery. For the stiffness of the sensor; in the internal model of the battery, Solid-phase stiffness (corresponding to solid parts such as positive and negative electrode materials of batteries). This refers to the liquid phase stiffness (corresponding to the diaphragm, electrolyte, and pore portion).

[0033] Figure 4 This demonstrates the evolution of the battery's mechanical state at different testing stages. In the static state, the battery is not subjected to external forces and is in a free state, with stress... During the pre-compression state, an initial pre-tightening force is applied through the clamps to bring the battery to its initial stress state. At this point, the sensor detects the initial compression and sets the relative displacement at this time. Under constant pressure (CPM) conditions, the external pressure is kept constant during charging. Battery volume expansion manifests as a change in displacement, resulting in a change in displacement amount. (as shown in the figure, extending downwards) In constant displacement (CDM) state, the total displacement constraint is kept constant during charging. The expansion of the battery volume is restricted by the mechanical structure, which translates into an increase in internal stress. At this point, the stress is changed from... Rise to For the series spring model, the corresponding total equivalent stiffness of the battery is... The reciprocal of is equal to the sum of the reciprocals of the stiffnesses of each component spring, that is... solid phase Much larger than the liquid phase Therefore, the model simplifies to ,Right now Therefore, this application proposes a battery dynamic equivalent stiffness calculation technique based on multi-physics coupling characteristics.

[0034] See Figure 1 As shown in the exemplary embodiment of this application, the method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics includes the following steps:

[0035] In constant displacement mode, the expansion force and surface temperature of the battery under different charging states are collected. The expansion force is converted into stress. The stress is thermally corrected based on the temperature rise change and thermal expansion coefficient to eliminate the influence of thermal expansion and obtain the actual stress of the battery in the full SOC range during charging.

[0036] In constant pressure mode, the displacement change of the battery under different states of charge during the charging process is collected and converted into strain. The strain is corrected based on the initial displacement related to the initial pressure and the sensor deformation to obtain the actual strain of the battery in the full SOC range during the charging process.

[0037] Based on the intrinsic properties of the battery solid / liquid phase materials and Hooke's law, the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress and temperature is calculated according to the actual stress and actual strain.

[0038] In this embodiment of the application, during battery testing, the large surface of the battery is clamped by the testing device. The displacement change is the thickness change data of the battery during the charging process, that is, the thickness change data between the two large surfaces of the battery. The initial displacement is the initial thickness data of the battery.

[0039] Specifically, the dynamic equivalent stiffness of the obtained battery can be described by the following formula:

[0040] ;

[0041] In the formula, These represent stress, the battery's state of charge (SOC), and the battery's temperature, respectively. Represents a function, This represents the dynamic equivalent stiffness of the battery.

[0042] This application achieves coupled testing of multiple physical fields (thermal, electrical, and mechanical) by simultaneously measuring the force, temperature, and displacement of the battery within the same experimental system. This effectively reflects the mechanical behavior of the battery under actual service conditions and overcomes the limitations of traditional single mechanical loading experiments. Furthermore, this application proposes a stress correction based on the coefficient of thermal expansion, improving the accuracy of stress calculation. It also considers the influence of initial pressure on initial displacement and the sensor compression displacement problem, correcting strain and improving the accuracy of strain calculation.

[0043] In this embodiment of the application, the stress The expansion force is obtained by dividing the area of ​​the battery subjected to the force, as shown in the calculation formula. ,in It is the area of ​​the battery that bears the force. It is an expansion force.

[0044] In this embodiment of the application, the coefficient of thermal expansion is expressed as: It is the relative rate of change of a unit length of material with temperature. The unit is ,in, This represents the initial displacement of the material. Temperature change The amount of material displacement change caused by this.

[0045] In this embodiment of the application, the actual stress is expressed as: Through the stress Subtract the change in temperature and the coefficient of thermal expansion It is obtained by multiplying by , and the calculation formula is: ,in, It is the stress obtained by converting the collected expansion force. It is the amount of temperature change measured in the experiment, that is, the amount of temperature rise.

[0046] In this embodiment of the application, the strain before modification is expressed as: It is obtained by dividing the measured displacement change by the initial displacement. In this application, the measured displacement change is equal to the uncorrected (without considering sensor deformation) battery displacement minus the initial displacement, and the calculation formula is as follows:

[0047] ;

[0048] In the formula, This represents the displacement change measured under constant pressure mode. This represents the uncorrected battery displacement, i.e., the measured battery displacement. This corresponds to the uncorrected initial displacement.

[0049] In this embodiment, after collecting the displacement changes of the battery under different states of charge during charging and converting them into strain, the influence of preload on the initial displacement and sensor compression on the expansion displacement is considered. Based on the initial displacement related to the initial pressure and the sensor deformation, the strain is adjusted accordingly. After correction, the actual strain of the solid-state active material across the entire SOC range during battery charging is obtained, calculated as follows:

[0050] ;

[0051] in, This is the actual displacement of the battery during the corrected charging process. This represents the initial displacement relative to the initial pressure. This represents the actual strain. In this application, the initial displacement related to the initial pressure is described. It takes into account the effect of initial pressure on initial displacement. The influence of the initial displacement It is obtained by modifying it after relating it to the initial stress.

[0052] In this embodiment, the actual battery displacement is the displacement after deducting sensor deformation, obtained by subtracting sensor deformation from the directly measured battery displacement data. In the constant pressure mode experiment, the pressure sensor itself exhibits deformation. Directly measured battery displacement / expansion measurement data The influence of sensor deformation needs to be eliminated in order to accurately calculate the actual displacement of the battery. Therefore, in this application, the influence of dynamic pressure on the sensor's compression displacement is considered, and the influence of sensor deformation is eliminated to improve the accuracy of the calculation. The corrected formula for calculating the actual displacement of the battery is as follows: .

[0053] Based on the above description, the charge state, stress, and dynamic equivalent stiffness under temperature coupling of this application can be obtained. Specifically, in the embodiments of this application, the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress, and temperature is... The calculation formula is as follows:

[0054] ;

[0055] in, This represents the corrected battery displacement during the charging process after removing sensor deformation, i.e., the corrected actual battery displacement.

[0056] In this embodiment, the full SOC range refers to the 0%–100% SOC range. In this application, after calculating the dynamic equivalent stiffness of the battery under multi-physics coupling conditions, the dynamic equivalent stiffness can be visualized under different SOC ranges and different initial pressures for convenient and intuitive observation.

[0057] In this embodiment of the application, during testing, two sets of testing devices can be used to measure the battery data. One is a constant displacement device (CDM) to measure the expansion force, and the other is a constant pressure device (CPM) to measure the expansion displacement. By synchronizing the expansion displacement and expansion force, the dynamic equivalent stiffness under multi-physics coupling conditions is finally calculated.

[0058] In this embodiment, the acquisition of battery expansion force under different charging states during charging in constant displacement mode involves applying a constant displacement constraint to the battery using a mechanical clamp of the constant displacement device. This directly converts the volume expansion changes during battery charging into a measurable mechanical signal, i.e., expansion force. Specifically, the constant displacement device, in addition to the mechanical clamp, also includes high-precision sensors (such as force sensors, thermocouples for temperature measurement), a control and data acquisition unit, and charging / discharging equipment.

[0059] In this application, the core working principle of the constant displacement device is to fix the total displacement of the battery and convert the volume expansion of the battery into a measurable mechanical signal, namely the measurable expansion force, through constant displacement constraint. This reveals the correlation between the expansion force and the state of charge (SOC) and the charge / discharge rate, providing data support for calculating the dynamic equivalent stiffness of the battery's multi-physics coupling characteristics and laying the foundation for the study of the multi-field coupling relationship of the battery during the charging process.

[0060] In this embodiment of the application, the displacement change of the battery under different states of charge during the charging process is collected in constant pressure mode. It uses a mechanical clamp with a constant pressure device to apply constant pressure to the battery, directly converting the volume expansion changes during the battery charging process into measurable displacement changes.

[0061] In addition to the mechanical clamps, the constant pressure device described in this application also includes high-precision sensors (such as displacement sensors and force sensors), a control and data acquisition unit, and charging and discharging equipment. The core working principle of the constant pressure device is to maintain a constant pressure on the battery by actively adjusting the mechanical displacement, thus directly converting the battery's volume expansion trend into a measurable displacement change (expansion displacement), revealing the correlation between the expansion displacement and the state of charge (SOC) and charge / discharge rate.

[0062] As shown in Figure 2, the constant displacement (CDM) device described in this application includes upper and lower fixed clamping frames 5 for providing overall support and constraint, four corner fastening bolts 1 for tightening with a torque wrench to subject the battery 100 to uniform preload in a rigid structure and achieve constant displacement constraint, a movable intermediate frame 4 located between the battery 100 and the force sensor 2 for transmitting expansion force, force sensors 2 installed at the lower ends of the four corner fastening bolts 1 for measuring the expansion force of the battery 100 during charging and discharging, and thermocouples 3 attached to the battery surface for real-time monitoring of temperature changes on the battery surface.

[0063] The constant displacement (CDM) device operates as follows: a fully discharged battery is placed in the test device, centered below the movable intermediate frame. The four corner bolts 1 are tightened evenly using a torque wrench to apply an initial preload to the battery, placing it in a constant displacement constraint state. The battery is then connected to the charge-discharge test system and data acquisition system for charge-discharge cycles. During the test, a force sensor records the expansion force F generated by the battery in real time, and thermocouples simultaneously collect battery surface temperature data, providing data support for subsequent thermal correction analysis. This method allows for the acquisition of constrained mechanical response characteristics of the battery under different states of charge (SOC) during charging.

[0064] The constant pressure (CPM) device, such as Figure 3 As shown, the device includes upper and lower fixed clamping frames 9 for providing overall support and constraint. Two displacement sensors 7 are symmetrically installed on both sides of the upper frame for real-time measurement of battery displacement changes. A pressure control terminal 6 is located at the center of the upper end and contacts the battery to apply and maintain a constant external pressure. The upper movable intermediate frame 4 and the lower movable intermediate frame 10 are respectively placed above and below the battery 100 to uniformly transmit pressure. A force sensor 8 is installed at the center of the bottom of the lower movable intermediate frame for real-time measurement of load changes of the battery during charging and discharging.

[0065] The constant pressure (CPM) device operates as follows: First, the battery is placed between the two movable intermediate frames above the force sensor, aligned with the pressure control terminal. Then, the target pressure is set, the pressure control terminal is activated, the force sensor provides real-time pressure feedback, and the terminal automatically adjusts to maintain a constant pressure. Next, the battery charging / discharging equipment and data acquisition system are connected to perform a charge / discharge cycle. During the test, the displacement sensor records the battery's initial displacement and displacement changes in real time, while the force sensor monitors the external load. This constant pressure testing device allows for accurate acquisition of the battery's displacement changes under different states of charge (SOC) at a constant pressure.

[0066] The lithium-ion battery in this invention can be a pouch battery, or a cylindrical battery, a square aluminum-cased battery, or a stacked battery, or other structural forms of lithium-ion batteries. As long as testing conditions are available for measuring parameters such as displacement changes, force, and temperature, the method described in this invention can be applied for testing and analysis.

[0067] In this application, during battery charge-discharge testing using the aforementioned constant pressure and constant displacement devices, data acquisition, data transmission, and data processing and analysis are all performed by a computer system. The computer collects pressure, displacement, and temperature data recorded by sensors in real time and transmits it to the computer system for processing. Computer software tools (such as MATLAB) are used to calculate and analyze the collected data, and the results can be visualized using various graphical methods. This achieves efficient evaluation and intuitive analysis of the battery's mechanical performance, significantly improving the convenience of data processing and result interpretation.

[0068] In this application, the units of the physical quantities of the data collected by the constant pressure device and the constant displacement device are specified as follows: displacement is in millimeters (mm), force is in Newtons (N), area is in square millimeters (mm²), stress and equivalent stiffness are in megapascals (MPa), coefficient of thermal expansion is in megapascals per degree Celsius (MPa / °C), temperature is in degrees Celsius (°C), and strain is a dimensionless quantity.

[0069] This application presents a method for calculating the dynamic equivalent stiffness of a battery based on multiphysics coupling characteristics. It utilizes a three-plate constant pressure and constant displacement device for testing, and calibrates the stress-strain curves of the pressure sensor to compensate for the measured displacement during battery expansion, obtaining the battery's true expansion displacement under dynamic pressure. By performing force analysis on the entire battery plane under constant pressure and constant displacement modes, and considering the electro-thermal-mechanical multi-field coupling characteristics during charging and discharging, it more realistically reflects the changes in the battery's dynamic equivalent stiffness. This method achieves accurate parameter characterization of battery expansion behavior under multiphysics coupling, providing key parameters for battery structural safety design and multiphysics simulation.

[0070] To further verify the effectiveness of the method described in this application and to visually demonstrate the improvement in stiffness calculation accuracy brought about by multiphysics correction, this embodiment compares the elastic modulus data before and after correction. The following, in conjunction with... Figures 5 to 7 A detailed explanation of the experimental data sources and analysis results is provided: This is achieved by comparing the elastic modulus obtained without correction (…). ")" and "the elastic modulus obtained after multiphysics correction using the method of this invention () ), calculate the difference between the two. The difference is then visualized in a three-dimensional coordinate system.

[0071] The following is about Figures 5 to 7 The coordinate axes are explained as follows: X-axis (SOC %), representing the battery's state of charge; Y-axis (initial pressure, MPa), representing the magnitude of the preload applied at the start of the test, covering different pressure levels from 0.01 MPa to 0.61 MPa; Z-axis (elastic modulus difference). The bar () represents the deviation of the calculation results before and after correction. The higher the bar, the greater the error in the calculation results if no correction is made.

[0072] like Figure 5 This demonstrates the improved accuracy of the calculated equivalent stiffness results achieved by applying only temperature / thermal expansion correction, as shown by the formula. By eliminating the thermal expansion stress caused by heat generated during battery charging and discharging, the thermal effect on stiffness calculation is significant (with large differences) in the low pressure and low SOC regions, proving the effectiveness of introducing the coefficient of thermal expansion. The necessity of performing stress thermal correction; such as Figure 6 This demonstrates the accuracy improvement achieved by correcting only sensor deformation, in computation... When using formula Eliminates the minute deformations that occur in the pressure sensor itself during the stress process. If this factor is ignored, the compression of the sensor will be misjudged as the compression of the battery, resulting in an underestimation of the battery stiffness. Figure 7 This demonstrates the overall accuracy improvement after comprehensively considering thermal expansion, sensor deformation, and initial displacement correction, in calculation... At that time, based on the complete calculation model of this application, it was derived that the modified actual stress was used simultaneously. and actual strain The difference in elastic modulus in this figure The overall value is the largest, indicating that the multiphysics coupling correction plays a decisive role in the accuracy of the final result.

[0073] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention.

[0074] Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the claims be included within the invention.

[0075] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A battery dynamic equivalent stiffness calculation method based on multi-physical field coupling characteristics, characterized in that, Include: In constant displacement mode, the expansion force and surface temperature of the battery under different charging states are collected. The expansion force is converted into stress. The stress is thermally corrected based on the temperature rise change and thermal expansion coefficient to eliminate the influence of thermal expansion and obtain the actual stress of the battery in the full SOC range during charging. In constant pressure mode, the displacement change of the battery under different states of charge during the charging process is collected and converted into strain. The strain is corrected based on the initial displacement related to the initial pressure and the sensor deformation to obtain the actual strain of the battery in the full SOC range during the charging process. Based on the intrinsic properties of the battery solid / liquid phase materials and Hooke's law, the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress and temperature is calculated according to the actual stress and actual strain.

2. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The stress is obtained by dividing the expansion force by the area of ​​the battery subjected to the force.

3. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The coefficient of thermal expansion is the relative rate of change of a material per unit length with temperature.

4. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The actual stress is obtained by subtracting the product of the temperature rise change and the coefficient of thermal expansion from the stress.

5. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The actual strain is obtained by dividing the corrected displacement change by the initial displacement related to the initial pressure. The corrected displacement change is equal to the actual displacement of the battery during the charging process minus the initial displacement related to the initial pressure.

6. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 5, characterized in that, The actual displacement of the battery is the displacement after removing the sensor deformation, which is obtained by subtracting the sensor deformation from the directly measured battery displacement data.

7. The method for calculating the dynamic equivalent stiffness of a battery based on multiphysics coupling characteristics according to claim 1, characterized in that, The formula for calculating the dynamic equivalent stiffness of the battery under the coupling of state of charge, stress, and temperature is as follows: ； in, Indicates dynamic equivalent stiffness. This represents the actual displacement of the battery during the charging process after removing sensor deformation. Indicates stress, Indicates the coefficient of thermal expansion. This represents the change in temperature. This represents the initial displacement related to the initial pressure.

8. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The full SOC range refers to the 0%–100% SOC range.

9. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The method of collecting the expansion force of the battery under different charging states during the charging process in constant displacement mode is to use a mechanical clamp of a constant displacement device to apply a constant displacement constraint to the battery, and directly convert the volume expansion change of the battery during the charging process into a measurable mechanical signal, namely expansion force.

10. The method for calculating the dynamic equivalent stiffness of a battery based on multi-physics coupling characteristics according to claim 1, characterized in that, The method of collecting the displacement change of the battery under different charging states during the charging process in constant pressure mode is to apply constant pressure to the battery using a mechanical clamp of a constant pressure device, so as to directly convert the volume expansion change of the battery during the charging process into a measurable displacement change.

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