A lithium battery internal stress prediction method and a battery stress prediction system based on a P4D electrochemical model

Abstract

The application discloses a lithium battery internal stress prediction method and a battery stress prediction system based on a P4D electrochemical model, relates to the technical field of battery production, and solves electrochemical fields, temperature fields and mechanical fields in sequence, establishes scale transfer relationships among active particles, electrodes and battery cells, obtains the position, occurrence time, migration track and corresponding risk indexes of the battery internal stress hot spots, sequentially couples the electrochemical fields, temperature fields and mechanical fields, can retain the in-plane electrochemical inhomogeneity caused by the tab position, current collector resistance and electrode size, obtains the lithium concentration, local current density and overpotential of the active particles at different spatial positions, reduces the local information loss caused by the traditional stress prediction method, improves the accuracy of the battery internal stress prediction, and performs layered verification by using voltage, temperature and constraint force, so that more reliable basis is provided for the mechanical state evaluation and structure optimization of the battery.

Description

Technical Field

[0001] This invention relates to the field of rechargeable battery manufacturing technology, and in particular to a method for predicting the internal stress of lithium batteries and a battery stress prediction system based on the P4D electrochemical model. Background Technology

[0002] Lithium-ion batteries are widely used in new energy vehicles and energy storage systems due to their good safety and long cycle life. During charging and discharging, lithium ions are inserted and extracted into the positive and negative electrode active materials, causing changes in the active particles and volume of the electrodes. Under the constraints of the separator, current collector, adjacent electrodes, and casing, non-uniform expansion occurs, resulting in internal stress. This stress can cause particle cracking, interface delamination, separator compression, and localized structural damage, thus affecting battery performance and lifespan. By simulating and predicting the internal stress generated by charging and discharging in lithium-ion batteries, we can assess the impact of the charging and discharging process on battery performance and lifespan, providing a basis for lithium-ion battery structure optimization, material improvement, and charging strategies.

[0003] Existing internal stress calculation models for lithium-ion batteries mainly include single-particle models, pseudo-two-dimensional models, and three-dimensional models. The single-particle model takes a single ideal particle as the object and simplifies the complex internal processes of the battery into a two-way coupling mechanism of electrochemistry and mechanics. It tracks the concentration change of a single representative particle during the lithium-ion insertion or extraction process. Since the entire porous electrode is simplified into a representative spherical particle, it assumes that the current is uniformly distributed in the electrode thickness direction and ignores the spatial position of the particles in the cell and the differences in local operating conditions. Especially during high-rate charge and discharge, the error in calculating the complex stress state caused by the battery charge and discharge process is relatively large.

[0004] Currently, P2D models or pseudo-3D coupled models exist. P2D models, however, remain limited by the one-dimensional assumption and cannot reflect macroscopic differences and microstructural fluctuations within the battery cell. Pseudo-3D coupled models, while capable of obtaining lithium concentration, potential, and local current density in the three-dimensional space of the cell and the radial space of the particles, treating the electrode or cell as a homogeneous continuum and calculating macroscopic deformation based on the overall state of charge or empirical expansion rate, suffer from several drawbacks. These traditional battery stress prediction models not only fail to consider the additional dimensions within the electrode particles and cannot simulate intercalation reactions within the particles, but also rely on spatial averaging approximations when dealing with electrochemical and heat transfer equations. This leads to homogenization errors in the calculation of microscopic particle concentration gradients, resulting in a lack of localized prediction information for the battery cell. This is particularly problematic during high-rate charge / discharge cycles or extreme thermal environments, leading to significant errors in predicting the internal stress of lithium batteries during charging and discharging. Summary of the Invention

[0005] The purpose of this invention is to address the problem that existing prediction models or methods for internal stress during the charging and discharging process of lithium batteries, due to neglecting the spatial position of electrode particles in the cell and differences in local operating conditions, or relying only on spatial average approximation, have homogenization errors in the calculation of microparticle concentration gradient, resulting in large prediction errors for internal stress during the charging and discharging process of lithium batteries. This invention provides a method for predicting internal stress of lithium batteries and a battery stress prediction system based on the P4D electrochemical model.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for predicting internal stress in lithium batteries, comprising the following steps:

[0008] S1. Obtain the basic parameters and usage condition parameters of the lithium battery under test; the basic parameters include: cell size, cell type, positive and negative electrode size, separator size, number of electrode layers, and tab parameters; the usage condition parameters include: charging and discharging current, ambient temperature, initial charge, saturated charge, and initial preload.

[0009] Based on the cell type, determine the radius of active particles, proportion of active material, density of active material, specific heat capacity, thermal conductivity, solid-phase diffusion coefficient, electrolyte diffusion coefficient, reaction rate constant, solid-phase conductivity, and electrolyte conductivity.

[0010] S2. Constructing the P4D electrochemical model:

[0011] Using the length, width, and thickness directions of the battery cell as three-dimensional spatial coordinates x, y, and z, respectively, and the radial direction from the center of the active particle to the surface as coordinate r, a P4D electrochemical model containing the three-dimensional space of the battery cell and the radial space of the particle is constructed.

[0012] The P4D electrochemical model includes: the solid-phase lithium diffusion equation of the active particles, the liquid-phase lithium transport equation, the local current density calculation formula, and the overpotential calculation formula.

[0013] Based on the charge conservation equation and boundary conditions, the P4D electrochemical model is used to solve for the expressions of solid-phase lithium concentration, liquid-phase lithium concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each coordinate position of the battery cell at the nth time node.

[0014] The local current density includes: solid phase current density, liquid phase current density, and current collector current density;

[0015] S3. Construct a three-dimensional thermal model of the battery cell:

[0016] Construct a reversible heat source Q based on the local current density. rev The calculation formula is given; based on the overpotential, the reaction polarization heat Q is constructed. actThe calculation formula; based on the solid-phase potential, liquid-phase potential, solid-phase current density, and liquid-phase current density, the ohmic thermal Q of the battery cell is constructed. ohm The calculation formula is derived from the solid-state current density and solid-state potential, and the Joule heating Q of the current collector is constructed. cc Therefore, the formula for calculating the local total heat production rate is as follows:

[0017] ;

[0018] Based on the material density, specific heat capacity, and thermal conductivity, the three-dimensional temperature field calculation formula for the battery cell is constructed as follows;

[0019] ;

[0020] S4. Calculate the chemical strain of the active particles:

[0021] Based on the solid-phase lithium concentration, the chemical strain for constructing active particles is calculated as follows:

[0022] ;

[0023] in, ;

[0024] Where, θ k Indicates the degree of lithium intercalation in the active particles, c s,k c represents the solid-phase lithium concentration of the k-th type of electrode active material. s,k,max β represents the maximum solid-phase lithium concentration of the k-th type of electrode active material. k Represents the chemical expansion coefficient; θ k,0 Indicates the degree of lithium insertion in the reference state; I represents the unit tensor;

[0025] S5. Calculate the particle-scale stress of the active particles:

[0026] Treating the active particles as spherical elastic bodies with concentration-dependent intrinsic strain, the formula for calculating the radial strain of the active particles is as follows:

[0027] ;

[0028] The formula for calculating the circumferential strain of active particles is constructed as follows:

[0029] ;

[0030] The radial strain and circumferential strain satisfy the equilibrium relationship:

[0031] ;

[0032] The formula for calculating particle-scale stress is as follows:

[0033] ;

[0034] Among them, C k This represents the elastic stiffness tensor of the active material. This represents the total strain of the active particles. Indicates the chemical strain of the active particles. This indicates the thermal strain of the active particles;

[0035] Based on the displacement continuity condition at the center of the active particles and the contact pressure boundary on the surface, the radial stress of the active particles in each region of the battery cell is obtained as follows:

[0036] ;

[0037] The circumferential stress of the active particles in each region of the battery cell was then calculated as follows:

[0038] ;

[0039] S6. Map the particle-scale strain of the active particles to the electrode scale, and calculate the chemical strain of the electrode. :

[0040] The volume-average formula for calculating the chemical strain of the active particles is as follows:

[0041] ;

[0042] Among them, R s,k Indicates the radius of the active particles;

[0043] Based on the proportion of active material and the scale correction coefficient, the chemical strain of the active particles is mapped to the chemical strain at the electrode scale using a mapping relationship. The mapping relationship is as follows:

[0044] ;

[0045] Where, ε s,k Indicates the volume fraction of active materials; Ξ k This represents the strain correction tensor from the particle scale to the electrode scale; the formula for calculating the strain correction tensor is:

[0046] ;

[0047] Among them, ξ x,k ξ y,k ξ z,k These represent the strain correction factors in the length, width, and thickness directions of the electrode, respectively.

[0048] S7. Calculate the thermal strain in each region of the battery cell:

[0049] Based on the three-dimensional temperature field calculation formula, the thermal strain of each region of the battery cell is constructed. The calculation formula is:

[0050] ;

[0051] Where m represents each region of the battery cell; α m T represents the thermal expansion coefficient tensor for each region; ref Indicates reference temperature;

[0052] S8. Construct a three-dimensional mechanical model of the battery cell:

[0053] The formula for calculating the total strain in each region of the battery cell is:

[0054] ;

[0055] Among them, u m (x,y,z,t) is the displacement vector within each region m of the battery cell;

[0056] Total strain in each region of the battery cell The decomposition formula is:

[0057] ;

[0058] Among them, the elastic strain of each region The calculation formula is:

[0059] ;

[0060] Based on the constitutive relation, the stress relationship for each region is constructed as follows:

[0061] ;

[0062] And construct the internal static equilibrium equations of the battery cell:

[0063] ;

[0064] Among them, C m b represents the stiffness tensor of different regions of the battery cell; m Indicates static force;

[0065] The three-dimensional stress and displacement of the battery cell at time node n are obtained by solving the problem.

[0066] Compared to traditional stress prediction methods that rely solely on the radial spatial average approximation of particles, the lithium battery internal stress prediction method described in this invention constructs a P4D electrochemical model, encompassing the three-dimensional space of the cell and the radial space of the particles. Combined with the construction of a three-dimensional thermal model and the calculation of chemical strain in the active particles, this method preserves the in-plane electrochemical inhomogeneities of the electrode positions and current collectors caused by charging and discharging in various regions of the cell. It obtains the lithium concentration, local current density, and overpotential of active particles at different spatial locations, reducing the loss of local information caused by traditional stress calculations using average state of charge or representative particles. Furthermore, by calculating chemical strain and particle stress based on the local lithium concentration of the particles, the particle chemical strain is mapped to the equivalent chemical strain of the electrodes, constructing particle-scale and electrode-scale... The continuous and traceable strain and stress transfer relationship between the temperature and cell scale enables the macroscopic stress of the cell to correspond to the local electrochemical state. In conjunction with the sequential coupling of electrochemical field, temperature field and mechanical field, the local electrochemical heat generation and three-dimensional temperature distribution are transferred to the mechanical model. Combined with the differences in electrode materials, membrane compression characteristics, interlayer contact, initial preload and external constraints, the influence of chemical expansion, thermal expansion and structural constraints on cell stress and deformation is comprehensively considered. The three-dimensional stress and displacement of the cell at time node n are obtained, which reduces the error of internal stress prediction during the charging and discharging process of lithium battery, significantly improves the accuracy of internal stress prediction caused by charging and discharging, and provides more reliable parameter basis for the mechanical state assessment and structural design of lithium battery.

[0067] Preferably, the lithium battery internal stress prediction method of the present invention further includes the following steps:

[0068] S9. Calculate the continuous stress of the battery cell over time:

[0069] Solving for the three-dimensional stress and displacement at multiple time points n, the continuous stress calculation formula for the three-dimensional stress of the battery cell over time is constructed as follows:

[0070] ;

[0071] S10. Construct multiple risk indicators corresponding to battery failure modes, and identify stress hotspots and hotspot migration trajectories:

[0072] Based on the continuous stress, risk indices for particle cracking, interface delamination, diaphragm compression, and current collector yielding are constructed respectively. The formula for calculating the comprehensive risk index is then established as follows:

[0073] ;

[0074] Among them, R p R represents the risk index of particle cracking. d R represents the interface delamination risk indicator. sep R represents the risk index of diaphragm compression.cc Indicators representing the risk of collective flow yielding;

[0075] Based on the comprehensive risk index, the formula for calculating the location of stress hotspots at each time point is as follows:

[0076] ;

[0077] Based on the locations of stress hotspots at multiple time points, the formula for calculating the hotspot migration trajectory is as follows:

[0078] ;

[0079] Based on the comprehensive risk index, determine the time when the comprehensive risk index is reached:

[0080] ;

[0081] The expression for the total distance of stress hotspot migration is:

[0082] ;

[0083] Then, the time of the first occurrence of the comprehensive risk, the time of maximum risk, the migration distance, and the duration are calculated.

[0084] As a preferred embodiment of the present invention, through steps S9 and S10, the location, initial occurrence time, maximum risk time, duration, and migration trajectory of stress hotspots are determined via continuous time nodes, thereby describing the spatiotemporal evolution of the stress concentration region. Furthermore, through a three-dimensional stress model, risk indicators for particle cracking, interface delamination, separator compression, and current collector yielding can be constructed respectively, and combined with corresponding material critical parameters to form a comprehensive risk assessment result for the battery cell, providing a basis for identifying different failure risks. By outputting multi-scale stress distribution, hotspot migration trajectories, and risk indicators, the effects of factors such as electrode thickness, number of unit layers, initial preload, charging rate, and ambient temperature can be compared, providing a more reliable basis for assessing the mechanical state, structural design, and optimizing operating conditions of lithium batteries.

[0085] Preferably, the lithium battery internal stress prediction method of the present invention constructs multiple risk indicators corresponding to battery failure modes, specifically including the following steps:

[0086] The formula for calculating the particle cracking risk index is as follows:

[0087] ;

[0088] in, θ represents the maximum circumferential tensile stress of the particle; fract Indicates the tensile strength of the active material;

[0089] The formula for calculating the interface delamination risk index is as follows:

[0090] ;

[0091] Where, σ n σ represents the normal stress at the interface. n > + =max(σ n ,0) represents the interface normal tensile stress portion; σ n,crit τ represents the critical tensile strength in the normal direction of the interface. int τ represents the interfacial shear stress. crit Indicates the critical shear strength of the interface;

[0092] The formula for calculating the current collector risk index is as follows:

[0093] ;

[0094] Where, σ vM σ represents the von Mises equivalent stress of the current collector; y Indicates the yield strength of the current collector;

[0095] The formula for calculating the diaphragm compression risk index is as follows:

[0096] ;

[0097] Where, ε sep ε represents the compressive strain in the thickness direction of the diaphragm. sep,crit p represents the critical compressive strain of the diaphragm. sep p represents the diaphragm contact pressure. sep,crit This indicates the critical contact pressure of the diaphragm.

[0098] Preferably, in the lithium battery internal stress prediction method of the present invention, step S8 further includes the step:

[0099] The formula for calculating the stress in the thickness direction of the membrane is:

[0100] ;

[0101] Among them, f comp This represents the nonlinear compression relationship of the diaphragm; σ ve (t) represents the viscoelastic stress component;

[0102] As a preferred embodiment of the present invention, by constructing a stress calculation formula in the thickness direction of the separator, the accuracy of capturing interface delamination and separator compression stress is improved, and the accuracy of predicting the internal stress of the battery cell of the present invention is further improved.

[0103] Preferably, in the lithium battery internal stress prediction method of the present invention, step S8 further includes setting interlayer contact relationships and external mechanical boundaries to obtain contact pressure and cell constraint force:

[0104] The electrodes and current collectors are bonded together; the electrodes and diaphragms are in a non-slip contact or bonded relationship; the battery cell and the housing are in a normal contact relationship.

[0105] Set the preset initial preload or initial compression displacement before charging and discharging, and keep the spacing between the external pressure plates constant during charging and discharging to form a constant displacement constraint condition; obtain the cell constraint force based on the boundary reaction force of the external pressure plates.

[0106] Preferably, the lithium battery internal stress prediction method of the present invention further includes, in a layered manner, verifying the P4D electrochemical model, the three-dimensional thermal model, and the three-dimensional mechanical model:

[0107] T1. Obtain the terminal voltage during the battery charging and discharging process using an electrical measuring device; obtain the surface temperature of the battery using a temperature measuring device; obtain the external constraint force of the battery using a force measuring device.

[0108] T2. Compare the overpotential with the terminal voltage to verify the P4D electrochemical model; compare the three-dimensional temperature with the surface temperature to verify the three-dimensional thermal model; compare the three-dimensional stress with the external constraint force to verify the three-dimensional mechanical model.

[0109] As a preferred embodiment of the present invention, the P4D electrochemical model, the three-dimensional thermal model and the three-dimensional mechanical model are verified in layers to form an electrochemical-thermal-mechanical layered verification chain, which is beneficial for identifying the source of model error and completing parameter calibration.

[0110] To achieve the objectives of this invention, the present invention provides the following technical solution:

[0111] A battery stress prediction system based on the P4D electrochemical model includes: an input module, an electrochemical simulation calculation module, a thermal simulation calculation module, a mechanical simulation calculation module, a coupled solution calculation module, a risk assessment calculation module, and a verification module;

[0112] The input module is used to obtain the basic parameters and usage condition parameters of the lithium battery under test;

[0113] The electrochemical simulation and calculation module is used to construct a P4D electrochemical model, which can solve for the expressions of solid-phase lithium concentration, liquid-phase lithium concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each coordinate position of the battery cell at the nth time node; it can construct the chemical strain of the active particles and calculate the chemical strain of the electrodes.

[0114] The thermal simulation calculation module is used to construct a three-dimensional thermal model of the battery cell; it can solve and calculate the thermal strain in each region of the battery cell.

[0115] The mechanical simulation calculation module is used to calculate the particle-scale stress of the active particles.

[0116] The coupled solution calculation module is used to construct a three-dimensional mechanical model, which can map the particle-scale strain of the active particles to the electrode scale and solve for the three-dimensional stress and displacement of the cell at time node n.

[0117] The risk assessment calculation module is used to construct multiple risk indicators corresponding to battery failure modes and identify stress hotspots and hotspot migration trajectories.

[0118] The verification module is used to perform tiered verification of the P4D electrochemical model, the three-dimensional thermal model, and the three-dimensional mechanical model.

[0119] The battery stress prediction system based on the P4D electrochemical model described in this invention can take battery structure, material parameters, operating conditions, and mechanical boundary conditions as inputs to establish a P4D electrochemical model that includes the three-dimensional space of the cell and the radial space of the particles. It sequentially solves for local electrochemical variables, local heat sources, three-dimensional temperature field, particle chemical strain, and particle-scale stress. It establishes multi-scale mechanical transmission relationships through particle-electrode-cell scale mapping. Based on the sequential coupling solution of electrochemistry-thermal-mechanical, it further constructs multi-failure mode risk indicators, identifies stress hotspots and their migration trajectories, and performs hierarchical verification by combining terminal voltage, surface temperature, and external constraint forces. It outputs stress prediction results and comprehensive risk assessment results at the particle scale, electrode scale, and cell scale more accurately and efficiently, thereby improving the accuracy of battery charge-discharge failure risk assessment.

[0120] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0121] 1. The lithium battery internal stress prediction method described above can preserve the in-plane electrochemical inhomogeneity of the electrode positions and current collectors in various regions of the battery cell caused by charging and discharging, and obtain the lithium concentration, local current density and overpotential of active particles at different spatial locations. This reduces the loss of local information caused by traditional methods of calculating stress using average state of charge or representative particles. It can construct a continuous and traceable strain and stress transmission relationship between particle scale, electrode scale and cell scale, so that the macroscopic stress of the battery cell can correspond to the local electrochemical state. It comprehensively considers the influence of chemical expansion, thermal expansion and structural constraints on the stress and deformation of the battery cell, and obtains the three-dimensional stress and displacement of the battery cell at time node n. This reduces the error in predicting the internal stress of the lithium battery during charging and discharging, significantly improves the accuracy of predicting the internal stress of the battery caused by charging and discharging, and provides more reliable parameter basis for the mechanical state assessment and structural design of lithium batteries.

[0122] 2. The battery stress prediction system can take battery structure, material parameters, operating conditions, and mechanical boundary conditions as inputs to establish a P4D electrochemical model that includes the three-dimensional space of the cell and the radial space of the particles. It sequentially solves for local electrochemical variables, local heat sources, three-dimensional temperature field, particle chemical strain, and particle-scale stress. It establishes multi-scale mechanical transmission relationships through particle-electrode-cell scale mapping. Based on the electrochemical-thermal-mechanical sequential coupling solution, it further constructs multi-failure mode risk indicators, identifies stress hotspots and their migration trajectories, and performs hierarchical verification by combining terminal voltage, surface temperature, and external constraint forces. It outputs stress prediction results and comprehensive risk assessment results at the particle scale, electrode scale, and cell scale more accurately and efficiently, thereby improving the accuracy of battery charge-discharge failure risk assessment. Attached Figure Description

[0123] Figure 1 This is the present invention;

[0124] Figure 2 This is the present invention;

[0125] Figure 3 This is the invention. Detailed Implementation

[0126] The present invention will now be described in detail with reference to the accompanying drawings.

[0127] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0128] Example 1:

[0129] refer to Figure 1 As shown, this embodiment discloses a method for predicting the internal stress of a lithium battery, including the following steps:

[0130] S1. Obtain the basic parameters and usage condition parameters of the lithium battery under test; the basic parameters include: cell size, cell type, positive and negative electrode size, separator size, number of electrode layers, and tab parameters; the usage condition parameters include: charging and discharging current, ambient temperature, initial charge, saturated charge, and initial preload.

[0131] Based on the cell type, determine the radius of active particles, proportion of active material, density of active material, specific heat capacity, thermal conductivity, solid-phase diffusion coefficient, electrolyte diffusion coefficient, reaction rate constant, solid-phase conductivity, and electrolyte conductivity.

[0132] S2. Constructing the P4D electrochemical model:

[0133] Using the length, width, and thickness directions of the battery cell as three-dimensional spatial coordinates x, y, and z, respectively, and the radial direction from the center of the active particle to the surface as coordinate r, a P4D electrochemical model containing the three-dimensional space of the battery cell and the radial space of the particle is constructed.

[0134] The P4D electrochemical model includes: the solid-phase lithium diffusion equation of the active particles, the liquid-phase lithium transport equation, the local current density calculation formula, and the overpotential calculation formula.

[0135] Based on the charge conservation equation and boundary conditions, the P4D electrochemical model is used to solve for the expressions of solid-phase lithium concentration, liquid-phase lithium concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each coordinate position of the battery cell at the nth time node.

[0136] The local current density includes: solid phase current density, liquid phase current density, and current collector current density;

[0137] S3. Construct a three-dimensional thermal model of the battery cell:

[0138] Construct a reversible heat source Q based on the local current density. rev The calculation formula is given; based on the overpotential, the reaction polarization heat Q is constructed. act The calculation formula; based on the solid-phase potential, liquid-phase potential, solid-phase current density, and liquid-phase current density, the ohmic thermal Q of the battery cell is constructed. ohm The calculation formula is derived from the solid-state current density and solid-state potential, and the Joule heating Q of the current collector is constructed. cc Therefore, the formula for calculating the local total heat production rate is as follows:

[0139] ;

[0140] Based on the material density, specific heat capacity, and thermal conductivity, the three-dimensional temperature field calculation formula for the battery cell is constructed as follows;

[0141] ;

[0142] S4. Calculate the chemical strain of the active particles:

[0143] Based on the solid-phase lithium concentration, the chemical strain for constructing active particles is calculated as follows:

[0144] ;

[0145] in, ;

[0146] Where, θ k Indicates the degree of lithium intercalation in the active particles, c s,k c represents the solid-phase lithium concentration of the k-th type of electrode active material. s,k,maxβ represents the maximum solid-phase lithium concentration of the k-th type of electrode active material. k Represents the chemical expansion coefficient; θ k,0 Indicates the degree of lithium insertion in the reference state; I represents the unit tensor;

[0147] S5. Calculate the particle-scale stress of the active particles:

[0148] Treating the active particles as spherical elastic bodies with concentration-dependent intrinsic strain, the formula for calculating the radial strain of the active particles is as follows:

[0149] ;

[0150] The formula for calculating the circumferential strain of active particles is constructed as follows:

[0151] ;

[0152] The radial strain and circumferential strain satisfy the equilibrium relationship:

[0153] ;

[0154] The formula for calculating particle-scale stress is as follows:

[0155] ;

[0156] Among them, C k This represents the elastic stiffness tensor of the active material. This represents the total strain of the active particles. Indicates the chemical strain of the active particles. This indicates the thermal strain of the active particles;

[0157] Based on the displacement continuity condition at the center of the active particles and the contact pressure boundary on the surface, the radial stress of the active particles in each region of the battery cell is obtained as follows:

[0158] ;

[0159] The circumferential stress of the active particles in each region of the battery cell was then calculated as follows:

[0160] ;

[0161] S6. Map the particle-scale strain of the active particles to the electrode scale, and calculate the chemical strain of the electrode. :

[0162] The volume-average formula for calculating the chemical strain of the active particles is as follows:

[0163] ;

[0164] Among them, R s,k Indicates the radius of the active particles;

[0165] Based on the proportion of active material and the scale correction coefficient, the chemical strain of the active particles is mapped to the chemical strain at the electrode scale using a mapping relationship. The mapping relationship is as follows:

[0166] ;

[0167] Where, ε s,k Indicates the volume fraction of active material; Ξ k This represents the strain correction tensor from the particle scale to the electrode scale; the formula for calculating the strain correction tensor is:

[0168] ;

[0169] Among them, ξ x,k ξ y,k ξ z,k These represent the strain correction factors in the length, width, and thickness directions of the electrode, respectively.

[0170] S7. Calculate the thermal strain in each region of the battery cell:

[0171] Based on the three-dimensional temperature field calculation formula, the thermal strain of each region of the battery cell is constructed. The calculation formula is:

[0172] ;

[0173] Where m represents each region of the battery cell; α m T represents the thermal expansion coefficient tensor for each region; ref Indicates reference temperature;

[0174] S8. Construct a three-dimensional mechanical model of the battery cell:

[0175] The formula for calculating the total strain in each region of the battery cell is:

[0176] ;

[0177] Among them, u m (x,y,z,t) is the displacement vector within each region m of the battery cell;

[0178] Total strain in each region of the battery cell The decomposition formula is:

[0179] ;

[0180] Among them, the elastic strain of each region The calculation formula is:

[0181] ;

[0182] Based on the constitutive relation, the stress relationship for each region is constructed as follows:

[0183] ;

[0184] And construct the internal static equilibrium equations of the battery cell:

[0185] ;

[0186] Among them, C m b represents the stiffness tensor of different regions of the battery cell; m Indicates static force;

[0187] The three-dimensional stress and displacement of the battery cell at time node n are obtained by solving the problem.

[0188] The solid-phase lithium diffusion equation, liquid-phase lithium transport equation, local current density calculation formula, and overpotential calculation formula of the active particles described in this invention can be obtained through existing P2D electrochemical models of active particles. In this preferred embodiment, the solid-phase lithium diffusion calculation formula inside the active particles is as follows:

[0189] ;

[0190] Among them, c s,k D represents the solid-phase lithium concentration in the active particles of the k-th type of electrode, where k=p represents the lithium iron phosphate cathode and k=n represents the graphite anode; s,k denoted by , r represents the solid-phase diffusion coefficient; r represents the radial coordinate of the particle; t represents time.

[0191] The formula for calculating liquid-phase lithium transport is:

[0192] ;

[0193] Among them, c e,k Indicates the lithium-ion concentration in the electrolyte; ε e,k Indicates the integral number of the electrolyzed liquid; t represents the effective diffusion coefficient; + Represents the lithium-ion transference number; a k Indicates the specific surface area of ​​the electrode; i loc,k The value represents the local interface current density; F represents the Faraday constant.

[0194] The local interface current density is calculated using the Butler–Volmer relation as follows:

[0195] ;

[0196] Among them, i0,k Represents the exchange current density; α a,k and α c,k Represents the charge transfer coefficients of the anode and cathode, respectively; R represents the gas constant; T represents the temperature; η k This indicates an electrode overpotential.

[0197] The formula for calculating electrode overpotential is:

[0198] ;

[0199] Among them, ϕ s,k and ϕ e,k U represents the solid-phase potential and the liquid-phase potential, respectively; k Represents the electrode equilibrium potential; θ k This indicates the normalized degree of lithium intercalation of the active particles.

[0200] By solving the solid-phase lithium diffusion equation, the liquid-phase lithium transport equation, the local current density relationship calculation formula, and the corresponding charge conservation equation and boundary conditions, the solid-phase lithium concentration, liquid-phase lithium ion concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each spatial location and time node are obtained.

[0201] In the three-dimensional thermal model described in this invention, the heat source can be constructed by referring to existing heat source calculation formulas; specifically, a reversible heat source. I represents electric current; T represents absolute temperature; U oc Represents open-circuit voltage; ∂U oc / ∂T represents the entropy coefficient; heat of reaction polarization a s i represents the specific surface area. loc The ohmic thermal property represents the local exchange current, and η represents the overpotential of the electrode; the ohmic thermal property of the battery cell. , σ s σ is the solid-state electronic conductivity; e ϕ is the effective ionic conductivity of the electrolyte. s ϕ is the solid-state potential. e Liquid phase potential; Joule heating of current collector J cc ρ is the current density of the current collector; cc The resistivity of the current collector.

[0202] The three-dimensional temperature field described in this invention can be calculated using a conventional temperature field equation. Preferably, in this embodiment, the three-dimensional temperature field equation is:

[0203] ;

[0204] Where ρ represents the material density; C pLet λ represent specific heat capacity and λ represent thermal conductivity. Using the three-dimensional temperature field equations, the formula for calculating the three-dimensional temperature field of the battery cell is:

[0205] .

[0206] The chemical strain calculation formula for constructing active particles described in this invention can be obtained through conventional chemical strain relationships for active particles. In this preferred embodiment, the formula for calculating the normalized degree of lithium intercalation of the positive and negative electrode active particles based on the solid-phase lithium concentration obtained from the P4D electrochemical model is as follows:

[0207] ;

[0208] Among them, c s,k,max This represents the maximum solid-phase lithium concentration of the k-th type of electrode active material;

[0209] The general formula for calculating the chemical strain of the active particles is:

[0210] ;

[0211] Among them, f k (θ k ) represents the relationship between the degree of lithium insertion and chemical strain of the k-th type of active material; I represents the unit tensor. k (θ k By using piecewise interpolation of the volume change curves or literature curves of lithium iron phosphate and graphite materials to measure the degree of lithium intercalation, the implementation method is further simplified, and the chemical strain calculation formula for the active particles is obtained as follows:

[0212] .

[0213] It should be noted that each region m in this invention is understood as a structural part of the battery cell. The battery cell actually has a layered structure. For example, m represents a part or region of the positive electrode, negative electrode, separator, aluminum current collector, copper current collector, or shell.

[0214] The constitutive relations described in this invention are specifically selected and set according to each region of the battery cell. For example, the constitutive relations include: the positive and negative electrodes adopt transversely isotropic equivalent elastic constitutive relations, the separator adopts a thickness-direction nonlinear viscoelastic compression constitutive relations, the positive and negative electrode current collectors adopt elastoplastic constitutive relations, and the shell adopts an elastic or elastoplastic constitutive relations.

[0215] To achieve the electrochemical-thermal-mechanical coupling solution of this invention, the charging and discharging process is divided into multiple time nodes. At the nth time node, steps S1 to S8 of this invention are executed to obtain the solution of the three-dimensional stress and displacement of the battery cell. Combined with S9, the multi-scale stress results of the current time node are saved, and the process proceeds to the next time node. S1 to S8 are executed repeatedly to obtain the continuous stress calculation formula, so as to obtain the continuous stress evolution results at the particle scale, electrode scale, and battery cell scale.

[0216] In a preferred embodiment, the following step is also included:

[0217] S9. Calculate the continuous stress of the battery cell over time:

[0218] Solving for the three-dimensional stress and displacement at multiple time points n, the continuous stress calculation formula for the three-dimensional stress of the battery cell over time is constructed as follows:

[0219] ;

[0220] S10. Construct multiple risk indicators corresponding to battery failure modes, and identify stress hotspots and hotspot migration trajectories:

[0221] Based on the continuous stress, risk indices for particle cracking, interface delamination, diaphragm compression, and current collector yielding are constructed respectively. The formula for calculating the comprehensive risk index is then established as follows:

[0222] ;

[0223] Among them, R p R represents the risk index of particle cracking. d R represents the interface delamination risk indicator. sep R represents the risk index of diaphragm compression. cc Indicators representing the risk of collective flow yielding;

[0224] Based on the comprehensive risk index, the formula for calculating the location of stress hotspots at each time point is as follows:

[0225] ;

[0226] Based on the locations of stress hotspots at multiple time points, the formula for calculating the hotspot migration trajectory is as follows:

[0227] ;

[0228] Based on the comprehensive risk index, determine the time when the comprehensive risk index is reached:

[0229] ;

[0230] The expression for the total distance of stress hotspot migration is:

[0231] ;

[0232] Then, the time of the first occurrence of the comprehensive risk, the time of maximum risk, the migration distance, and the duration are calculated.

[0233] In a preferred embodiment, the method further includes the step of: constructing multiple risk indicators corresponding to battery failure modes, specifically including the following steps:

[0234] The formula for calculating the particle cracking risk index is as follows:

[0235] ;

[0236] in, θ represents the maximum circumferential tensile stress of the particle; fract Indicates the tensile strength of the active material;

[0237] The formula for calculating the interface delamination risk index is as follows:

[0238] ;

[0239] Where, σ n σ represents the normal stress at the interface. n > + =max(σ n ,0) represents the interface normal tensile stress portion; σ n,crit τ represents the critical tensile strength in the normal direction of the interface. int τ represents the interfacial shear stress. crit Indicates the critical shear strength of the interface;

[0240] The formula for calculating the current collector risk index is as follows:

[0241] ;

[0242] Where, σ vM σ represents the von Mises equivalent stress of the current collector; y Indicates the yield strength of the current collector;

[0243] The formula for calculating the diaphragm compression risk index is as follows:

[0244] ;

[0245] Where, ε sep ε represents the compressive strain in the thickness direction of the diaphragm. sep,crit p represents the critical compressive strain of the diaphragm. sep p represents the diaphragm contact pressure. sep,crit This indicates the critical contact pressure of the diaphragm.

[0246] In a preferred embodiment, step S8 further includes the following step:

[0247] The formula for calculating the stress in the thickness direction of the membrane is:

[0248] ;

[0249] Among them, f comp This represents the nonlinear compression relationship of the diaphragm; σ ve (t) represents the viscoelastic stress component.

[0250] In a preferred embodiment, step S8 further includes setting interlayer contact relationships and external mechanical boundaries to obtain contact pressure and cell constraint force: the electrode and current collector are set to a binding relationship; the electrode and diaphragm are set to a non-slip contact relationship or a binding relationship; the cell and the shell are set to a normal contact relationship; a preset initial preload or initial compression displacement is set before charging and discharging, and the spacing of the external pressure plates remains unchanged during charging and discharging, thereby forming a constant displacement constraint condition; the cell constraint force is obtained according to the boundary reaction force of the external pressure plates.

[0251] In a preferred embodiment, the method further includes stratified verification of the P4D electrochemical model, the three-dimensional thermal model, and the three-dimensional mechanical model: T1, obtaining the terminal voltage during the battery charging and discharging process using an electrical measuring device; obtaining the surface temperature of the battery using a temperature measuring device; obtaining the external constraint force of the battery using a force measuring device; T2, verifying the P4D electrochemical model by comparing the overpotential with the terminal voltage; verifying the three-dimensional thermal model by comparing the three-dimensional temperature with the surface temperature; and verifying the three-dimensional mechanical model by comparing the three-dimensional stress with the external constraint force.

[0252] The comparison described in T2 of this invention is understood as a mathematical calculation, specifically, one or more of the following: root mean square error, maximum absolute error, peak error, and peak occurrence time error.

[0253] Through steps S1-S10 of this invention, the following scale stress prediction results can be output: radial and circumferential stresses of positive and negative electrode particles; equivalent stress and strain of positive and negative electrode electrodes; three-dimensional stress and displacement fields of the battery cell; interlayer contact pressure and external constraint force; spatial location of stress hotspots; the moment of first appearance of hotspots and the moment of maximum risk; hotspot migration trajectory; risk indicators for particle cracking, interface delamination, diaphragm compression, and current collector yielding; and comprehensive risk assessment results of the battery cell. Based on the above results, adjustment suggestions for electrode thickness, number of unit layers, initial preload, or charging rate are generated.

[0254] Example 2:

[0255] Specifically, this embodiment, based on Embodiment 1, takes a square stacked lithium iron phosphate battery as the research object. The battery includes a lithium iron phosphate positive electrode, a graphite negative electrode, a separator, an aluminum current collector, a copper current collector, positive and negative electrode tabs, and a casing. The cell capacity, external dimensions, electrode thickness, number of unit layers, and tab size are determined according to the actual cell.

[0256] First, the geometric, electrochemical, thermophysical, and mechanical parameters of the battery cell are obtained. Geometric parameters are obtained through cell design documents, disassembly measurements, or microscopic characterization; electrochemical parameters are obtained through material testing, literature data, and voltage curve calibration; thermophysical parameters are obtained through experimental measurements or literature data; and mechanical parameters are obtained through compression, tension, nanoindentation, or literature data.

[0257] refer to Figure 3 As shown, this invention establishes the three-dimensional spatial coordinates of the battery cell and the radial spatial coordinates of the active particles using a P4D electrochemical field model. The x, y, and z coordinates are established along the length, width, and thickness of the battery cell, respectively, while the radial coordinate r is established along the direction from the center of the active particle to its surface. A P4D electrochemical model is established in the four dimensions of x, y, z, and r to solve for the solid-phase lithium concentration, electrolyte lithium-ion concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential in the active particles of the lithium iron phosphate cathode and graphite anode.

[0258] Reversible heat, polarization heat, ohmic heat, and current collector Joule heat are calculated based on local current density, overpotential, potential gradient, and material entropy thermal coefficient. The local heat sources at each location are then transferred to a three-dimensional thermal model to obtain the cell temperature field. Particle chemical strain and radial and circumferential stresses are calculated based on the local lithium concentrations of the positive and negative electrode particles. The particle chemical strain is then mapped to the equivalent chemical strain of the electrode. The equivalent chemical strain of the electrode and the three-dimensional temperature field are transferred to the three-dimensional mechanical model of the cell to solve for the stress, strain, displacement, contact pressure, and external constraint forces of each material layer.

[0259] Risk indicators for particle cracking, interface delamination, diaphragm compression, and current collector yielding are extracted at each time point to determine the location and occurrence time of various risk hotspots. Based on the hotspot coordinates of continuous time points, hotspot migration trajectories are formed, and finally, multi-scale stress distribution, hotspot migration process, and comprehensive risk assessment results of the battery cell are output.

[0260] Specifically, the P4D electrochemical model includes a three-dimensional region of the battery cell and a radial region of the active particles. The positive electrode region, the separator region, and the negative electrode region are arranged sequentially along the thickness direction of the battery cell, and the positive and negative electrode tabs are set at predetermined positions in the battery cell to reflect the differences in in-plane current distribution caused by the current collector resistance and the position of the tabs.

[0261] The model uses the actual charge / discharge current as the current boundary and the initial state of charge (SOC) of the battery cell as the initial condition. Zero-flux boundaries are used at the centers of the positive and negative electrode particles, and the lithium flux at the particle surface is correlated with the local interface current density. The electrode-separator interface satisfies the conditions for continuous lithium-ion concentration and flux. Current input and potential reference boundaries are respectively set on the outer surfaces of the positive and negative electrode current collectors.

[0262] In one specific implementation, a constant current-constant voltage charging condition can be adopted. The battery is first charged at a predetermined rate to the cutoff voltage, and then the cutoff voltage is maintained until the current drops to a predetermined value. The local reaction heat, polarization heat, ohmic heat, and current collector Joule heat at each spatial location are obtained based on the P4D model and used as the volumetric heat source for the three-dimensional thermal model. A convective heat transfer boundary is set on the outer surface of the cell, and the ambient temperature is set as the actual experimental temperature. By solving step-by-step, the formula for calculating the solid-phase lithium concentration is obtained as follows:

[0263] ;

[0264] The formula for calculating local current density is:

[0265] ;

[0266] The formula for calculating the three-dimensional temperature field is:

[0267] ;

[0268] Among them, the solid-phase lithium concentration is used for subsequent chemical strain calculation, and the local temperature is used for thermal strain calculation and temperature-related material parameter correction.

[0269] The parameters of the P4D electrochemical model were first calibrated using measured terminal voltages, while the parameters of the three-dimensional thermal model were then calibrated using surface temperatures. The parameters of both models were confirmed in the order of electrochemical first, followed by thermal, to reduce uncertainties caused by simultaneous adjustments to different physical field parameters.

[0270] The chemical strain and particle stress of the active particles are calculated. More specifically, the lithium intercalation degree-chemical strain relationship is established for both the lithium iron phosphate cathode and the graphite anode. The formula for calculating the normalized lithium intercalation degree of the active particles is:

[0271] ;

[0272] Based on the SOC-volume change curves of lithium iron phosphate and graphite materials, the chemical strain relationship is established using piecewise linear interpolation or a continuous fitting function as follows:

[0273] ;

[0274] Among them, the lithium iron phosphate cathode uses the function fp(θp), and the graphite anode uses the function f n (θn When a complete SOC-volume change curve is missing, the linear Vegard relationship can be used:

[0275] ;

[0276] Where, β k θ is the chemical expansion coefficient. k,0 For reference degree of lithium intercalation.

[0277] The active particles are then considered as spherical elastic bodies. A boundary condition with zero radial displacement is set at the particle center, and a free boundary or predetermined contact pressure is set on the particle surface. Based on the particle radial concentration and chemical strain, the radial stress and circumferential stress of the particles are solved, and the maximum circumferential tensile stress on the particle surface, the compressive stress at the particle center, and the time of their occurrence are extracted.

[0278] For lithium iron phosphate and graphite systems, a small-strain linear elastic model is preferred; for materials with large volume changes, such as silicon-based anodes, the linear elastic model can be replaced with a finite-strain or elastoplastic model. These replacements do not alter the core relationship in calculating particle stress driven by local P4D concentration.

[0279] This invention achieves particle-electrode-cell dimensional transfer and three-dimensional mechanical solution. Specifically, for example, it performs particle volume averaging of the chemical strain of particles at each spatial location of the cell.

[0280] ;

[0281] By combining the volume fraction of the active material and the orientation correction coefficient, the equivalent chemical strain of the electrode is obtained:

[0282] ;

[0283] in:

[0284] ;

[0285] Where, ξ x,k ξ y,k ξ z,k These represent strain correction factors in the length, width, and thickness directions of the electrode, respectively, and are used to reflect pore compression, particle rearrangement, binder constraint, and electrode anisotropy. These correction factors can be obtained through calculation using representative volume elements, single-electrode expansion tests, or cell constraint force inversion.

[0286] In the cell mechanical model, the positive and negative electrodes preferably adopt transversely isotropic equivalent elastic constitutive models, the separator preferably adopts a thickness-direction nonlinear viscoelastic compression constitutive model, the copper and aluminum current collectors adopt elastoplastic constitutive models, and the shell adopts an elastic or elastoplastic constitutive model.

[0287] A bonding relationship is established between the electrodes and the current collector. Under structural integrity conditions, a bonding relationship or non-slip contact relationship is established between the electrodes and the diaphragm; a normal contact relationship is established between the cell stack and the housing or external pressure plate. A predetermined initial preload or compression displacement is applied to the cells before charging and discharging, and then the spacing of the external pressure plates is kept constant.

[0288] At each time point, the equivalent chemical strain and temperature field of the electrodes are mapped to a mechanical mesh to solve for: the three-dimensional stress field of the battery cell; the three-dimensional displacement field of the battery cell; the interlayer shear stress of the electrodes; the compressive strain of the separator; the interlayer contact pressure; the equivalent stress of the current collector; and the reaction force of the external pressure plate. In a simplified embodiment, both the positive and negative electrodes and the separator can be made of equivalent linear elastic materials; when it is necessary to improve the prediction capability of the constraint force, the separator adopts a nonlinear viscoelastic model. Both the simplified and preferred methods retain the relationship of particle chemical strain transmission to the electrodes and the battery cell.

[0289] In this embodiment, stress hotspot identification and risk assessment are specifically carried out, for example, risk indicators are constructed for different failure modes.

[0290] The risk of particle cracking is characterized by the ratio of the maximum circumferential tensile stress of the particle to the particle fracture strength; the risk of interface delamination is characterized by the ratio of the interface normal tensile stress or shear stress to the corresponding critical strength; the risk of diaphragm compression is characterized by the ratio of the compressive strain or contact pressure in the thickness direction of the diaphragm to the critical value; and the risk of current collector yielding is characterized by the ratio of von Mises equivalent stress to the material yield strength.

[0291] At each time point t n The maximum value and spatial location of each risk indicator are determined. The location corresponding to the maximum risk indicator is defined as the stress risk hotspot at the current time point. The formula for calculating this hotspot is:

[0292] ;

[0293] By sequentially connecting the hotspot locations at consecutive time points, a stress hotspot migration trajectory is formed. Record: the moment the hotspot first reaches the risk threshold; the moment the maximum risk occurs; the material layer where the hotspot is located; the spatial coordinates of the hotspot; the migration distance of the hotspot; the migration speed of the hotspot; the duration of the hotspot; and the corresponding failure mode. The optimal comprehensive risk index is the maximum value among the risk indices for particle cracking, interface delamination, diaphragm compression, and current collector yielding.

[0294] This invention achieves tiered verification of voltage, temperature, and constraint force. In this preferred embodiment, an experimental verification system for voltage, temperature, and constraint force is established. The lithium iron phosphate cell to be tested is placed between two parallel pressure plates, one of which is fixed, while the other pressure plate is subjected to an initial compression displacement via a displacement adjustment mechanism, and its position is locked after reaching a predetermined initial preload. A force sensor is positioned between the cell and the pressure plates to continuously measure the constraint force during the charging and discharging process.

[0295] The battery cell is connected to a charge / discharge testing device to apply predetermined charge / discharge conditions and record the terminal voltage and current. Multiple temperature measurement points are set on the surface of the battery cell, preferably including the area near the tabs, the center of the battery cell, and the area away from the tabs. The surface temperature is recorded using thermocouples or infrared thermal imaging devices.

[0296] The experiment was conducted in the following order: ① The battery cell was adjusted to the predetermined initial state of charge (SOC); ② It was allowed to stand at the predetermined ambient temperature until thermal equilibrium was reached; ③ An initial preload was applied and the spacing between the pressure plates was locked; ④ Constant current-constant voltage charging or charge-discharge cycles were performed at a predetermined rate; ⑤ Voltage, current, temperature, and constraint force were collected simultaneously; ⑥ The measured terminal voltage was compared with the voltage calculated by the P4D model; ⑦ The measured surface temperature was compared with the temperature calculated by the three-dimensional thermal model; ⑧ The measured constraint force was compared with the pressure plate reaction force of the mechanical model; ⑨ The electrochemical, thermal, and mechanical parameters were corrected sequentially based on the error results.

[0297] Model evaluation metrics include root mean square error, maximum absolute error, peak error, and peak occurrence time error. Electrochemical, thermal, and mechanical parameters are calibrated sequentially to avoid inconsistent parameter identification caused by simultaneous changes in multiple physical field parameters.

[0298] Through the above steps S1~S10, this invention achieves the analysis of the influence of structural parameters and operating conditions. Specifically, for example, by changing the electrode thickness, electrode area, number of unit layers, initial preload, ambient temperature and charging rate, while keeping other parameters unchanged, the influence of different parameters on stress hotspots and risk indicators is compared.

[0299] For each set of operating conditions, the extracted data includes: maximum circumferential tensile stress of particles, maximum interfacial shear stress, maximum diaphragm compressive strain, maximum current collector equivalent stress, comprehensive risk index, the first occurrence time of hotspots, hotspot migration distance, and peak constraint force. Based on the above results, the main structural or operating parameters that increase risk are determined, and corresponding recommendations for adjusting electrode thickness, number of unit layers, initial preload, or charging rate are formulated.

[0300] Example 3:

[0301] refer to Figure 2As shown, this embodiment discloses a battery stress prediction system based on the P4D electrochemical model, which realizes the lithium battery internal stress prediction method described in Embodiment 1, including: an input module, an electrochemical simulation calculation module, a thermal simulation calculation module, a mechanical simulation calculation module, a coupled solution calculation module, a risk assessment calculation module, and a verification module;

[0302] The input module is used to acquire the basic parameters and usage conditions of the lithium battery under test; the electrochemical simulation calculation module is used to construct a P4D electrochemical model, which can solve for the expressions of solid-phase lithium concentration, liquid-phase lithium concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each coordinate position of the battery cell at the nth time node; it can construct the chemical strain of active particles and calculate the chemical strain of the electrodes; the thermal simulation calculation module is used to construct a three-dimensional thermal model of the battery cell; it can solve for the thermal strain of each region of the battery cell; the mechanical simulation calculation module is used to calculate the particle-scale stress of active particles; the coupled solution calculation module is used to construct a three-dimensional mechanical model, which can map the particle-scale strain of the active particles to the electrode scale and solve for the three-dimensional stress and displacement of the battery cell at time node n; the risk assessment calculation module is used to construct multiple risk indicators corresponding to battery failure modes and identify stress hotspots and hotspot migration trajectories; the verification module is used to perform hierarchical verification of the P4D electrochemical model, the three-dimensional thermal model, and the three-dimensional mechanical model.

[0303] The P4D model described in this invention can be understood as a high-fidelity multiphysics coupled simulation model. Based on the traditional three-dimensional spatial structure, it adds the calculation simulation of the solid-phase diffusion dimension and the time evolution dimension inside the electrode particles. The core principle is to solve the electrochemical reaction, heat generation and mechanical deformation together to simulate and calculate the particle diffusion-induced stress and thermal stress during the battery charging and discharging process.

[0304] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting internal stress in a lithium battery, characterized in that, Including the following steps: S1. Obtain the basic parameters and usage condition parameters of the lithium battery under test; the basic parameters include: cell size, cell type, positive and negative electrode size, separator size, number of electrode layers, and tab parameters; the usage condition parameters include: charging and discharging current, ambient temperature, initial charge, saturated charge, and initial preload. Based on the cell type, determine the radius of active particles, proportion of active material, density of active material, specific heat capacity, thermal conductivity, solid-phase diffusion coefficient, electrolyte diffusion coefficient, reaction rate constant, solid-phase conductivity, and electrolyte conductivity. S2. Constructing the P4D electrochemical model: Using the length, width, and thickness directions of the battery cell as three-dimensional spatial coordinates x, y, and z, respectively, and the radial direction from the center of the active particle to the surface as coordinate r, a P4D electrochemical model containing the three-dimensional space of the battery cell and the radial space of the particle is constructed. The P4D electrochemical model includes: the solid-phase lithium diffusion equation of the active particles, the liquid-phase lithium transport equation, the local current density calculation formula, and the overpotential calculation formula. Based on the charge conservation equation and boundary conditions, the P4D electrochemical model is used to solve for the expressions of solid-phase lithium concentration, liquid-phase lithium concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each coordinate position of the battery cell at the nth time node. The local current density includes: solid phase current density, liquid phase current density, and current collector current density; S3. Construct a three-dimensional thermal model of the battery cell: Construct a reversible heat source Q based on the local current density. rev The calculation formula is given; based on the overpotential, the reaction polarization heat Q is constructed. act The calculation formula; based on the solid-phase potential, liquid-phase potential, solid-phase current density, and liquid-phase current density, the ohmic thermal Q of the battery cell is constructed. ohm The calculation formula is derived from the solid-state current density and solid-state potential, and the Joule heating Q of the current collector is constructed. cc Therefore, the formula for calculating the local total heat production rate is as follows: ； Based on the material density, specific heat capacity, and thermal conductivity, the three-dimensional temperature field calculation formula for the battery cell is constructed as follows; ； S4. Calculate the chemical strain of the active particles: Based on the solid-phase lithium concentration, the chemical strain for constructing active particles is calculated as follows: ； in, ; Where, θ k Indicates the degree of lithium intercalation in the active particles, c s,k c represents the solid-phase lithium concentration of the k-th type of electrode active material. s,k,max β represents the maximum solid-phase lithium concentration of the k-th type of electrode active material. k Represents the chemical expansion coefficient; θ k,0 Indicates the degree of lithium insertion in the reference state; I represents the unit tensor; S5. Calculate the particle-scale stress of the active particles: Treating the active particles as spherical elastic bodies with concentration-dependent intrinsic strain, the formula for calculating the radial strain of the active particles is as follows: ； The formula for calculating the circumferential strain of active particles is constructed as follows: ； The radial strain and circumferential strain satisfy the equilibrium relationship: ； The formula for calculating particle-scale stress is as follows: ； Among them, C k This represents the elastic stiffness tensor of the active material. This represents the total strain of the active particles. Indicates the chemical strain of the active particles. This indicates the thermal strain of the active particles; Based on the displacement continuity condition at the center of the active particles and the contact pressure boundary on the surface, the radial stress of the active particles in each region of the battery cell is obtained as follows: ； The circumferential stress of the active particles in each region of the battery cell was then calculated as follows: ； S6. Map the particle-scale strain of the active particles to the electrode scale, and calculate the chemical strain of the electrode. : The volume-average formula for calculating the chemical strain of the active particles is as follows: ； Among them, R s,k Indicates the radius of the active particles; Based on the proportion of active material and the scale correction coefficient, the chemical strain of the active particles is mapped to the chemical strain at the electrode scale using a mapping relationship. The mapping relationship is as follows: ； Where, ε s,k Indicates the volume fraction of active materials; Ξ k This represents the strain correction tensor from the particle scale to the electrode scale; the formula for calculating the strain correction tensor is: ； Among them, ξ x,k ξ y,k ξ z,k These represent the strain correction factors in the length, width, and thickness directions of the electrode, respectively. S7. Calculate the thermal strain in each region of the battery cell: Based on the three-dimensional temperature field calculation formula, the thermal strain of each region of the battery cell is constructed. The calculation formula is: ； Where m represents each region of the battery cell; α m T represents the thermal expansion coefficient tensor for each region; ref Indicates reference temperature; S8. Construct a three-dimensional mechanical model of the battery cell: The formula for calculating the total strain in each region of the battery cell is: ； Among them, u m (x,y,z,t) is the displacement vector within each region m of the battery cell; Total strain in each region of the battery cell The decomposition formula is: ； Among them, the elastic strain of each region The calculation formula is: ； Based on the constitutive relation, the stress relationship for each region is constructed as follows: ； And construct the internal static equilibrium equations of the battery cell: ； Among them, C m b represents the stiffness tensor of different regions of the battery cell; m Indicates static force; The three-dimensional stress and displacement of the battery cell at time node n are obtained by solving the problem.

2. The method for predicting internal stress of a lithium battery according to claim 1, characterized in that, It also includes the following steps: S9. Calculate the continuous stress of the battery cell over time: Solving for the three-dimensional stress and displacement at multiple time points n, the continuous stress calculation formula for the three-dimensional stress of the battery cell over time is constructed as follows: ； S10. Construct multiple risk indicators corresponding to battery failure modes, and identify stress hotspots and hotspot migration trajectories: Based on the continuous stress, risk indices for particle cracking, interface delamination, diaphragm compression, and current collector yielding are constructed respectively. The formula for calculating the comprehensive risk index is then established as follows: ； Among them, R p R represents the risk index of particle cracking. d R represents the interface delamination risk indicator. sep R represents the risk index of diaphragm compression. cc Indicators representing the risk of collective flow yielding; Based on the comprehensive risk index, the formula for calculating the location of stress hotspots at each time point is as follows: ； Based on the locations of stress hotspots at multiple time points, the formula for calculating the hotspot migration trajectory is as follows: ； Based on the comprehensive risk index, determine the time when the comprehensive risk index is reached: ； The expression for the total distance of stress hotspot migration is: ； Then, the time of the first occurrence of the comprehensive risk, the time of maximum risk, the migration distance, and the duration are calculated.

3. The method for predicting internal stress of a lithium battery according to claim 2, characterized in that, It also includes the step of constructing multiple risk indicators corresponding to battery failure modes, specifically including the following steps: The formula for calculating the particle cracking risk index is as follows: ； in, θ represents the maximum circumferential tensile stress of the particle; fract Indicates the tensile strength of the active material; The formula for calculating the interface delamination risk index is as follows: ； Where, σ n σ represents the normal stress at the interface. n > + =max(σ n ,0) represents the interface normal tensile stress portion; σ n,crit τ represents the critical tensile strength in the normal direction of the interface. int τ represents the interfacial shear stress. crit Indicates the critical shear strength of the interface; The formula for calculating the current collector risk index is as follows: ； Where, σ vM σ represents the von Mises equivalent stress of the current collector; y Indicates the yield strength of the current collector; The formula for calculating the diaphragm compression risk index is as follows: ； Where, ε sep ε represents the compressive strain in the thickness direction of the diaphragm. sep,crit p represents the critical compressive strain of the diaphragm. sep p represents the diaphragm contact pressure. sep,crit This indicates the critical contact pressure of the diaphragm.

4. The method for predicting internal stress of a lithium battery according to claim 1, characterized in that, S8 further includes the following steps: The formula for calculating the stress in the thickness direction of the membrane is: ； Among them, f comp This represents the nonlinear compression relationship of the diaphragm; σ ve (t) represents the viscoelastic stress component.

5. The method for predicting internal stress of a lithium battery according to claim 1, characterized in that, The S8 further includes setting the interlayer contact relationship and external mechanical boundary to obtain contact pressure and cell constraint force: The electrodes and current collectors are bonded together; the electrodes and diaphragms are in a non-slip contact or bonded relationship; the battery cell and the housing are in a normal contact relationship. Set the preset initial preload or initial compression displacement before charging and discharging, and keep the spacing between the external pressure plates constant during charging and discharging to form a constant displacement constraint condition; obtain the cell constraint force based on the boundary reaction force of the external pressure plates.

6. The method for predicting internal stress of a lithium battery according to claim 1, characterized in that, It also includes stratified validation of the P4D electrochemical model, three-dimensional thermal model, and three-dimensional mechanical model: T1. Obtain the terminal voltage during the battery charging and discharging process using an electrical measuring device; obtain the surface temperature of the battery using a temperature measuring device; obtain the external constraint force of the battery using a force measuring device. T2. Compare the overpotential with the terminal voltage to verify the P4D electrochemical model; compare the three-dimensional temperature with the surface temperature to verify the three-dimensional thermal model; compare the three-dimensional stress with the external constraint force to verify the three-dimensional mechanical model.

7. A battery stress prediction system based on the P4D electrochemical model, characterized in that, The method for predicting the internal stress of a lithium battery as described in any one of claims 1-6 includes: an input module, an electrochemical simulation calculation module, a thermal simulation calculation module, a mechanical simulation calculation module, a coupled solution calculation module, and a verification module; The input module is used to obtain the basic parameters and usage condition parameters of the lithium battery under test; The electrochemical simulation and calculation module is used to construct a P4D electrochemical model, which can solve for the expressions of solid-phase lithium concentration, liquid-phase lithium concentration, solid-phase potential, liquid-phase potential, local current density, and overpotential at each coordinate position of the battery cell at the nth time node; it can construct the chemical strain of the active particles and calculate the chemical strain of the electrodes. The thermal simulation calculation module is used to construct a three-dimensional thermal model of the battery cell; it can solve and calculate the thermal strain in each region of the battery cell. The mechanical simulation calculation module is used to calculate the particle-scale stress of the active particles. The coupled solution calculation module is used to construct a three-dimensional mechanical model, which can map the particle-scale strain of the active particles to the electrode scale and solve for the three-dimensional stress and displacement of the cell at time node n. The risk assessment calculation module is used to construct multiple risk indicators corresponding to battery failure modes and identify stress hotspots and hotspot migration trajectories; the verification module is used to perform hierarchical verification of the P4D electrochemical model, three-dimensional thermal model and three-dimensional mechanical model.

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