A cross-scale prediction method for fast-charging swelling behavior of lithium-ion batteries

Abstract

This invention discloses a cross-scale prediction method for the expansion behavior of lithium-ion batteries during fast charging, relating to the field of lithium-ion battery safety monitoring technology. The method includes: establishing an electrochemical model with lithium plating kinetics based on a pseudo-two-dimensional framework to obtain the spatiotemporal distribution of lithium-ion concentration and lithium plating current density; establishing a particle-electrode cross-scale expansion strain model to obtain the electrochemically driven negative electrode thickness strain and the compressive strain induced by contact radius changes, and introducing an effective contact characteristic radius to characterize dynamic contact radius changes; establishing a mechanically coupled expansion model under different mechanical constraint boundaries, using geometrically compatible equations to uniformly handle three types of constraint boundaries: free expansion, elastic clamps, and rigid clamps, constructing a cross-scale prediction method model; and performing parameter identification to predict the cell expansion displacement or expansion force under arbitrary charging rates and constraint conditions. This invention achieves high-precision prediction of battery expansion behavior under high-rate fast charging conditions.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery safety monitoring technology, and in particular to a cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries. Background Technology

[0002] Lithium-ion batteries, as the core energy unit for electric transportation and grid-scale energy storage, inherently face a contradiction between rapid charging and operational safety: while increasing the charging rate significantly shortens charging time, it also significantly exacerbates the risk of thermal runaway. Before thermal runaway occurs, lithium-ion batteries typically undergo a series of internal degradation processes, including electrolyte decomposition, gas evolution, and damage to the solid electrolyte interface film, leading to abnormal internal pressure accumulation, manifested as a noticeable expansion response in the cell casing or electrode assembly. Compared to traditional diagnostic signals such as terminal voltage and surface temperature, expansion signals respond to these internal anomalies earlier, providing more timely warnings before thermal runaway occurs. However, the nominal expansion behavior of lithium-ion batteries is influenced by multiple factors, including charging rate, state of charge, and external mechanical constraints, exhibiting strong nonlinearity and operating condition dependence. Fixed threshold warning schemes struggle to reliably distinguish between nominal expansion and abnormal expansion induced by precursors to thermal runaway under complex operating conditions. Research indicates that constructing residual signals based on nominal expansion behavior models and using them as anomaly detection criteria is a more robust early warning strategy. Therefore, accurately characterizing the nominal expansion behavior of batteries is a crucial prerequisite for achieving highly reliable early detection of thermal runaway.

[0003] In the field of battery expansion behavior modeling, existing research can be divided into two categories: lumped-parameter mechanical models and expansion modeling based on electrochemical models. Regarding lumped-parameter mechanical models, Garrick et al. first established the mechanical coupling relationship between lithium intercalation-induced electrode volumetric strain and shell constraint stiffness based on the solid-phase mass conservation equation of porous electrodes. Subsequent researchers further simplified the lithium intercalation-induced volumetric strain into a piecewise or linear function of the state of charge, combining equivalent mechanical models, nonlinear equivalent stiffness, or Kelvin element series equivalent constraint springs to predict expansion forces under different aging states, temperature conditions, and pre-pressure conditions. Regarding expansion modeling based on electrochemical models, Rieger et al. first incorporated the concentration-dependent lattice volume change of electrode materials into the physicochemical modeling framework, simulating the battery thickness evolution at different discharge rates. Subsequent researchers systematically modeled concentration gradient-induced non-uniform lithium intercalation expansion based on a pseudo-two-dimensional electrochemical model, effectively reproducing the evolution of the expansion curve with rate. Wang et al. first quantitatively characterized the expansion overshoot induced by lithium plating under high-rate charging.

[0004] However, the existing technologies still have the following shortcomings: the lumped-parameter mechanical model simplifies the electrode expansion driving term to a linear function of the state of charge, which cannot characterize the electrochemical kinetics under high-rate charging, resulting in a serious lack of prediction accuracy under high-rate conditions; existing electrochemical expansion models treat non-uniform expansion due to concentration gradient and expansion overshoot induced by lithium plating separately, lacking a unified characterization framework, and neither lithium plating side reactions nor mechanical constraint boundary conditions are systematically included; existing models are generally based on the assumption of free expansion, and the expansion response under different mechanical constraint boundary conditions is not included in the modeling scope; during the charging process, the particle contact radius changes due to the rigid in-plane constraint of the copper foil and the stretching effect of the binder, making the equivalent modulus characterized by static compression testing no longer applicable to dynamic conditions, and existing models do not model this mechanism; in addition, the cross-scale mechanical transmission chain from the particle-scale electrochemical state to the macroscopic expansion of the cell is also missing in existing work, and the coupling relationship between external pressure and the effect of changing the electrode pore structure on ion transport impedance and the number of effective active particles has never been introduced into the expansion prediction framework. Therefore, there is still a lack of a complete expansion prediction framework that can simultaneously characterize concentration gradient expansion and lithium plating expansion overshoot, cover multiple mechanical constraint boundaries, and include the mechano-electrochemical feedback coupling path. Summary of the Invention

[0005] The purpose of this invention is to propose a cross-scale prediction method for the expansion behavior of lithium-ion batteries during fast charging. This method simultaneously characterizes two mechanisms: non-uniform expansion due to concentration gradient and lithium plating expansion overshoot. It constructs a complete cross-scale mechanical transmission chain from particle deformation to macroscopic expansion of the cell and uniformly handles three mechanical constraint boundary conditions: free, elastic clamp, and rigid clamp, thereby achieving high-precision expansion prediction under high-rate fast charging conditions.

[0006] To achieve the above objectives, this invention provides a cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries, the specific steps of which are as follows: Step S1: Obtain the current and electrochemical parameters of the battery, and establish a P2D electrochemical model covering three regions—graphite anode, separator, and NCM cathode—along the battery thickness direction based on the pseudo-two-dimensional P2D framework. Step S2: Based on the battery's current and electrochemical parameters, obtain the electrochemical spatiotemporal distribution information of lithium-ion concentration distribution and lithium plating current density inside the battery through an electrochemical model; Step S3: Based on the electrochemical spatiotemporal distribution information, establish a particle-electrode cross-scale expansion strain model to obtain the electrochemically driven negative electrode thickness strain and the negative electrode compressive strain induced by the change in contact radius. Step S4: Establish a mechanically coupled expansion model under different mechanical constraint boundaries, couple each strain component through geometrically compatible equations, uniformly handle the three constraint boundaries of free expansion, elastic clamp and rigid clamp, and construct a cross-scale prediction model. Step S5: Identify model parameters and substitute the identified parameters into the cross-scale prediction model to predict the cell expansion displacement or expansion force under arbitrary rate and constraint conditions.

[0007] Preferably, in step S3, the specific steps are as follows: Step S31: Based on the lithium ion concentration distribution, establish a nonlinear piecewise mapping between the volumetric strain of the graphite unit cell and the negative electrode charge state; Step S32: Perform volume-weighted integration on the local cell volume strain at each radial position inside the graphite particle to obtain the equivalent volume expansion strain of a single graphite particle. Step S33: Based on the lithium plating current density, the cumulative molar amount of lithium metal deposited per unit particle is obtained by integrating over time; assuming that the deposited lithium metal uniformly covers the particle surface in a spherical distribution, the porosity index k, which varies with the external constraint pressure, is introduced, and combined with the molar volume of lithium metal, the particle volumetric strain and radius strain caused by lithium plating are obtained. Step S34: Superimpose the particle volumetric strain caused by lithium intercalation and lithium plating to obtain the total volumetric strain of the anode particles and convert it into total radial strain; calculate the equivalent elastic modulus and Poisson's ratio of the graphite-lithium metal two-phase composite by weighting according to the volume fraction of each phase. Step S35: Based on the fact that the Young's modulus of copper foil is much greater than that of the composite, the copper foil is equivalent to a rigid in-plane constraint, and the elastic strain in the particle plane is zero; combined with the symmetry condition, the generalized Hooke's law is applied to derive the equivalent strain expression in the thickness direction of the particles, and the equivalent strain in the thickness direction is decomposed into an electrochemically driven expansion component and a constraint stress compression component. Step S36: Establish a dynamic change model of particle contact radius, and introduce the effective contact feature radius as a single identifiable parameter for unified characterization; Step S37: Integrate the electrochemically driven thickness expansion component of a single particle layer along the anode thickness direction to obtain the electrochemically driven anode thickness strain; integrate the compression component induced by the contact radius change along the anode thickness direction to obtain the anode compressive strain induced by the contact radius change.

[0008] Preferably, in step S32, the equivalent volumetric expansion strain of a single graphite particle is obtained by volume-weighted integration of the local cell volumetric strain at each radial position inside the graphite particle, as shown in the following formula: ; in, This is the anode region. t For the current moment, Where is the radius of the anode particles. It is in an anode charge state. The initial charge state of the anode. The variable is the integral variable, representing the local coordinates along the radial direction inside the anode particle. The equivalent volumetric expansion strain of a single graphite particle. This represents a nonlinear piecewise mapping between the volumetric strain of graphite unit cells and the negative electrode charge state. This represents the initial volume of the anode particles.

[0009] Preferably, in step S33, the particle volumetric strain caused by lithium plating is modeled as a spherical distribution where the deposited lithium metal uniformly covers the particle surface, as shown in the following formula: ; in, This refers to the volumetric strain of a single anode particle caused by lithium plating. This refers to the molar amount of lithium metal. Let be the molar volume of lithium metal. k It is the porosity index.

[0010] Preferably, in step S34, the equivalent elastic modulus and Poisson's ratio of the graphite-lithium metal two-phase composite are calculated by weighting according to the volume fraction of each phase, as shown in the following formula: ; in, The equivalent elastic modulus and Poisson's ratio of the two-phase composite , Poisson's ratio, For elastic modulus, Elastic modulus and Poisson's ratio of lithium metal , The equivalent volumetric expansion strain of a single graphite particle. This refers to the volumetric strain of a single anode particle caused by lithium plating. The elastic modulus and Poisson's ratio of graphite particles .

[0011] Preferably, in step S35, the copper foil applies a rigid in-plane constraint to the anode particles, and the elastic strain in the particle plane is zero. The equivalent strain in the particle thickness direction is derived from the generalized Hooke's law, as shown in the following formula: ; in, The thickness-direction equivalent strain of a single anode particle under rigid in-plane constraint of copper foil is considered. The equivalent Poisson ratio of the two complexes. The total strain of the anode particle radius is calculated by considering the contributions from both lithium intercalation and lithium plating. The equivalent elastic modulus of the two composites. This represents the stress experienced by the anode particles in the thickness direction. The equivalent strain along the particle thickness direction is decomposed into an electrochemically driven expansion component and a constrained stress compressive component; the formula for the electrochemically driven expansion component is as follows: ; in, This is an electrochemically driven thickness-direction expansion component. The total strain of anode particle radius, which is a combination of the contributions from lithium intercalation and lithium plating; The formula for the compressive component of constrained stress is as follows: ; in, The thickness direction compression component is driven by the thickness direction constraint force.

[0012] Preferably, in step S36, the dynamic change of the particle contact radius is determined by two mechanisms: the rigid in-plane constraint of the copper foil forces the particle to expand only in the thickness direction, and the particle gradually changes from a sphere to an elongated ellipsoid, reducing the radius of curvature at the z-axis contact end; at the same time, the z-axis elongation of the particle produces a JKR-like peeling effect on the adhesive contact bond, further reducing the contact radius; both together produce additional compressive strain that cannot be characterized by static compression testing. By introducing an effective contact feature radius A unified characterization of the combined effect of the two mechanisms is required to satisfy... Extended Kalman filtering was used to identify the expansion data under quasi-static conditions. The identification results were then used as general parameters applicable to all operating conditions. This refers to the contact radius between particles during the charging process. This represents the static contact radius of the battery.

[0013] Preferably, the particle volumetric strain is independent of the internal concentration gradient distribution and is determined solely by the average particle concentration. Extending this equivalence to the electrode scale, the positive electrode contraction strain becomes the cumulative charge, as shown in the following formula: ; in, For cathode contraction strain, The thickness of the cathode electrode. The number of electrode layers. The total strain represents the approximately linear volume contraction within the lithium intercalation degree range of 0.9 to 0.35. This represents the initial cathode charge state. This is the final state of cathode charge. For battery thickness, The rated charging capacity under quasi-static operating conditions, This represents the cumulative charging amount.

[0014] Preferably, in step S4, the geometrically compatible equation couples electrochemically driven expansion strain, positive electrode contraction strain, thermal expansion strain, contact radius change-induced compressive strain, and power-law nonlinear constitutive compressive strain of the composite electrode within a unified framework; the three boundary conditions of free expansion, elastic clamp, and rigid clamp correspond to direct solution, iterative solution of constraint force, and solution of expansion force under zero displacement condition, respectively, and the three constraints are unified in the same equation system.

[0015] Preferably, in step S5, the key parameter identification adopts a two-step sequential strategy: The first step is to use the measured expansion amount under quasi-static charging at a charging rate of 0.05C with elastic clamp constraint as the observation value, and to identify the convergence value of the effective contact feature radius by extended Kalman filtering; The second step involves substituting the identified effective contact feature radius into the cross-scale prediction model, using the measured expansion amount under the 1C charging rate constrained by the elastic clamp as the observation value, and then identifying the convergence value of the thermal expansion coefficient again through extended Kalman filtering.

[0016] Therefore, this invention proposes a cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries, with the following beneficial effects: (1) This invention covers four constraint conditions in the charging rate range of 0.05C to 3.5C: free expansion, elastic clamp (700N, 900N pre-tightening force) and rigid clamp (500N pre-tightening force). The maximum relative error between expansion displacement and expansion force prediction does not exceed 6.84%, and the average absolute error and root mean square error do not exceed 2.69% and 2.98% of the total increment, respectively, thus achieving high-precision expansion prediction under high-rate fast charging conditions.

[0017] (2) This invention simultaneously characterizes the non-uniform lithium insertion expansion induced by concentration gradient and the expansion overshoot induced by lithium plating within the same pseudo-two-dimensional electrochemical framework, filling the gap in existing models that treat the two mechanisms separately, and maintaining reasonable prediction accuracy under high-rate conditions near the lithium plating threshold.

[0018] (3) Starting from the lithium ion concentration distribution inside the particles, this invention establishes a complete cross-scale mechanical transmission chain from micro to macro, through the radial strain of the particles, the change in the contact state between the particles, the electrode thickness strain, and the macroscopic expansion of the battery cell. This can explain the cause of the difference in expansion response under different constraints from the mechanism level.

[0019] (4) The physical mechanism of the reduction of particle contact radius caused by the rigid in-plane constraint of copper foil and the tensile effect of adhesive during the charging process proposed in this invention introduces the effective contact characteristic radius for quantitative characterization, which solves the problem of the failure of the equivalent modulus in static compression test under dynamic working conditions. The ablation experiment proves that this is the main source of constraint compression under dynamic working conditions.

[0020] (5) In this invention, the three common engineering constraints of free expansion, elastic clamp and rigid clamp are solved in the same geometrically compatible equation framework. There is no need to build independent models for different constraints. It has good engineering applicability and generalization ability.

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 This is a flowchart of a cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to the present invention. Figure 2 This is a flowchart of parameter identification in this invention; Figure 3 This is a schematic diagram of the battery thickness variation and terminal voltage estimation results without clamps in an embodiment of the present invention; wherein, (a) is the battery thickness variation estimation result at different charging rates without clamps, and (b) is the battery terminal voltage estimation result at different charging rates without clamps. Figure 4 This is a schematic diagram of the battery thickness change and expansion force estimation results under a 700N pre-tightening force of the elastic clamp in an embodiment of the present invention; wherein, (a) is the battery thickness change estimation result under a 700N pre-tightening force of the elastic clamp at different charging rates, and (b) is the battery expansion force estimation result under a 700N pre-tightening force of the elastic clamp at different charging rates. Figure 5 This is a schematic diagram showing the estimation result of battery expansion force under a rigid clamp preload of 500N in an embodiment of the present invention. Detailed Implementation

[0023] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0024] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0025] Example 1 like Figure 1 As shown, this invention provides a cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries, with the following specific steps: Step S1: Obtain the current and electrochemical parameters of the battery, and establish a P2D electrochemical model covering three regions—graphite anode, separator, and NCM cathode—along the battery thickness direction based on the pseudo-two-dimensional P2D framework. To accurately capture the spatial distribution characteristics of concentration and lithium plating effect within the electrode, an electrochemical model covering three regions—graphite anode, separator, and NCM cathode—was established based on the P2D framework. A one-dimensional coordinate system was established along the battery thickness direction, and the coordinates of each region were defined as follows: Anode region ,in For the copper foil current collector side, For the anode / diaphragm interface, Single-layer anode thickness; diaphragm region ,in For the anode / diaphragm interface, For the cathode / diaphragm interface, Diaphragm thickness; cathode region ,in For the aluminum foil current collector side, For the cathode diaphragm interface, This represents the thickness of a single-layer cathode. The number of layers for both the anode and cathode of the battery is [number missing]. The electrode length is Width is This embodiment uses standard electrochemical notation, with positive values ​​corresponding to the oxidation direction and negative values ​​corresponding to the reduction direction, and the electrode surface current density. Represented as: (1); in Total current. Specific surface area of ​​anode and cathode. , They are respectively: (2); in and These represent the number of effective active particles at the anode and cathode, respectively. Where is the radius of the anode particles. The radius of the cathode particle is denoted as .

[0026] Based on specific surface area, the volume current density of the anode and cathode and They are represented as follows: (3); During charging, the current density of the lithium intercalation reaction at the anode Anode lithium plating reaction current density Cathode delithiation reaction current density Liquid lithium-ion concentration in the anode, diaphragm, and cathode regions Described by the Nernst-Planck equations: (4); in, This indicates the porosity of the anode, diaphragm, and cathode regions. The effective diffusion coefficients for the anode, diaphragm, and cathode regions are based on the Bruggeman modified relation. Where is the lithium-ion transference number, and F is the Faraday constant. This represents the liquid phase lithium-ion concentration in the anode, diaphragm, and cathode regions. Let the spatial coordinates along the battery thickness direction correspond to the local coordinates within the anode, separator, and cathode regions, respectively. This represents the volume current density at the anode and cathode; since there is no electrochemical reaction within the membrane, .

[0027] The current collector side satisfies the zero flux boundary condition: (5); The concentration and flux continuity conditions are satisfied at the anode / diaphragm interface and the diaphragm / cathode interface, respectively: (6); (7); Based on the theory of concentrated solutions, the liquid phase potential gradient is composed of both Ohmic conduction and diffusion potential caused by the concentration gradient, and the liquid phase potential in each region is... satisfy: (8); in The effective liquid phase ionic conductivity of each region. The gas constant is... Temperature. Liquid current density in each region. Taking the current collector side as the zero flux boundary condition, the result obtained from the charge conservation integral is: Since there is no electrochemical reaction within the diaphragm, the liquid phase current density of the diaphragm is uniformly distributed and equal to the surface current density. Using the cathode / diaphragm interface as the global liquid phase potential reference zero point, the boundary value of the liquid phase potential on the anode side is obtained by integrating equation (8) along the diaphragm region: (9); in, The integral variable represents the local spatial coordinates of the anode and cathode along the thickness direction; Using formula (9) as the starting point for integrating the anodic liquid phase potential, we solve for the liquid phase potential distribution in each region by combining it with formula (8).

[0028] Step S2: Based on the battery's current and electrochemical parameters, obtain the electrochemical spatiotemporal distribution information of lithium-ion concentration distribution and lithium plating current density inside the battery through an electrochemical model; Lithium ion concentration in anode and cathode particles In spherical coordinate system The following follows Fick's Second Law: (10); in, is the lithium-ion solid-phase diffusion coefficient within each electrode particle; The particle center satisfies symmetrical boundary conditions, and the flux at the particle surface is determined by the reaction current density. (11); Solid-state electron transport follows Ohm's law, and the solid-state potentials at the anode and cathode are... satisfy: (12); in, The effective conductivity of the solid phase of each electrode. This represents the volume fraction of the active material for each electrode.

[0029] The diaphragm side satisfies the zero flux condition, while the current collector side is subject to a current boundary condition. (13); Based on electrode reaction kinetics, the current density of each electrode reaction is described by the Butler-Volmer equation, and the anode lithium intercalation current density... for: (14); in, This is the rate constant for the anodic lithium intercalation reaction. The maximum lithium-ion concentration of the anode particles, and the overpotential of the anode lithium intercalation reaction. Represented as: (15); in, This is the anode equilibrium potential. This represents the lithium-ion concentration on the surface of the anode particles. The equivalent resistance of the SEI film is... Indicates the thickness of the SEI film. This indicates the conductivity of the SEI film.

[0030] Anode lithium plating reaction current density It can be represented as: (16); in, This represents the rate constant for the lithium deposition reaction at the anode. This represents the lithium deposition nucleation barrier threshold.

[0031] The results indicate that lithium deposition on graphite surfaces faces a significant nucleation barrier. This embodiment takes Overpotential of anodic lithium plating reaction Represented as: (17); Cathode delithiation current density for: (18); in, This represents the rate constant of the cathode delithiation reaction. The maximum lithium-ion concentration of the cathode particles, and the overpotential of the cathode delithiation reaction. Represented as: (19); in, This is the cathode equilibrium potential. This represents the lithium-ion concentration on the surface of the cathode particles.

[0032] Based on charge conservation, the integral of the electrode reaction current density along the electrode thickness direction must satisfy: (20); By combining equations (4) to (20), the spatiotemporal distribution of each electrochemical quantity is obtained, and then... Determine the battery terminal voltage ;in, This represents the contact resistance.

[0033] Step S3: Based on the electrochemical spatiotemporal distribution information, establish a particle-electrode cross-scale expansion strain model to obtain the electrochemically driven negative electrode thickness strain and the negative electrode compressive strain induced by the change in contact radius. Based on the lithium ion concentration distribution inside the obtained anode particles Current density of lithium plating reaction A model for lattice volume expansion caused by lithium intercalation and a model for surface-additional volume expansion caused by lithium deposition were established. The equivalent thickness-direction strain of particles under the rigid constraint of copper foil was determined by combining the generalized Hooke's law.

[0034] Graphite cell volume strain With anodic charge state The relationship is nonlinear, and it can be represented as an anode charge state. Functions: (twenty one); Anode charge state Defined as: (twenty two); Due to the lithium-ion concentration gradient within the particle, the local volume expansion at various radial positions is uneven. Taking the initial state as a reference, the position... The equivalent volumetric expansion strain of a single graphite particle is represented by the volume-weighted integral of the local expansion: (twenty three); in, This represents the initial charge state of the anode. The variable is the integral variable, representing the local coordinates along the radial direction inside the anode particle. The equivalent volumetric expansion strain of a single graphite particle. This represents a nonlinear piecewise mapping between the volumetric strain of graphite unit cells and the negative electrode charge state. This represents the initial volume of the anode particles.

[0035] Assuming isotropic volume change of particles under free expansion conditions, the intrinsic radius expansion strain of a single anode particle is... for: (twenty four); During lithium plating, the cumulative molar amount of lithium metal deposited by a single anode particle for: (25); The precipitated lithium metal exhibits sparse porosity, and the porosity exponent is [value missing] under different pressures. The values ​​will differ (in this embodiment, the value is 0.59 without preload; under the preload condition described in this embodiment, the value is 0.34). Assuming the deposited lithium metal uniformly covers the particle surface in a spherical distribution, the particle volumetric strain caused by lithium deposition... for: (26); in, denoted as , where is the molar volume of lithium metal.

[0036] Particle radius strain caused by lithium plating for: (27); Combining lithium intercalation and lithium deposition, the total strain of anode particle radius is calculated. The formula is as follows: (28); The equivalent elastic modulus and Poisson's ratio of the two-phase composite consisting of graphite particles and precipitated lithium metal are calculated by weighting the volume fraction of each phase and are uniformly expressed as follows: (29); in ; In this embodiment, the Young's modulus of the graphite particles Poisson's ratio Young's modulus of lithium metal Poisson's ratio Under maximum lithium plating conditions, the volume fraction of the lithium metal phase is less than 2%. Based on this, the calculated equivalent modulus and Poisson's ratio are approximately 9.96 GPa and 0.2624, respectively, primarily dominated by graphite properties. Therefore, in this embodiment, the elastic modulus and Poisson's ratio of the composite are taken as typical graphite values. Since the anode particles are attached to the copper foil via a binder, the Young's modulus E of the copper foil... Cu ≈120 GPa, much larger than the composite modulus (10 GPa), can be approximated as a rigid in-plane constraint, according to the generalized Hooke's law: (30); in, The actual strains in the x, y, and z directions. The intrinsic strain (free expansion strain) is in the x, y, and z directions. The stresses are in the x, y, and z directions. The equivalent elastic modulus of the composite. The equivalent Poisson's ratio for the complex; Under this constraint, the elastic strain within the anode particle surface is zero, that is: From symmetry, we can obtain The stress on the anode particles along the z-axis ,and Substituting the above conditions into formula (30), we get: (31); Formula (31) gives the equivalent strain in the thickness direction of a single anode particle under rigid in-plane constraint of copper foil. Formula (31) is decomposed into an electrochemically driven expansion component. Particle compression component caused by constraint stress : (32); (33); in, P It can be based on the macroscopic constraints experienced during battery expansion. F e Based on the relationships between forces, we obtain: (34); in, , The contact radius between the anode particles; The contact radius differs between static and charging conditions: During static compression testing, the measured equivalent compressive modulus of the composite electrode already includes the contribution of anode particle contact compression, but the battery is in an uncharged state at this time, and its contact radius... The compaction process of the anode electrode is determined by this; since the stress required for the compaction process is much greater than the stress generated in actual operation, It can be considered a constant; among which, This represents the static contact radius of the battery.

[0037] However, during charging, according to the generalized Hooke's law, the rigid in-plane constraint of the copper foil causes the particle expansion strain to concentrate along the z-axis, resulting in zero in-plane strain. This anisotropic strain causes the particles to gradually evolve from spherical to elongated ellipsoids, thus reducing the radius of curvature at the z-axis contact end. Simultaneously, the elongation of the particles along the z-axis exerts an equivalent tensile effect on the adhesive contact bonds, further reducing the contact radius. These two effects together influence the interparticle contact radius during charging. When the value is less than the static reference value, the granular-scale compression caused by the macroscopic constraint force is no longer equivalent to the portion included in the static test, resulting in additional compressive strain. It can be expressed as: (35); in, This refers to the contact radius between particles during the charging process. This refers to the static contact radius of the battery. The size is determined by the electrode compaction process parameters and is difficult to quantify independently under actual working conditions; The formation process of [the substance] is similar to the desorption process in JKR's adhesive contact theory in terms of contact mechanics, but the driving mechanisms are different, so JKR theory is not directly applicable. Given [this]... and It is difficult to make independent prior estimates based solely on material constitutive parameters and process parameters, so an equivalent contact characteristic radius is introduced. As a single identification parameter, it uniformly represents the combined effect of the two and is defined as: (36); Electrochemically driven anode thickness strain and the anodic compressive strain caused by the change in contact radius It can be obtained by integrating along the anode thickness direction using formulas (32) and (33): (37); (38); in, This represents the initial thickness of the battery.

[0038] The cathode undergoes shrinkage during charging. In this embodiment, XRD results show that the NCM523 cathode exhibits approximately linear volume shrinkage within a delithiation degree ranging from 0.1 to 0.65, with a total strain of... Based on cathode particle concentration distribution It can be seen that under charging conditions (maximum 3.5C), the degree of local delithiation at various locations of the cathode particles falls within the aforementioned linear range. Since the cell volume has a linear relationship with the local lithium concentration, the volume-weighted integral of the particle volumetric strain is equivalent to directly substituting the average particle concentration into the linear relationship. That is, the particle volumetric strain is independent of the internal concentration gradient distribution and is determined solely by the average particle concentration. This equivalence extends further to the electrode scale: the overall volume change of the anode is equivalent to being determined by the average electrode concentration, i.e., it depends only on the total amount of lithium ions extracted and the cumulative charging amount. Unique correspondence. Assuming isotropic contraction, the cathode contraction strain... For cumulative charging amount Linear functions: (39); in, The rated charging capacity under quasi-static operating conditions, This represents the initial cathode charge state. This is the final state of cathode charging.

[0039] Step S4: Establish a mechanically coupled expansion model under different mechanical constraint boundaries, couple each strain component through geometrically compatible equations, uniformly handle the three constraint boundaries of free expansion, elastic clamp and rigid clamp, and construct a cross-scale prediction model. A macroscopic mechanical coupling model is established based on electrode-scale strain. During battery charging, thermal effects occur, causing macroscopic thermal expansion. Therefore, the overall thermal expansion strain of the battery is... Expressed as: (40); in, The coefficient of thermal expansion is The surface temperature of the battery. The ambient temperature is considered. Multiple studies have shown that aluminum-plastic film encapsulation provides almost no constraint on battery expansion; under fixture-free conditions, the macroscopically observable thickness strain of the battery is minimal. This can be expressed as: (41); in, For electrochemical kinetic anodic expansion, Electrochemically driven cathode contraction strain Thermal expansion strain driven by temperature; In most cases, batteries are used with clamps. During battery expansion, the clamps create a restraining force on the electrodes. F e Macroscopic thickness strain of battery under fixture Electrochemical kinetic anodic expansion and temperature-driven thermal expansion strain Electrochemically driven cathode contraction strain and binding force F e Anodic compressive strain caused by related contact radius changes and the overall compressive strain of the composite electrode Through the strain response of the fixture Determined by geometric compatibility coupling: (42); in, , is the spring constant.

[0040] Overall equivalent Young's modulus of composite electrode The results, characterized by static compression experiments, conform to a power-law form. Based on the nonlinear elastic constitutive relation, the stress-strain relationship along the overall electrode thickness is: (43); in, The force acting on the electrode is h, and the actual thickness of the battery after compression is h. denoted as , and b is the power-law coefficient of the overall equivalent Young's modulus of the composite electrode. The pressure applied in the thickness direction of the battery can be used to obtain the compressive strain of the composite electrode caused by the constraint force. It can be represented as: (44); in, This represents the preload applied by the clamp. Substituting the constitutive expressions for each strain into formula (42), we obtain... State equilibrium equations: (45); In this embodiment, for the rigid fixture working condition, Formula 45 can be rewritten as: (46); The macroscopic thickness expansion strain of the battery without clamps can be obtained by calculating formula (41). By iteratively solving equation (45) or equation (46), the macroscopic thickness expansion strain of the battery under the two constraint conditions can be obtained. Or the expansion force measured by a mechanical sensor .

[0041] Step S5: Identify model parameters and substitute the identified parameters into the cross-scale prediction model to predict the cell expansion displacement or expansion force under arbitrary rate and constraint conditions.

[0042] like Figure 2 As shown, the equivalent contact characteristic radius, using the measured expansion amount under the 0.05C charging condition with elastic clamp constraint as the observation value, is obtained through the extended Kalman filter algorithm and used as a universal parameter for all operating conditions. Similarly, the thermal expansion coefficient, using the measured expansion amount under the 1C charging condition with elastic clamp constraint as the observation value, is also obtained through the extended Kalman filter algorithm and used as a universal parameter for all operating conditions. Both parameters are applied universally to all rate and constraint conditions, utilizing sequential identification to avoid the coupling problem and convergence difficulties associated with simultaneous identification of multiple parameters.

[0043] like Figures 3-5 As shown, the predicted battery expansion behavior under various constraints during high-rate charging is presented. Figure 3 It can be seen that the maximum error in estimating the battery thickness change without clamps is no more than 10.98 micrometers, accounting for 5.11% of the total change, and the maximum error in estimating the terminal voltage is no more than 40 mV, verifying the accuracy of the battery thickness change estimation and electrochemical state estimation without clamps. Figure 4 It can be seen that the maximum error in surface thickness variation under the elastic clamp is no more than 10.94 micrometers, accounting for 4.23% of the total variation, and the maximum error in expansion force is no more than 7.99 N, accounting for 6.00% of the total variation, thus verifying the estimation capability of the proposed method under elastic boundaries. Figure 5 It can be seen that the maximum error in estimating the expansion force under rigid fixtures is no more than 19.33 N, which is 4.33% of the total variation, thus verifying the estimation capability of the proposed method under rigid boundaries.

[0044] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0045] Therefore, this invention provides a cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries, which solves the problems of existing models being unable to uniformly represent the two expansion mechanisms, lacking cross-scale mechanical transmission chains, static compression modulus failure under dynamic conditions, and the need to model different constraints separately and repeatedly calibrate parameters. It achieves high-precision fast-charging expansion prediction across the full rate range and under various constraints.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries, characterized in that, The specific steps are as follows: Step S1: Obtain the current and electrochemical parameters of the battery, and establish a P2D electrochemical model covering three regions—graphite anode, separator, and NCM cathode—along the battery thickness direction based on the pseudo-two-dimensional P2D framework. Step S2: Based on the battery's current and electrochemical parameters, obtain the electrochemical spatiotemporal distribution information of lithium-ion concentration distribution and lithium plating current density inside the battery through an electrochemical model; Step S3: Based on the electrochemical spatiotemporal distribution information, establish a particle-electrode cross-scale expansion strain model to obtain the electrochemically driven negative electrode thickness strain and the negative electrode compressive strain induced by the change in contact radius. Step S4: Establish a mechanically coupled expansion model under different mechanical constraint boundaries, couple each strain component through geometrically compatible equations, uniformly handle the three constraint boundaries of free expansion, elastic clamp and rigid clamp, and construct a cross-scale prediction model. Step S5: Identify model parameters and substitute the identified parameters into the cross-scale prediction model to predict the cell expansion displacement or expansion force under arbitrary rate and constraint conditions.

2. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 1, characterized in that, In step S3, the specific steps are as follows: Step S31: Based on the lithium ion concentration distribution, establish a nonlinear piecewise mapping between the volumetric strain of the graphite unit cell and the negative electrode charge state; Step S32: Perform volume-weighted integration on the local cell volume strain at each radial position inside the graphite particle to obtain the equivalent volume expansion strain of a single graphite particle. Step S33: Based on the lithium plating current density, the cumulative molar amount of lithium metal deposited per unit particle is obtained by integrating over time; assuming that the deposited lithium metal uniformly covers the particle surface in a spherical distribution, the porosity index k, which varies with the external constraint pressure, is introduced, and combined with the molar volume of lithium metal, the particle volumetric strain and radius strain caused by lithium plating are obtained. Step S34: Superimpose the particle volumetric strain caused by lithium intercalation and lithium plating to obtain the total volumetric strain of the anode particles and convert it into total radial strain; calculate the equivalent elastic modulus and Poisson's ratio of the graphite-lithium metal two-phase composite by weighting according to the volume fraction of each phase. Step S35: Based on the fact that the Young's modulus of copper foil is much greater than that of the composite, the copper foil is equivalent to a rigid in-plane constraint, and the elastic strain in the particle plane is zero; combined with the symmetry condition, the generalized Hooke's law is applied to derive the equivalent strain expression in the thickness direction of the particles, and the equivalent strain in the thickness direction is decomposed into an electrochemically driven expansion component and a constraint stress compression component. Step S36: Establish a dynamic change model of particle contact radius, and introduce the effective contact feature radius as a single identifiable parameter for unified characterization; Step S37: Integrate the electrochemically driven thickness expansion component of a single particle layer along the anode thickness direction to obtain the electrochemically driven anode thickness strain; integrate the compression component induced by the contact radius change along the anode thickness direction to obtain the anode compressive strain induced by the contact radius change.

3. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 2, characterized in that, In step S32, the equivalent volumetric expansion strain of a single graphite particle is obtained by volume-weighted integration of the local cell volumetric strain at each radial position inside the graphite particle, as shown in the following formula: ； in, This is the anode region. t For the current moment, Where is the radius of the anode particles. It is in an anode charge state. This represents the initial charge state of the anode. The variable is the integral variable, representing the local coordinates along the radial direction inside the anode particle. The equivalent volumetric expansion strain of a single graphite particle. This represents a nonlinear piecewise mapping between the volumetric strain of graphite unit cells and the negative electrode charge state. This represents the initial volume of the anode particles.

4. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 3, characterized in that, In step S33, the particle volumetric strain caused by lithium plating is modeled as a spherical distribution where the deposited lithium metal uniformly covers the particle surface, as shown in the following formula: ； in, This refers to the volumetric strain of a single anode particle caused by lithium plating. This refers to the molar amount of lithium metal. Let be the molar volume of lithium metal. k It is the porosity index.

5. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 4, characterized in that, In step S34, the equivalent elastic modulus and Poisson's ratio of the graphite-lithium metal two-phase composite are calculated by weighting according to the volume fraction of each phase, as shown in the following formula: ； in, The equivalent elastic modulus and Poisson's ratio of the two-phase composite , Poisson's ratio, For elastic modulus, Elastic modulus and Poisson's ratio of lithium metal , The equivalent volumetric expansion strain of a single graphite particle. This refers to the volumetric strain of a single anode particle caused by lithium plating. The elastic modulus and Poisson's ratio of graphite particles .

6. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 5, characterized in that, In step S35, the copper foil applies a rigid in-plane constraint to the anode particles, and the elastic strain in the particle plane is zero. The equivalent strain in the particle thickness direction is derived from the generalized Hooke's law, as shown in the following formula: ； in, The thickness-direction equivalent strain of a single anode particle under rigid in-plane constraint of copper foil is considered. The equivalent Poisson ratio of the two complexes. The total strain of the anode particle radius is calculated by considering the contributions from both lithium intercalation and lithium plating. The equivalent elastic modulus of the two composites. This represents the stress experienced by the anode particles in the thickness direction. The equivalent strain along the particle thickness direction is decomposed into an electrochemically driven expansion component and a constrained stress compressive component; the formula for the electrochemically driven expansion component is as follows: ； in, This is an electrochemically driven thickness-direction expansion component. The total strain of anode particle radius, which is a combination of the contributions from lithium intercalation and lithium plating; The formula for the compressive component of constrained stress is as follows: ； in, The thickness direction compression component is driven by the thickness direction constraint force.

7. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 6, characterized in that, In step S36, the dynamic change of the particle contact radius is determined by two mechanisms: the rigid in-plane constraint of the copper foil forces the particle to expand only in the thickness direction, and the particle gradually changes from a sphere to an elongated ellipsoid, and the radius of curvature of the z-axis contact end decreases; at the same time, the z-axis elongation of the particle produces a JKR-like peeling effect on the adhesive contact bond, further reducing the contact radius; the two together produce additional compressive strain that cannot be characterized by static compression test. By introducing an effective contact feature radius A unified characterization of the combined effect of the two mechanisms is required to satisfy... Extended Kalman filtering was used to identify the expansion data under quasi-static conditions. The identification results were then used as general parameters applicable to all operating conditions. This refers to the contact radius between particles during the charging process. This represents the static contact radius of the battery.

8. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 7, characterized in that, The particle volumetric strain is independent of the internal concentration gradient distribution and is determined solely by the average particle concentration. Extending this equivalence to the electrode scale, the positive electrode contraction strain becomes the cumulative charge, as shown in the following formula: ； in, For cathode contraction strain, The thickness of the cathode electrode. The number of electrode layers. The total strain represents the approximately linear volume contraction within the lithium intercalation degree range of 0.9 to 0.

35. This represents the initial cathode charge state. This is the final state of cathode charge. For battery thickness, The rated charging capacity under quasi-static operating conditions, This represents the cumulative charging amount.

9. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 8, characterized in that, In step S4, the geometrically compatible equation couples electrochemically driven expansion strain, positive electrode contraction strain, thermal expansion strain, contact radius change-induced compressive strain, and power-law nonlinear constitutive compressive strain of the composite electrode within a unified framework; the three boundary conditions of free expansion, elastic clamp, and rigid clamp correspond to direct solution, iterative solution of constraint force, and solution of expansion force under zero displacement condition, respectively, and the three constraints are unified in the same equation system.

10. The cross-scale prediction method for the fast-charging expansion behavior of lithium-ion batteries according to claim 9, characterized in that, In step S5, the key parameter identification adopts a two-step sequential strategy: The first step is to use the measured expansion amount under quasi-static charging at a charging rate of 0.05C with elastic clamp constraint as the observation value, and to identify the convergence value of the effective contact feature radius by extended Kalman filtering; The second step involves substituting the identified effective contact feature radius into the cross-scale prediction model, using the measured expansion amount under the 1C charging rate constrained by the elastic clamp as the observation value, and then identifying the convergence value of the thermal expansion coefficient again through extended Kalman filtering.

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