CN110633496B - A Method for Determining Thermal Stress and Temperature During Discharge of Li-ion Batteries Based on Thermal-Mechanical Coupled Model - Google Patents

Abstract

The invention discloses a method for determining thermal stress and temperature in a lithium ion battery discharging process based on a thermal-force coupling model, which relates to the field of lithium ion battery thermal expansion and stress calculation, and the method establishes a thermal expansion model by using a lithium ion battery three-dimensional geometric scale, and comprises the following specific steps: (1) Selecting a single battery cell, and acquiring three-dimensional geometric parameters, mechanical and thermodynamic initial parameters of the single battery cell; (2) Establishing a thermal-force coupling model of a three-dimensional electrical core scale according to a thermal expansion coefficient, a temperature difference and a coupling mechanism of a stress-strain relation; (3) Testing the battery temperature and the lug temperature, and verifying the effectiveness of the model; (4) The temperature distribution and the expansion displacement and the stress along the x, y and z directions of the battery are obtained. The invention provides a certain guidance basis for the expansion model of the battery cell on the macroscopic scale and the expansion behavior and rupture prediction of the battery cell in the charging and discharging process.

Description

A thermal-mechanical coupling model based on thermal stress and stress during discharge of lithium-ion batteries How to determine the temperature

technical field

The invention belongs to the field of thermal expansion and stress calculation of lithium-ion batteries, and in particular relates to a method for determining thermal stress and temperature during the discharge process of lithium-ion batteries based on a thermal-mechanical coupling model.

Background technique

Lithium-ion batteries are widely used in electronic equipment, electric vehicles and energy storage power stations due to their excellent performance, but there have also been many safety accidents. During the charging and discharging process of lithium-ion batteries, especially in the high-rate charging and discharging process, there will be local high temperature phenomenon, and high temperature will cause thermal expansion, which will lead to thermal stress. When the generated stress is large, it will Accompanied by the cracking and falling off of the electrode material, and the poor contact of each part of the battery cell due to the expansion of the battery cell, it will eventually lead to an increase in internal resistance, capacity decay, and battery failure. Therefore, predicting the stress of the battery can effectively prevent battery failure. The safety of lithium-ion batteries is guaranteed.

At present, the traditional experimental method is difficult to observe the expansion behavior of the battery cell during the charging and discharging process and predict the stress, and the thermal expansion model on the macro scale of the battery cell is difficult to verify the validity of the model and difficult to establish the model. less. Therefore, the present invention breaks through the limitations of the two, and proposes a method for determining thermal stress and temperature in the lithium-ion battery discharge process based on a thermal-mechanical coupling model. According to the coupling mechanism of thermal expansion coefficient, temperature difference and stress-strain relationship, a thermal-mechanical coupling model was established; then the validity of the model was verified by the experimentally measured temperature and tab temperature to ensure the accuracy of the model; Look at the expansion displacement and stress distribution in the three directions of x, y, and z. The invention can calculate the stress and temperature suffered by the battery core during the discharge process of the lithium ion battery, and can observe the expansion behavior of the battery core, which can provide a certain guiding basis for predicting the expansion and rupture behavior of the battery core.

SUMMARY OF THE INVENTION

The invention provides a method for determining thermal stress and temperature during the discharge process of lithium-ion batteries based on a thermal-mechanical coupling model. By establishing a three-dimensional macroscopic thermal-mechanical coupling model of the battery cell and through effective experimental verification, the battery is finally obtained. The temperature distribution of the core during the discharge process, the thermal stress distribution and the expansion displacement distribution along the three directions of x, y, and z reveal the relationship between the expansion phenomenon of the core and the temperature.

The technical scheme adopted in the present invention is: a method for determining thermal stress and temperature in the lithium-ion battery discharge process based on a thermal-mechanical coupling model, including the following steps: Step 1, select a single battery cell, and obtain its three-dimensional geometry Parameters, initial parameters of mechanics and thermodynamics; step 2, according to the coupling mechanism of thermal expansion coefficient, temperature difference and stress-strain relationship, establish a thermal-mechanical coupling model of three-dimensional cell scale; step 3, test the battery temperature and tab temperature, Verify the validity of the model; step 4, obtain the temperature distribution of the battery and the expansion displacement and stress along the three directions of x, y, and z.

The model in step 2 is a thermal-mechanical coupling model of the three-dimensional cell scale. The basic theory of the model includes two aspects, (1) stress-strain relationship (2) energy conservation equation. The process of building the model is described below:

(1) Stress-strain relationship

Think of the battery as an anisotropic heat conductor and an isotropic linear elastic body. The coupling of stress and temperature is achieved through thermal expansion. The relationship between strain and temperature caused by thermal stress is shown in formula (1), where ε _ij is the strain component, α is the thermal expansion coefficient, and δ _ij is the Dirac delta function. When i=j Its value is 1, otherwise its value is 0, and ΔT is the temperature difference. According to the formula, when the temperature difference is greater, the strain is greater, so the thermal stress is also greater.

In the presence of thermal stress, the stress-strain relationship is expressed according to formula (2),

where σ _ij is the stress component, E is Young's modulus, and ν is Poisson's ratio.

The hydrostatic stress (σ _h ) and von Mises stress (σ _v ) are given by equations (3) and (4):

σ _ν = |σ _r -σ _θ | (4)

where σ _r is the radial stress, and σ _θ is the tangential stress.

The boundary conditions are as follows: constraints are set on the four surfaces around the surface of the battery cell, so that the battery only expands along the thickness direction, namely:

u _y ＝0, u _z ＝0 (5)

(2) Energy Conservation Equation

The cell is regarded as an anisotropic heat conductor, and the governing equations and boundary conditions of the thermal model are listed in Table 1. Its heat generation follows the Bernardi heat generation rate equation, see formula (7). The former is reversible heat, which is generated by the entropy change of the electrode material and depends on the entropy coefficient (dU ₀ /dT); the latter is irreversible heat, which is generated by the battery itself caused by internal resistance. Heat loss considers heat convection and heat radiation.

Table 1 Thermal model governing equations and boundary conditions

In the thermal model, the battery is equivalent to an anisotropic heat conductor, and the aggregate specific heat capacity, density, and thermal conductivity are shown in formulas (11)-(14) respectively, where the thermal conductivity is divided into direction) and perpendicular to the pole piece (y direction: thickness direction).

(3) Coupling process

Stress and heat are coupled through the temperature of the battery. When the temperature changes, the temperature difference ΔT of the battery will also change, which will lead to the change of thermal strain in formula (1), and the change of thermal strain will lead to the total The change of strain and total stress, and the change of stress will in turn lead to the change of battery temperature, so as to realize the coupling of thermal-mechanical model. This process is reproduced in the multiphysics field coupling software COMSOLMultiphysics. The coupling process and calculation process are shown in Figure 1. The symbols and terms appearing in the present invention are shown in Table 2.

Symbols and terms that appear in the present invention in table 2

The validity verification of the model in step 3 adopts the following steps:

(1) First arrange several thermocouples on the surface of the battery to measure the temperature of the battery during the discharge process, and connect the battery to the force measuring device;

(2) Fully charge the battery through the charging method of constant current and then constant voltage, and set the charging cut-off voltage according to the battery material;

(3) Perform constant current discharge on the battery, and set the discharge cut-off voltage according to the battery material;

(4) compare the average temperature curve obtained by the experiment with the simulated value;

(5) Carry out parameter correction according to the result of the above step (4), and obtain a corrected thermal-mechanical coupling model.

Compared with the prior art, the present invention has the following advantages: 1. It makes up for the deficiency that the traditional experimental method is difficult to predict the thermal stress of the battery during the discharge process, and also improves the thermal-mechanical coupling model system; 2. Establishes a three-dimensional battery cell The scale thermal-mechanical coupling model can not only reproduce the three-dimensional geometric structure of the battery, but also obtain the temperature distribution and thermal stress distribution of the battery cell during the discharge process; 3. It can dynamically observe the lithium-ion battery during the discharge process. The expansion phenomenon and displacement changes are convenient for analyzing the expansion behavior and stress changes of the battery during the entire discharge process; 4. The establishment of numerical simulation methods and models saves resources and manpower, and has guiding significance for the thermal and mechanical safety of lithium-ion batteries 5. The thermal-mechanical coupling model of the three-dimensional macro scale established by the inventive method can verify the validity of the model through experiments, which ensures the accuracy of the model, and also provides a basis for the subsequent stress of the lithium-ion battery charge and discharge cycle process on this three-dimensional model. 6. It provides a research foundation and research basis for researchers and developers of lithium-ion battery stress numerical simulation researchers and developers, and provides technical support for the thermal safety and mechanical safety of lithium-ion batteries.

Description of drawings

Fig. 1 is the coupling mechanism and principle of the thermal-mechanical coupling model in the present invention.

Fig. 2 is a graph showing the variation of the battery entropy coefficient and internal resistance with the depth of discharge in the embodiment of the present invention.

Fig. 3 is the schematic diagram of model geometry and grid in the embodiment of the present invention, wherein, Fig. 3 (a) is the schematic diagram of model geometry in the embodiment of the present invention, Fig. 3 (b) is the schematic diagram of model grid in the embodiment of the present invention .

Fig. 4 is an experimental and simulated comparison graph of the average temperature of the battery core and the temperature of the positive and negative tabs in the embodiment of the present invention.

Fig. 5 is a temperature distribution diagram of the battery under different discharge times (5s, 900s, 2700s, 3600s) in the embodiment of the present invention.

Fig. 6 is the von Mises stress curve that the battery is subjected to along x, y, z three directions under different discharge times (0s, 900s, 1800s, 2700s, 3600s) in the embodiment of the present invention, wherein (0,0 ) point is the geometric center of the cell.

Fig. 7 is a diagram showing the displacement distribution of the battery under different discharge times (5s, 900s, 2700s, 3600s) in the embodiment of the present invention, which is deformed and enlarged by 5000 times.

Fig. 8 is a curve diagram of the expansion displacement of the battery along the x, y, and z directions under different discharge times (0s, 900s, 1800s, 2700s, 3600s) in the embodiment of the present invention, where (0,0) point is the geometric center of the cell.

Detailed ways

In order to facilitate the understanding of the present invention, the following will describe the present invention more comprehensively and in detail in conjunction with examples, but the protection scope of the present invention is not limited to the following specific examples.

Example

Taking a 105Ah lithium iron phosphate/graphite battery as an example, calculate the temperature and stress distribution during the discharge process of the lithium-ion battery, and describe the present invention in a comprehensive and detailed manner. The method is not limited to the thermal-mechanical coupling of this type of lithium-ion battery The construction of the model and the calculation of temperature and stress are applicable to all lithium-ion batteries. The method is mainly divided into the following four parts: (1) Establishment of thermal-mechanical coupling model; (2) Validation of the model; (3) Temperature distribution of the battery during discharge; (4) Stress distribution of the battery during discharge and expansion behavior.

1. First, describe the model building part, which is divided into 2 steps, as follows:

Step 1, model parameter acquisition. The mechanical parameters of the cell and the thermodynamic parameters of the material are obtained according to the method of literature research, and these parameters are listed in Table 3 and Figure 2.

Step two, the establishment of a three-dimensional thermal-mechanical coupling model at the cell scale. The model geometry and grid are shown in Figure 3. The model contains three computational domains: the negative tab (the material is copper), the positive tab (the material is aluminum), and the main body of the battery (isotropic elastomer and anisotropic thermal conductivity Body), the layered structure inside the cell is not considered to simplify the model. The mesh construction adopts the method of freely subdividing the tetrahedral mesh, which contains 9777 tetrahedral elements, 1926 triangular elements, 206 edge elements and 24 vertex elements, and has passed the mesh independence test.

Table 3 Thermal-mechanical coupling model parameters

Note: "-" indicates that the item does not exist or is not considered.

2. Validation of the model

The validation steps of the model are as follows:

(1) First arrange several thermocouples on the surface of the battery to measure the temperature of the battery during the discharge process, and connect the battery to the force measuring device;

(2) Charge the battery with constant current and then constant voltage at a rate of 1C. The charging cut-off voltage is 3.65V, and the battery is fully charged;

(3) Discharge the battery with a constant current at a rate of 1C, and set the cut-off voltage to 2.65V;

(4) Compare the positive pole lug temperature, negative pole lug temperature, and battery average temperature curve obtained in the experiment with the simulated value;

(5) Carry out parameter correction according to the result of the above step (4), and obtain a corrected thermal-mechanical coupling model.

It can be seen from Figure 4 that the initial temperature of the battery, the temperature at the end of discharge, and the trend of the overall temperature curve are basically consistent with the experimental values. The difference is that the temperature difference in the experiment is large due to the influence of environmental conditions, while the temperature difference in the simulation is relatively small due to the relatively ideal environment, but this is within the allowable range of error, which can roughly ensure the accuracy of the model.

3. The temperature distribution of the battery during the discharge process

Figure 5 shows the distribution of temperature and its isovalue surface when the cell is discharged for 5s, 900s, 2700s and 3600s. During the discharge process, the internal center temperature of the cell is the highest and the surface temperature is relatively low. It can be seen from the isotherm distribution that the temperature is along the cell The center decreases to the surroundings, but the overall temperature difference is small; and the temperature of the positive tab is higher than that of the negative tab. This is because the positive tab is aluminum, and the negative tab is a composite of aluminum and copper. The heat conduction of the positive tab is The coefficient is lower than the negative tab, resulting in more heat generation in the positive tab, so the temperature is higher than that of the negative tab. This also corresponds to the analysis of stress below, the higher the temperature, the greater the thermal expansion force, that is, the greater the stress.

4. Stress distribution and expansion behavior of the battery during discharge

Figure 6. The von Mises stress variation curves of the battery cell along three directions at different discharge times. It can be seen from the figure that the stress on the surface of the battery cell is very small at the beginning of the discharge and can be ignored. The stress on the surface of the core increases, and the deformation also increases, until the end of 3600s discharge, the stress on the surface of the cell is the largest, and the maximum stress is about 10000N/m ² . The trend of the stress change curve along the x and z directions is basically the same. The stress in the center of the cell is relatively large, and there is a "plateau period" in the center along the outward direction, and then there is a trend of "falling first and then rising" at the edge. It is due to the boundary setting constraints that lead to stress fluctuations; while the change curve along the y direction is relatively smooth, the stress in the middle of the cell is the highest, and gradually decreases to both sides. The following displacement change curve will further explain this phenomenon.

The change of the cell thickness is characterized by the displacement of the cell during the discharge process. Since only one discharge process is simulated, the thickness change is relatively small. Figure 7 shows the change of the displacement of the cell during discharge of 5s, 900s, 2700s, and 3600s, and each sub-graph contains the displacement change diagram of the zy plane and the three-dimensional stereo. It can be seen from the figure that as the discharge time increases, the overall displacement of the battery cell increases, and the displacement at the center of the battery core is the largest, and the displacement at the tab is also larger, which is also consistent with the middle part of the battery core and the pole. The temperature at the ear is relatively high, the stress and expansion force are relatively large, and the maximum displacement at the end of the discharge is 3.04 μm; from the displacement change diagram of the zy plane, it can be seen that as the discharge time prolongs, the cell along the thickness The directional expansion is more obvious, and the tabs have obvious expansion. From this trend, it can be seen that the thickness of the cell will change more obviously after multiple cycles. Figure 8 is the displacement change curve of the battery cell along three different directions (x, y, z directions) at different discharge times, and the dotted line in the figure is the center of each plane. It can be seen from the three figures: as the discharge time increases, the displacement along the three directions increases; from the displacement change diagram along the x direction, it can be seen that from the middle of the cell to the outside, the displacement presents The trend of first increasing and then decreasing, the position corresponding to the peak point is the position of the tab, and the displacement decreases after crossing the tab, which is caused by the stress concentration at the tab; the displacement along the y direction is the largest, and from the middle of the cell Increase linearly to both sides until the outermost displacement of the cell is the largest; from the displacement change diagram along the z direction, it can be seen that it is similar to the displacement change along the x direction, and the peak point on the right is still due to the stress concentration of the tab , and the peak point on the left is due to the setting of the battery bottom constraint; the displacement changes along the x and y directions are symmetrically distributed, but the displacement changes along the z direction are not symmetrically distributed, which is due to the top tab of the battery Existence, the stress concentration at the lug part causes the expansion along the z direction to approach the tab area.

Claims (6)

1. A method for determining thermal stress and temperature in a lithium ion battery discharge process based on a thermal-force coupling model is characterized by comprising the following steps:

selecting a single battery cell, and acquiring three-dimensional geometric parameters, mechanical and thermodynamic initial parameters of the single battery cell;

step two, establishing a thermal-force coupling model of a three-dimensional electrical core scale according to a thermal expansion coefficient, a temperature difference and a coupling mechanism of a stress-strain relation; stress and heat are coupled through the temperature of the battery, when the temperature changes, the temperature difference delta T of the battery also changes, so that the change of thermal strain is caused, the change of thermal strain further causes the change of total strain and total stress, and the change of stress in turn causes the change of the temperature of the battery, so that the coupling of a thermal-force model is realized;

step three, measuring the temperature of the battery and the temperature of the lug through experiments, and verifying the effectiveness of the model;

and step four, obtaining the temperature distribution of the battery and the expansion displacement and stress along the x, y and z directions.

2. The method of claim 1, wherein the thermal-mechanical coupling model is a three-dimensional cell macro-scale thermal expansion model, and the model geometry of the thermal-mechanical coupling model comprises a cell body, and positive and negative electrode tabs, and the stress, expansion behavior, and temperature distribution of the cell body and the positive and negative electrode tabs can be obtained.

3. The method for determining the thermal stress and the temperature in the discharging process of the lithium ion battery based on the thermal-mechanical coupling model according to claim 1, wherein the thermal strain is a quantity related to the thermal expansion coefficient and the cell temperature difference according to a coupling mechanism of the thermal expansion coefficient, the temperature difference and a stress-strain relation, so that the coupling of the stress and the heat transfer physical field is realized.

4. The method for determining the thermal stress and the temperature in the discharging process of the lithium ion battery based on the thermal-mechanical coupling model is characterized in that in the third step of the method, the temperature of the battery and the temperature of the tab are determined through experiments, and then compared with simulation data, so that the effectiveness of the model is fully verified.

5. The method for determining the thermal stress and the temperature in the discharging process of the lithium ion battery based on the thermal-mechanical coupling model according to claim 1, wherein a three-dimensional cell-scale macroscopic thermal-mechanical coupling model can observe the temperature distribution of the battery during the discharging process of the cell.

6. The method for determining the thermal stress and the temperature in the discharging process of the lithium ion battery based on the thermal-force coupling model according to claim 1, wherein a three-dimensional cell-scale macroscopic thermal-force coupling model can observe the expansion displacement and the stress of the cell in the x, y and z directions in the discharging process.

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