CN110633496B - Method for determining thermal stress and temperature in lithium ion battery discharging process based on thermal-force coupling model - Google Patents
Method for determining thermal stress and temperature in lithium ion battery discharging process based on thermal-force coupling model Download PDFInfo
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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
Technical Field
The invention belongs to the field of lithium ion battery thermal expansion and stress calculation, and particularly relates to a method for determining thermal stress and temperature in a lithium ion battery discharging process based on a thermal-force coupling model.
Background
Lithium ion batteries are widely applied to electronic equipment, electric vehicles and energy storage power stations due to excellent performance, and meanwhile, many safety accidents occur. In the process of charging and discharging of the lithium ion battery, particularly in the process of charging and discharging with high multiplying power, a local high temperature phenomenon can occur, the high temperature can cause thermal expansion, and further thermal stress is generated, when the generated stress is larger, the thermal stress can be accompanied with the cracking and falling of electrode materials, and poor contact of all parts of the battery cell caused by the expansion of the battery cell can finally cause the increase of internal resistance, the attenuation of capacity and the failure of the battery, so that the stress of the battery can be predicted, the failure of the battery can be effectively prevented, and the safety of the lithium ion battery is guaranteed.
At present, the expansion behavior of the battery cell in the charging and discharging process and the stress prediction are difficult to observe by the traditional experimental method, and the thermal expansion model on the macroscopic scale of the battery cell is less researched due to the factors that the model effectiveness is difficult to detect, the model establishment is difficult and the like. Therefore, the invention breaks through the limitations of the two and provides a method for determining the thermal stress and the temperature in the discharge process of the lithium ion battery based on a thermal-force coupling model, which comprises the steps of firstly obtaining the geometric parameters of a battery cell, the mechanical and thermodynamic related parameters and establishing a thermal-force coupling model according to the coupling mechanism of the thermal expansion coefficient, the temperature difference and the stress-strain relation; the validity of the model is verified through the temperature measured by experiments and the temperature of the lug, so that the accuracy of the model is ensured; and then, expansion displacement and stress distribution of the cell along the x, y and z directions are obtained. The invention can calculate the stress and temperature of the battery cell in the discharging process of the lithium ion battery, can observe the expansion behavior of the battery cell, and can provide a certain guidance basis for the prediction of the expansion and rupture behaviors of the battery cell.
Disclosure of Invention
The invention provides a method for determining thermal stress and temperature in a lithium ion battery discharging process based on a thermal-force coupling model, which is characterized in that the temperature distribution, the thermal stress distribution and the expansion displacement distribution along the x, y and z directions of a battery cell in the discharging process are finally obtained through establishing the thermal-force coupling model of the three-dimensional macroscopic scale of the battery cell and effective experimental verification, and the relationship between the expansion phenomenon of the battery cell and the temperature is revealed.
The technical scheme adopted by the invention is as follows: a method for determining thermal stress and temperature in a lithium ion battery discharging process based on a thermal-force coupling model comprises 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; step three, measuring the temperature of the battery and the temperature of the lug by an experiment, 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.
The model in the step two is a three-dimensional electrical core scale heat-force coupling model, and the basic theory of the model comprises two aspects, (1) stress-strain relation and (2) energy conservation equation. The following describes the process of model building:
(1) Stress-strain relationship
The cell is considered to be an anisotropic thermal conductor and an isotropic linear elastomer. In which the coupling of stress and temperature is achieved by thermal expansion, the strain induced by thermal stress is related to temperature by the equation (1), in which ij Is the strain component, alpha is the coefficient of thermal expansion, delta ij For the Dirac delta function, when i = j, the value is 1, otherwise the value is 0, Δ T is the temperature difference, and it can be known from the formula that when the temperature difference is larger, the strain is larger, and therefore the thermal stress is larger.
The stress-strain relationship in the presence of thermal stress is expressed by equation (2),
wherein σ ij For the stress component, E is the Young's modulus and ν is the Poisson's ratio.
Hydrostatic stress (σ) h ) And von Mises stress (σ) v ) Given by equations (3) and (4):
σ ν ＝|σ r -σ θ | (4)
wherein sigma r For radial stress, σ θ Is the tangential stress.
The boundary conditions are as follows: the restraint is set up on four surfaces all around on the electricity core surface, only makes the battery expand along thickness direction, promptly:
u y ＝0,u z ＝0 (5)
(2) Energy conservation equation
The cell was considered an anisotropic thermal conductor and the thermal model control equations and boundary conditions are listed in table 1. Its heat production follows the Bernardi heat generation rate equation, see equation (7), the former being reversible heat, produced by entropy change of the electrode material, depending on the entropy coefficient (dU) 0 A size of/dT); the latter is irreversible heat, caused by the internal resistance of the cell itself. Heat loss takes into account thermal convection and thermal radiation.
TABLE 1 thermal model control equation and boundary conditions
In the thermal model, the battery is equivalent to an anisotropic heat conductor, and the lumped specific heat capacity, density and thermal conductivity are respectively shown in formulas (11) - (14), wherein the thermal conductivity is divided into two types, namely parallel to the pole pieces (x and z directions) and perpendicular to the pole pieces (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 Δ T of the battery also changes, which results in the change of thermal strain in the formula (1), and the change of thermal strain further results in the change of total strain and total stress in the formula (2), and the change of stress in turn results in the change of the temperature of the battery, so that the coupling of the thermal-force model is realized. The process is reproduced in the multi-physics coupling software COMSOLMULITY, and the coupling process and the calculation process are shown in figure 1. The symbols and terms appearing in the present invention are shown in Table 2.
TABLE 2 symbols and terms appearing in the present invention
The validity verification of the model in the third step adopts the following steps:
(1) Firstly, arranging a plurality of thermocouples on the surface of a battery to measure the temperature of the battery in the discharging process, wherein the battery is connected with a force measuring device;
(2) Fully charging the battery by a constant-current-first and constant-voltage-second charging method, and setting a charging cut-off voltage according to a battery material;
(3) Performing constant current discharge on the battery, and setting a discharge cut-off voltage according to a battery material;
(4) Comparing the average temperature curve obtained by the experiment with the simulation value;
(5) And (4) carrying out parameter correction according to the result of the step (4) to obtain a corrected thermal-force coupling model.
Compared with the prior art, the invention has the advantages that: 1. the defect that the traditional experimental method is difficult to predict the thermal stress borne by the battery in the discharging process is overcome, and a thermal-force coupling mold system is also perfected; 2. a thermal-force coupling die type of a three-dimensional cell scale is established, so that not only can the three-dimensional geometric structure of the battery be reproduced, but also the temperature distribution and the thermal stress distribution of the cell in the discharging process can be obtained; 3. the expansion phenomenon and displacement change condition of the lithium ion battery in the discharging process can be dynamically observed, and the expansion behavior and stress change of the battery in the whole discharging process can be conveniently analyzed; 4. the establishment of the numerical simulation method and the model saves resources and manpower, and has guiding significance on the thermal safety and the mechanical safety of the lithium ion battery; 5. the three-dimensional macro-scale heat-force coupling model established by the method can verify the effectiveness of the model through experiments, ensures the accuracy of the model, and lays a foundation for stress and expansion research and multi-factor research in the subsequent lithium ion battery charging and discharging cycle process of the three-dimensional model; 6. the stress numerical simulation test device provides a research basis and a research basis for lithium ion battery stress numerical simulation researchers and developers, and provides technical support for the thermal safety and the mechanical safety of the lithium ion battery.
Drawings
FIG. 1 illustrates the coupling mechanism and principle of the thermal-force coupling model of the present invention.
Fig. 2 is a graph of the variation of the entropy coefficient and the internal resistance of the battery with the depth of discharge in an embodiment of the present invention.
Fig. 3 is a schematic diagram of a model geometry and a mesh in an embodiment of the present invention, in which fig. 3 (a) is a schematic diagram of a model geometry in an embodiment of the present invention, and fig. 3 (b) is a schematic diagram of a model mesh in an embodiment of the present invention.
Fig. 4 is a graph showing experimental and simulated comparison of the average temperature of the battery cell and the temperatures of the positive and negative electrode tabs in the embodiment of the present invention.
FIG. 5 is a graph showing temperature profiles of the cells at different discharge times (5 s,900s,2700s,3600 s) in the example of the present invention.
Fig. 6 is a graph of von Mises stress in the battery along x, y, and z directions at different discharge times (0 s,900s,1800s,2700s,3600 s) in the embodiment of the present invention, wherein the (0, 0) point is the geometric center of the cell.
Fig. 7 is a displacement distribution diagram of the battery according to the example of the present invention at different discharge times (5 s,900s,2700s,3600 s), distorted to be shown by a magnification of 5000 times.
Fig. 8 is a graph showing the expansion displacement variation of the battery in the x, y, z directions at different discharge times (0 s,900s,1800s,2700s, 3600s) in the embodiment of the present invention, wherein the (0, 0) point is the geometric center of the cell.
Detailed Description
In order to facilitate understanding of the present invention, the present invention will be described in more detail with reference to the following examples, but the scope of the present invention is not limited to the following specific examples.
Examples
Taking 105Ah lithium iron phosphate/graphite battery as an example, the temperature and stress distribution in the discharging process of the lithium ion battery are calculated, and the method is comprehensively and specifically described. The method mainly comprises the following four parts: (1) establishing a thermal-force coupling model; (2) verifying the validity of the model; (3) temperature distribution of the battery during discharge; (4) Stress distribution and swelling behavior of the cell during discharge.
1. Firstly, a model building part is described, which is divided into 2 steps as follows:
step one, obtaining model parameters. The mechanical parameters of the cell and the thermodynamic parameters of the material were obtained according to the literature research method, and these parameters are listed in table 3 and fig. 2.
And step two, establishing a battery cell scale three-dimensional thermal-force coupling model. Model geometry and mesh see fig. 3, the model contains three computational domains: the battery cell comprises a negative electrode tab (made of copper), a positive electrode tab (made of aluminum), a battery cell main body (an isotropic elastomer and an anisotropic heat conductor), and a layered structure inside the battery cell is not considered, so that the model is simplified. The mesh construction adopts a method of freely dividing tetrahedral meshes, which comprises 9777 tetrahedral units, 1926 triangular units, 206 edge units and 24 vertex units, and passes mesh independence test.
TABLE 3 Heat-force coupling die parameters
Note: "-" indicates that the item is not present or is not considered.
2. Validation of models
The validity verification steps of the model are as follows:
(1) Firstly, arranging a plurality of thermocouples on the surface of a battery to measure the temperature of the battery in the discharging process, wherein the battery is connected with a force measuring device;
(2) Carrying out constant-current-first-constant-voltage charging process on the battery at a rate of 1C, wherein the charging cut-off voltage is 3.65V, and fully charging the battery;
(3) Constant current discharging is carried out on the battery at the multiplying power of 1C, and the cut-off voltage is set to be 2.65V;
(4) Comparing the anode tab temperature, the cathode tab temperature and the average cell temperature curve obtained by the experiment with the analog value;
(5) And (4) carrying out parameter correction according to the result of the step (4) to obtain a corrected thermal-force coupling model.
It can be seen from fig. 4 that the initial temperature of the battery, the temperature at the end of discharge, and the trend of the overall temperature curve are substantially consistent with the experimental values, and the temperature at the end of discharge is about 49 ℃, so that the accuracy of the model is ensured.
3. Temperature distribution of battery during discharge
Fig. 5 shows the temperature and the distribution of the isosurface thereof when the cells discharge for 5s,900s,2700s and 3600s, the temperature is the highest at the center of the interior of the cell during the discharge process, the surface temperature is lower, and the temperature is reduced along the center of the cell to the periphery through the distribution of the isotherms, but the total temperature difference is smaller; and the temperature of the anode tab is higher than that of the cathode tab, because the anode tab is aluminum, the cathode tab is the composition of aluminum and copper, and the heat conductivity coefficient of the anode tab is lower than that of the cathode tab, the anode tab generates more heat, and the temperature of the anode tab is higher than that of the cathode tab. This also corresponds to the analysis of the stresses below, the higher the temperature the greater the thermal expansion force, i.e. the greater the stress.
4. Stress distribution and expansion behavior of battery during discharge
Fig. 6 shows the change curves of von Mises stress of the battery cell along three directions at different discharge times, as can be seen from the graph, the stress on the surface of the battery cell at the beginning of the discharge is very small and can be ignored, along with the progress of the discharge, the stress on the surface of the battery cell increases, the deformation also increases, and the stress on the surface of the battery cell is maximum until the end of the discharge of 3600s, and the maximum stress is 10000N/m 2 Left and right. The trends of stress change curves along the x direction and the z direction are basically consistent, the stress of the center part of the battery cell is larger, the center part has a section of 'plateau phase' along the outward direction, and then the trend of 'descending first and then rising back' appears at the edge, which is caused by stress fluctuation due to the boundary setting constraint; the change curve along the y direction is smooth, the stress in the middle of the battery cell is highest, and gradually decreases towards two sides, and the displacement change curve behind the battery cell will further explain the phenomenon.
The change of the cell thickness is represented by the displacement of the cell in the discharging process, and the thickness change is relatively small because the discharging process is simulated only once. Fig. 7 is a graph showing the variation of displacement of the cell during discharging at 5s,900s,2700s and 3600s, and each subgraph comprises a displacement variation graph of a zy plane and a three-dimensional solid. 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 central part of the battery cell is the largest, and the displacement at the tab is also larger, which corresponds to the higher temperature, the larger stress and the larger expansion force at the middle part of the battery cell and the tab, and the maximum displacement is 3.04 μm when the discharge is finished; as can be seen from the displacement change diagram of the zy plane, along with the extension of the discharge time, the expansion of the battery cell along the thickness direction is obvious, and the tab has obvious expansion, and the trend shows that after the battery cell is subjected to multiple cycles, the thickness can be changed more obviously. Fig. 8 is a graph showing the displacement variation of the cells along three different directions (x, y, z directions) for different discharge times, wherein the dotted line is the central portion of each plane. As can be seen from the three figures: as the discharge time increases, the displacement in all three directions increases; from the displacement change graph along the x direction, the displacement tends to increase and then decrease from the middle part of the battery cell to the outside, the corresponding position of the peak point, namely the position of the tab, is reduced after passing the tab, and the displacement is caused by the stress concentration at the tab; the displacement along the y direction is maximum, and the displacement is linearly increased from the middle of the battery cell to two sides until the displacement of the outermost side of the battery cell is maximum; as can be seen from the displacement change graph along the z direction, the right peak point is still due to the stress concentration of the tab, and the left peak point is due to the arrangement of the battery bottom constraint, which is similar to the displacement change along the x direction; the displacement changes along the x direction and the y direction are symmetrically distributed, while the displacement changes along the z direction are not symmetrically distributed, because the stress concentration at the lug position causes the expansion along the z direction to be close to the lug area due to the existence of the battery top lug.
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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