A design method for a battery module

Abstract

A battery module design method includes the following steps: S1: Calculate the battery module gap; S2: Calculate the compressibility range of the buffer material and find the corresponding CFD stress range; S3: Calculate the preload range of the battery module and compare it with the target preload range; if the preload is not within the target range, adjust the rules and design parameters, and repeatedly verify the preload until the requirements are met; S4: Calculate the compression increase rate of the buffer material; S5: Calculate the upper limit of the EOL compressibility of the buffer material and find the corresponding CFD stress; S6: Calculate the expansion force of the battery module and compare it with the upper limit J of the cell expansion force; if the expansion force is greater than or equal to the upper limit J of the cell expansion force, adjust the design parameters, recalculate the expansion force until the expansion force design meets the requirements, and re-verify the preload. This method solves the problems of low design and production efficiency and high quality control costs in battery module design and production.

Description

Technical Field

[0001] This invention belongs to the field of batteries, and in particular relates to a design method for a battery module. Background Technology

[0002] As a core component of the new energy industry, the performance of lithium-ion batteries directly determines the development of the industry. During charging and discharging, the positive and negative electrode materials continuously intercalate and deintercalate lithium, leading to changes in particle volume and consequently, cell thickness. This directly affects the battery's lifespan and cycle life. As batteries age, they expand in the later stages of their lifespan, increasing thickness, internal resistance, and capacity decay. Research indicates that applying a certain preload force can ensure a tight connection between components in the battery module, preventing loosening or deformation during use. This improves the module's conductivity and heat dissipation, thus enhancing its overall performance. It also slows down battery expansion, extending battery life. Therefore, verifying the battery module's BOL (Break-Off) preload force and EOL (End-Off) expansion force is crucial in battery module design.

[0003] Currently, existing technologies for controlling pre-tightening force typically use pre-compression fixtures to clamp the battery cells to their theoretical dimensions before shaping the module. This inevitably leads to problems such as the battery being crushed, lacking expansion space and posing safety hazards, or the module being difficult to install in a box after pre-compression packaging. When implementing pre-tightening methods, precise control of clamping force and deformation is crucial. Excessive clamping force may damage or deform the battery cells, while insufficient clamping force may fail to ensure tight contact between the cells. Many factors influence the packaging pre-tightening force, primarily the compression of the buffer material between the cells and CFD stress. Without verification, multiple experiments may be required to reach a conclusion, significantly reducing the efficiency of battery module design and production. It may even prevent accurate assessment of the battery module's performance and safety during the design phase, hindering optimization and improvement of the battery module design, or resulting in inconsistent battery module quality, increasing the difficulty and cost of quality control. Summary of the Invention

[0004] The technical problem solved by this invention is to provide a design method for battery modules, which solves the problems of low design and production efficiency and high quality control costs in battery modules.

[0005] The basic solution provided by this invention is a design method for a battery module, which specifically includes the following steps:

[0006] S1: Calculate the battery module gap X based on the material parameters of the battery module;

[0007] S2: Calculate the compressibility range [E1,E2] of the buffer material. Based on the CFD stress curve data of the buffer material corresponding to the compressibility range [E1,E2], find the CFD stress range [F1,F2] corresponding to the compressibility range [E1,E2].

[0008] S3: Calculate the preload range [G1,G2] of the battery module based on the CFD stress range [F1,F2], and compare the preload range [G1,G2] of the battery module with the target preload range [H1,H2] of the battery module:

[0009] If the target preload lower limit H1 is less than the battery module preload lower limit G1, and the target preload upper limit H2 is greater than the battery module preload upper limit G2, then the preload design meets the requirements; otherwise, adjust the design parameters according to the preload parameter adjustment rules, and repeat steps S1 to S5 until the preload design meets the requirements.

[0010] S4: Calculate the compression increase rate P of the buffer material;

[0011] S5: Calculate the upper limit of the EOL compression ratio Q of the buffer material based on the compression increase rate P of the buffer material, and find the CFD stress R corresponding to the upper limit of the EOL compression ratio Q of the buffer material based on the CFD stress curve data of the buffer material.

[0012] S6: Calculate the expansion force U of the battery module based on the CFD stress R, and compare the expansion force U of the battery module with the upper limit J of the cell expansion force:

[0013] If the expansion force U is less than the upper limit of the cell expansion force J, the design meets the requirements. Otherwise, adjust the design parameters according to the expansion force parameter adjustment rules, repeat steps S4 to S6 until the expansion force design meets the requirements, and re-verify the preload force.

[0014] Preferably, in step S1, the material parameters include the module design length A, end plate thickness B, and cell thickness C, and the battery module gap X includes the gap X1 between the cell and the end plate and the gap X2 between the cells. The battery module gap X is calculated based on the module design length A, end plate thickness B, and cell thickness C.

[0015] The design length A of the module has the following relationship:

[0016] A = L a ±T a

[0017] In the formula, L a T represents the theoretical length of the battery module. a For battery module length tolerance;

[0018] The end plate thickness B has the following relationship:

[0019] B = L b ±T b

[0020] In the formula, L b T represents the theoretical thickness of the end plate. b For end plate thickness tolerance;

[0021] The cell thickness C has the following relationship:

[0022] C = L c ±T c

[0023] In the formula, L c T represents the theoretical length of the battery module. c This refers to the battery module length tolerance.

[0024] More preferably, the battery module gap X is calculated according to the following formula:

[0025]

[0026] In the formula, N a N represents the number of battery modules. b N represents the number of end plates. c L represents the number of battery cells. a L is the theoretical length of the battery module. b L is the theoretical thickness of the end plate. c T represents the theoretical thickness of the battery cell. a T represents the battery module length tolerance. b For end plate thickness tolerance, T c For cell thickness tolerance, N x This refers to the amount of cushioning material.

[0027] Preferably, in step S2, the formula for calculating the compressibility range [E1, E2] of the buffer material is as follows:

[0028]

[0029] In the formula, E2 is the upper limit of the compressibility of the cushioning material, and L d T represents the theoretical thickness of the cushioning material. d For the thickness tolerance of the cushioning material, L x T represents the theoretical gap between battery modules. x This refers to the battery module clearance tolerance.

[0030]

[0031] In the formula, E1 is the lower limit of the compressibility of the cushioning material, and L d T represents the theoretical thickness of the cushioning material.d For the thickness tolerance of the cushioning material, L x T represents the theoretical gap between battery modules. x This refers to the clearance tolerance of the battery module.

[0032] Preferably, in step S3, the preload parameter adjustment rule includes adjusting the battery module material parameters and the battery module assembly size parameters. The preload parameter adjustment rule is to first adjust the battery module material parameters, and if the preload still does not meet the requirements, then adjust the battery module assembly size parameters.

[0033] More preferably, when adjusting the battery module material parameters, the theoretical values, tolerance values, and contact areas of the buffer material are adjusted according to the preload parameter adjustment rules. First, the theoretical values ​​of the materials are adjusted, then the tolerance values ​​are adjusted, and finally the contact areas of the buffer material are adjusted.

[0034] Preferably, in step S4, the formula for calculating the compression increase rate P of the buffer material is as follows:

[0035] P = L c ×K / L d

[0036] In the formula, L c L represents the theoretical thickness of the battery cell. d Where K is the theoretical thickness of the buffer material, and K is the cell expansion rate.

[0037] Preferably, the formula for calculating the upper limit Q of the compressibility of the buffer material EOL in step S5 is as follows:

[0038] Q = P + E2

[0039] In the formula, P is the compression increase rate of the buffer material, and E2 is the upper limit of the compression rate of the buffer material.

[0040] The principles and advantages of this invention are as follows:

[0041] 1. By verifying the BOL preload and EOL expansion force of the battery module, accurate data on the performance and safety of the battery module are provided, which provides strong support for the design and optimization of the battery module. The verification can ensure tight contact between cells and between cells and the module frame during the assembly process, prevent structural damage caused by poor contact, and thus improve the safety performance of the battery module.

[0042] 2. Simultaneous verification of the battery module's BOL preload and EOL expansion force provides a more comprehensive understanding of the battery module's state under actual operating conditions. This ensures that the interaction between the two is fully considered, avoiding the interactive effects overlooked by separate verifications and improving the overall verification accuracy. Compared to existing methods that verify each force separately, this method reduces the number of repeated adjustments, minimizing the time and labor costs associated with repetitive operations, and effectively improving battery module design and production efficiency. Simultaneous verification allows for a more accurate assessment of the rationality of the battery module's design and manufacturing process, enabling timely identification and resolution of design defects, optimization of product performance, and improved battery module quality, while reducing the difficulty and cost of quality control. Furthermore, it ensures the stability and consistency of preload and expansion force throughout the battery module's entire lifecycle, reducing system instability caused by changes in a single factor. It also generates more complete data records, facilitating subsequent analysis and problem tracking, and improving data consistency and traceability.

[0043] 3. During the verification process, by using reasonable parameter adjustment rules, prioritizing the adjustment of battery module material parameters in the preload and expansion force parameter adjustments, and then adjusting the battery module assembly size parameters, the error of human operation can be reduced, the accuracy of verification results can be improved, and the operation steps of verification and adjustment can be simplified, unnecessary repetitive operations can be reduced, and work efficiency can be improved. Reasonable parameter adjustment rules can be flexibly adjusted according to different working conditions and environmental conditions to ensure that the battery module can work normally under various conditions. Attached Figure Description

[0044] Figure 1 This is a flowchart of the present invention;

[0045] Figure 2 This is a schematic diagram of the battery module structure of the present invention;

[0046] Figure 3 This is a front view of the battery module structure of the present invention. Detailed Implementation

[0047] The following detailed description illustrates the specific implementation method:

[0048] The specific implementation process is as follows: (See details) Figures 1 to 3 A design method for a battery module, specifically including the following steps:

[0049] S1: Calculate the battery module gap X based on the material parameters of the battery module. The material parameters include the module's design length A, end plate thickness B, cell thickness C, double-sided adhesive thickness, spray adhesive thickness, and the thickness of other heat insulation materials, etc.

[0050] In this embodiment, the structure of the battery module is as follows: Figures 2 to 3As shown, the battery module includes battery cells 2, end plates 1, and buffer material 3. Material parameters include the module's design length A, end plate thickness B, and battery cell thickness C; the battery module gap X includes the gap X1 between the battery cell and the end plate, and the gap X2 between battery cells; the module's design length A has the following relationship:

[0051] A = L a ±T a ;

[0052] In the formula, L a T represents the theoretical length of the battery module. a For battery module length tolerance;

[0053] In this implementation, the module's design length A = 667 ± 1.5 mm;

[0054] The end plate thickness B has the following relationship:

[0055] B = L b ±T b ;

[0056] In the formula, L b T represents the theoretical thickness of the end plate. b For end plate thickness tolerance;

[0057] In this implementation, the end plate thickness B = 14 ± 0.2 mm;

[0058] The cell thickness C has the following relationship:

[0059] C = L c ±T c ;

[0060] In the formula, L c T represents the theoretical length of the battery module. c For battery module length tolerance;

[0061] In this implementation, the cell thickness C = 50 ± 0.3 mm;

[0062] Calculate the battery module gap X according to the following formula based on the module's design length A, end plate thickness B, and cell thickness C:

[0063]

[0064] In the formula, N a N represents the number of battery modules. b N represents the number of end plates. c L represents the number of battery cells. a L is the theoretical length of the battery module. b L is the theoretical thickness of the end plate. c T represents the theoretical thickness of the battery cell. aT represents the battery module length tolerance. b For end plate thickness tolerance, T c For cell thickness tolerance, N x This refers to the amount of cushioning material.

[0065] In this embodiment, the number of battery modules N a The number of end plates is 1, and the number of end plates is N. b The number of cells is 2, and the number of cells is N. c The value is 20, and the battery module gap X = 3 ± 1.35 mm.

[0066] S2: Calculate the compression ratio range [E1, E2] of the buffer material based on the gap X between the battery modules. Based on the CFD stress curve data of the buffer material corresponding to the compression ratio range [E1, E2], find the CFD stress range [F1, F2] corresponding to the compression ratio range [E1, E2]. In this embodiment, the buffer material is foam.

[0067] In step S2, the formula for calculating the compressibility range [E1, E2] of the buffer material is as follows:

[0068]

[0069] In the formula, E2 is the upper limit of the compressibility of the cushioning material, and L d T represents the theoretical thickness of the cushioning material. d For the thickness tolerance of the cushioning material, L x T represents the theoretical gap between battery modules. x This refers to the battery module clearance tolerance.

[0070]

[0071] In the formula, E1 is the lower limit of the compressibility of the cushioning material, and L d T represents the theoretical thickness of the cushioning material. d For the thickness tolerance of the cushioning material, L x T represents the theoretical gap between battery modules. x This refers to the clearance tolerance of the battery module.

[0072] Among them, the theoretical gap L of the battery module x The following relationship exists:

[0073]

[0074] In the formula, N a N represents the number of battery modules. b N represents the number of end plates. c L represents the number of battery cells. a L is the theoretical length of the battery module. b L is the theoretical thickness of the end plate. cN represents the theoretical thickness of the battery cell. x This refers to the amount of cushioning material.

[0075] Battery module gap tolerance T x The following relationship exists:

[0076]

[0077] In the formula, N a N represents the number of battery modules. b N represents the number of end plates. c T represents the number of battery cells. a T represents the battery module length tolerance. b For end plate thickness tolerance, T c For cell thickness tolerance, N x This refers to the amount of cushioning material.

[0078] In this implementation, the theoretical thickness L of the buffer material d The tolerance for the thickness of the cushioning material is 4, and the tolerance for the thickness of the cushioning material is T. d The compression ratio is 0.4, the upper limit of the compression ratio of the buffer material E2 is 30%, the lower limit of the compression ratio of the buffer material E1 is 20%, [E1,E2]=[20%,30%];

[0079] Based on the CFD stress curve data of the foam corresponding to the compression ratio range [20%, 30%] of the cushioning material, the CFD stress range [F1, F2] corresponding to the compression ratio range [E1, E2] is found to be [0.03MPa, 0.9MPa].

[0080] S3: Calculate the preload range [G1,G2] of the battery module based on the CFD stress range [F1,F2], and compare the preload range [G1,G2] of the battery module with the target preload range [H1,H2] of the battery module:

[0081] If the target preload lower limit H1 is less than the battery module preload lower limit G1, and the target preload upper limit H2 is greater than the battery module preload upper limit G2, then the preload design meets the requirements; otherwise, adjust the design parameters according to the preload parameter adjustment rules, and repeat steps S1 to S5 until the preload design meets the requirements.

[0082] The preload range [G1, G2] of the battery module is calculated according to the formula G = F × S, wherein the lower limit of the battery module preload range is calculated according to the following formula:

[0083] G1 = F1 × S

[0084] In the formula, G1 is the lower limit of the pre-tightening force range of the battery module, F1 is the lower limit of the CFD stress range corresponding to the compression ratio range [E1,E2], and S is the contact area between the buffer material and the cell.

[0085] The upper limit of the preload force range for the battery module is calculated according to the following formula:

[0086] G2 = F2 × S

[0087] In the formula, G2 is the upper limit of the pre-tightening force range of the battery module, F2 is the upper limit of the CFD stress range corresponding to the compression ratio range [E1,E2], and S is the contact area between the buffer material and the battery cell.

[0088] Based on the calculation results, the preload range of the battery module can be determined as [G1, G2] = [1200N, 3600N].

[0089] In this embodiment, the target preload range of the battery module is set as [H1,H2] = [1000N,5000N]. The calculated preload range of the battery module is within the target preload range, so the preload design meets the requirements.

[0090] In step S3, the preload parameter adjustment rule includes adjusting the battery module material parameters and the battery module assembly dimension parameters. The rule prioritizes adjusting the battery module material parameters; if the preload still does not meet the requirements, then the battery module assembly dimension parameters are adjusted. The battery module materials include end plates, battery cells, and buffer materials. When adjusting the battery module material parameters in the preload parameter adjustment rule, the theoretical values, tolerance values, and contact area of ​​the buffer materials are adjusted first, followed by the tolerance values, and finally the contact area of ​​the buffer materials.

[0091] In another embodiment, the target preload range of the battery module is set as [H1,H2] = [2000N,5000N]. The calculated preload range of the battery module is not within the target preload range, so the preload design does not meet the requirements.

[0092] Adjust the theoretical thickness L of the cushioning material according to the preload parameter adjustment rules. d The preload is 4.5mm; recalculate the preload.

[0093] The compressibility range of the cushioning material is [E1, E2] = [29%, 37%];

[0094] The CFD stress range [F1, F2] is [0.03MPa, 0.9MPa] = [0.08MPa, 0.12MPa].

[0095] The preload range of the battery module is [G1, G2] = [3200N, 4800N]. This preload range is within the target preload range [H1, H2] = [2000N, 5000N]. Therefore, the adjusted design meets the preload design requirements.

[0096] S4: Based on the expansion dimension M of the battery cell and the theoretical thickness of the buffer material, the compression increase rate P of the buffer material is calculated.

[0097] The formula for calculating the expansion dimension M of the battery cell is as follows:

[0098] M = K × L c

[0099] In the formula, L c Where K is the theoretical thickness of the battery cell, and K is the cell expansion rate.

[0100] The formula for calculating the compression increase rate P of the cushioning material is as follows:

[0101] P = M / L d

[0102] In the formula, M is the expansion dimension of the battery cell, and L... d This represents the theoretical thickness of the buffer material.

[0103] In this embodiment, the theoretical thickness L of the buffer material d =4mm, theoretical cell thickness L c =50mm, cell expansion rate K=1%, so the cell expansion size =0.5mm, and the compression increase rate of the buffer material P=12.5%.

[0104] S5: Calculate the upper limit of the EOL compression ratio Q of the buffer material based on the compression increase rate P of the buffer material, and find the CFD stress R corresponding to the upper limit of the EOL compression ratio Q of the buffer material based on the CFD stress curve data of the buffer material.

[0105] The formula for calculating the upper limit of the compressibility Q of the buffer material EOL in step S5 is as follows:

[0106] Q = P + E2

[0107] In the formula, P is the compression increase rate of the buffer material, and E2 is the upper limit of the compression rate of the buffer material.

[0108] In this embodiment, the upper limit of the compression ratio of the buffer material EOL is Q = 12.5% ​​+ 30% = 42.5%.

[0109] Based on the CFD stress curve data of the foam, the corresponding CFD stress R is found to be 0.5 MPa.

[0110] S6: Calculate the expansion force U of the battery module based on the CFD stress R, and compare the expansion force U of the battery module with the upper limit J of the cell expansion force:

[0111] If the expansion force U is less than the upper limit of the cell expansion force J, the design meets the requirements. Otherwise, adjust the design parameters according to the expansion force parameter adjustment rules, repeat steps S4 to S6 until the expansion force design meets the requirements, and re-verify the preload force.

[0112] The formula for calculating the expansion force U of the battery module is as follows:

[0113] U = R × S

[0114] In the formula, R is the CFD stress corresponding to the upper limit of EOL compression ratio Q, and S is the contact area between the buffer material and the battery cell.

[0115] In this embodiment, the upper limit of the cell expansion force J = 40000N, and the expansion force of the battery module U = 0.5 × 40000 = 20000N. This expansion force is less than the upper limit of the cell expansion force J, so the design meets the requirements.

[0116] The expansion force parameter adjustment rules include prioritizing the adjustment of battery module material parameters, including sequentially adjusting the theoretical values, tolerance values, and contact area of ​​the end plate, cell, and buffer material. If the expansion force requirements are still not met after adjusting the battery module material parameters, the battery module assembly size parameters are then adjusted.

[0117] The above are merely embodiments of the present invention. Commonly known structures and characteristics are not described in detail here. Those skilled in the art are aware of all common technical knowledge in the field prior to the application date or priority date, are aware of all existing technologies in that field, and have the ability to apply conventional experimental methods prior to that date. Those skilled in the art can, under the guidance of this application, improve and implement this solution in combination with their own capabilities. Some typical known structures or methods should not be obstacles for those skilled in the art to implement this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the structure of the present invention. These should also be considered within the scope of protection of the present invention, and will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A design method for a battery module, characterized in that, Specifically, the following steps are included: S1: Calculate the battery module gap X based on the material parameters of the battery module; S2: Calculate the compressibility range [E1,E2] of the buffer material. Based on the CFD stress curve data of the buffer material corresponding to the compressibility range [E1,E2], find the CFD stress range [F1,F2] corresponding to the compressibility range [E1,E2]. S3: Calculate the preload range [G1,G2] of the battery module based on the CFD stress range [F1,F2], and compare the preload range [G1,G2] of the battery module with the target preload range [H1,H2] of the battery module: If the lower limit of the target preload H1 is less than the lower limit of the battery module preload G1, and the upper limit of the target preload H2 is greater than the upper limit of the battery module preload G2, then the preload design meets the requirements; otherwise, adjust the design parameters according to the preload parameter adjustment rules, and repeat steps S1 to S3 until the preload design meets the requirements. S4: Calculate the compression increase rate P of the buffer material; S5: Calculate the upper limit of the EOL compression ratio Q of the buffer material based on the compression increase rate P of the buffer material, and find the CFD stress R corresponding to the upper limit of the EOL compression ratio Q of the buffer material based on the CFD stress curve data of the buffer material. S6: Calculate the expansion force U of the battery module based on the CFD stress R, and compare the expansion force U of the battery module with the upper limit J of the cell expansion force: If the expansion force U is less than the upper limit of the cell expansion force J, the design meets the requirements. Otherwise, adjust the design parameters according to the expansion force parameter adjustment rules, repeat steps S4 to S6 until the expansion force design meets the requirements, and re-verify the preload force.

2. The design method of the battery module according to claim 1, characterized in that: In step S1, the material parameters include the module design length A, end plate thickness B, and cell thickness C. The battery module gap X includes the gap X1 between the cell and the end plate and the gap X2 between cells. The battery module gap X is calculated based on the module design length A, end plate thickness B, and cell thickness C. The design length A of the module has the following relationship: A=L a ±T a In the formula, L a T represents the theoretical length of the battery module. a For battery module length tolerance; The end plate thickness B has the following relationship: B=L b ±T b In the formula, L b T represents the theoretical thickness of the end plate. b For end plate thickness tolerance; The cell thickness C has the following relationship: C=L c ±T c In the formula, L c T represents the theoretical length of the battery module. c This refers to the battery module length tolerance.

3. The design method of the battery module according to claim 2, characterized in that: Calculate the battery module gap X using the following formula: In the formula, N a N represents the number of battery modules. b N represents the number of end plates. c L represents the number of battery cells. a L is the theoretical length of the battery module. b L is the theoretical thickness of the end plate. c T represents the theoretical thickness of the battery cell. a T represents the battery module length tolerance. b For end plate thickness tolerance, T c For cell thickness tolerance, N x This refers to the amount of cushioning material.

4. The design method of the battery module according to claim 1, characterized in that: In step S2, the formula for calculating the compressibility range [E1, E2] of the buffer material is as follows: In the formula, E2 is the upper limit of the compressibility of the cushioning material, and L d T represents the theoretical thickness of the cushioning material. d For the thickness tolerance of the cushioning material, L x T represents the theoretical gap between battery modules. x This refers to the battery module clearance tolerance. In the formula, E1 is the lower limit of the compressibility of the cushioning material, and L d T represents the theoretical thickness of the cushioning material. d For the thickness tolerance of the cushioning material, L x T represents the theoretical gap between battery modules. x This refers to the clearance tolerance of the battery module.

5. The design method of the battery module according to claim 1, characterized in that: In step S3, the preload parameter adjustment rule includes adjusting the battery module material parameters and the battery module assembly size parameters. The preload parameter adjustment rule is to first adjust the battery module material parameters, and if the preload still does not meet the requirements, then adjust the battery module assembly size parameters.

6. The design method of the battery module according to claim 5, characterized in that: The battery module material parameters include the theoretical value, tolerance value, and contact area of ​​the buffer material for each material. When adjusting the battery module material parameters in the preload parameter adjustment rules, the theoretical value of the material is adjusted first, then the tolerance value is adjusted, and finally the contact area of ​​the buffer material is adjusted.

7. The design method of the battery module according to claim 1, characterized in that: In step S4, the formula for calculating the compression increase rate P of the buffer material is as follows: P=L c ×K / L d In the formula, L c L represents the theoretical thickness of the battery cell. d Where K is the theoretical thickness of the buffer material, and K is the cell expansion rate.

8. The design method of the battery module according to claim 1, characterized in that: The formula for calculating the upper limit of the compressibility Q of the buffer material EOL in step S5 is as follows: Q = P + E2 In the formula, P is the compression increase rate of the buffer material, and E2 is the upper limit of the compression rate of the buffer material.

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