A cylindrical battery design method based on archimedes spiral formula

Abstract

The application discloses a cylindrical battery design method based on an Archimedes spiral formula, which completes the calculation of the winding number of the positive electrode, the negative electrode and two layers of the separator by the Archimedes spiral equation, then carries out winding simulation on the four groups of components respectively, establishes the relationship curve of the winding number, the winding radius and the winding curve xy of the four groups of components on the battery simulation diagram, obtains the xy coordinate values of the corresponding winding curve of the four groups of components, and completes the winding design of the cylindrical battery. The application guarantees that the diameter of the winding core is completely consistent with the preset diameter after the winding of the positive electrode, the negative electrode and the separator is completed, and the winding core cannot enter the shell. Moreover, the method can simulate the cross-section condition of the winding core after winding in the execl table directly, can more intuitively judge the diameter of the winding core, the wrapping condition of the negative electrode to the positive electrode and other information, and provides great convenience for the design of the winding core.

Description

Technical Field

[0001] This invention relates to the field of cylindrical battery design, and more specifically to a cylindrical battery design method based on Archimedes' spiral formula. Background Technology

[0002] Wound batteries are battery cells assembled through a winding process. Due to their numerous significant advantages, they have been widely used in fields such as new energy vehicles. These batteries possess high-rate discharge capabilities, with a maximum discharge rate of up to 18C, enabling rapid energy release. Simultaneously, wound batteries operate stably within an extreme temperature range of -55℃ to 75℃, ensuring reliability under various environmental conditions. Furthermore, they feature high energy density, stable output voltage, and excellent shock resistance, making them ideal for high-performance applications such as electric vehicles and hybrid vehicles. The design of wound batteries eliminates free electrolyte, allowing them to be placed in any orientation, and they can be charged to over 95% capacity within 40 minutes, meeting the demands of fast charging. Their ultra-long service life can reach over 8 years, significantly reducing maintenance costs. With the rapid development of the new energy industry, batteries using different material types (such as lithium-ion and sodium-ion batteries) are flourishing. Therefore, a rational and efficient battery core design has become a crucial aspect of cylindrical battery production.

[0003] Currently, the common method in the battery industry is to calculate the required length of the positive electrode based on the battery's design capacity. The length of the negative electrode, separator, and other rolled materials is then increased based on empirical values, referencing the positive electrode length. The cross-sectional areas of the different rolled materials (positive electrode, negative electrode, separator) are then added together and compared with the inner cross-sectional area of ​​the battery casing. The difference between the two areas must not exceed 5mm². 2 If the length is too large or too small, the core may not be able to fit into the casing or there may be large gaps in the casing. This requires redesigning the lengths of the positive and negative electrodes, which greatly reduces the accuracy and efficiency of the design. Moreover, the area method cannot visually show the wrapping of the positive and negative electrodes on the battery plates. According to the design principle of batteries, the negative electrode must wrap the positive electrode, and the separator must wrap the positive and negative electrode plates and separate them. If the length of the negative electrode or the separator is insufficient, the produced battery will have a great safety hazard. On the other hand, if the length is too long, there will be problems such as wasting materials and reducing the energy density of the battery. Summary of the Invention

[0004] To address the aforementioned problems, this invention aims to provide a cylindrical battery design method based on Archimedes' spiral equation. This method uses the Archimedes' spiral equation to calculate the number of winding turns for the positive electrode, negative electrode, and two-layer separator in a single operation. Then, it simulates the winding process for each of the four components, obtaining the xy-coordinate values ​​of their corresponding winding curves. This completes the cylindrical battery winding design and ensures that the core diameter perfectly matches the preset diameter after the positive electrode, negative electrode, and separator are wound, preventing any issues with the core failing to fit into the casing. Furthermore, this method can directly simulate the cross-section of the wound core in an Excel spreadsheet, allowing for a more intuitive assessment of the core diameter, the extent to which the negative electrode wraps around the positive electrode, and other information, greatly facilitating core design.

[0005] This invention is achieved through the following technical solution: a cylindrical battery design method based on the Archimedes spiral formula. The method calculates the number of winding turns for the positive electrode, negative electrode, and two-layer separator in one step using the Archimedes spiral equation. Then, winding simulations are performed on the four components respectively. Relationship curves between the number of winding turns, the in-wind radius, and the xy-coordinate of the winding curves for the four components are established on the battery simulation diagram. The xy-coordinate values ​​of the corresponding winding curves for the four components are obtained, thus completing the cylindrical battery winding design. The winding simulation process for each component specifically includes the following steps: Let A be the winding angle θ of a certain component. n , winding radius value R n Let Bn be the coordinate of the corresponding winding angle position X. n and Y n Where An takes values ​​from 0° to 360°*Q, and Bn = b + *(An*PI() / 180), X n = B n *COS(A n *PI() / 180), Y n1 = B n *SIN(A n *PI() / 180), where b is the in-roll radius of the component, and multiple X n and Y n Connecting the scattered points yields the component curve, where n1 is a natural number of 0, 1, 2, ..., n, and Q is the number of wraps around the component. The four groups of components can be simulated on the same graph. The helical parameters are calculated as follows: t is the thickness of the basic unit in the core.

[0006] Positive electrode curve winding simulation: Let A be the positive electrode curve winding angle θ. n1 , winding radius value R n1 Let it be B n1, and establish the corresponding winding angle position coordinate X. n1 and Y n1An1 takes values ​​from 0° to 360°*Q 正 Bn1 = b1 + *(An1*PI() / 180), X n1 = B n1 *COS(A n1 *PI() / 180), Y n1 = B n1 *SIN(A n1 *PI() / 180), where Q 正 b1 is the number of turns of the positive electrode plate, and b1 is the in-winding radius of the positive electrode plate. Multiple X... n1 and Y n1 Connecting the scattered points yields the positive electrode curve, where n1 is a natural number of 0, 1, 2, ..., n.

[0007] Negative electrode curve winding simulation: Let A be the negative electrode curve winding angle θ. n2 Its winding radius value R n2 Let it be Bn2, and establish the corresponding winding angle position coordinates X. n2 and Y n2 An2 takes values ​​from 0° to 360°*Q 负 Bn1 = b2 + *(An2*PI() / 180), X n2 = B n2 *COS(A n2 *PI() / 180), Y n2 = B n2 *SIN(A n2 *PI() / 180), where Q 负 b2 is the number of turns of the negative electrode, and b2 is the in-winding radius of the negative electrode. Connecting multiple scattered points of Xn2 and Yn2 yields the negative electrode curve, where n2 is a natural number of 0, 1, 2, ..., n.

[0008] Simulation of the first diaphragm curve winding: Let A be the winding angle θ of the negative electrode curve. n3 Its winding radius value R n3 Let it be Bn3, and establish the corresponding winding angle position coordinates X. n3 and Y n3 A n3 Values ​​range from 0° to 360°* Q 隔 Bn3 = b3 + *(An3*PI() / 180), X n3 = B n3 *COS(A n3 *PI() / 180), Y n3 = B n3 *SIN(An3 *PI() / 180), where Q 隔1 b3 is the number of turns of the first diaphragm winding, and b3 is the in-winding radius of the first diaphragm. Connecting multiple scattered points of Xn3 and Yn3 yields the curve of the first diaphragm, where n3 is a natural number of 0, 1, 2, ..., n.

[0009] Simulation of the second diaphragm curve winding: Let A be the winding angle θ of the negative electrode curve. n4 Its winding radius value R n4 Let it be Bn4, and establish the corresponding winding angle position coordinates X. n4 and Y n4 A n4 Values ​​range from 0° to 360°* Q 隔 Bn4 = b4 + *(An4*PI() / 180), X n4 = B n4 *COS(A n4 *PI() / 180), Y n4 = B n4 *SIN(A n4 *PI() / 180), where Q is the value of 180. 隔2 The second diaphragm has the number of turns, b4 is the in-winding radius of the second diaphragm, and the curve of the second diaphragm is obtained by connecting multiple Xn4 and Yn4 scatter points, where n4 is a natural number of 0, 1, 2...n.

[0010] Number of turns of positive electrode Q 正 The specific calculation method is: (R1-R0) / t, where R1 is the core radius and R0 is the core needle radius; The helical parameters are calculated as follows: t is the thickness of the basic unit in the core.

[0011] Based on Archimedes' spiral formula, the number of turns Q of the negative electrode sheet is... 负 The specific calculation method is as follows: (R1+2t) 负 +2t 隔 -R0+2t 负 +2t 隔 ) / t, where t 负 t represents the thickness of the negative electrode sheet. 隔 This refers to the diaphragm thickness. Both diaphragms have the same thickness.

[0012] Number of diaphragm winding turns Q 隔 The specific calculation method is as follows: Qdiaphragm1 = (R1 + 4t)2 隔 -R0+4t 隔 ) / t, Qdiaphragm2 = (R1 + 2t ... 负 +4t 隔 -R0+2t负 +4t 隔 ) / t.

[0013] The battery winding core is an Archimedean spiral. According to relevant theories, the relationship between the radius r of the winding core and the total rotation angle ϕ can be calculated by the following formula: When the radius of the core coil needle is r0, then: The calculation method for the helical parameter 'a' is as follows: t is the thickness of the basic building block in the core. For a cylindrical battery, t is equivalent to the thickness of the positive and negative electrode sheets and the thickness of the two separators, such as... Figure 1 As shown. Based on Archimedes' spiral theory, according to the formula... Calculate the arc length of the core core and the arc length of the core as a whole, and the difference between the two is the winding length of the positive electrode sheet.

[0014] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0015] This invention uses the Archimedes' spiral equation to calculate the number of winding turns for the positive electrode, negative electrode, and two-layer separator in a single operation. Then, it simulates the winding process for each of the four components, obtaining the xy-coordinate values ​​of the corresponding winding curves for each component. This completes the cylindrical battery winding design. The method ensures that after the positive electrode, negative electrode, and separator are wound, the core diameter will perfectly match the preset diameter, preventing the core from failing to fit into the casing. Furthermore, the method provides precise calculation in one step, eliminating the need for rework and modification of winding parameters, thus achieving a complete process design in one step. Moreover, this method can directly simulate the cross-section of the wound core in an Excel spreadsheet, allowing for a more intuitive assessment of the core diameter, the extent to which the negative electrode wraps around the positive electrode, and other information, greatly facilitating core design. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0017] Figure 1 This is a schematic diagram of the thickness of the basic unit of the core in this invention.

[0018] Figure 2 This is a simulation diagram of the winding process of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0020] Example 1

[0021] Table 1 shows the common outer diameter, casing thickness, and internal space diameter of cylindrical batteries.

[0022]

[0023] This embodiment uses an 18650 battery as an example. Some specific parameters are: positive electrode thickness 138μm; negative electrode thickness 210μm; separator thickness 24μm; core basic unit thickness t = (138+210+24*2)μm = 396μm; helix parameter a = t / 2π = 63.027μm. The core core winding needle diameter is 3.5mm, and the rotation arc of the hollow core part ϕ = r / a = 1.75mm / 63.027 μm = 27.77, corresponding to the number of turns ϕ / 2π = 27.77 / (2*3.14) = 4.42. Figure 1 As shown. The internal space diameter of the shell is 17.5mm. Considering the expansion space of the core and the space of the multiple-wound diaphragm and negative electrode, the core diameter is 17mm. Therefore, the rotational radius ϕ containing the hollow core is ϕ = r / a = (17 / 2) mm / 63.027 μm = 134.94, corresponding to the number of turns ϕ / 2π = 134.94 / (2*3.14) = 21.49. Thus, the actual number of turns for the positive electrode is 21.49 - 4.42 = 17.07. According to the helix arc length formula... The length of the rotating arc in the hollow core is l=24.44mm, and the length of the rotating arc containing the hollow core is l=574.03mm. Therefore, the actual length of the positive electrode is 573.03-24.44=549.59mm. The theoretically calculated length of the positive electrode matches the actual measured value of 549.68mm.

[0024] In the Excel simulation process, the positive electrode curve is plotted. Based on the calculations above, the positive electrode sheet is wound 17.07 times, with a rotation angle of 17.07 * 360 = 6145.2. Then, the formula is entered into Excel according to the table below. Since there is a winding needle in the middle, the formula (r = b + a \cdot \theta ) is used, where a is the helical parameter, b is the winding radius of 1.75, and the maximum value in column A is 6145.2. The design formula is shown in Table 2: (Note: In the embodiment, A(θ) can be set with an interval angle according to the actual curve simulation requirements, such as 0.5°, 1°, etc.)

[0025]

[0026] The negative electrode curve is plotted based on battery design principles. The negative electrode sheet must completely wrap around the positive electrode sheet, and all negative electrode windings should be inside the positive electrode sheet. Therefore, the winding radius of the negative electrode is b = 1.75 - 0.2 = 1.55. A space needs to be reserved on the outermost ring for welding the negative electrode tabs. Therefore, the maximum value of A is 6520. Based on the arc length formula, the length of the negative electrode sheet is calculated to be 584.75 mm. The design formula is shown in Table 3.

[0027]

[0028] The separator curve is plotted because a wound battery consists of two separators wound with positive and negative electrode plates. Therefore, the separator plotting is divided into the first separator and the second separator. According to battery design principles, the separator must completely wrap around the positive and negative electrodes and separate them. During the winding process, half of the separator is wound in one turn before being wound into the positive and negative electrode plates. When winding up, it is wound in one more turn to completely wrap the battery electrode plates. The in-wound radius of the first separator 1 is b = 1.75 - 0.5 = 1.25, and the in-wound radius of the second separator 2 is b = 1.75 - 0.7 = 1.05. The maximum value of A is 6910. According to the arc length formula, the length of the two separators can be calculated to be 609.7 mm. The design formula is shown in Table 5.

[0029]

[0030] By selecting all the data from columns C and D of the above curve formulas for the positive electrode, negative electrode, separator 1, and separator 2, and inserting them into a scatter plot, a complete battery winding simulation diagram can be created. For example... Figure 2 As shown.

[0031] Based on the formula above, the positive electrode length of this 18650 battery is 549.69 mm, the negative electrode length is 584.75 mm, and the length of separator 1 and separator 2 is 609.7 mm. The actual data from disassembling the battery are: positive electrode length 549.68 mm, negative electrode length 584.5 mm, and separator 1 and separator 2 length 609.5 mm. The length simulated in Excel has an error of less than 0.3 mm from the actual length of the battery electrodes, which is higher than the manufacturing level of half of the machines.

[0032] In addition, adjusting the winding radius and the number of turns can simulate the electrode rolls of wound cylindrical batteries such as 21700 and 4680. Furthermore, based on this simulation diagram, a series of operations such as the electrode tab welding position and the adhesive application position can also be simulated.

[0033] Existing technology for setting the electrode tabs involves first determining a position based on experience, starting the winding process, and then determining whether the tab position is suitable after winding is complete. If the position is incorrect, adjustments are made, which may involve multiple adjustments until the tab appears in the preset position. Our new technology, however, can directly and accurately calculate the tab position. For example, if we want to place the tab at a certain location in the simulation diagram, we can calculate the required tab space at a certain length of the electrode sheet. This one-step calculation method saves a lot of trouble.

[0034] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A cylindrical battery design method based on Archimedes' spiral formula, characterized in that, The Archimedes spiral equation is used to calculate the number of turns for the positive electrode, negative electrode, and two-layer separator in one step. Then, winding simulations are performed on the four groups of components respectively. The relationship curves of the number of turns, winding radius, and winding curve xy of the four groups of components are established on the battery simulation diagram. The xy coordinate values ​​of the corresponding winding curves of the four groups of components are obtained, and the winding design of the cylindrical battery is completed. The winding simulation process of each component specifically includes the following steps: Let A be the winding angle θ of a certain component. n , winding radius value R n Let it be B n Establish the corresponding winding angle position coordinates X n and Y n A n Values ​​range from 0° to 360° , , , Where b is the in-contraction radius of the component, and multiple X n and Y n Connecting the scattered points yields the component curve, where n is a natural number and Q is the number of wraps around the component. The four groups of components can then be simulated on the same graph. The helical parameters are calculated as follows: t is the thickness of the basic unit in the core; the calculation process for the positive electrode winding length includes: according to the formula Calculate the arc length of the core core and the arc length of the entire core separately; the difference between the two is the positive electrode winding length. The rotation angle; Wherein, based on the Archimedes spiral formula, the positive electrode sheet winding number Q 正 The specific calculation method is: (R1-R0) / t, R1 is the radius of the winding core, R0 is the radius of the winding core needle; the negative electrode sheet winding number Q 负 The specific calculation method is: (R1+2t 负 +2t 隔 -R0+2t 负 +2t 隔 ) / t, wherein t 负 The thickness of the negative electrode sheet, t 隔 The thickness of the separator; the winding number of the separator Q 隔1 =(R1+4t 隔 -R0+4t 隔 ) / t, the winding number of the separator Q 隔2 =(R1+2t 负 +4t 隔 -R0+2t 负 +4t 隔 ) / t; The method ensures that after the positive electrode, negative electrode, and separator are wound, the diameter of the core is consistent with the preset diameter, preventing the core from failing to fit into the shell. It also provides accurate calculation in one step, eliminating the need for rework to modify winding parameters. The process design is completed in one step, and the cross-sectional situation of the wound core after winding can be directly simulated in the Excel spreadsheet, providing a more intuitive judgment of the diameter of the wound core and the wrapping of the negative electrode with the positive electrode.

Images