Design method of shear band microstructure, microstructure, shear band and tire

Abstract

The present disclosure relates to a design method for a shear band microstructure, a microstructure, a shear band and a tire. The method includes: defining a design region and determining a design variable; the design region is the minimum periodic unit of the shear band microstructure; the design variable is the filling material in the design region; constructing a material matrix of the design region and determining an objective function; performing finite element analysis on the design region and calculating an equivalent elastic modulus; calculating the sensitivity of each grid in the design region based on the equivalent elastic modulus; updating the design variables based on the sensitivity; calculating the target value of the objective function after updating the design variables and judging whether the target value meets a convergence condition; when the convergence condition is met, outputting the design region as a shear band microstructure; when the convergence condition is not met, returning to the step of performing finite element analysis on the design region and calculating the equivalent elastic modulus of the design region. The shear band microstructure obtained by the method is applied to the shear band to improve the load-bearing capacity of the non-pneumatic tire.

Description

Technical Field

[0001] The present disclosure relates to the technical field of non-pneumatic tires, and in particular to a design method for a shear band microstructure, a microstructure, a shear band and a tire. Background Art

[0002] Tires are one of the important parts of a vehicle. They are the only part of a vehicle that connects to the road. They support the vehicle, cushion impacts, transmit driving force, transmit braking force, provide ride comfort, and ensure the smoothness of the vehicle. The safety performance of a vehicle during driving is closely related to the safety of the tires. Traditional pneumatic tires cannot solve the problem of tire blowouts due to their own structural limitations, so the safety performance of tires cannot be effectively improved. Compared with pneumatic tires, non-pneumatic tires have the advantages of no need for inflation, explosion-proof, safety, durability, low rolling resistance, economy, and easy processing and molding. Since they do not require inflation, non-pneumatic tires do not have problems such as tire blowouts, which improves the driving safety of vehicles and has broad market and development prospects.

[0003] In the related art, typical non-pneumatic tire structures include spoke-type non-pneumatic tires, honeycomb-type non-pneumatic tires, and spring-type non-pneumatic tires, etc., and their main structures include rubber treads, tough support structures, rigid rims, and annular shear bands. In order to enhance the load-bearing capacity of non-pneumatic tires, the shear bands usually adopt a "sandwich" structure, that is, the shear bands are composed of an elastic shear layer and two radially inner and outer spacers attached to the elastic shear layer; although the "sandwich" shear band structure enhances the load-bearing capacity of non-pneumatic tires, due to the small load-bearing capacity of the tires, they are only used in low-speed scenes such as engineering vehicles and lawn mowers, which limits the application scenarios of the tires. Summary of the invention

[0004] In order to solve the above technical problems, the present disclosure provides a design method of a shear band microstructure, a microstructure, a shear band and a tire.

[0005] In a first aspect, the present disclosure provides a method for designing a shear band microstructure, comprising:

[0006] Define a design region and determine design variables; wherein the design region refers to the smallest periodic unit of the shear band microstructure, the design region includes N grids, N is a positive integer; the design variables are the filling materials in the design region;

[0007] constructing a material matrix of the design region and determining an objective function of the design region;

[0008] Performing finite element analysis on the design area to calculate the equivalent elastic modulus of the design area;

[0009] Calculating the sensitivity of each mesh in the design area based on the equivalent elastic modulus of the design area;

[0010] Based on the sensitivity, updating the design variables;

[0011] Calculating the target value of the objective function after updating the design variables, and determining whether the target value satisfies the convergence condition;

[0012] When the convergence condition is met, the design region is output as a shear band microstructure; and when the convergence condition is not met, returning to the step of performing finite element analysis on the design region and calculating the equivalent elastic modulus of the design region.

[0013] Optionally, the filling material in the design area includes a first material or a second material; when the filling material is the first material, the design variable is Ce=1; when the filling material is the second material, the design variable is Ce=0; the initial value of the design variable is that the design area is completely filled with the first material; wherein e is a positive integer from 1 to N.

[0014] Optionally, determining the objective function of the design area includes: the objective function is a maximization function, and the objective function is calculated using the following formula:

[0015]

[0016] Among them, F(x) is the objective function; and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus.

[0017] Optionally, performing finite element analysis on the design area to calculate the equivalent elastic modulus of the design area includes:

[0018] The equivalent elastic modulus of the design area is calculated using the following formula:

[0019]

[0020] Ku=∫ Y B T EdY;

[0021]

[0022] in, is the equivalent elastic modulus of the design area; H represents homogenization; i, j, k and l are the subscripts of the equivalent elastic modulus, indicating its regional position in the design area, i, j, k and l are all positive integers; Y is the area of ​​the design area, I is a 3×3 unit matrix; B is the strain matrix of the design area; B T represents the transposed matrix of the strain matrix; u is the internal displacement field of the design area; K is the stiffness matrix of the design area; p1 is the penalty factor; E e，ijkl is the elastic modulus of the e-th grid; Indicates that the e-th grid filling material is the elastic modulus of the first material; Indicates that the e-th grid filling material is the elastic modulus of the second material; e is a positive integer from 1 to N.

[0023] Optionally, calculating the sensitivity of each grid in the design area based on the equivalent elastic modulus of the design area includes:

[0024] The sensitivity is calculated using the following formula:

[0025]

[0026] in, and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus; Ce is a design variable, which takes a value of 0 or 1, and e is a positive integer from 1 to N.

[0027] Optionally, updating the design variables based on the sensitivity includes:

[0028] Based on the sensitivity, the filling material of the grid whose sensitivity meets the preset update condition is replaced from the first material to the second material.

[0029] Optionally, before calculating the target value of the objective function after updating the design variables and judging whether the target value satisfies a convergence condition, the method further comprises:

[0030] Calculating the volume fraction of the first material after updating the design variables, and determining whether the volume fraction of the first material satisfies the constraint condition of the objective function;

[0031] The constraint condition of the objective function is: V1 = V * ;

[0032] When the constraint condition is met, executing the calculation of the target value of the target function after updating the design variables, and judging whether the target value meets the convergence condition; and

[0033] When the constraint condition is not satisfied, returning to the step of performing finite element analysis on the design area and calculating the equivalent elastic modulus of the design area;

[0034] Wherein, V1 is the volume fraction of the first material in the design area; V * is the volume fraction constraint value of the first material in the design region.

[0035] Optionally, the convergence condition includes: a target value of the objective function meets a preset accuracy requirement.

[0036] In a second aspect, the present disclosure also provides a shear band microstructure formed by any of the design methods described above.

[0037] In a third aspect, the present disclosure further provides a shear band, comprising the above-mentioned shear band microstructure arranged periodically.

[0038] In a fourth aspect, the present disclosure further provides a non-pneumatic tire, comprising: the above-mentioned shear belt.

[0039] Compared with the prior art, the technical solution provided by the present invention has the following advantages:

[0040] The present disclosure provides a design method for a shear band microstructure, a microstructure, a shear band and a tire, the design method comprising: defining a design region and determining design variables; wherein the design region refers to the minimum periodic unit of the shear band microstructure, the design region includes N grids, N is a positive integer; the design variables are the filling materials in the design region; constructing a material matrix of the design region and determining the objective function of the design region; performing finite element analysis on the design region and calculating the equivalent elastic modulus of the design region; calculating the sensitivity of each grid in the design region based on the equivalent elastic modulus of the design region; updating the design variables based on the sensitivity; calculating the target value of the objective function after updating the design variables and judging whether the target value meets the convergence condition; outputting the design region as a shear band microstructure when the convergence condition is met; and returning to the step of performing finite element analysis on the design region and calculating the equivalent elastic modulus of the design region when the convergence condition is not met. Thus, the shear band microstructure obtained by the method is applied to the shear band, which can improve the load-bearing capacity of the non-pneumatic tire. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0043] Figure 1 A schematic flow chart of a method for designing a shear band microstructure provided in an embodiment of the present disclosure;

[0044] Figure 2 A schematic diagram of the structure of the design area provided for the embodiment of the present disclosure;

[0045] Figure 3 for Figure 2 A schematic diagram of the structure of a local enlarged portion of the design area shown;

[0046] Figure 4 A schematic flow chart of another method for designing a shear band microstructure provided by an embodiment of the present disclosure;

[0047] Figure 5 A schematic flow chart of another method for designing a shear band microstructure provided in an embodiment of the present disclosure;

[0048] Figure 6 A schematic diagram of a shear band microstructure provided by an embodiment of the present disclosure;

[0049] Figure 7 A schematic structural diagram of a 3×3 shear band microstructure provided in an embodiment of the present disclosure;

[0050] Figure 8 A schematic diagram of the structure of a non-pneumatic tire provided in an embodiment of the present disclosure;

[0051] Fig. 9 It is a static rigidity simulation diagram of a non-pneumatic tire using a sandwich shear band in the related art;

[0052] Fig.10 A static rigidity simulation diagram of a non-pneumatic tire using a microstructure shear band provided in an embodiment of the present disclosure;

[0053] Fig.11 A diagram showing stress results of a non-pneumatic tire using a sandwich shear band in the related art;

[0054] Fig.12 A diagram showing stress results for a non-pneumatic tire using a microstructured shear band according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0055] In order to more clearly understand the above-mentioned objectives, features and advantages of the present disclosure, the scheme of the present disclosure will be further described below. It should be noted that the embodiments of the present disclosure and the features in the embodiments can be combined with each other without conflict.

[0056] In the following description, many specific details are set forth to facilitate a full understanding of the present disclosure, but the present disclosure may also be implemented in other ways different from those described herein; it is obvious that the embodiments in the specification are only part of the embodiments of the present disclosure, rather than all of the embodiments.

[0057] In the related art, the shear layer in the "sandwich" shear band structure is usually made of polyurethane elastomer, such as thermoplastic polyurethane elastomer, cast polyurethane elastomer or mixed polyurethane elastomer. However, the non-pneumatic wheel belt with such a shear band structure still has the defect of low load-bearing capacity, which limits the application scenarios of the tire.

[0058] In order to solve the above technical problems, the embodiment of the present disclosure provides a design method for a shear band microstructure, a microstructure, a shear band and a tire, the design method comprising: defining a design area and determining design variables; wherein the design area refers to the minimum periodic unit of the shear band microstructure, the design area includes N grids, N is a positive integer; the design variable is the filling material in the design area; constructing a material matrix of the design area, determining the objective function of the design area; performing finite element analysis on the design area, calculating the equivalent elastic modulus of the design area; calculating the sensitivity of each grid in the design area based on the equivalent elastic modulus of the design area; updating the design variables based on the sensitivity; calculating the target value of the objective function after updating the design variables, and judging whether the target value meets the convergence condition; when the convergence condition is met, outputting the design area as a shear band microstructure; and when the convergence condition is not met, returning to perform a finite element analysis on the design area, and calculating the equivalent elastic modulus of the design area. Thus, the shear band microstructure obtained by the method is applied to the shear band, which can improve the load-bearing capacity of the non-pneumatic tire.

[0059] Combine the following Figure 1-Figure 12 , a design method for a shear band microstructure, a microstructure, a shear band and a tire provided in an embodiment of the present disclosure are exemplarily described.

[0060] Figure 1 A schematic diagram of a process flow of a shear band microstructure design method provided in an embodiment of the present disclosure. Figure 1 , the method comprising:

[0061] S110, define the design area and determine the design variables.

[0062] The design region refers to the smallest periodic unit of the shear band microstructure, and the design region includes N grids, where N is a positive integer; the design variable is the filling material in the design region.

[0063] The design area refers to the smallest periodic unit of the shear band microstructure, that is, the repeating unit; several shear band microstructures are periodically arranged to form a shear band.

[0064] Among them, the design area is customized and divided into several grids, each grid is filled with material; the filling material includes at least a first material and a second material, and the design variables are defined according to the filling material in the grid; for example, when the filling material is defined as the first material, the design variable value is 1; when the filling material is the second material, the design variable value is 0; or when the filling material is the first material, the design variable value is 0; when the filling material is the second material, the design variable value is 1; the value of the design variable can be defined according to the needs and is not limited here.

[0065] The first material includes at least one of steel, carbon fiber and glass fiber; the second material includes at least one of natural or artificial rubber, polyurethane and polyurethane elastomer.

[0066] Among them, the initial value of the design variable can be set to fill the entire design area with the first material; the entire design area with the second material; or a preset proportion of grids in the design area are filled with the first material, and the remaining grids are filled with the second material; the setting of the initial value of the design variable can be flexibly set according to the requirements of the design method of the shear band microstructure, and is not limited here.

[0067] For example, Figure 2-Figure 3 As shown, Figure 2 A schematic diagram of the structure of the design area provided for the embodiment of the present disclosure; Figure 3 for Figure 2 A partial enlarged structural diagram of the design area shown. Figure 2 , the design area is defined as a square with 50×50 grids, that is, the design area includes 2500 grids. Figure 3 , the design variable is the filling material of each grid, the filling material includes the first material or the second material; when the filling material is the first material, the design variable is Ce=1; when the filling material is the second material, the design variable is Ce=0; e=1, 2, 3...2500.

[0068] It is understandable that Figure 2 The shape of the design area is shown as a square, including 2500 grids, but it does not constitute a limitation on the design method of the shear band microstructure provided by the embodiment of the present disclosure. In other embodiments, the shape and scale of the design area can be defined according to the requirements of the design method of the shear band microstructure, which is not limited here.

[0069] S120, constructing a material matrix of the design area and determining an objective function of the design area.

[0070] The material matrix corresponding to the two-dimensional design area is a 3×3-order matrix, as follows:

[0071]

[0072] Among them, E H is the material matrix corresponding to the design area, and is the element of the matrix, is the equivalent elastic modulus of the material matrix, that is, the equivalent elastic modulus of the design area.

[0073] According to S=E H ×R (S is stress, R is strain), R strain is in three directions, namely horizontal x, vertical y and lateral xy, and the corresponding stresses in the three directions are horizontal tension, vertical tension and lateral shear.

[0074] In the material matrix E H middle, Corresponding to the horizontal direction, it is the tensile modulus of the design area; Corresponding to the vertical direction, it is the tensile modulus of the design area; Corresponding to the lateral direction, it is the shear modulus of the design area.

[0075]

[0076] This paper expects the designed shear band microstructure to have high tensile modulus and low shear modulus. Therefore, the objective function for determining the design area is:

[0077]

[0078] Among them, F(x) is the objective function, which is the maximization function; and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus; the value range of w1 and w2 is 0~1, and w1+w2=1.

[0079] S130. Perform finite element analysis on the design area to calculate the equivalent elastic modulus of the design area.

[0080] Specifically, the finite element method is used to analyze the elastic mechanical properties of the design area and calculate the equivalent elastic modulus of the design area. The equivalent elastic modulus of the design area is calculated by combining the following formulas.

[0081]

[0082] Ku=∫ Y B T EdY;

[0083]

[0084] in, is the equivalent elastic modulus of the design area, H represents homogenization, i, j, k and l are the subscripts of the equivalent elastic modulus, indicating its regional position in the design area, i, j, k and l are all positive integers; Y is the area of ​​the design area; I is a 3×3 unit matrix; B is the strain matrix of the design area; B T represents the transposed matrix of the strain matrix; u is the internal displacement field of the design area; K is the stiffness matrix of the design area; p1 is the penalty factor, which is 3; Ce is the design variable, which is 0 or 1; e is a positive integer from 1 to N; E e，ijkl is the elastic modulus of the e-th grid; Indicates that the e-th grid filling material is the elastic modulus of the first material; Indicates that the e-th mesh filling material is the elastic modulus of the second material.

[0085] S140. Calculate the sensitivity of each mesh in the design area based on the equivalent elastic modulus of the design area.

[0086] Specifically, sensitivity is the influence of the design variable on the target value of the objective function. The sensitivity can be calculated by taking the derivative of the objective function with respect to the design variable; that is, the sensitivity is calculated using the following formula:

[0087]

[0088] in, and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus; Ce is the design variable, which takes a value of 0 or 1, and e is a positive integer from 1 to N.

[0089] S150. Update the design variables based on the sensitivity.

[0090] Specifically, based on the sensitivity, the filling material of the grids whose sensitivity meets the preset update condition is replaced from the first material to the second material. For example, all the grids in the design area are sorted in descending order of sensitivity, and the filling material of the grids in the last 2% (or the first 2%) of the sensitivity sorting is replaced from the first material to the second material; or the filling material of the grids whose sensitivity is less than a specific value (or greater than a specific value) is replaced from the first material to the second material.

[0091] It should be noted that the embodiment of the present disclosure only exemplarily shows the updating of design variables based on the order of sensitivity, but does not constitute a limitation on the design method of shear band microstructure provided by the embodiment of the present disclosure. In other implementations, other methods known to those skilled in the art can also be used to update the design variables, which are not limited here.

[0092] It can be understood that the embodiment of the present disclosure only exemplarily presets the update condition as the last 2% (or the first 2%) and less than a specific value (or greater than a specific value), but does not constitute a limitation on the design method of the shear band microstructure provided by the embodiment of the present disclosure. In other implementations, the range of the preset update condition can be set according to the requirements of the design method of the shear band microstructure, such as 1%, 5% or 10%, which is not limited here.

[0093] S160, calculating the target value of the objective function after updating the design variables, and determining whether the target value meets the convergence condition.

[0094] Specifically, S160 can be divided into:

[0095] S161. Calculate the target value of the target function after updating the design variables.

[0096] Among them, after the design variables are updated, the filling materials in the grid of the design area change, the distribution of the filling materials in the design area changes, and the material matrix corresponding to the design area also changes. Therefore, it is necessary to recalculate the target value of the objective function after the design variables are updated.

[0097] S162. Determine whether the target value meets the convergence condition.

[0098] Among them, when the convergence condition is met, the judgment result is yes (Y), and S170 is executed; and when the convergence condition is not met, the judgment result is no (N), and it returns to execute S130 "perform finite element analysis on the design area and calculate the equivalent elastic modulus of the design area".

[0099] S170. Output the designed region as a shear band microstructure.

[0100] Specifically, the design region where the target value meets the convergence condition is output as the shear band microstructure, and the output shear band microstructure has a high tensile modulus and a low shear modulus. Since the design region is the minimum periodic unit of the shear band microstructure, the output shear band microstructure is periodically arranged to obtain a shear band structure, and the obtained shear band also has a high tensile modulus and a low shear modulus. The shear band is prone to shear deformation, which improves the load-bearing capacity of the non-pneumatic tire.

[0101] The disclosed embodiment provides a design method for a shear band microstructure, the design method comprising: defining a design region and determining design variables; wherein the design region refers to the minimum periodic unit of the shear band microstructure, the design region includes N grids, N is a positive integer; the design variables are the filling materials in the design region; constructing a material matrix of the design region, and determining the objective function of the design region; performing finite element analysis on the design region, and calculating the equivalent elastic modulus of the design region; calculating the sensitivity of each grid in the design region based on the equivalent elastic modulus of the design region; updating the design variables based on the sensitivity; calculating the target value of the objective function after updating the design variables, and judging whether the target value meets the convergence condition; when the convergence condition is met, outputting the design region as the shear band microstructure; and when the convergence condition is not met, returning to the step of performing finite element analysis on the design region and calculating the equivalent elastic modulus of the design region. Thus, the shear band microstructure obtained by the method is applied to the shear band, which can improve the load-bearing capacity of the non-pneumatic tire.

[0102] In some embodiments, the filling material in the design area includes the first material or the second material; when the filling material is the first material, the design variable is Ce=1; when the filling material is the second material, the design variable is Ce=0; the initial value of the design variable is that the design area is completely filled with the first material; wherein e is a positive integer from 1 to N.

[0103] In some embodiments, the filling material in the design area includes the first material or the second material; when the filling material is the first material, the design variable is Ce=1; when the filling material is the second material, the design variable is Ce=0; the initial value of the design variable is that the design area is completely filled with the second material; wherein e is a positive integer from 1 to N.

[0104] In some embodiments, Figure 4 FIG. 1 is a flow chart of another method for designing a shear band microstructure according to an embodiment of the present disclosure. Figure 4 Before S160 "calculating the target value of the target function after updating the design variables and judging whether the target value satisfies the convergence condition", the method further includes:

[0105] S180, calculating the volume fraction of the first material after the design variables are updated, and determining whether the volume fraction of the first material satisfies the constraint conditions of the objective function.

[0106] Specifically, when the constraint conditions are met, the target value of the objective function after the design variables are updated is calculated to determine whether the target value meets the convergence conditions; and when the constraint conditions are not met, the step of returning to perform finite element analysis on the design area and calculating the equivalent elastic modulus of the design area is returned.

[0107] Among them, the constraint condition of the objective function is: V1=V* ; V1 is the volume fraction of the first material in the design area; V * is the volume fraction constraint value of the first material in the design area, and its value range is between 0 and 100%.

[0108] For example, if in step S110 “Define design region and determine design variables”, the initial value of the design variable Ce=1, e is a positive integer from 1 to N, that is, the grids in the design region are all filled with the first material, and the volume fraction of the first material is 100%; and V * If the first material is replaced by the second material by iteratively updating the design variables, the volume fraction of the first material is reduced to 10% to meet the constraint condition. If the initial value of the design variable Ce=0 is defined in the step S110 "Define the design region and determine the design variables", e is a positive integer from 1 to N, that is, the grids in the design region are all filled with the second material, and the volume fraction of the first material is 0%; and V * If it is set to 10%, it is necessary to iteratively update the design variables to replace the second material with the first material so that the volume fraction of the first material increases to 10% to meet the constraint condition.

[0109] In some embodiments, the convergence condition includes: the target value of the objective function meets a preset accuracy requirement.

[0110] Specifically, since the number of grids included in the design area is large, when the constraints are met, there are various distributions of filling materials in the design area. Therefore, it is necessary to judge whether the target value of the objective function meets the convergence conditions. Since the objective function is a maximization function, it is expected that the target value of the design area tends to the maximum value; at the same time, considering the stability of the output shear band microstructure, the target value of the design area is required to meet the preset accuracy requirements at the same time. For example, the target values ​​of the design area are sorted in order from large to small, and the top 10% or the top M (for example, 10) of the target values ​​are selected to calculate the relative deviation, and the design area corresponding to the target value with the smallest relative deviation is used as the shear band microstructure output, and the output shear band microstructure has a higher stability; or the design area corresponding to the target value with a relative deviation less than a preset threshold (for example, 1%, 2% or 5%) is used as the shear band microstructure output, so that the number of output shear band microstructures may be multiple.

[0111] It should be noted that this embodiment only exemplarily shows the relative deviation of the target value as the preset accuracy index, but does not constitute a limitation on the design method of the shear band microstructure provided by the embodiment of the present disclosure. In other embodiments, the preset accuracy index may select other parameters known to those skilled in the art, such as absolute deviation, which is not limited here.

[0112] For example, Figure 5 FIG. 1 is a flow chart of another method for designing a shear band microstructure provided by an embodiment of the present disclosure. Figure 5 , the method comprising:

[0113] S201. Start.

[0114] S210. Define initial design variables and objectives.

[0115] The initial design variables are defined as follows: the design domain is a square with a 50×50 grid, the design variables are the material options for each grid, C ab = 0 or 1, where a and b represent the grid area, representing the grid of the ath row and the bth column respectively; when C ab = 0, it is the second material (such as rubber), C ab =1, it is the first material (such as steel), let C ab =Ce, e=1, 2, 3...2500.

[0116] The material matrix corresponding to the two-dimensional design area is a 3×3-order matrix, as follows:

[0117]

[0118] Where EH is the material matrix corresponding to the design area, and is the element of the matrix, is the equivalent elastic modulus of the material matrix, that is, the equivalent elastic modulus of the design area.

[0119] Define your goals:

[0120]

[0121] Constraints of the objective function: V1 = V * ;

[0122] Among them, F(x) is the objective function, which is the maximization function; and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus; the value range of w1 and w2 is 0-1, and w1+w2=1; V1 is the volume fraction of the first material in the design area; V * It is the volume fraction constraint value of the first material in the design area, and its value range is between 0 and 100%.

[0123] S220, mechanical properties analysis of shear band microstructure.

[0124] Specifically, the equivalent elastic modulus is selected as the mechanical property index of the shear band microstructure; S220 can be subdivided into S221 and S222, and the equivalent elastic modulus of the design area is calculated jointly by the following formula.

[0125] S221. Uniform calculation of shear band microstructure.

[0126] S222. Obtain the equivalent elastic modulus of the design area.

[0127]

[0128] Ku=∫ Y B T EdY;

[0129] in, is the equivalent elastic modulus of the design area, H represents homogenization, i, j, k and l are the subscripts of the equivalent elastic modulus, indicating its regional position in the design area, i, j, k and l are all positive integers; Y is the area of ​​the design area; I is a 3×3 unit matrix; B is the strain matrix of the design area; B T represents the transposed matrix of the strain matrix; u is the internal displacement field of the design area; K is the stiffness matrix of the design area.

[0130] S230: Calculate target sensitivity.

[0131] Specifically, this step can be divided into:

[0132] S231. Sensitivity analysis.

[0133] S232, sensitivity filtering.

[0134] The equivalent elastic modulus of each grid in the design area is calculated by the following formula:

[0135]

[0136] Among them, E e，ijkl is the elastic modulus of the e-th grid; Indicates that the e-th grid filling material is the elastic modulus of the first material; Indicates that the e-th grid filling material is the elastic modulus of the second material; p1 is the penalty factor, which is 3; Ce is the design variable, which is 0 or 1; e is a positive integer from 1 to N.

[0137] Among them, sensitivity is the influence of the design variable on the target value of the objective function. The sensitivity can be calculated by taking the derivative of the objective function with respect to the design variable; that is, the sensitivity is calculated using the following formula:

[0138]

[0139] in, and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus; Ce is the design variable, which takes a value of 0 or 1, and e is a positive integer from 1 to N.

[0140] S240. Update design variables.

[0141] Specifically, all meshes in the design area are sorted in descending order of sensitivity, and the filling material of the last 2% (or first 2%) of the meshes in the sensitivity sorting is replaced from the first material to the second material.

[0142] S250: Determine whether convergence has occurred.

[0143] Specifically, this step can be subdivided into S251 "determine whether the material volume fraction converges" and S252 "determine whether the target value converges". First, determine whether the volume fraction of the first material meets the constraint conditions, and then determine whether the function value of the objective function converges (the target value is large and has good stability); when the above two conditions are met at the same time, stop updating and iterating the design variables, output the design area as the shear band microstructure, and execute S202; otherwise, return to execute S220 "shear band microstructure mechanical properties analysis".

[0144] S202, end.

[0145] It should be noted that due to the comprehensive consideration of the stability and maximization of the target value, the target value of the shear band microstructure finally output is not the global optimum (i.e., the maximum target value), but the shear band microstructure with a larger target value and the best stability is selected for output.

[0146] Based on the same inventive concept, the embodiment of the present disclosure also provides a shear band microstructure, which is formed by any of the above-mentioned design methods and has corresponding beneficial effects. In order to avoid repeated description, it will not be repeated here.

[0147] For example, Figure 6 FIG. 1 is a schematic diagram of a shear band microstructure provided by an embodiment of the present disclosure. Figure 6 The shear band microstructure is formed by any one of the shear band microstructure design methods provided in the above embodiments; the shear band microstructure is a centrally symmetrical figure, consisting of a first material and a second material; wherein the first material is in the form of black thin strips, with the center of the shear band microstructure as the origin of symmetry, symmetrically distributed in the shear band microstructure, dividing the shear band microstructure into nine approximately square sub-regions, and the second material fills the sub-regions.

[0148] It should be noted that the shear band microstructure is related to the V * Value related, V * The larger the value, the greater the volume fraction of the first material in the output shear band microstructure and the thicker the black stripes.

[0149] Based on the above implementation, the present disclosure also provides a shear band. Figure 7 As shown, the shear band includes the above-mentioned shear band microstructure arranged periodically, which has corresponding beneficial effects. In order to avoid repeated description, it will not be repeated here.

[0150] For example, Figure 7 As shown, 9 shear band microstructures are arranged periodically to form a 3×3 shear band microstructure.

[0151] Among them, the shear belt can be produced by the following methods:

[0152] Method 1: Use the black thin strip structure (i.e., the first material) in the 3D printed shear band microstructure, and then pour the raw rubber (the second material) into the 3D printed shear band microstructure for integrated vulcanization molding.

[0153] Method 2: Use weaving equipment to weave the black thin strip structure (i.e., the first material) in the shear band microstructure, and then pour raw rubber (the second material) into the weaved shear band microstructure for integrated vulcanization molding.

[0154] Based on the above-mentioned implementation manner, the present disclosure also provides a non-pneumatic tire. Figure 8 FIG. 1 is a schematic diagram of the structure of a non-pneumatic tire provided by an embodiment of the present disclosure. Figure 8 The non-pneumatic tire 100 includes: the above-mentioned shear band, which has corresponding beneficial effects. In order to avoid repeated description, it will not be repeated here.

[0155] For example, Figure 8 As shown, the non-pneumatic tire includes: the shear band 101 provided in the above embodiment, and the shear band 101 includes a periodically arranged shear band microstructure. Since the shear band microstructure has a higher tensile modulus and a lower shear modulus, the shear band microstructure is applied to the non-pneumatic tire to improve the load-bearing capacity of the non-pneumatic tire.

[0156] In some embodiments, the first material is provided as steel and the second material is provided as rubber.

[0157] In this way, the sandwich shear band of the polyurethane elastomer is replaced by the shear band having the shear band microstructure, which not only improves the load-bearing capacity of the non-pneumatic tire, but also reduces the production cost because the price of rubber is much lower than that of the polyurethane elastomer.

[0158] Exemplarily, the shear layer of the sandwich shear band is usually made of thermoplastic polyurethane elastomer or cast polyurethane elastomer, whose Young's modulus is 50 MPa; in the shear band with a shear band microstructure in this embodiment, the first material is set to steel, and the second material is set to rubber, and the Young's modulus of the rubber is 6 MPa; a non-pneumatic tire using a sandwich shear band and a non-pneumatic tire using a microstructure shear band are compared and tested. Under the condition that the weight and volume of the shear band are equal, the volume fraction of steel is 10%, and the same displacement is loaded, the non-pneumatic tire using the microstructure shear band has a greater load-bearing capacity of 179N; while the load-bearing capacity of the non-pneumatic tire using the sandwich shear band is only 121N.

[0159] For example, Figure 9-12 As shown, Fig. 9 It is a static rigidity simulation diagram of a non-pneumatic tire using a sandwich shear band in the related art; Fig.10 A static rigidity simulation diagram of a non-pneumatic tire using a microstructure shear band provided in an embodiment of the present disclosure; Fig.11 A diagram showing stress results of a non-pneumatic tire using a sandwich shear band in the related art; Fig.12 The stress result diagram of a non-pneumatic tire with a microstructure shear band provided by an embodiment of the present disclosure. Fig. 9 and Fig.10 , under the same displacement, the non-pneumatic tire with microstructure shear band generates a larger ground reaction force, that is, the non-pneumatic tire with microstructure shear band has a larger stiffness and a stronger ability to resist deformation. Fig.11 and Fig.12 Under the same displacement, the stress generated by the non-pneumatic tire using the microstructure shear band is mainly distributed in the microstructure shear band, and the stress distribution is relatively uniform; while the stress generated by the non-pneumatic tire using the sandwich shear band is mainly distributed on the steel ring structure on both sides of the shear band along the radial direction of the tire; This shows that the microstructure shear band has a higher utilization rate of structural materials and is more effective in bearing.

[0160] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0161] The above description is only a specific embodiment of the present disclosure, so that those skilled in the art can understand or implement the present disclosure. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure will not be limited to the embodiments described herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for designing a shear band microstructure, characterized in that: include: Define a design region and determine design variables; wherein the design region is the minimum periodic unit of the shear band microstructure, the design region includes N grids, N is a positive integer; the design variables are the filling materials in the design region; constructing a material matrix of the design region and determining an objective function of the design region; Finite element analysis is performed on the design area, and the equivalent elastic modulus of the design area is calculated using the following formula: To=∫ Y B T EdY; Based on the equivalent elastic modulus of the design area, the sensitivity of each grid in the design area is calculated using the following formula: Based on the sensitivity, updating the design variables; Calculating the target value of the objective function after updating the design variables, and determining whether the target value satisfies the convergence condition; When the convergence condition is met, the design region is output as a shear band microstructure; and when the convergence condition is not met, returning to the step of performing finite element analysis on the design region and calculating the equivalent elastic modulus of the design region; in, is the equivalent elastic modulus of the design area; H represents homogenization; i, j, k and l are the subscripts of the equivalent elastic modulus, indicating its regional position in the design area, i, j, k and l are all positive integers; Y is the area of ​​the design area, I is a 3×3 unit matrix; B is the strain matrix of the design area; B T represents the transposed matrix of the strain matrix; u is the internal displacement field of the design area; K is the stiffness matrix of the design area; p1 is the penalty factor; E e，ijkl is the elastic modulus of the e-th grid; Indicates that the e-th grid filling material is the elastic modulus of the first material; Indicates that the elastic modulus of the e-th grid filling material is the second material; e is a positive integer from 1 to N; and is the tensile modulus of the design area; is the shear modulus of the design area; w1 is the weight coefficient of the tensile modulus; w2 is the weight coefficient of the shear modulus; Ce is the design variable, and its value is 0 or 1.

2. The method according to claim 1, characterized in that The filling material in the design region includes a first material or a second material; when the filling material is the first material, the design variable is Ce=1; when the filling material is the second material, the design variable is Ce=0; The initial value of the design variable is that the design region is completely filled with the first material.

3. The method according to claim 2, characterized in that The determining of the objective function of the design area includes: the objective function is a maximization function, and the objective function is calculated using the following formula: Among them, F(x) is the objective function.

4. The method according to claim 2, characterized in that: The updating of the design variables based on the sensitivity comprises: Based on the sensitivity, the filling material of the grid whose sensitivity meets the preset update condition is replaced from the first material to the second material.

5. The method according to claim 4, characterized in that Before calculating the target value of the target function after updating the design variables and judging whether the target value satisfies the convergence condition, the method further comprises: Calculating the volume fraction of the first material after updating the design variables, and determining whether the volume fraction of the first material satisfies the constraint condition of the objective function; The constraint condition of the objective function is: V1 = V * ; When the constraint condition is met, executing the calculation of the target value of the target function after updating the design variables, and judging whether the target value meets the convergence condition; and When the constraint condition is not satisfied, returning to the step of performing finite element analysis on the design area and calculating the equivalent elastic modulus of the design area; Wherein, V1 is the volume fraction of the first material in the design area; V * is the volume fraction constraint value of the first material in the design region.

6. The method according to claim 5, characterized in that The convergence condition includes: the target value of the objective function meets a preset accuracy requirement.

7. A shear band microstructure, characterized in that: The method is formed by the design method according to any one of claims 1 to 6.

8. A shear band, characterized in that: A shear band microstructure comprising a periodically arranged shear band as claimed in claim 7.

9. A non-pneumatic tire, characterized in that: include: A shear tape as claimed in claim 8.

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