Non-pneumatic wheel with negative Poisson's ratio structure, optimization method and related system

Abstract

The present invention discloses a non-pneumatic wheel with a negative Poisson's ratio (NPR-R) structure, an optimization method, and a related system. Based on the parameters of the NPR-R non-pneumatic wheel, a relative density model, a peak force (PCF) model, and a unit mass energy absorption (SEA) model are established for the NPR-R wheel. A multi-objective optimization mathematical model is established, targeting the minimum relative density, minimum PCF, and maximum SEA of the NPR-R wheel, with the NPR-R wheel's structural parameters as design variables. This multi-objective discrete robust optimization design method, combining the continuous Taguchi method, improved grey relational analysis (IGRA), and principal component analysis, is used to form a multi-objective discrete robust optimization method. The multi-objective optimization mathematical model is then optimized to determine the NPR-R wheel's structural parameters. This method not only enhances the safety and stability of all-terrain vehicles during driving but also improves the impact resistance of NPR-R non-pneumatic tires.

Description

Technical Field

[0001] The present invention relates to the field of wheels, and in particular to a non-pneumatic wheel for an all-terrain vehicle with a negative Poisson's ratio structure, an optimization method and a related system. Background Art

[0002] The ATV racing event, held in rivers, woods, and shrubs, integrates rural tourism with outdoor sports, generating new product formats and addressing the current overly single and unsustainable development model of rural tourism. This has injected new momentum into the comprehensive promotion of rural revitalization. However, ATVs currently have a drawback: rough terrain and foreign objects can easily cause tire blowouts. Therefore, a non-pneumatic wheel with a negative Poisson's ratio structure and its optimization method for all-terrain vehicles have been proposed, which can further improve the safety and stability of ATVs.

[0003] The traditional positive Poisson's ratio structure will expand laterally when subjected to axial compression and contract laterally when subjected to axial tension, while the negative Poisson's ratio structure will contract laterally when subjected to axial compression and expand laterally when subjected to axial tension, which is completely opposite to the positive Poisson's ratio structure. This special mechanical property gives it excellent performance in energy absorption, shear resistance, compression resistance and impact resistance, and it can easily cope with harsh terrains such as beaches and riverbeds. Summary of the Invention

[0004] Purpose of the invention: In order to solve the problem that foreign objects on rugged roads are more likely to cause "tire blowouts", the present invention provides an optimization method for non-pneumatic wheels with a negative Poisson's ratio structure.

[0005] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A method for optimizing non-pneumatic wheels with negative Poisson's ratio structures is proposed. First, a finite element simulation model (NPR-DAM) is established. NPR-DAM stands for negative Poisson's ratio double-arrow microstructure. The optimization problem is defined, and simulation analysis is performed to obtain response parameters. A multi-objective discrete robust optimization design approach is then developed by integrating the continuous Taguchi method, an improved grey relational analysis method, and principal component analysis. Based on this, a multi-objective optimization mathematical model is established, targeting minimum relative density, minimum PCF, and maximum SEA of the NPR-DAM, with the structural parameters of the NPR-DAM as optimization variables. The multi-objective optimization design is then carried out, including the following steps:

[0007] Step 1: According to the parameters of the non-pneumatic wheel with negative Poisson's ratio structure, the relative density model, peak force PCF model and unit mass energy absorption SEA model of NPR-DAM are established.

[0008] Step 2: Based on the established relative density model, peak force PCF model, and unit mass energy absorption SEA model, a multi-objective optimization mathematical model is established with the minimum relative density, minimum PCF, and maximum SEA of NPR-DAM as the goals and the structural parameters of NPR-DAM as the design variables.

[0009] Step 3: A multi-objective discrete robust optimization design method is formed by integrating the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method to perform multi-objective optimization on the multi-objective optimization mathematical model and obtain the structural parameters of NPR-DAM.

[0010] Preferably, the multi-objective optimization mathematical model is:

[0011] Design var:N,D l ,Ds,θ1,θ2

[0012]

[0013] Where N is the number of microstructure units, D l is the thickness of the long beam, D S is the thickness of the short beam, θ1 is the angle between the long beam and the vertical direction, θ2 is the angle between the short beam and the vertical direction, SEA is the energy absorption per unit mass, θ2 is the angle between the short beam and the vertical direction, θ'2 represents the angle between the short beam and the vertical direction after compression, L is the half width of the microstructure unit, The compression displacement is The force used when M is the structural mass, PCF is the peak force, is the relative density of NPR-DAM, D is the thickness of the beam, and θ1 is the angle between the long beam and the vertical direction.

[0014] Preferably, the design method of integrating the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method in step 3 to form a multi-objective discrete robust optimization is specifically as follows: the principal component analysis method is to describe the variance-covariance structure through the design standard of linear combination, and determine the design variables and noise factors according to the defined optimization problem. The noise factor and design variable samples are collected by the experimental design DOE method and placed in an orthogonal table. The penalty function is calculated based on the response index obtained by the finite element model simulation analysis, and the signal-to-noise ratio SNR of the penalty function is calculated. The best and worst reference series of each performance index are selected, the coefficient of grey relational degree is calculated, the principal component analysis is performed and the relative correlation between the evaluation index value of each evaluation object and the optimal solution and the worst solution is calculated, and then the relative closeness between the evaluation value and the optimal value is calculated, and the optimal solution is obtained based on the closeness.

[0015] Preferably, the penalty function formula is:

[0016]

[0017] Where, F new (x) is the objective function after penalty, F(x) is the original objective function. M(x) represents the penalty function vector, v i It represents the violation amount of the i-th constraint function, P is the number of samples, and C is the penalty function coefficient.

[0018] Preferably, the formula for the signal-to-noise ratio SNR is:

[0019] Big features: Small features:

[0020] In the formula, n represents the number of times the experiment is repeated, y ij represents the jth repeated test of the i-th experiment.

[0021] Preferably, data normalization is performed:

[0022]

[0023] In the formula, the element x of the decision matrix is ij represents the jth indicator value of the i-th alternative design, and the element X of the standardized matrix ij Represents x ij Normalized value.

[0024] The best and worst reference series selected:

[0025]

[0026] Where, represents the optimal reference sequence, Represents the worst reference sequence.

[0027] Calculate the grey relational coefficient:

[0028]

[0029] Where, is the optimal reference series grey relational coefficient, is the grey relational coefficient of the worst reference series, and β is called the discrimination coefficient.

[0030] The relative correlation between the evaluation index value of each evaluation object and the optimal solution and the worst solution is:

[0031]

[0032] Where, is the relative correlation between the evaluation index value of each evaluation object and the optimal solution, is the relative correlation between the evaluation index value of each evaluation object and the worst solution, i=1,2,…,m, m is, n is, W k is the weight of each indicator.

[0033] The structure of variance-covariance is:

[0034]

[0035] Where Rk is the variance-covariance structure, k = 1, 2, ..., n, n is the number of performance indicators, For sequence and The covariance of . represent the standard deviation of the series.

[0036] The corresponding eigenvalues ​​and eigenvectors are calculated from the correlation coefficient array:

[0037]

[0038] Where λ k is the eigenvalue, and V ik Its corresponding eigenvector, I N is the N-dimensional identity matrix.

[0039] The square of the eigenvector corresponding to the maximum eigenvalue is set as the weighting coefficient W k .

[0040] Preferably, the relative closeness to the optimal solution:

[0041]

[0042] Where h i Indicates the relative closeness to the optimal solution.

[0043] Another object of the present invention is to provide a non-pneumatic wheel for an all-terrain vehicle with a negative Poisson's ratio structure, comprising a wheel tread (1), a negative Poisson's ratio internal support structure (2), and a wheel hub (3), wherein the wheel tread (1) and the negative Poisson's ratio internal support structure (2) form a function-oriented integrated structure, and the wheel tread (1) is provided with pattern blocks and pattern grooves for increasing the grip between the wheel tread and the road surface and ensuring the vehicle's anti-skid force. The negative Poisson's ratio internal support structure (2) is connected to the wheel hub (3) by extrusion, interlocking, and bonding. The negative Poisson's ratio internal support structure (2) comprises two layers of negative Poisson's ratio support arrow-shaped microstructures, each layer of microstructures comprising a plurality of support units. The structural parameters of the negative Poisson's ratio support arrow-shaped microstructure NPR-DAM are obtained by the non-pneumatic wheel optimization method of the negative Poisson's ratio structure.

[0044] Another object of the present invention is to provide a non-pneumatic wheel optimization system with a negative Poisson's ratio structure, which is used to implement the non-pneumatic wheel optimization method with a negative Poisson's ratio structure, including a multi-objective optimization mathematical model unit and a solution unit, wherein:

[0045] The multi-objective optimization mathematical model unit is used to establish a multi-objective optimization mathematical model with the minimum relative density, minimum PCF, and maximum SEA of NPR-DAM as objectives and the structural parameters of NPR-DAM as design variables.

[0046] The solution unit is used to integrate the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method to form a multi-objective discrete robust optimization design method to perform multi-objective optimization on the multi-objective optimization mathematical model and optimize the structural parameters of the NPR-DAM.

[0047] Another object of the present invention is to provide an electronic device comprising: at least one processor, at least one memory, and a communication interface. The processor, memory, and communication interface are in communication with each other. The memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the method for optimizing a non-pneumatic wheel with a negative Poisson's ratio structure.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention adopts a multi-objective discrete robust optimization design method formed by integrating the continuous Taguchi method, the improved grey relational analysis IGRA method and PCA to obtain the optimal negative Poisson's ratio double-arrow microstructure parameters, further improving the lightweight and impact resistance of the negative Poisson's ratio structure non-pneumatic wheel. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is an assembly diagram of a non-pneumatic tire with a negative Poisson's ratio internal support structure.

[0051] Figure 2 This is a front view of the internal support structure with a negative Poisson's ratio.

[0052] Figure 3 It is a front view and a partial enlarged view of the internal support structure with a negative Poisson's ratio.

[0053] Figure 4 It is a microstructure diagram of the internal support structure with negative Poisson's ratio.

[0054] Figure 5 It is a flow chart of the optimization method of the internal support structure with negative Poisson's ratio. DETAILED DESCRIPTION

[0055] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0056] A non-pneumatic wheel for an all-terrain vehicle with a negative Poisson's ratio structure, such as Figure 1 As shown, the wheel comprises a tread 1, a negative Poisson's ratio internal support structure 2, and a hub 3. The hub 3 has rims at both ends. The negative Poisson's ratio internal support structure 2 is connected to the hub 3 by extrusion, interlocking, and bonding. The hub 3 is provided with positioning holes and a reinforcement support structure for reinforcing the negative Poisson's ratio internal support structure 2. The wheel tread 1 and the negative Poisson's ratio internal support structure 2 form a function-oriented integrated structure. The wheel tread 1 is provided with tread blocks and grooves that enhance grip between the wheel and the road surface and ensure the vehicle's resistance to sideslip. This embodiment utilizes a function-oriented integrated design approach for the tread and negative Poisson's ratio internal support structure. This novel design approach and method improve the durability of a non-pneumatic tire with a negative Poisson's ratio structure.

[0057] like Figure 2-3 As shown, the negative Poisson's ratio internal support structure 2 includes two layers of negative Poisson's ratio support arrow-shaped microstructures, and each layer of microstructure contains multiple support units. A single support unit is a negative Poisson's ratio structure with a certain concave shape composed of long cell walls and short cell walls. Among them, the number N of microstructure units in the negative Poisson's ratio internal support structure 2 is specifically set according to actual conditions, and the manufacturing material of the negative Poisson's ratio internal support structure is any one of alloy, aluminum, steel, ceramic composite material, rubber composite material and resin plastic, and is produced using manufacturing processes including 3D printing, bonding, material molding, thermal curing and shaping processing. It is specifically set according to the vehicle model quality requirements and driving conditions during the design process. The structural parameters of the negative Poisson's ratio support arrow-shaped microstructure NPR-DAM are obtained by the non-pneumatic wheel optimization method of the negative Poisson's ratio structure.

[0058] like Figure 4 As shown, the arrow-shaped microstructure with a negative Poisson's ratio shrinks laterally when subjected to axial compression and expands laterally when subjected to axial tension, a behavior completely opposite to that of a positive Poisson's ratio structure. This unique mechanical property provides excellent energy absorption, shear resistance, compression resistance, and impact resistance, enhancing vehicle stability and driving comfort on rugged mountainous surfaces. By employing a double-layered arrow-shaped negative Poisson's ratio support structure and non-pneumatic tires instead of traditional pneumatic tires, the present invention can easily handle harsh terrain such as beaches and riverbeds.

[0059] This embodiment uses a negative Poisson's ratio double-arrow microstructure non-pneumatic tire to replace the traditional pneumatic tire. The negative Poisson's ratio structure non-pneumatic wheel has special mechanical properties of "cohesion under pressure" and "becoming stronger with pressure", which can prevent sharp objects from piercing the tire and causing a blowout, greatly improving the safety and operational stability of the all-terrain vehicle during driving.

[0060] A non-pneumatic wheel optimization method with a negative Poisson's ratio structure first establishes an NPR-DAM finite element simulation model, defines the optimization problem, performs simulation analysis to obtain the response parameters, and then forms a multi-objective discrete robust optimization MODRO design method by integrating the continuous Taguchi method, the improved grey relational analysis method, and the principal component analysis. Based on this, with the minimum relative density, minimum PCF, and maximum SEA of the NPR-DAM as the goals, and the structural parameters of the NPR-DAM as the optimization variables, a multi-objective optimization mathematical model is established, and a multi-objective optimization design is carried out, such as Figure 5 As shown, the specific steps include:

[0061] Step 1: According to the parameters of the non-pneumatic wheel with negative Poisson's ratio structure, the relative density model, peak force PCF model and unit mass energy absorption SEA model of NPR-DAM are established.

[0062] The specific methods for establishing the NPR-DAM finite element simulation model, defining the optimization problem, and performing simulation analysis to obtain the response parameters are as follows: establishing the finite element simulation analysis model through the finite element pre-processing software; determining the optimization target, design parameter variables and design constraints; setting the corresponding parameters in the finite element pre-processing software to perform simulation analysis to obtain the response parameters.

[0063] The relative density model of NPR-DAM is:

[0064]

[0065] in, is the relative density of NPR-DAM, ρ is the equivalent density, ρ s is the density of the matrix material, N is the number of microstructure units, and D is the thickness of the beam (assuming that the long and short beams D l 、D S thickness), L is the half-width of the microstructure unit, θ1 is the angle between the long beam and the vertical direction, and θ2 is the angle between the short beam and the vertical direction.

[0066] The total energy E absorbed during the structural deformation process can be expressed as:

[0067]

[0068] Here, δ represents the compression displacement, and F(δ) represents the force applied when the compression displacement is δ.

[0069] During a collision, PCF represents the maximum value of the collision force between the energy-absorbing structure and the collision contact surface. The peak force PCF model is:

[0070]

[0071] Where PCF is the peak force, The compression displacement is is the force used when the short beam is compressed, and θ'2 represents the angle between the short beam and the vertical direction after compression.

[0072] In addition, during the compression process, the unit mass energy absorption SEA model is:

[0073]

[0074] Among them, SEA is the energy absorbed per unit mass, M is the structural mass

[0075] The optimized design variables are as follows:

[0076] The structural parameters are the number of microstructure units N, the thickness of the long and short beams D l 、D S , the angles θ1 and θ2 between the long and short beams and the vertical direction.

[0077] Step 2: Based on the established relative density model, peak force PCF model, and unit mass energy absorption SEA model, with the minimum relative density, minimum PCF, and maximum SEA of NPR-DAM as the goals, and the structural parameters of NPR-DAM as the design variables, a multi-objective optimization mathematical model is established, and a multi-objective optimization design is carried out to obtain the optimal NPR-DAM structural parameters.

[0078] In another embodiment, the multi-objective optimization mathematical model is:

[0079] Design var:N,D l ,Ds,θ1,θ2(5)

[0080]

[0081] Where N is the number of microstructure units, D l is the thickness of the long beam, D S is the thickness of the short beam, θ1 is the angle between the long beam and the vertical direction, θ2 is the angle between the short beam and the vertical direction, SEA is the energy absorption per unit mass, θ2 is the angle between the short beam and the vertical direction, θ'2 represents the angle between the short beam and the vertical direction after compression, L is the half width of the microstructure unit, The compression displacement is The force used when M is the structural mass, PCF is the peak force, is the relative density of NPR-DAM, D is the thickness of the beam, and θ1 is the angle between the long beam and the vertical direction.

[0082] Too many negative Poisson's ratio microstructure units will cause the mass of the structure to surge, which is not conducive to the lightweight design of the structure; the angle between the microstructure units should not be too small. A smaller angle between the microstructure units will also lead to an increase in the relative density of the double-arrow negative Poisson's ratio structure, and the cell wall thickness should be kept within a reasonable range to avoid excessive stress concentration. The cell wall thickness should be set between 1 mm and 2.5 mm.

[0083] Step 3: A multi-objective discrete robust optimization design method is formed by integrating the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method to perform multi-objective optimization on the multi-objective optimization mathematical model and obtain the structural parameters of NPR-DAM.

[0084] In another embodiment, step 3 integrates the continuous Taguchi method, the improved grey relational analysis (IGRA) method, and the principal component analysis method to form a multi-objective discrete robust optimization design method. Specifically, the Taguchi method is an effective parametric design and experimental planning method. The principal component analysis method describes the variance-covariance structure through linear combination design criteria, and determines the design variables and noise factors based on the defined optimization problem. The noise factor and design variable samples are collected and placed in an orthogonal table using the experimental design (DOE) method. The penalty function is calculated based on the response index obtained from the finite element model simulation analysis, and the signal-to-noise ratio (SNR) of the penalty function is calculated. The optimal and worst reference series for each performance index are selected, the grey relational coefficient is calculated, the principal component analysis is performed, and the relative correlation between the evaluation index value of each evaluation object and the optimal solution and the worst solution is calculated. The relative proximity between the evaluation value and the optimal value is then calculated, and the optimal solution is obtained based on the proximity.

[0085] In another embodiment, the penalty function formula is:

[0086]

[0087] Where, F new (x) is the objective function after penalty, F(x) is the original objective function. M(x) represents the penalty function vector, v i represents the violation of the i-th constraint function, P is the number of samples, and C is the penalty function coefficient. The penalty function coefficient C is taken to be 10 times the original objective function.

[0088] Preferably, the formula for the signal-to-noise ratio SNR is:

[0089] Big features: Small features:

[0090] In the formula, n represents the number of times the experiment is repeated, y ij represents the jth repeated test of the i-th experiment.

[0091] Preferably, data normalization is performed:

[0092]

[0093] In the formula, the element x of the decision matrix is ij represents the jth indicator value of the i-th alternative design, and the element X of the standardized matrix ij Represents x ij Normalized value.

[0094] The best and worst reference series selected:

[0095]

[0096] Where, represents the optimal reference sequence, Represents the worst reference sequence.

[0097] Calculate the grey relational coefficient:

[0098]

[0099] Where, is the optimal reference series grey relational coefficient, is the grey relational coefficient of the worst reference series, β is called the discrimination coefficient, which generally takes a value between 0 and 1, and is taken as 0.7 in the present invention.

[0100] The relative correlation between the evaluation index value of each evaluation object and the optimal solution and the worst solution is:

[0101]

[0102] Where, is the relative correlation between the evaluation index value of each evaluation object and the optimal solution, is the relative correlation between the evaluation index value of each evaluation object and the worst solution, i=1,2,…,m, m is, n is, W k is the weight of each indicator.

[0103] The structure of variance-covariance is:

[0104]

[0105] Where Rk is the variance-covariance structure, k = 1, 2, ..., n, n is the number of performance indicators, For sequence and The covariance of . represent the standard deviation of the series.

[0106] The corresponding eigenvalues ​​and eigenvectors are calculated from the correlation coefficient array:

[0107]

[0108] Where λ k is the eigenvalue, and V ik Its corresponding eigenvector, I N is the N-dimensional identity matrix.

[0109] The square of the eigenvector corresponding to the maximum eigenvalue is set as the weighting coefficient W k .

[0110] Preferably, the relative closeness to the optimal solution:

[0111]

[0112] Where h i Indicates the relative closeness to the optimal solution.

[0113] Sort by proximity, the larger the proximity, the closer to the optimal solution.

[0114] The present invention takes the minimum relative density, minimum peak force PCF, and maximum specific energy absorption SEA of NPR-DAM as the goals, and uses the structural parameters of NPR-DAM as optimization variables to carry out multi-objective optimization design to further improve the performance of negative Poisson's ratio structural non-pneumatic tires.

[0115] In another embodiment, a non-pneumatic wheel optimization system with a negative Poisson's ratio structure is provided, which is used to implement the non-pneumatic wheel optimization method with a negative Poisson's ratio structure, and includes a multi-objective optimization mathematical model unit and a solution unit, wherein:

[0116] The multi-objective optimization mathematical model unit is used to establish a multi-objective optimization mathematical model with the minimum relative density, minimum PCF, and maximum SEA of NPR-DAM as objectives and the structural parameters of NPR-DAM as design variables.

[0117] The solution unit is used to integrate the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method to form a multi-objective discrete robust optimization design method to perform multi-objective optimization on the multi-objective optimization mathematical model and optimize the structural parameters of the NPR-DAM.

[0118] In another embodiment, an electronic device is provided, comprising: at least one processor, at least one memory, and a communication interface. The processor, memory, and communication interface are in communication with each other. The memory stores program instructions executable by the processor, and the processor invokes the program instructions to perform the method for optimizing a non-pneumatic wheel with a negative Poisson's ratio structure.

[0119] The present invention utilizes the special mechanical properties of the negative Poisson's ratio double-arrow microstructure NPR-DAM, which is "cohesive under pressure" and "stronger with pressure," to achieve greater resistance to plastic deformation when under load, better maintain shape and dimensional stability, reduce deformation and distortion caused by harsh road conditions, and improve the safety and stability of all-terrain vehicles during driving. A multi-objective discrete robust optimization design method, formed by integrating the continuous Taguchi method, the improved grey relational analysis IGRA method, and PCA, is used to obtain the optimal structural parameters of the negative Poisson's ratio double-arrow microstructure, further improving the lightweight and impact resistance of the negative Poisson's ratio structured non-pneumatic wheel. Taking the minimum relative density, minimum peak force PCF, and maximum specific energy absorption SEA of the NPR-DAM as the goals, and using the structural parameters of the NPR-DAM as optimization variables, a multi-objective optimization design is carried out to further improve the performance of the negative Poisson's ratio structured non-pneumatic tire.

[0120] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for optimizing a non-pneumatic wheel with a negative Poisson's ratio structure, characterized in that: A non-pneumatic wheel for an all-terrain vehicle with a negative Poisson's ratio structure includes a negative Poisson's ratio internal support structure, wherein the negative Poisson's ratio internal support structure includes two layers of negative Poisson's ratio support arrow-shaped microstructures, each layer of the microstructure includes a plurality of support units, and a single support unit is a negative Poisson's ratio structure with a concave shape composed of a long cell wall and a short cell wall; and the steps are as follows: Step 1: Based on the parameters of the non-pneumatic wheel with negative Poisson's ratio structure, the relative density model, peak force PCF model and unit mass energy absorption SEA model of NPR-DAM are established; Step 2: Based on the established relative density model, peak force PCF model, and unit mass energy absorption SEA model, a multi-objective optimization mathematical model is established with the minimum relative density, minimum PCF, and maximum SEA of the NPR-DAM as the goals and the structural parameters of the NPR-DAM as the design variables; The multi-objective optimization mathematical model is: Design was Objective: ; Subject to: ; Where N is the number of microstructure units, D l is the thickness of the long beam, D S is the thickness of the short beam, θ1 is the angle between the long beam and the vertical direction, θ2 is the angle between the short beam and the vertical direction, SEA is the energy absorbed per unit mass, represents the angle between the short beam and the vertical direction after compression, L is the half-width of the microstructure unit, The compression displacement is The force used when M is the mass of the structure, is the peak force, is the relative density of NPR-DAM, D is the thickness of the beam; Step 3: A multi-objective discrete robust optimization design method is formed by integrating the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method to perform multi-objective optimization on the multi-objective optimization mathematical model and obtain the structural parameters of NPR-DAM.

2. The method for optimizing a non-pneumatic wheel with a negative Poisson's ratio structure according to claim 1, characterized in that: In step 3, the continuous Taguchi method, improved grey relational analysis (IGRA) method and principal component analysis (PCA) method are integrated to form a multi-objective discrete robust optimization design method. Specifically, the PCA method describes the variance-covariance structure through linear combination of design criteria, and determines the design variables and noise factors according to the defined optimization problem. The noise factors and design variable samples are collected and placed in an orthogonal table through the experimental design DOE method; The penalty function is calculated based on the response index obtained from the finite element model simulation analysis, and then the signal-to-noise ratio (SNR) of the penalty function is calculated. The optimal and worst reference series of each performance index are selected, and the coefficient of grey correlation is calculated. The principal component analysis is performed and the relative correlation between the evaluation index value of each evaluation object and the optimal solution and the worst solution is calculated. The relative closeness between the evaluation value and the optimal value is calculated, and the optimal solution is obtained based on the closeness.

3. The non-pneumatic wheel optimization method with a negative Poisson's ratio structure according to claim 2, characterized in that: The penalty function formula is: Where, F new (x) is the objective function after penalty, F(x) is the original objective function; M(x) represents the penalty function vector, v i Indicates the i The amount of constraint violation for a constraint function, is the number of samples, and C is the penalty function coefficient.

4. The non-pneumatic wheel optimization method with a negative Poisson's ratio structure according to claim 3, characterized in that: The formula for signal-to-noise ratio (SNR) is: Big features: ; Towards Small features: Where, represents the number of times the experiment is repeated, y ij Indicates the i The first experiment j Repeat the test.

5. The non-pneumatic wheel optimization method with a negative Poisson's ratio structure according to claim 4, characterized in that: Data normalization processing: ； In the formula, the element x of the decision matrix is ij represents the jth indicator value of the ith alternative design, and the element X ij Represents x ij Normalized value; The best and worst reference series selected: ； ； Where, represents the optimal reference sequence, represents the worst reference sequence; Calculate the grey relational coefficient: ； Where, is the optimal reference series grey relational coefficient, is the grey relational coefficient of the worst reference series, and β is called the discrimination coefficient; The relative correlation between the evaluation index value of each evaluation object and the optimal solution and the worst solution is: Where, is the relative correlation between the evaluation index value of each evaluation object and the optimal solution, is the relative correlation between the evaluation index value of each evaluation object and the worst solution, , W k is the weight of each indicator; The structure of variance-covariance is: ； Where, is the variance-covariance structure, , is the number of performance indicators, For sequence and covariance of represent the standard deviation of the series; The corresponding eigenvalues ​​and eigenvectors are calculated from the correlation coefficient array: Where, is the eigenvalue, and Its corresponding eigenvector, is the N-dimensional identity matrix; The square of the eigenvector corresponding to the maximum eigenvalue is set as the weighting coefficient W k .

6. The non-pneumatic wheel optimization method with a negative Poisson's ratio structure according to claim 5, characterized in that: Relative closeness to the optimal solution: ； Where, Indicates the relative closeness to the optimal solution.

7. A non-pneumatic wheel for an all-terrain vehicle with a negative Poisson's ratio structure, characterized by: The invention comprises a wheel tread (1), a negative Poisson's ratio internal support structure (2) and a wheel hub (3), wherein the wheel tread (1) and the negative Poisson's ratio internal support structure (2) form a function-oriented integrated structure, and the wheel tread (1) is provided with tread blocks and tread grooves for increasing the grip between the wheel tread and the road surface and ensuring the vehicle's anti-skid force; the negative Poisson's ratio internal support structure (2) is connected to the wheel hub (3) by extrusion, interlocking and bonding; the negative Poisson's ratio internal support structure (2) comprises two layers of negative Poisson's ratio support arrow-shaped microstructures, each layer of microstructures comprising a plurality of support units; the structural parameters of the negative Poisson's ratio support arrow-shaped microstructure NPR-DAM are obtained by the non-pneumatic wheel optimization method of the negative Poisson's ratio structure according to any one of claims 1 to 6.

8. A non-pneumatic wheel optimization system with a negative Poisson's ratio structure, characterized in that: The non-pneumatic wheel optimization method for realizing the negative Poisson's ratio structure according to any one of claims 1 to 6 comprises a multi-objective optimization mathematical model unit and a solution unit, wherein: The multi-objective optimization mathematical model unit is used to establish a multi-objective optimization mathematical model with the minimum relative density, minimum PCF, and maximum SEA of the NPR-DAM as the objectives and the structural parameters of the NPR-DAM as the design variables; The solution unit is used to integrate the continuous Taguchi method, the improved grey relational analysis IGRA method and the principal component analysis method to form a multi-objective discrete robust optimization design method to perform multi-objective optimization on the multi-objective optimization mathematical model and optimize the structural parameters of the NPR-DAM.

9. An electronic device, characterized in that: include: at least one processor, at least one memory, and a communication interface; The processor, memory and communication interface communicate with each other; The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the non-pneumatic wheel optimization method with a negative Poisson's ratio structure according to any one of claims 1-6.

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