A carcass profile design method for improving tire durability

Abstract

This invention discloses a tire carcass profile design method to improve tire durability. The invention includes the following steps: S1, establishing a tire finite element model; S2, constructing a parameterized tire carcass profile model based on Bézier curve theory; S3, extracting tire durability performance evaluation indicators; S4, performing local optimization design of the tire carcass profile based on orthogonal experiments; S5, performing global optimization design of tire carcass profile design variables based on the GPR-MIGA algorithm; S6, analyzing and verifying the mechanical mechanism of the optimized scheme. This invention, through establishing a tire finite element model, constructing a parameterized tire carcass profile model based on Bézier curve theory, extracting tire durability performance evaluation indicators, performing local optimization design of the tire carcass profile based on orthogonal experiments, performing global optimization design of tire carcass profile design variables based on the GPR-MIGA algorithm, and analyzing and verifying the mechanical mechanism of the optimized scheme, allows technicians to effectively reduce tire durability and increase tire lifespan by designing the tire carcass profile during tire research and development.

Description

Technical Field

[0001] This invention relates to the field of tire profile design and performance optimization technology, specifically to a tire carcass profile structure design method for improving tire durability. Background Technology

[0002] Against the backdrop of the continuous evolution of the automotive industry, the impact of tire durability on vehicle driving safety, operational efficiency, and total lifecycle costs is becoming increasingly prominent. Durability refers to a tire's ability to resist wear, fatigue, cracks, and structural failure during long-term use, directly determining its lifespan and reliability under complex operating conditions. Especially with the rapid development of distributed electric drive heavy-duty vehicles, tires must frequently withstand high-load starts, braking, and severe impacts from complex road conditions. This leads to a high concentration of strain energy density in critical areas such as the tire shoulder, significantly increasing the risk of fatigue damage and directly causing phenomena such as tire shoulder gaps, delamination, and cord breakage. To ensure vehicle driving safety in harsh environments and reduce replacement frequency, improving tire durability has become a key research direction in tire design and automotive engineering.

[0003] The tire carcass profile, as the core skeleton of the tire structure, directly affects the mechanical properties of the carcass layers and the tire's durability. In the field of tire carcass profile design, existing methods are mostly based on force balance theory to derive profile equations. For example, Chinese Patent Publication No. CN111506965A discloses a tire structure design method that improves tire durability by calculating a balanced profile. However, the profile equation derived theoretically contains many assumptions and simplifications, and key parameters are difficult to obtain, resulting in significant limitations in application. Existing research on optimizing tire performance through structural design mainly focuses on adjusting the structural parameters of the belt layer. For example, Chinese Patent Publication No. CN121168163A performs parametric modeling and optimization of the belt layer ends. However, it ignores the fact that tire load-bearing capacity is primarily determined by the shape of the tire carcass profile, and its input variables and optimization algorithms are prone to problems such as limited sample sizes and getting trapped in local optimization. Another type of method, such as Chinese Patent Publication No. CN119459185A, optimizes performance by adjusting the radius of curvature of the profile. However, current methods for profile design do not consider the continuity of the profile geometry, which can easily lead to curvature discontinuity, resulting in local stress concentration in the tire and consequently a decrease in tire durability.

[0004] Therefore, in order to solve the above problems and optimize tire durability through tire carcass profile design, a structural design method that can achieve continuous curvature of the tire carcass profile is needed, supported by existing research and mathematical methods. This method should be combined with a high-precision, global optimization algorithm to achieve efficient improvement in tire durability. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the existing contour design methods are mainly derived through force balance equations, which contain many assumptions and simplifications and have limited applications. In order to solve the above problems, a tire carcass contour structure design method that improves tire durability is provided.

[0006] The object of this invention is achieved in the following manner: A method for designing tire carcass profile structure to improve tire durability includes the following steps: S1. Establishment of tire finite element model: A two-dimensional finite element model of the tire is established by using the tire material distribution map, and a corresponding three-dimensional finite element model is established with reference to the tire rated air pressure and rated load. S2. Construction of a parameterized tire carcass profile model based on Bézier curve theory: Based on the two-dimensional finite element model of the tire in step S1, the discrete node coordinates of the tire carcass cord layer in the two-dimensional uninflated state are extracted. Combining the stress characteristics of the tire carcass profile, five positions are selected as key nodes: the highest point of the tire carcass profile, the end point of the belt layer, the widest point of the tire carcass profile, the end point of the tire carcass reverse wrapping, and the lowest point of the profile. Based on the key nodes, the tire carcass profile is divided into four regions with half of the tire carcass profile as the target. Bézier curves are used to fit each region piecewise. By applying collinear constraints to the control points at the connection points of the Bézier curves of adjacent regions, the profile segments are smoothly spliced, and the parameterized mathematical equations of the tire carcass profile of each region are obtained. Finally, the coordinates of the control points of the Bézier curves of each region are obtained by iteratively solving the weighted sum of squared Euclidean distances from discrete nodes to the Bézier curves as the objective function, and the parameterized model representing the tire carcass profile is obtained. S3. Extraction of tire durability performance evaluation indicators: Based on the three-dimensional finite element model of the tire under load conditions in step S1, the cross-section at the ground contact center of the tire contact area is selected as the object, and the maximum strain energy density at the end of the belt layer in this cross-section is extracted. SED max To represent the cumulative rate of tire fatigue damage, and by comparing the maximum strain energy density SED max The values ​​are used to evaluate the tire durability and the quality of the tire profile design using a negative correlation method. S4. Tire carcass profile design based on orthogonal experiment: Based on the parameterized model of the tire carcass profile in step S2, considering the specification requirements of the tire production mold, and ensuring that the outermost geometric structure and parameters of the tire remain unchanged, only the ordinate of the control points of the Bezier curve in the sidewall area is selected as the design variable to specify the orthogonal experiment scheme. For the design scheme generated by the orthogonal experiment, the material distribution diagrams of different tire carcass profile schemes are drawn, and the finite element models of different design schemes are established according to step S1. According to step S3, the tire durability performance evaluation index is extracted. The order of influence of each design variable on the durability performance evaluation index is determined by range analysis, and the optimal combination of design variables is initially obtained. The durability performance improvement effect of the tire carcass profile scheme corresponding to the optimal combination of design variables is verified again through steps S2 and S3. S5. Global Optimization Design of Tire Carcass Contour Variables Based on GPR-MIGA Algorithm: Addressing the challenge of efficiently optimizing contour structure parameters due to the large number of design variables, a Gaussian Process Regression (GPR) model is selected as a surrogate model. This model can learn nonlinear mappings from small-scale samples, providing prediction confidence intervals. The model is trained using orthogonal experimental schemes and optimal combinations of design variables as training samples, and its generalization ability is verified. Based on this, the Multi-Island Genetic Algorithm (MIGA) is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and the tire finite element model corresponding to the globally optimized design scheme is established through the process of step S1. S6. Optimization Scheme Mechanical Mechanism Analysis and Verification: Based on the finite element model of the global optimization design scheme established in step S5, the mechanical mechanism of the optimized scheme is verified. SED max The optimization effect was investigated, and the changes in the mechanical property parameters of the tire carcass cords before and after optimization were compared. The mechanical property parameters include the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, in order to reveal the mechanical mechanism of the improved durability.

[0007] Further, in step S1, a tire finite element simulation model is established. The two-dimensional cross-section of the tire is imported into HYPERMESH software for mesh generation. Then, using uniaxial tensile test data of the rubber of various tire components, different hyperelastic constitutive models are selected for fitting to obtain the material parameters, which are then assigned to each tire component. Finally, by applying inflation pressure and load, a three-dimensional finite element model of the tire under load conditions is established; including the following steps: S11. Use AutoCAD software to draw a two-dimensional cross-sectional material distribution diagram of the tire. S12. Import the drawn two-dimensional tire cross-section into HYPERMESH software for mesh generation. Use CGAX3H and CGAX4H elements for rubber material and SFMGAX1 elements for cord material through rebar reinforcing rib element model to generate a two-dimensional finite element model of the tire. S13. Based on the uniaxial tensile test data of rubber, Neo-Hookean, Yeoh, Mooney-Rivlin (N=1), and Mooney-Rivlin (N=2) hyperelastic constitutive models were selected for fitting. The model that balances fitting accuracy and model stability was selected as the constitutive model of the rubber material, and the material parameters of each rubber component were obtained. S14. Using the *SYMMETRIC MODEL GENERATION,REVOLVE command, rotate the two-dimensional model 360° to generate a three-dimensional finite element model. Define the rim and road surface as analytical rigid bodies, and apply tire boundary conditions including inflation pressure and ground load to simulate the actual ground load conditions of the tire.

[0008] Further, in step S2, a parameterized model of the tire carcass profile is constructed using Bézier curves. Using Abaqus software, with the tire carcass cords as the target, specific mesh nodes are selected for the cords and a node set is created. The discrete node coordinates of the tire carcass cord node set in the uninflated state of the two-dimensional finite element model are extracted. Key points of the profile are selected for region division. Finally, a fifth-order Bézier curve is selected to fit the tire carcass profile of each region and collinearity constraints are applied to achieve smooth segmentation and splicing of the tire carcass profile. This includes the following steps: S21. Use Abaqus software to create a set of tire carcass outline nodes, and extract the discrete node coordinates of the tire carcass cord layer in the two-dimensional finite element model of the tire, and remove nodes that are not easily changed near the tire bead. S22. Based on the curvature variation characteristics of the tire body contour, the highest point of the contour, the end point of the belt layer, the widest point of the contour, the end point of the tire body reverse wrapping, and the lowest point of the contour are used as key nodes to divide the tire body contour into four regions: including the tread region A, the upper side region B, the lower side region C, and the tire body reverse wrapping region D. The upper side region B and the lower side region C are selected as the contour design regions, and the other regions are used as reference regions for subsequent smooth splicing. S23. A fifth-order Bézier curve is used to fit the discrete nodes of each region. The fifth-order Bézier curve is expanded into the form of parametric equations as follows: (4) Each segment of a fifth-order Bézier curve has 6 control points, denoted as ( A 0 ,B 0 )to( A 5,B 5 By defining the collinearity constraint of the control points at the segment connection by making the cross product of three vectors equal to 0, the smooth splicing of multiple Bézier curves is achieved, ensuring the continuity of the curvature of the tire body contour. S24. By calculating the weighted sum of squares of the Euclidean distances from discrete nodes to the Bézier curves as the objective function, the coordinates of the control points of the Bézier curves in each region are obtained by iterative solution, forming a parametric model of the tire contour that can be characterized by the Bézier equation.

[0009] The collinearity constraint in S23 is achieved through the following mathematical expression: ,in( x 1, y 1) is the second to last control point of the previous area, ( x 3, y 3) is the second control point in the next area. x 2, y 2) This is the connection control point between the two areas.

[0010] In step S3, based on the three-dimensional finite element model of the tire under load conditions obtained in step S1, with the ground contact center section of the tire contact area as the target, SENER is selected in the Abaqus post-processing interface. The mesh only retains the area of ​​the tire shoulder near the end of the belt layer, and the maximum strain energy density at the end of the belt layer is obtained according to the contour map. SED max The value is negatively correlated with the tire's durability. The higher the value, the greater the deformation of the tire during contact with the ground, the more energy is stored in the deformation, and the more likely the tire will fail due to fatigue.

[0011] In step S4, local optimization design of the tire carcass contour is achieved based on orthogonal experiments. Control points with significant influence on the tire carcass contour shape within the design area are selected. The ordinates of these control points are used as design variables. The variation amplitudes of each design variable are set and determined to be at different levels. An orthogonal array is selected according to the orthogonal experimental design principles to determine the design scheme, and material distribution diagrams are drawn for each scheme. Following steps S1 and S3, finite element models of each scheme are established, and evaluation indicators are extracted. Range analysis is used to determine the primary and secondary influences of each design variable on the evaluation indicators. Based on the range analysis results, the optimal combination of design variables is initially obtained. Finally, the durability performance improvement effect of the optimal combination of design variables is verified using the finite element method. This includes the following steps: S41. By changing the control points, select the ordinate of the control points that have a greater impact on the shape of the tire body within the design area as the design variable, while keeping the abscissa of the control points fixed. Set the change amplitude of each design variable and determine it to be at different levels, while keeping the position of other control points fixed. S42. Select an orthogonal array to determine the design scheme according to the orthogonal experimental design principle. Draw the corresponding Bézier curve as the new tire carcass outline according to different design schemes. Draw the tire two-dimensional cross-sectional material distribution diagram of different tire carcass outlines using AutoCAD software. Adjust the shape and distribution of the tire carcass layer mesh in the two-dimensional finite element model of the tire according to the new cross-section. Establish the three-dimensional finite element model of the tire with different tire carcass outline schemes according to step S1. S43. Based on the finite element models of different schemes in S42 and the tire durability performance evaluation index in S3, obtain the maximum strain energy density at the end of the belt layer for each scheme. SED max Calculate the different levels of each design variable SED max The mean and range are used to determine the design variables. SED max The order of influence of the variables was determined, and the optimal combination of design variables was initially determined. S44. Draw the tire carcass outline based on the optimal combination of design variables and establish a finite element model for simulation calculation. SED max The durability improvement effect was verified by comparing the initial tire body structure design scheme.

[0012] In step S5, the global optimization design of the tire carcass profile design variables is achieved based on the GPR-MIGA algorithm. Using the orthogonal experimental scheme and the optimal combination of design variables determined in steps S42 and S43 as training samples, the design variables and target data are imported into MATLAB. A surrogate model is obtained through Gaussian process regression (GPR) training, and the generalization ability of the model is further verified. The model is then imported into Isight software for MATLAB-Isight joint optimization. The multi-island genetic algorithm (MIGA) in Isight is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and a finite element model of the global optimization design scheme is established through step S1; this includes the following steps: S51, with n The sample consists of a group of orthogonal experimental schemes plus a set of optimal combinations of tire carcass profile design variables. The input is the combination of the ordinates of the control points of the design variables, and the output is the corresponding... SED max Construct a sample dataset; S52. Construct the GPR proxy model, which is expressed in the following form: In the formula, It is Gaussian noise. For noise variance, f (x It follows a Gaussian process, determined by the mean function. m ( x and covariance function (kernel function) k ( x , x’ Defined as follows: In application, the sample dataset is divided into training and test sets in a 7:3 ratio, and the RBF radial basis function is selected as the kernel function, which is expressed as follows: in, Let be the signal variance, and Λ be a diagonal matrix whose diagonal elements are the squares of the length scale parameters of each dimension. Hyperparameters are automatically adjusted using Bayesian optimization. Finally, model training is completed by maximizing the marginal likelihood function. The expression for maximizing the marginal likelihood function is: in, X For input points, y The output value of the observation, I It is an identity matrix, and then the correlation coefficient is used. R 2 Verify the model's fitting accuracy and generalization ability; S53. Global optimization is achieved through the MIGA algorithm. The trained GPR surrogate model is imported into the Isight software. Parameters such as the range of design variables, subpopulation size, number of islands, generation number, crossover rate, and mutation rate for the MIGA algorithm are set. SED max Minimize the optimization objective and iteratively search for the optimal combination of control points to obtain the globally optimal combination of control points. S54. Predict the globally optimal combination of control points using the GPR surrogate model. SED max Based on step S1, a finite element model of the global optimization design scheme is established, and finite element analysis of it under load is carried out. In step S6, the finite element model of the global optimization design scheme established in step S54 is verified. SED max The optimization effect is compared with the result of the optimal combination of design variables in step S4. Finally, the changes in the mechanical properties of the tire carcass cord before and after optimization are compared to reveal the mechanical mechanism of improved durability. The optimization includes the following steps: S61. Perform simulation calculations based on step S3 to obtain the global optimized design scheme. SED max The results are then compared with the predictions from the GPR surrogate model in step S54 to further verify the effectiveness of the optimized model. S62, Optimize the global design scheme SED max The results were compared with those of the initial scheme and the scheme with the best combination of design variables to verify the feasibility of the global optimization method. S63. Perform tire carcass cord force analysis on the tire carcass layers. Perform post-processing in Abaqus software to extract the S11 stress of the tire carcass cord at the tire ground contact center section before and after optimization. Analyze the uniformity of cord force distribution and the changes in cord tension in key areas. Compare the mechanical property parameters before and after optimization, including the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, to explain the mechanical principles of the durability performance design.

[0013] The beneficial effects of this invention are as follows: Compared with the prior art, this invention establishes a finite element model of the tire under load and uses Bézier curves for regional splicing and fitting to obtain a parameterized model of the tire carcass profile with continuous curvature and smooth splicing. The profile shape can be flexibly modified by adjusting the coordinates of the control points to achieve the design of different tire carcass profiles. The end of the belt layer at the tire ground contact center section is extracted through simulation calculation. SED max As a durability performance evaluation index, it is used to evaluate the durability performance of tires with different designs; Using specified control points as design variables, an orthogonal experimental design was developed, and the optimal combination of tire carcass design variables was initially obtained through range analysis. The durability performance improvement effect of the optimal combination of design variables was verified using finite element analysis. A surrogate model was trained using Gaussian process regression with existing designs as training samples. Finally, a multi-island genetic optimization algorithm was used to globally optimize the design variable combination, yielding the minimum... SED max The optimization scheme was proposed, and the durability improvement effect of the global optimization scheme was verified by finite element method. The changes in the mechanical properties of tire carcass cords before and after optimization were compared, revealing the mechanical mechanism of durability improvement. This provides technical support for tire companies to develop tire products with improved durability and reduces R&D and testing costs. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a two-dimensional finite element model of a tire.

[0015] Figure 2 This is a schematic diagram of a three-dimensional finite element model of a tire.

[0016] Figure 3 This is a schematic diagram of the set of nodes representing the fetal body contour.

[0017] Figure 4 This is a schematic diagram showing the division of the fetal body outline area.

[0018] Figure 5 This is a schematic diagram of the parametric model of the fetal body contour.

[0019] Figure 6 This is a cloud map showing the maximum strain energy density at the end of the belt layer at the tire ground contact center section.

[0020] Figure 7 The maximum strain energy density cloud diagram at the end of the belt layer is the optimal combination of design variables.

[0021] Figure 8 This is a schematic diagram of a Gaussian process regression training model.

[0022] Figure 9 This is a schematic diagram of the iterative process of the multi-island genetic algorithm.

[0023] Figure 10 The maximum strain energy density cloud map at the end of the belt layer in the global optimization design scheme.

[0024] Figure 11 To optimize the stress of the tire cord S11 at the front tire contact center section.

[0025] Figure 12 To optimize the stress of the tire cord S11 at the rear tire ground contact center section.

[0026] Wherein 1-the set of fetal body contour nodes, 2-the end point of the belt layer, 3-the widest point of the contour, and 4-the end point of the fetal body reverse wrapping. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0028] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same technical meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0029] A method for designing tire carcass profile structure to improve tire durability includes the following steps: S1. Establishment of tire finite element model: A two-dimensional finite element model of the tire is established by using the tire material distribution map, and a corresponding three-dimensional finite element model is established with reference to the tire rated air pressure and rated load. S2. Construction of a parameterized tire carcass profile model based on Bézier curve theory: Based on the two-dimensional finite element model of the tire in step S1, the discrete node coordinates of the tire carcass cord layer in the two-dimensional uninflated state are extracted. Combining the stress characteristics of the tire carcass profile, five locations are selected as key nodes: the highest point of the tire carcass profile, the end point of the belt layer, the widest point of the tire carcass profile, the end point of the tire carcass reverse wrapping, and the lowest point of the profile. Based on the key nodes, the tire carcass profile is divided into four regions with half of the tire carcass profile as the target. Bézier curves are used to fit each region piecewise. The parametric equation of the Bézier curve is: in, Q ( t ( ) represents the coordinates of each point on the Bézier curve. P k To control the polygon's first k One vertex, n This represents the number of control points for the Bézier curve. B k,n ( t ) are Bernstein basis functions, defined as follows: By applying collinear constraints to the control points at the connection points, smooth segmentation and splicing of the contour are achieved, resulting in the parametric mathematical equations of the tire body contour for each region. Collinearity constraints are achieved by ensuring that the cross product of three vectors is zero. in,( x 1, y 1) is the second to last control point of the previous area, ( x 3, y 3) is the second control point in the next area. x 2, y 2) As the connection control points between the two regions, the coordinates of the control points of the Bézier curve in each region are obtained by iteratively solving the weighted sum of squared Euclidean distances from discrete nodes to the Bézier curve as the objective function, thus obtaining a parameterized model representing the tire body contour. S3. Extraction of tire durability performance evaluation indicators: Based on the three-dimensional finite element model of the tire under load conditions in step S1, the cross-section at the ground contact center of the tire contact area is selected as the object, and the maximum strain energy density at the end of the belt layer in this cross-section is extracted. SED max To represent the cumulative rate of tire fatigue damage, and by comparing the maximum strain energy density SED max The values ​​are used to evaluate the tire durability and the quality of the tire profile design using a negative correlation method. S4. Tire carcass profile design based on orthogonal experiment: Based on the parameterized model of the tire carcass profile in step S2, considering the specification requirements of the tire production mold, and ensuring that the outermost geometric structure and parameters of the tire remain unchanged, only the ordinate of the control points of the Bezier curve in the sidewall area is selected as the design variable to specify the orthogonal experiment scheme. For the design scheme generated by the orthogonal experiment, the material distribution diagrams of different tire carcass profile schemes are drawn, and the finite element models of different design schemes are established according to step S1. According to step S3, the tire durability performance evaluation index is extracted, and the order of influence of each design variable on the evaluation index is determined by range analysis. The optimal combination of design variables is initially obtained, and the durability performance improvement effect of the tire carcass profile scheme corresponding to the optimal combination of design variables is verified again through steps S2 and S3. S5. Global Optimization Design of Tire Carcass Contour Variables Based on GPR-MIGA Algorithm: Addressing the challenge of efficiently optimizing contour structure parameters due to the large number of design variables, a Gaussian Process Regression (GPR) model is selected as a surrogate model. This model can learn nonlinear mappings from small-scale samples, providing prediction confidence intervals and solving the problem of limited sample size and high time consumption in single finite element simulations. The model is trained using orthogonal experimental schemes and optimal combinations of design variables, and its generalization ability is verified. Based on this, a multi-island genetic algorithm (MIGA) is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and the tire finite element model corresponding to the globally optimized design scheme is established through the process of step S1. S6. Optimization Scheme Mechanical Mechanism Analysis and Verification: Based on the finite element model of the global optimization design scheme established in step S5, the mechanical mechanism of the optimized scheme is verified. SED max The optimization effect was investigated, and the changes in the mechanical property parameters of the tire carcass cords before and after optimization were compared. The mechanical property parameters include the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, in order to reveal the mechanical mechanism of the improved durability.

[0030] In step S1, a finite element simulation model of the tire is established. The two-dimensional cross-section of the tire is imported into HYPERMESH software for mesh generation. Then, using uniaxial tensile test data of rubber for various tire components, different hyperelastic constitutive models are selected for fitting to obtain material parameters, which are then assigned to each tire component. Finally, by applying inflation pressure and load, a three-dimensional finite element model of the tire under load conditions is established. This includes the following steps: S11. Use AutoCAD software to draw a two-dimensional cross-sectional material distribution diagram of the tire. S12. Import the drawn two-dimensional tire cross-section into HYPERMESH software for mesh generation. Use CGAX3H and CGAX4H elements for rubber material and SFMGAX1 elements for cord material through rebar reinforcing rib element model to generate a two-dimensional finite element model of the tire. S13. Based on the uniaxial tensile test data of rubber, Neo-Hookean, Yeoh, Mooney-Rivlin (N=1), and Mooney-Rivlin (N=2) hyperelastic constitutive models were selected for fitting. The model that balances fitting accuracy and model stability was selected as the constitutive model of the rubber material, and the material parameters of each rubber component were obtained. S14. Using the *SYMMETRIC MODEL GENERATION,REVOLVE command, rotate the two-dimensional model 360° to generate a three-dimensional finite element model. Define the rim and road surface as analytical rigid bodies, and apply tire boundary conditions including inflation pressure and ground load to simulate the actual ground load conditions of the tire.

[0031] In step S2, a parameterized model of the tire carcass contour is constructed using Bézier curves. Abaqus software is used, with the tire carcass cords as the target, specific mesh nodes are selected for the cords, and a node set is created. The discrete node coordinates of the tire carcass cord node set in the uninflated state of the two-dimensional finite element model are extracted. Key contour points are selected for region division. Finally, a fifth-order Bézier curve is selected to fit the tire carcass contour of each region and collinearity constraints are applied to achieve smooth segmentation and splicing of the tire carcass contour. The steps include: S21. Use Abaqus software to create a set of tire carcass outline nodes, and extract the discrete node coordinates of the tire carcass cord layer in the two-dimensional finite element model of the tire, and remove nodes that are not easily changed near the tire bead. S22. Based on the curvature variation characteristics of the tire body contour, the highest point of the contour, the end point of the belt layer, the widest point of the contour, the end point of the tire body reverse wrapping, and the lowest point of the contour are used as key nodes to divide the tire body contour into four regions (including tread region A, upper sidewall region B, lower sidewall region C, and tire body reverse wrapping region D). The upper sidewall region B and the lower sidewall region C are selected as the contour design regions, and the other regions are used as reference regions for subsequent smooth splicing. S23. A fifth-order Bézier curve is used to fit the discrete nodes of each region. The fifth-order Bézier curve is expanded into the form of parametric equations as follows: Each segment of a fifth-order Bézier curve has 6 control points, denoted as ( A 0, B 0) to ( A 5, B5) By defining the collinearity constraint of the control points at the segment connection by making the cross product of three vectors equal to 0, the smooth splicing of multiple Bézier curves is achieved, ensuring the continuity of the curvature of the tire body contour. S24. By calculating the weighted sum of squares of the Euclidean distances from discrete nodes to the Bézier curves as the objective function, the coordinates of the control points of the Bézier curves in each region are obtained by iterative solution, forming a parametric model of the tire contour that can be characterized by the Bézier equation.

[0032] It is important to emphasize that this invention uses Bézier curves to fit the tire carcass profile piecewise, and introduces a collinearity constraint method where the cross product of three vectors is zero to achieve smooth piecewise splicing. The shape is globally determined by the control points of the Bézier curve, making adjustments intuitive and ensuring high-order continuity within each segment. The collinearity constraint forces the control points of adjacent curve segments to be collinear at the connection point, thus ensuring tangential continuity (G1 continuity). This avoids common geometric cusps or abrupt tangent changes during the fitting process, and is a key technical means to ensure a smooth tire carcass profile and eliminate local stress concentrations.

[0033] In step S3, based on the three-dimensional finite element model of the tire under load conditions obtained in step S1, with the ground contact center section of the tire contact area as the target, SENER is selected in the Abaqus post-processing interface. The mesh only retains the area of ​​the tire shoulder near the end of the belt layer, and the maximum strain energy density at the end of the belt layer is obtained according to the contour map. SED max This value indicates the quality of tire durability. The higher the value, the greater the deformation of the tire during contact with the ground, the more energy is stored in the deformation, and the more likely the tire will fail due to fatigue.

[0034] In step S4, local optimization design of the tire carcass contour is achieved based on orthogonal experiments. Control points with significant influence on the tire carcass contour shape within the design area are selected. The ordinates of these control points are used as design variables. The variation amplitudes of each design variable are set and determined to be at different levels. An orthogonal array is selected according to the orthogonal experimental design principles to determine the design scheme, and material distribution diagrams are drawn. Following steps S1 and S3, finite element models of each scheme are established, and evaluation indicators are extracted. Range analysis is used to determine the primary and secondary influences of each design variable on the evaluation indicators. Based on the range analysis results, the optimal combination of design variables is initially obtained. Finally, the durability performance improvement effect of the optimal combination of design variables is verified using the finite element method. This includes the following steps: S41. By changing the control points, select the vertical coordinates of the control points that have a greater impact on the shape of the tire body within the design area as the design variables, while keeping the horizontal coordinates of the control points fixed. Set the variation range of the design variables to -10mm, 0mm, and 10mm, and determine them as horizontal 1, 2, and 3 respectively. Keep the positions of other control points fixed. S42. Select an orthogonal array to determine the design scheme according to the orthogonal experimental design principle. Draw the corresponding Bézier curve as the new tire carcass outline according to different design schemes. Draw the tire two-dimensional cross-sectional material distribution diagram of different tire carcass outlines using AutoCAD software. Adjust the shape and distribution of the tire carcass layer mesh in the two-dimensional finite element model of the tire according to the new cross-section. Establish the three-dimensional finite element model of the tire with different tire carcass outline schemes according to step S1. S43. Based on the finite element models of different schemes in S42 and the tire durability performance evaluation index in S3, obtain the maximum strain energy density at the end of the belt layer for each scheme. SED max Calculate the different levels of each design variable SED max The mean and range are used to determine the design variables. SED max The order of influence of the variables was determined, and the optimal combination of design variables was initially determined. S44. Draw the tire carcass outline based on the optimal combination of design variables and establish a finite element model for simulation calculation. SED max The durability improvement effect was verified by comparing the initial tire body structure design scheme.

[0035] In step S5, the global optimization design of the tire carcass profile design variables is achieved based on the GPR-MIGA algorithm. Using the orthogonal experimental scheme and the optimal combination of design variables determined in steps S42 and S43 as training samples, the design variables and target data are imported into MATLAB. A surrogate model is obtained through Gaussian process regression (GPR) training, and the generalization ability of the model is further verified. The model is then imported into Isight software for MATLAB-Isight joint optimization. The multi-island genetic algorithm (MIGA) in Isight is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and a finite element model of the global optimization design scheme is established through step S1; this includes the following steps: S51, with n The sample consists of a group of orthogonal experimental schemes plus a set of optimal combinations of tire carcass profile design variables. The input is the combination of the ordinates of the control points of the design variables, and the output is the corresponding... SED max Construct a sample dataset; S52. Construct the GPR proxy model, which is expressed in the following form: In the formula, It is Gaussian noise. For noise variance, f (x It follows a Gaussian process, determined by the mean function. m ( x and covariance function (kernel function) k ( x , x’ Defined as follows: In application, the sample dataset is divided into training and test sets in a 7:3 ratio, and the RBF radial basis function is selected as the kernel function, which is expressed as follows: in, Let be the signal variance, and Λ be a diagonal matrix whose diagonal elements are the squares of the length scale parameters of each dimension. Hyperparameters are automatically adjusted using Bayesian optimization. Finally, model training is completed by maximizing the marginal likelihood function. The expression for maximizing the marginal likelihood function is: in, X For input points, y The output value of the observation, I It is an identity matrix, and then the correlation coefficient is used. R 2 Verify the model's fitting accuracy and generalization ability; S53. Global optimization is achieved through the MIGA algorithm. The trained GPR surrogate model is imported into the Isight software. Parameters such as the range of design variables, subpopulation size, number of islands, generation number, crossover rate, and mutation rate for the MIGA algorithm are set. SED max Minimize the optimization objective and iteratively search for the optimal combination of control points to obtain the globally optimal combination of control points. S54. Predict the globally optimal combination of control points using the GPR surrogate model. SED max Based on step S1, a finite element model of the global optimization design scheme is established, and finite element analysis of it under load is carried out. In step S6, the finite element model of the global optimization design scheme established in step S54 is verified. SED max The optimization effect is compared with the result of the optimal combination of design variables in step S4. Finally, the changes in the mechanical properties of the tire carcass cord before and after optimization are compared to reveal the mechanical mechanism of improved durability. The optimization includes the following steps: S61. Perform simulation calculations based on step S3 to obtain the global optimized design scheme. SED max The results are then compared with the predictions from the GPR surrogate model in step S54 to further verify the effectiveness of the optimized model. S62, Optimize the global design scheme SED max The results were compared with those of the initial scheme and the scheme with the best combination of design variables to verify the feasibility of the global optimization method. S63. Perform tire carcass cord force analysis on the tire carcass layers. Perform post-processing in Abaqus software to extract the S11 stress of the tire carcass cord at the tire ground contact center section before and after optimization. Analyze the uniformity of cord force distribution and the changes in cord tension in key areas. Compare the mechanical property parameters before and after optimization, including the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, to explain the mechanical principles of the durability performance design.

[0036] The present invention will now be described in detail using the 12R22.5 all-steel radial truck tire as a specific embodiment. It should be noted that this embodiment is only used to further illustrate the present invention and should not be construed as a limitation on the scope of protection of the present invention. Those skilled in the art can make some non-essential improvements and adjustments based on the above content of the present invention.

[0037] This invention provides a tire carcass profile structure design method to improve tire durability, the method comprising the following steps: S1. Establishment of tire finite element model: Discretize the two-dimensional cross-sectional material distribution map of the tire into finite element mesh elements, and then use the uniaxial tensile test data of rubber of various tire components to select different hyperelastic constitutive models for fitting to obtain the material parameters, and assign them to various tire components. Then, by applying inflation pressure and load, establish a three-dimensional finite element model of the tire under load conditions. First, AutoCAD software is used to draw a two-dimensional cross-sectional material distribution diagram of the tire. The drawn two-dimensional tire cross-section is then imported into Hypermesh software for mesh generation. CGAX3H and CGAX4H elements are used for the rubber material, and SFMGAX1 elements are used for the cord material, which is modeled using rebar reinforcing elements. This generates a two-dimensional finite element model of the tire. Figure 1As shown, the model has 3536 nodes and 3314 elements. Secondly, based on the uniaxial tensile test data of rubber, Neo-Hookean, Yeoh, Mooney-Rivlin (N=1), and Mooney-Rivlin (N=2) hyperelastic constitutive models were selected for fitting. Considering the model stability under large strain conditions of heavy-duty tires, the Mooney-Rivlin (N=1) constitutive model was finally selected, and the material parameters of each rubber component were obtained, as shown in Table 1. Finally, the two-dimensional model was rotated 360° using the *SYMMETRIC MODEL GENERATION,REVOLVE command to generate a three-dimensional finite element model. The rim and road surface were defined as analytical rigid bodies, and tire boundary conditions including an actual inflation pressure of 0.91 MPa and a ground load of 34790 N were applied to simulate the actual ground load condition of the tire. The resulting three-dimensional finite element model of the tire is shown in Table 1. Figure 2 As shown.

[0038] Table 1 Material parameters of tire rubber components S2. Construction of a parameterized tire carcass profile model based on Bézier curve theory: Based on the two-dimensional finite element model of the tire in step S1, the discrete node coordinates of the tire carcass cord layer in the two-dimensional uninflated state are extracted. Combining the stress characteristics of the tire carcass profile, five locations are selected as key nodes: the highest point of the tire carcass profile, the end point of the belt layer, the widest point of the tire carcass profile, the end point of the tire carcass reverse wrapping, and the lowest point of the profile. Based on the key nodes, the tire carcass profile is divided into four regions with half of the tire carcass profile as the target. Bézier curves are used to fit each region piecewise. The parametric equation of the Bézier curve is: in, Q ( t ( ) represents the coordinates of each point on the Bézier curve. P k To control the polygon's first k One vertex, n This represents the number of control points for the Bézier curve. B k,n ( t ) are Bernstein basis functions, defined as follows: By applying collinear constraints to the control points at the connection points, smooth segmentation and splicing of the contour are achieved, resulting in the parametric mathematical equations of the tire body contour for each region. Collinearity constraints are achieved by ensuring that the cross product of three vectors is zero. in,( x 1, y1) is the second to last control point of the previous area, ( x 3, y 3) is the second control point in the next area. x 2, y 2) As the connection control points between the two regions, the coordinates of the control points of the Bézier curve in each region are obtained by iteratively solving the weighted sum of squared Euclidean distances from discrete nodes to the Bézier curve as the objective function, thus obtaining a parameterized model representing the tire body contour. Specifically, Abaqus software was used to create a tire carcass outline node set 1, and the discrete node coordinates of the tire carcass cord layers in the two-dimensional finite element model of the tire were extracted. Nodes that were not easily changed near the bead were removed, and the resulting tire carcass outline node set is shown below. Figure 3 As shown; based on the curvature variation characteristics of the tire carcass, using the highest point of the contour, the end point of the belt layer 2, the widest point of the contour 3, the end point of the carcass reverse wrapping 4, and the lowest point of the contour as key nodes, the tire carcass contour is divided into four regions (including tread region A, upper sidewall region B, lower sidewall region C, and carcass reverse wrapping region D), as shown. Figure 4 As shown, the upper tire side region B and the lower tire side region C are selected as the contour design areas, and other regions are used as reference areas for subsequent smooth splicing. A fifth-order Bézier curve is used to fit the discrete nodes of each region. The fifth-order Bézier curve is expanded into a parametric equation as follows: Each segment of a fifth-order Bézier curve has 6 control points, denoted as ( A 0, B 0) to ( A 5, B 5) By defining the collinearity constraint of control points at the segmented connection points through a three-point vector cross product of 0, smooth splicing of multiple Bézier curves is achieved, ensuring the continuity of the tire carcass curvature. The coordinates of the control points of the Bézier curves in each region are obtained iteratively by calculating the weighted sum of squared Euclidean distances from discrete nodes to the Bézier curves as the objective function, forming a parameterized model of the tire carcass contour that can be characterized by the Bézier equation, such as... Figure 5 As shown in Table 2, the final coordinates of the four fitting control points are as follows.

[0039] Table 2 Coordinates of control points for four segments of fifth-order Bézier curves

[0040] S3. Extraction of tire durability performance evaluation indicators: Based on the three-dimensional finite element model of the tire under load conditions obtained in step S1, the cross-section at the center of the tire contact patch is selected as the object, and the maximum strain energy density at the end of the belt layer within this cross-section is extracted. SED max To represent the cumulative rate of tire fatigue damage, and by comparing the maximum strain energy density SEDmax The values ​​are used to evaluate tire durability and the quality of tire profile design using a negative correlation method. The maximum strain energy density cloud diagram at the tire contact center section of the belt layer end is shown in the figure. Figure 6 As shown, the original scheme is obtained. SED max It is 0.1308 mJ / mm 3 ; S4. Tire carcass profile design based on orthogonal experiment: Based on the parameterized model of the tire carcass profile in step S2, considering the specification requirements of the tire production mold, and ensuring that the outermost geometric structure and parameters of the tire remain unchanged, only the ordinate of the control points of the Bezier curve in the sidewall area is selected as the design variable to specify the orthogonal experiment scheme. For the design scheme generated by the orthogonal experiment, the material distribution diagrams of different tire carcass profile schemes are drawn, and the finite element models of different design schemes are established according to step S1. According to step S3, the tire durability performance evaluation index is extracted, and the order of influence of each design variable on the evaluation index is determined by range analysis. The optimal combination of design variables is initially obtained, and the durability performance improvement effect of the tire carcass profile scheme corresponding to the optimal combination of design variables is verified again through steps S2 and S3. Specifically, firstly, by changing the control points, the ordinates of the control points within the design area that have a significant impact on the tire body contour shape are selected as design variables; here, region two is chosen. P 2 , P 4 and Region 3 P 1 ,、 P 3 The vertical coordinate of the control points is fixed, while the horizontal coordinate of the control points remains unchanged. The variation range of the design variables is set to -10mm, 0mm, and 10mm, which are respectively determined as horizontal 1, 2, and 3. The positions of other control points are fixed and do not change. Secondly, the orthogonal array is selected according to the orthogonal experimental design principle to determine the design scheme, as shown in Table 3. The corresponding Bézier curves are drawn as the new tire carcass outline according to different design schemes. The two-dimensional cross-sectional material distribution diagram of the tire with different tire carcass outlines is drawn using AutoCAD software. The shape and distribution of the tire carcass layer mesh in the two-dimensional finite element model of the tire are adjusted according to the new cross-section. The three-dimensional finite element model of the tire with different tire carcass outline schemes is established according to step S1. Table 3 L9(34) orthogonal array

[0041] Based on the finite element models of different schemes and the tire durability performance evaluation index of S3, the maximum strain energy density at the end of the belt layer of each scheme was obtained. SED max Calculate the different levels of each design variable SEDmax The mean and range of the values ​​are shown in Table 4. The results of the range analysis are used to determine the impact of the design variables. SED max The order of influence was determined, and the optimal combination of design variables was initially identified as A2B1C3D2. Finally, based on the optimal combination of design variables, the tire carcass outline was drawn and a finite element model was established for simulation calculation. SED max The durability improvement effect was verified by comparing the initial tire carcass structure design scheme. The maximum strain energy density cloud diagram at the end of the belt layer of the optimal combination of design variables is shown in the figure. Figure 7 As shown, the optimal combination of design variables can be obtained. SED max It is 0.1216 mJ / mm 3 This represents a 7.03% reduction compared to the original design, indicating an improvement in durability.

[0042] Table 4 Range Analysis of Orthogonal Experiments

[0043] S5. Global Optimization Design of Tire Body Contour Variables Based on GPR-MIGA Algorithm: Since the sample size is only 10, the Gaussian Process Regression (GPR) model, as a classic surrogate model suitable for learning nonlinear mappings from small-scale samples and providing prediction confidence intervals, can solve scenarios with small sample sizes and high time consumption in a single finite element simulation. The model is trained on the training samples, and its generalization ability is verified. Based on this, the Multi-Island Genetic Algorithm (MIGA) is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and the tire finite element model corresponding to the globally optimized design scheme is established through the process of step S1. Specifically, the sample consists of nine orthogonal experimental schemes plus one optimal combination of tire carcass profile design variables. The input is the combination of the ordinates of the control points of the design variables, and the output is the corresponding... SED max First, construct a sample dataset; then, construct a GPR proxy model using MATLAB, whose expression is as follows: In the formula, It is Gaussian noise. For noise variance, f ( x It follows a Gaussian process, determined by the mean function. m ( x and covariance function (kernel function) k ( x , x’Defined as follows: In application, the sample dataset is divided into training and test sets in a 7:3 ratio, and the RBF radial basis function is selected as the kernel function, which is expressed as follows: in, Let be the signal variance, and Λ be a diagonal matrix whose diagonal elements are the squares of the length scale parameters of each dimension. Hyperparameters are automatically adjusted using Bayesian optimization. Finally, model training is completed by maximizing the marginal likelihood function. The expression for maximizing the marginal likelihood function is: in, X For input points, y The output value of the observation, I It is an identity matrix, and then the correlation coefficient is used. R 2 The model's fitting accuracy and generalization ability were verified, and the final hyperparameter results are as follows: =1.48×10 -4 , =1.04×10 -4 The length scales are 13.19, 26.13, and 2.37 × 10⁻⁶, respectively. 5 4.3×10 5 0.09×10 5 The training was completed through 30 iterations, and the trained model results are as follows: Figure 8 As shown, for the training set R 2 =0.99, the test set R 2 =0.95, indicating good generalization ability; Next, global optimization is achieved using the MIGA algorithm. The trained GPR surrogate model is then imported into the Isight software, and the range of values ​​for the design variables is set. y 1 The diameter is 490mm-510mm. y 2 The diameter is 426.5 mm to 446.5 mm. y 3 The diameter is 394.3mm-414.3mm. y 4 The range is 340mm-360mm. The MIGA algorithm has a subpopulation size of 10, an island count of 10, a generation count of 10, a crossover rate of 1.0, a mutation rate of 0.01, a migration rate of 0.01, a migration interval of 5, an optimal number of individuals per evolution of 1, a penalty function cardinality of 0, a penalty function multiplier of 1000, and a penalty function exponent of 2.SED max The optimization objective is to minimize the value of the target value through iterative optimization. After 1001 iterations, the globally optimal combination of control points is found after the 946th iteration, as follows: Figure 9 As shown; finally, the global optimal control point combination is predicted using the GPR surrogate model. SED max It is 0.1198 mJ / mm 3 Based on step S1, a finite element model of the global optimization design scheme is established, and finite element analysis of it under load is carried out. S6. Optimization Scheme Mechanical Mechanism Analysis and Verification: Based on the finite element model of the global optimization design scheme established in step S5, the mechanical mechanism of the optimized scheme is verified. SED max The optimization effect was investigated, and the changes in the mechanical property parameters of the tire carcass cords before and after optimization were compared. The mechanical property parameters include the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, in order to reveal the mechanical mechanism of the improved durability.

[0044] Specifically, simulation calculations are performed based on step S3 to obtain the globally optimized design scheme. SED max It is 0.1205 mJ / mm 3 The error between the prediction results and those of the GPR surrogate model was 0.58%, further validating the effectiveness of the optimization model; simultaneously, the global optimization design scheme was... SED max The results of the global optimization design scheme are compared with those of the initial scheme and the optimal combination of design variables. The maximum strain energy density cloud map at the end of the belt layer is shown in the figure below. Figure 10 As shown, the optimized SED max Compared to the original scheme, the performance was reduced by 7.87%, and compared to the orthogonal test scheme, the tire durability performance was further reduced, verifying the feasibility of the method. Finally, tire carcass cord force analysis was performed on the tire carcass layers, and post-processing was carried out in Abaqus software to extract and optimize the S11 stress of the tire carcass cords at the tire contact center section before and after the test. Figure 11 and Figure 12 As shown, the optimized tire carcass cord force distribution is more uniform, the maximum tension in the bead area is reduced from 204.1923 MPa to 195.0111 MPa, a reduction of about 4.71%, and the minimum tension in the tread area is increased from 67.8168 to 68.0122, an increase of about 0.29%, which alleviates the stress concentration in the cords and thus improves the tire's durability.

[0045] The final global optimization results conclude that this invention provides a tire carcass profile design method to improve tire durability. Through complete parametric modeling and global optimization of the 12R22.5 all-steel radial truck tire carcass profile, the final... SED max Compared to the original solution, the cost was reduced by 7.87%, and the optimized design results were better, providing tire R&D personnel with a new method for product design based on tire performance.

[0046] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several changes and improvements without departing from the overall concept of the present invention, and these should also be considered within the scope of protection of the present invention.

Claims

1. A method of designing a carcass profile structure for improving the durability of a tire, characterized in that: Includes the following steps: S1. Establishment of tire finite element model: A two-dimensional finite element model of the tire is established by using the tire material distribution map, and a corresponding three-dimensional finite element model is established with reference to the tire rated air pressure and rated load. S2. Construction of a parameterized tire carcass profile model based on Bézier curve theory: Based on the two-dimensional finite element model of the tire in step S1, the discrete node coordinates of the tire carcass cord layer in the two-dimensional uninflated state are extracted. Combining the stress characteristics of the tire carcass profile, five positions are selected as key nodes: the highest point of the tire carcass profile, the end point of the belt layer, the widest point of the tire carcass profile, the end point of the tire carcass reverse wrapping, and the lowest point of the profile. Based on the key nodes, the tire carcass profile is divided into four regions with half of the tire carcass profile as the target. Bézier curves are used to fit each region piecewise. By applying collinear constraints to the control points at the connection points of the Bézier curves of adjacent regions, the profile segments are smoothly spliced. The parameterized mathematical equations of the tire carcass profile of the above four regions are obtained. Finally, the coordinates of the control points of the Bézier curves in each region are obtained by iteratively solving the weighted sum of squared Euclidean distances from the discrete nodes to the Bézier curves as the objective function, and the parameterized model representing the tire carcass profile is obtained. S3, tire durability performance evaluation index extraction: based on the three-dimensional finite element model of the tire under the load condition in step S1, selecting the ground contact center section of the tire contact area as the object, extracting the maximum strain energy density of the belt end part in the section SED max to represent the cumulative rate of tire fatigue damage, and by comparing the numerical value of the maximum strain energy density SED max , the negative correlation is used to evaluate the tire durability life and the advantages and disadvantages of the tire body contour design scheme. S4. Tire carcass profile design based on orthogonal experiment: Based on the parameterized model of the tire carcass profile in step S2, considering the specification requirements of the tire production mold, and ensuring that the outermost geometric structure and parameters of the tire remain unchanged, only the ordinate of the control points of the Bezier curve in the sidewall area is selected as the design variable to specify the orthogonal experiment scheme. For the design scheme generated by the orthogonal experiment, the material distribution diagrams of different tire carcass profile schemes are drawn, and the finite element models of different design schemes are established according to step S1. According to step S3, the tire durability performance evaluation index is extracted. The order of influence of each design variable on the durability performance evaluation index is determined by range analysis, and the optimal combination of design variables is initially obtained. The durability performance improvement effect of the tire carcass profile scheme corresponding to the optimal combination of design variables is verified again through steps S2 and S3. S5. Global Optimization Design of Small-Sample Tire Carcass Design Variables Based on GPR-MIGA Algorithm: Addressing the challenge of efficiently optimizing contour structure parameters due to the large number of tire carcass design variables, a Gaussian Process Regression (GPR) model is selected as a surrogate model. This model can learn nonlinear mappings from small-scale samples, providing prediction confidence intervals. The model is trained using orthogonal experimental schemes and optimal combinations of design variables as training samples, and its generalization ability is verified. Based on this, the Multi-Island Genetic Algorithm (MIGA) is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and the tire finite element model corresponding to the globally optimized design scheme is established through the process of step S1. S6. Optimization Scheme Mechanical Mechanism Analysis and Verification: Verification based on the finite element model of the global optimization design scheme established in step S5. SED max The optimization effect was investigated, and the changes in the mechanical property parameters of the tire carcass cords before and after optimization were compared. The mechanical property parameters include the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, in order to reveal the mechanical mechanism of the improved durability.

2. The tire carcass profile structure design method for improving tire durability according to claim 1, characterized in that: In step S1, a finite element simulation model of the tire is established. The two-dimensional cross-section of the tire is imported into HYPERMESH software for mesh generation. Then, using uniaxial tensile test data of rubber for various tire components, different hyperelastic constitutive models are selected for fitting to obtain material parameters, which are then assigned to each tire component. Finally, by applying inflation pressure and load, a three-dimensional finite element model of the tire under load conditions is established. This includes the following steps: S11. Use AutoCAD software to draw a two-dimensional cross-sectional material distribution diagram of the tire. S12. Import the drawn two-dimensional tire cross-section into HYPERMESH software for mesh generation. Use CGAX3H and CGAX4H elements for rubber material and SFMGAX1 elements for cord material through rebar reinforcing rib element model to generate a two-dimensional finite element model of the tire. S13. Based on the uniaxial tensile test data of rubber, Neo-Hookean, Yeoh, Mooney-Rivlin (N=1), and Mooney-Rivlin (N=2) hyperelastic constitutive models were selected for fitting. The model that balances fitting accuracy and model stability was selected as the constitutive model of the rubber material, and the material parameters of each rubber component were obtained. S14. Using the *SYMMETRIC MODEL GENERATION,REVOLVE command, rotate the two-dimensional model 360° to generate a three-dimensional finite element model. Define the rim and road surface as analytical rigid bodies, and apply tire boundary conditions including inflation pressure and ground load to simulate the actual ground load conditions of the tire.

3. The tire carcass profile structure design method for improving tire durability according to claim 1, characterized in that: In step S2, a parameterized model of the tire carcass profile is constructed using Bézier curves. Abaqus software is used, with the tire carcass cords as the target, specific mesh nodes are selected for the cords, and a node set is created. The discrete node coordinates of the tire carcass cord node set in the uninflated state of the two-dimensional finite element model are extracted. Key points of the tire carcass profile are selected for region division. Finally, a fifth-order Bézier curve is selected to fit the tire carcass profile of each region and collinearity constraints are applied to achieve smooth segmentation and splicing of the tire carcass profile. The steps include: S21. Use Abaqus software to create a set of tire carcass outline nodes, and extract the discrete node coordinates of the tire carcass cord layer in the two-dimensional finite element model of the tire, and remove nodes that are not easily changed near the tire bead. S22. Based on the curvature variation characteristics of the tire body contour, five key points are identified: the highest point of the tire body contour, the end point of the belt layer, the widest point of the contour, the end point of the tire body reverse wrapping, and the lowest point of the contour. The tire body contour is divided into four regions: the tread region A, the upper sidewall region B, the lower sidewall region C, and the tire body reverse wrapping region D. The upper sidewall region B and the lower sidewall region C are selected as the contour design regions, and the other regions are used as reference regions for subsequent smooth splicing. S23. A fifth-order Bézier curve is used to fit the discrete nodes of each region. The fifth-order Bézier curve is expanded into the form of parametric equations as follows: (4) Each segment of a fifth-order Bézier curve has 6 control points, denoted as ( A 0 ,B 0 )to( A 5 ,B 5 By defining the collinearity constraint of the control points at the segment connection by making the cross product of three vectors equal to 0, the smooth splicing of multiple Bézier curves is achieved, ensuring the continuity of the curvature of the tire body contour. S24. By calculating the weighted sum of squares of the Euclidean distances from discrete nodes to the Bézier curves as the objective function, the coordinates of the control points of the Bézier curves in each region are obtained by iterative solution, forming a parametric model of the tire contour that can be characterized by the Bézier equation.

4. The tire carcass profile structure design method for improving tire durability according to claim 3, characterized in that: The collinearity constraint in S23 is achieved through the following mathematical expression: ,in( x 1, y 1) is the second to last control point of the previous area, ( x 3, y 3) is the second control point in the next area. x 2, y 2) This is the connection control point between the two areas.

5. The tire carcass profile structure design method for improving tire durability according to claim 1, characterized in that: In step S3, based on the three-dimensional finite element model of the tire under load conditions obtained in step S1, and taking the ground contact center section of the tire contact area as the target, the maximum strain energy density at the end of the belt layer is obtained in the Abaqus post-processing interface. SED max The value is negatively correlated with the tire's durability. In other words, the higher the value, the greater the deformation of the tire during contact with the ground, the more energy is stored in the deformation, and the more likely the tire will fail due to fatigue.

6. The tire carcass profile structure design method for improving tire durability according to claim 1, characterized in that: In step S4, the optimal local design of the tire carcass contour is achieved based on orthogonal experiments. Control points with significant influence on the tire carcass contour shape within the design area are selected. The ordinates of these control points are used as design variables. The variation amplitudes of each design variable are set and determined to be at different levels. An orthogonal array is selected according to the orthogonal experimental design principles to determine the design scheme, and material distribution diagrams are drawn for each scheme. Following steps S1 and S3, finite element models of each scheme are established, and evaluation indicators are extracted. Range analysis is used to determine the primary and secondary influences of each design variable on the evaluation indicators. Based on the range analysis results, the optimal combination of design variables is initially obtained. Finally, the durability performance improvement effect of the optimal combination of design variables is verified using the finite element method. This includes the following steps: S41. Considering the specification requirements of tire production molds, under the premise of ensuring that the outermost geometric structure and parameters of the tire remain unchanged, only the vertical coordinates of the control points that have a greater impact on the tire body contour shape within the design area are selected as design variables, while the horizontal coordinates of the control points remain unchanged. The variation amplitude of each design variable is set and determined to be at different levels, while the positions of other control points are fixed and unchanged. S42. Select an orthogonal array to determine the design scheme according to the orthogonal experimental design principle. Draw the corresponding Bézier curve as the new tire carcass outline according to different design schemes. Draw the tire two-dimensional cross-sectional material distribution diagram of different tire carcass outlines using AutoCAD software. Adjust the shape and distribution of the tire carcass layer mesh in the two-dimensional finite element model of the tire according to the new cross-section. Establish the three-dimensional finite element model of the tire with different tire carcass outline schemes according to step S1. S43. Based on the finite element models of different schemes in S42 and the tire durability performance evaluation index in S3, obtain the maximum strain energy density at the end of the belt layer for each scheme. SED max Calculate the different levels of each design variable SED max The mean and range are used to determine the design variables. SED max The order of influence of the variables was determined, and the optimal combination of design variables was initially determined. S44. Draw the corresponding tire carcass profile based on the optimal combination of tire carcass profile design variables, establish a finite element model, and perform simulation calculations. SED max The durability improvement effect was verified by comparing the initial tire body structure design scheme.

7. The tire carcass profile structure design method for improving tire durability according to claim 1, characterized in that: In step S5, the global optimization design of the tire carcass profile design variables is achieved based on the GPR-MIGA algorithm. Using the orthogonal experimental scheme and optimal scheme determined in steps S42 and S43 as training samples, the design variables and target data are imported into MATLAB. A surrogate model is obtained through Gaussian process regression (GPR) training, and the generalization ability of the model is further verified. The model is then imported into Isight software for MATLAB-Isight joint optimization. The multi-island genetic algorithm (MIGA) in Isight is used to globally optimize the combination of design variables to minimize the maximum strain energy density at the end of the belt layer. SED max To optimize the objective, the globally optimal combination of design variables is obtained, and a finite element model of the global optimization design scheme is established through step S1; this includes the following steps: S51, with n The sample consists of a group of orthogonal experimental schemes plus a set of optimal combinations of tire carcass profile design variables. The input is the combination of the ordinates of the control points of the design variables, and the output is the corresponding... SED max Construct a sample dataset; S52. Construct the GPR proxy model, which is expressed in the following form: In the formula, It is Gaussian noise. For noise variance, f ( x It follows a Gaussian process, determined by the mean function. m ( x and covariance function (kernel function) k ( x , x’ Defined as follows: In application, the sample dataset is divided into training and test sets in a 7:3 ratio, and the RBF radial basis function is selected as the kernel function, which is expressed as follows: in, Let be the signal variance, and Λ be a diagonal matrix whose diagonal elements are the squares of the length scale parameters of each dimension. Hyperparameters are automatically adjusted using Bayesian optimization. Finally, model training is completed by maximizing the marginal likelihood function. The expression for maximizing the marginal likelihood function is: in, X For input points, y The output value of the observation, I It is an identity matrix, and then the correlation coefficient is used. R 2 Verify the model's fitting accuracy and generalization ability; S53. Global optimization is achieved through the MIGA algorithm. The trained GPR surrogate model is imported into the Isight software. Parameters such as the range of design variables, subpopulation size, number of islands, generation number, crossover rate, and mutation rate for the MIGA algorithm are set. SED max Minimize the optimization objective and iteratively search for the optimal combination of control points to obtain the globally optimal combination of control points. S54. Predict the globally optimal control point combination using the GPR surrogate model. SED max Based on step S1, establish a tire finite element model for the global optimization design scheme, and conduct finite element analysis of it under load.

8. The tire carcass profile structure design method for improving tire durability according to claim 1, characterized in that: In step S6, the finite element model of the global optimization design scheme established in step S54 is used to verify... SED max The optimization effect is compared with the result of the optimal combination of design variables in step S4. Finally, the changes in the mechanical properties of the tire carcass cord before and after optimization are compared to reveal the mechanical mechanism of improved durability. The optimization includes the following steps: S61. Perform simulation calculations based on step S3 to obtain the global optimized design scheme. SED max The results are then compared with the prediction results of the GPR surrogate model in step S54 to further verify the effectiveness of the optimized model. S62, Optimize the global design scheme SED max The results were compared with those of the initial scheme and the scheme with the best combination of design variables to verify the feasibility of the global optimization method. S63. Perform tire carcass cord force analysis on the tire carcass layers. Perform post-processing in Abaqus software to extract the S11 stress of the tire carcass cord at the tire ground contact center section before and after optimization. Analyze the uniformity of cord force distribution and the changes in cord tension in key areas. Compare the mechanical property parameters before and after optimization, including the cord tension in the tread area, the cord tension in the bead area, and the overall cord tension, to explain the mechanical principles of the durability performance design.

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