A multi-rubber tire fatigue failure positioning method based on equivalent stress field reconstruction

Abstract

The application discloses a kind of based on equivalent stress field reconstruction's multi-rubber tire fatigue failure positioning method, and the application provides the following scheme: S1, establish the three-dimensional finite element model of multi-rubber tire, the coordinates of effective rubber component node on target section and stress-strain data are extracted automatically;S2, construct the characteristic database covering multi-order Ogden constitutive parameter, match parameter and calculate node hydrostatic pressure and equivalent stress based on continuous medium damage mechanics equation;S3, construct node local topological neighborhood, set up isolatedness determination condition, filter false high stress singular point;S4, to effective calculation node, execute principal component analysis dimension reduction and limited side length triangulation interpolation, reconstruct two-dimensional continuous equivalent stress nephogram, and then locate tire internal fatigue crack initiation position.The application breaks through the technical link of multi-component joint fatigue prediction, and greatly improves the precision and intuitiveness of failure positioning.

Description

Technical Field

[0001] This invention relates to the fields of tire durability performance prediction, finite element numerical simulation analysis, and data processing technology, and particularly to a fatigue failure location method for multi-rubber tires based on equivalent stress field reconstruction. This method is especially suitable for fatigue crack initiation location and life assessment of large off-highway mining dump truck tires with extremely complex stress distribution and containing interfaces between various rubber compounds and reinforcing materials. Background Technology

[0002] Tires are the core components of vehicles, transmitting traction, bearing the vehicle's weight, and cushioning road impacts. During actual service, tires repeatedly withstand complex multi-axle alternating loads of tens or even hundreds of tons, accompanied by large deformations and intense heat generation. The tire's interior is a complex multi-rubber composite structure woven from the tread, sidewall, tread layer, airtight layer, various belt layers, and carcass materials. This structure results in numerous interfaces with abrupt changes in material properties within the tire (especially the interface between the steel wire skeleton and the rubber matrix). Under long-term high-load operation, these interfaces and surrounding areas are highly susceptible to fatigue damage and crack initiation, ultimately leading to tire delamination or blowout failure. Therefore, accurately predicting the fatigue failure location of the complex multi-rubber structure within the tire is of crucial engineering significance for improving tire durability.

[0003] Existing methods for predicting rubber fatigue life are mostly based on continuum damage mechanics, typically using uniaxial or biaxial fatigue tensile tests to obtain correlation models between specific parameters such as equivalent stress and fatigue life. However, there are significant limitations when applying this theory and traditional finite element post-processing methods to full-size multi-component tire models. First, existing finite element software struggles to coordinate rubber formulations with different Ogden hyperelastic constitutive parameters, heavily relying on manual selection of single material regions for data extraction. This makes it impossible to achieve fully automated batch processing and constitutive mapping of massive amounts of nodal data across materials, resulting in extremely low efficiency in fatigue calculations of the overall structure. Second, at the interface between the skeleton and rubber with significant stiffness differences, the finite element calculation matrix is ​​prone to stress singularities. The solved local stresses may exhibit non-physical amplifications. If these false high-stress points are used directly as fatigue judgment criteria without verification, it will lead to distorted predictions that deviate significantly from the actual failure locations observed in bench tests. Furthermore, conventional commercial software cannot directly reverse-map the composite damage parameters obtained by the user's secondary depth calculation back to the multi-component cross-section for continuous cloud map display. The lack of a global damage visualization and reconstruction mechanism makes it difficult for R&D personnel to intuitively locate weak points, which greatly restricts the efficiency of engineering R&D and the accuracy of assessment.

[0004] Therefore, there is an urgent need for a method that can accurately, efficiently, and non-contactly locate tire cracks in order to overcome the shortcomings of existing technologies. Summary of the Invention

[0005] The technical problems to be solved by the present invention are the technical bottlenecks in the prior art, such as the difficulty of automatic matching across materials, the prediction distortion caused by mesh singularity, and the lack of intuitive visualization reconstruction methods. In order to solve the above problems, a fatigue failure localization method for multi-rubber tires based on equivalent force field reconstruction is provided.

[0006] The object of this invention is achieved in the following manner: A fatigue failure localization method for multi-rubber tires based on equivalent stress field reconstruction, the method comprising the following steps: S1: Establish the finite element model and locate the target section: A three-dimensional finite element model of a multi-rubber tire containing various rubber components and rigid skeleton materials was established, and finite element solutions were performed under load conditions. Then, based on the finite element analysis results, the contact center section of the loaded tire was locked as the target section by determining the extreme value of vertical displacement. S2: Extract node data of valid rubber components: On the target cross section, valid rubber components are automatically identified and skeleton material units are masked based on whitelist rules; then, the spatial coordinates, principal stresses and principal strains of all valid rubber unit nodes on the cross section are extracted to form the original calculation dataset. S3: Automatic matching of hyperelastic constitutive parameters: A feature database containing Ogden hyperelastic constitutive model parameters for various rubber materials is constructed. Then, the original computational dataset is traversed, and the corresponding constitutive model parameters are automatically retrieved and matched from the feature database based on the material identifier attached to each node. S4: Point-by-point calculation of equivalent stress: Based on the Ogden constitutive parameters matched at each node and the extracted principal stress and principal strain data, the hydrostatic pressure at each node is calculated based on the mechanics theory of incompressible hyperelastic materials. Then, based on the continuum damage mechanics equation, the equivalent stress of each node characterizing the multiaxial fatigue damage driving force is calculated to generate the initial calculation dataset. S5: Spatial neighborhood filtering for false singularities: For numerical singularities generated at material interfaces and stiffness transition regions in finite element calculations, the set of spatial nearest neighbor nodes of the target node is obtained. Then, the equivalent stress of the target node is compared with the median equivalent stress of the set of nearest neighbor nodes. If the target node meets the set isolation multiple anomaly judgment condition and there are no high-stress nodes in its neighborhood that meet the support ratio, the target node is judged as a false singularity and is removed. The nodes that are not removed are retained as valid calculation nodes. S6: Reconstruct the equivalent stress cloud map in a reduced dimension and locate the failure location: Principal component analysis is performed on the selected and retained effective computation nodes to reduce their three-dimensional spatial coordinates and rotate them onto a unified two-dimensional feature plane. Then, a triangulation interpolation algorithm with a maximum side length limit threshold is performed on the projected point set to map and render the equivalent stress values ​​of the effective computation nodes onto the topological mesh, reconstructing and generating a continuous equivalent stress cloud map of the multi-rubber cross-section. Finally, the region of maximum equivalent stress concentration in the continuous equivalent stress cloud map is extracted globally and accurately located as the actual physical location of fatigue failure in the multi-rubber tire.

[0007] The specific method for locking the target section in step S1 is as follows: by finding the spatial azimuth angle where the minimum value of the vertical coordinate of the node is located, and combining it with the set angle tolerance threshold, the contact center section is located.

[0008] The whitelist rules in step S2 include keywords for rubber components, while the blacklist rules for the shielding skeleton material unit include keywords for steel wire and cord. The extracted node data specifically includes node spatial coordinates, principal stress, and principal strain.

[0009] The feature database mentioned in step S3 contains parameters of the third-order Ogden hyperelastic constitutive model for various rubber materials, including shear modulus. m j and nonlinear exponent α j , where j=1,2,3.

[0010] In step S4, the formula for calculating the hydrostatic pressure p is:

[0011] In the formula, n Let Ogden be the order of the constitutive model. m j and α j These are the constitutive parameters obtained from the experiment. l k The principal direction elongation is extracted based on the principal strain. s k These are the Cauchy principal stresses in the corresponding directions; The formula for calculating the equivalent stress Seq at each node is: In the formula, W Let be the strain energy function. For the node at the th i The effective second Piola-Kirchhoff principal stress after damage evolution in the principal direction, specifically calculated including the hydrostatic pressure. p and the strain energy function WPartial derivative with respect to principal elongation.

[0012] The specific conditions for determining a false singularity in step S5 are as follows: obtain the set of nearest neighbor nodes of the target node, and calculate the median of the equivalent stress of the set as the benchmark value; if the equivalent stress of the target node is higher than the set multiple of the benchmark value, and the number of high-stress nodes in its neighborhood that meet the set support ratio is less than the preset threshold, then the target node is determined to be a false singularity.

[0013] The specific process of principal component analysis dimensionality reduction rotation projection in step S6 is as follows: obtain the set of three-dimensional spatial coordinates of effective computing nodes, analyze their spatial distribution characteristics to extract the principal direction parameters of the target section, construct spatial coordinate transformation relationship based on the principal direction parameters, and adaptively rotate and project the three-dimensional spatial coordinates onto a unified two-dimensional feature plane.

[0014] The specific process of triangulation interpolation reconstruction in step S6 is as follows: Delaunay triangulation is performed on the projection point set in the two-dimensional feature plane; a maximum side length threshold is set, and triangular cells with side lengths greater than the threshold are automatically traversed and removed from the triangulated mesh to eliminate erroneous mesh connections in the hollow structure of the tire or across the component area; color interpolation rendering is performed on the retained triangular mesh facets using the equivalent stress values ​​of the effective computation nodes.

[0015] Step S6 also includes: extracting the lower and upper percentiles of the equivalent stress values ​​of all valid calculation nodes, and performing color saturation truncation on the equivalent stress values ​​below the lower percentile or above the upper percentile to enhance the visual contrast of the cloud map in high-risk fatigue failure hotspot areas.

[0016] The step S6 is followed by a closed-loop verification step: obtaining the cross-sectional failure image of the actual tire bench fatigue failure test, and comparing the predicted physical location of fatigue failure with the actual crack initiation and propagation location in the experimental image to verify the spatial location, thereby completing the closed-loop evaluation of the fatigue durability performance of multi-rubber tires.

[0017] The beneficial effects of this invention are as follows: This invention establishes a closed-loop system covering the entire process from automated extraction of bottom-level node data, mapping of constitutive parameters of multiple rubber compounds, intelligent spatial filtering of numerical singularities, to the final reconstruction of two-dimensional continuous damage cloud maps and experimental verification. This system achieves high-precision, fully automated, and visualized localization of fatigue failure locations in complex multi-rubber tires. By constructing a feature database covering Ogden hyperelastic constitutive parameters of various rubber formulations, and automatically retrieving matching parameters based on the material identifiers attached to nodes, batch processing and equivalent stress calculation of massive node data across materials can be completed without manual selection of different rubber regions one by one. Addressing the numerical singularity problem that easily arises in finite element calculations at material interfaces and stiffness transition regions, this invention proposes a singularity filtering method based on spatial neighborhood consistency constraints: by comparing the equivalent stress of the target node with the median of its nearest neighbor set, and combining this with the support ratio of high-stress nodes within the neighborhood, false high-stress singularities are intelligently identified and eliminated. This step effectively avoids interference from non-physical numerical anomalies in fatigue failure localization, making the prediction results closer to the actual crack initiation location. Attached Figure Description

[0018] Figure 1 A schematic diagram of the overall process of the method of the present invention.

[0019] Figure 2 Finite element model of multi-rubber tire and schematic diagram of load conditions.

[0020] Figure 3 A diagram illustrating the multi-material partitioning and mesh generation of the tire target cross-section.

[0021] Figure 4 A schematic diagram comparing the predicted equivalent stress (Seq) field with the experimental failure location. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0023] 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.

[0024] A fatigue failure localization method for multi-rubber tires based on equivalent stress field reconstruction includes the following steps: S1: Establish a three-dimensional finite element model of a multi-rubber tire containing various rubber components and rigid skeleton materials, apply load conditions under actual service environment and perform finite element calculations; based on the finite element analysis results, determine the extreme value of vertical displacement and lock the contact center section of the loaded tire as the target section; S2: Automatically identify effective pure rubber material components on the target cross section, shielding skeleton material units such as steel wire and cord; traverse and extract the spatial coordinates of all effective rubber unit nodes on the cross section, and extract the principal stress and principal strain data of each node accordingly to form the original calculation data; S3: Based on various rubber formulations of actual tire components, construct a feature database containing parameters of multiple rubber Ogden hyperelastic constitutive models; traverse the original cross-section dataset generated in S2, and automatically retrieve and match the corresponding Ogden material parameters from the feature database based on the specific material identifiers attached to each node; S4: Combining the Ogden material parameters matched at each node and the extracted principal stress and principal strain data, the triaxial hydrostatic pressure at each node is calculated based on the mechanics theory of incompressible hyperelastic materials; then, based on the damage mechanics equation of continuous medium, the equivalent stress of each node characterizing the multiaxial fatigue damage driving force of the material is obtained, and the initial calculation dataset is generated. S5: For numerical singularities generated by finite element calculations at different material interfaces and stiffness transition regions, obtain the set of spatial nearest neighbor nodes of the target node; compare the equivalent stress of the target node with the median of the equivalent stress of its nearest neighbor node set; if the target node meets the set isolation multiple anomaly judgment condition and there are no high-stress nodes in its neighborhood that meet the support ratio, then the target node is judged as a false singularity caused by the computational mesh and is removed, and the nodes that are not removed are retained as valid computational nodes.

[0025] S6: Principal Component Analysis (PCA) is performed on the valid computational nodes retained in S5 to reduce their 3D spatial coordinates and rotate and project them onto a unified 2D feature plane. A triangulation interpolation algorithm with a maximum side length constraint threshold is then applied to the projected point set to map and render the equivalent stress values ​​of the valid computational nodes onto a topological mesh, reconstructing a continuous equivalent stress cloud map of the multi-component cross-section. The region of maximum equivalent stress concentration in the continuous equivalent stress cloud map is globally extracted and precisely located as the actual physical location of fatigue failure in the multi-component tire. Finally, cross-sectional failure images from actual tire bench fatigue failure experiments are obtained. The predicted fatigue failure physical location is spatially compared and verified with the actual crack initiation and propagation locations in the experimental images, completing the closed-loop evaluation of the fatigue durability performance of the multi-component tire.

[0026] In steps S1 and S2: By finding the azimuth angle where the minimum value of the vertical coordinate of the node is located, and combining it with the set angle tolerance threshold, the contact center section is located. Based on a whitelist rule containing keywords related to rubber components and a blacklist rule containing keywords related to skeleton materials, non-rubber structures are automatically filtered from the target cross-section; the extracted node data specifically includes: node spatial coordinates, principal stresses, and principal strains.

[0027] In step S4, the formula for calculating the hydrostatic pressure p is:

[0028] In the formula, n Let Ogden be the order of the constitutive model. m j and α j These are the constitutive parameters obtained from the experiment. l k The principal direction elongation is extracted based on the principal strain. s k This represents the Cauchy principal stress in the corresponding direction.

[0029] In step S4, the formula for calculating the equivalent stress Seq at each node is:

[0030] In the formula, W Let be the strain energy function. For the node at the th i The effective second Piola-Kirchhoff principal stress after damage evolution in the principal direction, specifically calculated including the hydrostatic pressure. p and the strain energy function W Partial derivative with respect to principal elongation.

[0031] In step S5, the specific criteria for singularity filtering based on spatial neighborhood consistency constraints are as follows: Obtain the set of nearest neighbor nodes of the target node and extract the equivalent stress benchmark value of the set; compare the equivalent stress of the target node with the equivalent stress benchmark value. If the equivalent stress of the target node is abnormally higher than the benchmark value, mark it as a suspected singularity; for the suspected singularity, count the number of high-stress nodes in its nearest neighbor set that meet a set ratio; if the number is less than the preset minimum number of supports, determine that the target node is a false singularity caused by finite element calculation.

[0032] In step S6, the specific process of coordinate dimensionality reduction and rotation projection is as follows: Obtain the set of three-dimensional spatial coordinates of the effective computing nodes, analyze the spatial distribution characteristics of the coordinate set, and extract the principal direction parameter of the target section; construct a spatial coordinate transformation relationship based on the principal direction parameter, adaptively rotate and project the three-dimensional spatial coordinates of the effective computing nodes onto a unified two-dimensional feature plane, so as to achieve dimensionality reduction and tiling of the section data.

[0033] In step S6, the reconstruction process of the continuous equivalent stress patch cloud map is as follows: Within the two-dimensional feature plane, Delaunay triangulation is performed on the two-dimensional projection point set; a maximum side length threshold is set, and triangular units with side lengths greater than the maximum side length threshold in the triangulation network are automatically traversed and removed to eliminate erroneous mesh connections in the hollow structure of the tire or across component regions; color interpolation rendering is performed on the retained triangular mesh facets using the equivalent stress values ​​of the effective computed nodes.

[0034] Step S6 further includes: When reconstructing the continuous equivalent stress cloud map, the lower and upper percentiles of the equivalent stress values ​​of all valid calculation nodes are extracted; the equivalent stress values ​​below the lower percentile or above the upper percentile are truncated by color saturation to enhance the visual contrast of the cloud map in high-risk fatigue failure hotspot areas.

[0035] This invention provides a method for locating fatigue failure in multi-rubber tires based on equivalent stress field reconstruction. This embodiment uses a 16.00R25 off-highway mining dump truck all-steel radial tire as an example. This tire has a complex internal structure including a tread, sidewall, tactile rubber, belt layer, and carcass. The detailed implementation process of this method is as follows: S1. Construct a finite element model of a multi-rubber tire and locate the target section: S11. Based on the actual tire's structural dimensions and material distribution, a two-dimensional axisymmetric finite element mesh model of the tire was established using the finite element analysis software (ABAQUS). The rubber matrix was discretized using CGAX4H (incompressible quadrilateral elements) or CGAX3H (triangular elements), while the steel wire and cord skeleton were defined using Rebar elements.

[0036] The two-dimensional model is then rotated 360° around the tire's circumference to generate a complete three-dimensional solid tire model, such as... Figure 2 As shown. An analytical rigid body of the road surface is established. In the static or steady-state rolling analysis step, an inflation pressure of 0.8 MPa is applied to the inner surface of the tire cavity, and a vertical concentrated load is applied to the road surface reference point. The calculation is submitted, generating finite element analysis results including nodal coordinates, stress field, and strain field.

[0037] S12: Under three-dimensional loading, the area most prone to fatigue failure in a tire is typically located near the ground contact center section, where the compression deformation is most severe and the sinking is greatest. The tire finite element model is set to rotate around the global coordinate system Y-axis, with cross-sections distributed in the XZ plane. The three-dimensional coordinates of any node in space after loading deformation are defined as (X, Y, Z), and its spatial polar angle is... i The calculation formula is: In order to accurately pinpoint the azimuth angle of the center section under maximum load thetarget This embodiment uses the extreme vertical displacement of nodes for spatial positioning. Specifically: the direction of tire compression and sinking is set as the negative Z-axis. In the target steady-state load frame of the finite element analysis, all effective rubber element nodes are extracted and traversed to find the node with the smallest vertical coordinate (i.e., Z-axis coordinate value). This node represents the physical extreme position where the tire is flattened to the bottom under the current load. The spatial coordinates of the node containing this vertical minimum point are obtained and substituted into the polar angle formula mentioned above to obtain: The calculated result thetarget The target azimuth angle of the contact center section of the multi-rubber tire is locked as the absolute spatial reference for subsequent extraction of full-section node data.

[0038] S2. Multi-component material identification and multi-dimensional node data extraction S21. Establish a whitelist for identifying valid rubber units, mapping cross-sectional attribute strings to standard material labels. For example, map TREAD to tread rubber (Rub_Tread), APEX to triangular rubber (Rub_Apex), etc.

[0039] At the same time, a blacklist of skeleton materials is established, and data extraction of units such as REBAR, BEAD, and STEEL is skipped.

[0040] S22. Set the cross-sectional angle tolerance threshold to 2°. For any valid rubber node, calculate its polar angle and the angular deviation from the target cross-section. If the node is within the threshold, it is determined that the node is located within the target study cross-section. Extract the node's maximum / intermediate / minimum principal strain, maximum / intermediate / minimum Cauchy principal stress, and node coordinates, and write them into the original cross-sectional dataset.

[0041] S3. Establish a feature database containing parameters of the third-order Ogden hyperelastic constitutive model for various rubber formulations. Each row corresponds to a material label, and the parameters include shear modulus. not and nonlinear exponent αi ( i =1,2,3), as shown in Table 1. Traverse each node in the original cross-section dataset, and based on the material label bound to its element, precisely match and call the corresponding [material] from the database. not and αi The parameter set is used for subsequent single-point mechanical state calculations.

[0042] Table 1 Material parameters of tire rubber components

[0043] S4. Point-by-point calculation of equivalent stress based on continuous medium damage mechanics: S41. Strain tensor transformation and hydrostatic pressure solution: For any node, use its nominal principal strain NE k Calculate the principal elongation in the three principal directions l k (k=1, 2, 3): Based on the theory of incompressible hyperelastic materials mechanics, the strain energy density function of the third-order Ogden model is calculated. W : Triaxial hydrostatic pressure of the node under load p Based on any main direction k of Cauchy Principal stress s k Solve for the equation: S42, Equivalent stress Seq Calculation: According to the damage mechanics equations of continuous media, the effective second... Piola-Kirchhoff Principal stress Related to the hydrostatic pressure p and the partial derivatives of the strain energy function with respect to the principal elongation: Further calculation of equivalent stress Seq It characterizes the energy driving force for the initiation of fatigue cracks in rubber under complex multiaxial alternating stress conditions, and its calculation expression is: Complete the calculations for all valid nodes and generate an initial computational dataset containing coordinates and Seq values.

[0044] S5. Singularity filtering based on spatial neighborhood consistency constraints: For numerical singularities generated at material interfaces during finite element analysis, the spatial nearest neighbor set of the target node is extracted, and the median of the equivalent stress within this neighborhood is calculated. The equivalent stress of the target node is compared with the median. If the stress value of the target node exhibits an extreme isolated abrupt change and lacks continuous support from surrounding high-stress nodes, the node is determined to be a singularity and is discarded, retaining only the true and valid calculation nodes.

[0045] S6. Two-dimensional reconstruction of the equivalent force field of the cross section, failure location and experimental verification: The three-dimensional spatial coordinates of the effective computational nodes are extracted, and the principal direction of the cross-sectional spatial distribution is obtained through principal component analysis (PCA). Based on this principal direction, a rotation matrix is ​​constructed to adaptively rotate and project the three-dimensional node coordinates onto a two-dimensional plane. In the two-dimensional plane, a triangulation algorithm with a maximum side length constraint is performed on the nodes, and color interpolation rendering is performed using the equivalent stress values ​​of the nodes to reconstruct and generate a continuous equivalent stress cloud map of multiple rubber cross sections.

[0046] In the continuous equivalent stress cloud map output after dimensionality reduction rotation and interpolation reconstruction, the fatigue damage distribution trend of the cross-section can be observed intuitively. After eliminating the interference of spurious singularities at the skeleton interface, the cloud map shows that the global equivalent stress value is the largest, appearing as a bright yellow, precisely located in the rubber matrix region at the ends of the 2nd and 3rd belt layers. Based on this, the present invention determines that the ends of the 2nd and 3rd belt layers are the predicted locations where fatigue crack initiation is most likely to occur in the tire.

[0047] To verify the accuracy of the above predictions, an indoor rolling bench durability test was conducted on a tire of the same specification. After the tire reached fatigue failure, it was dissected to obtain fatigue failure images of the actual cross-section. Observation of the actual dissected images clearly shows that the actual fatigue crack initiation source is also located at the ends of the second and third belt layers, and the crack has clearly torn and propagated along the edge of the belt layer.

[0048] A direct comparison reveals that, for example Figure 4 As shown, the high stress concentration locations predicted by the reconstructed cloud map perfectly match the physical locations of fatigue crack initiation in the actual bench test (both located at the ends of the 2nd and 3rd belt layers). This result intuitively and powerfully verifies the accuracy of the multi-component equivalent stress calculation and singularity filtering algorithm of this invention, successfully realizing the engineering closed loop for tire fatigue failure location.

[0049] This invention constructs a feature database covering Ogden hyperelastic constitutive parameters for various rubber formulations, and automatically retrieves matching parameters by combining the material identifiers attached to nodes. This eliminates the need for manual selection of different rubber regions one by one, enabling batch processing and equivalent stress calculation of massive node data across materials.

[0050] To address the numerical singularity problem that easily arises in finite element method (FEM) calculations at material interfaces and regions of abrupt stiffness changes, this invention proposes a singularity filtering method based on spatial neighborhood consistency constraints. This method intelligently identifies and eliminates false high-stress singularities by comparing the equivalent stress of the target node with the median of its nearest neighbor set, and combining this with the support ratio of high-stress nodes within the neighborhood. This step effectively avoids interference from non-physical numerical anomalies in fatigue failure localization, making the predicted results closer to the actual crack initiation location.

[0051] This invention projects the selected effective computational nodes onto a two-dimensional feature plane using principal component analysis for dimensionality reduction. It then employs Delaunay triangulation with a maximum side length constraint and color interpolation rendering to reconstruct a continuous equivalent stress contour map of multiple rubber cross-sections. Compared to existing vector maps generated using the Kriging method, the contour map of this invention can adaptively eliminate erroneous connections in the hollow structure of the tire or across component regions, and visually display the global damage distribution in the form of continuous color patches. Researchers can quickly identify high-risk fatigue areas without complex post-processing.

[0052] After predicting the failure location, this invention further verifies the prediction results by spatially comparing them with anatomical images from actual tire bench fatigue failure experiments. This closed-loop process not only demonstrates the reliability of the prediction method but also provides a directly quantifiable evaluation basis for subsequent tire structure optimization, filling the gap in spatial verification in existing technologies.

[0053] The technical solution of this invention fully considers the actual working conditions of large off-highway mining tires, which are subjected to extremely complex stresses and involve interfaces between various rubber compounds and skeleton materials. Through equivalent stress field reconstruction and singularity filtering, the internal crack initiation locations of typical stress concentration areas such as the belt layer endpoints and carcass wrapping points can be accurately located, providing a powerful simulation tool for tire durability design under high load and large deformation conditions.

[0054] In summary, this invention has achieved significant technological advancements in terms of automation, prediction accuracy, visualization intuitiveness, and engineering verification closed loop. It overcomes long-standing technical bottlenecks in existing technologies, such as difficulties in cross-material joint calculations, large interface interference, and lack of global display, and has broad industrial application value.

[0055] 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 for locating fatigue failure in multi-rubber tires based on equivalent stress field reconstruction, characterized in that: The method includes the following steps: S1: Establish the finite element model and locate the target section: A three-dimensional finite element model of a multi-rubber tire containing various rubber components and rigid skeleton materials was established, and finite element solutions were performed under load conditions. Then, based on the finite element analysis results, the contact center section of the loaded tire was locked as the target section by determining the extreme value of vertical displacement. S2: Extract node data of valid rubber components: On the target cross section, valid rubber components are automatically identified and skeleton material units are masked based on whitelist rules; then, the spatial coordinates, principal stresses and principal strains of all valid rubber unit nodes on the cross section are extracted to form the original calculation dataset. S3: Automatic matching of hyperelastic constitutive parameters: A feature database containing Ogden hyperelastic constitutive model parameters for various rubber materials is constructed. Then, the original computational dataset is traversed, and the corresponding constitutive model parameters are automatically retrieved and matched from the feature database based on the material identifier attached to each node. S4: Point-by-point calculation of equivalent stress: Based on the Ogden constitutive parameters matched at each node and the extracted principal stress and principal strain data, the hydrostatic pressure at each node is calculated based on the mechanics theory of incompressible hyperelastic materials. Then, based on the continuum damage mechanics equation, the equivalent stress of each node characterizing the multiaxial fatigue damage driving force is calculated to generate the initial calculation dataset. S5: Spatial neighborhood filtering for false singularities: For numerical singularities generated at material interfaces and stiffness transition regions in finite element calculations, the set of spatial nearest neighbor nodes of the target node is obtained. Then, the equivalent stress of the target node is compared with the median equivalent stress of the set of nearest neighbor nodes. If the target node meets the set isolation multiple anomaly judgment condition and there are no high-stress nodes in its neighborhood that meet the support ratio, the target node is judged as a false singularity and is removed. The nodes that are not removed are retained as valid calculation nodes. S6: Reconstruct the equivalent stress cloud map in a reduced dimension and locate the failure location: Principal component analysis is performed on the selected and retained valid computation nodes, and their three-dimensional spatial coordinates are reduced in dimension, rotated and projected onto a unified two-dimensional feature plane; Then, a triangulation interpolation algorithm with a maximum side length limit threshold is executed on the projection point set to map and render the equivalent stress values ​​of the effective calculation nodes into the topological mesh, and reconstruct and generate a continuous equivalent stress cloud map of the multi-rubber cross section; finally, the maximum equivalent stress concentration area in the continuous equivalent stress cloud map is extracted globally and accurately located as the actual fatigue failure physical location of the multi-rubber tire.

2. The fatigue failure localization method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The specific method for locking the target section in step S1 is as follows: by finding the spatial azimuth angle where the minimum value of the vertical coordinate of the node is located, and combining it with the set angle tolerance threshold, the contact center section is located.

3. The fatigue failure location method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The whitelist rules in step S2 include keywords for rubber components, while the blacklist rules for the shielding skeleton material unit include keywords for steel wire and cord. The extracted node data specifically includes node spatial coordinates, principal stress, and principal strain.

4. The fatigue failure location method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The feature database mentioned in step S3 contains parameters of the third-order Ogden hyperelastic constitutive model for various rubber materials, including shear modulus. μ j and nonlinear exponent α j , where j=1,2,3.

5. The fatigue failure localization method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: In step S4, the formula for calculating the hydrostatic pressure p is:

6. In the formula, n Let Ogden be the order of the constitutive model. μ j and α j These are the constitutive parameters obtained from the experiment. λ k The principal direction elongation is extracted based on the principal strain. σ k These are the Cauchy principal stresses in the corresponding directions; The formula for calculating the equivalent stress Seq at each node is: In the formula, W Let be the strain energy function. For the node at the th i The effective second Piola-Kirchhoff principal stress after damage evolution in the principal direction, specifically calculated including the hydrostatic pressure. p and the strain energy function W Partial derivative with respect to principal elongation.

7. The fatigue failure localization method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The specific conditions for determining a false singularity in step S5 are as follows: obtain the set of nearest neighbor nodes of the target node, and calculate the median of the equivalent stress of the set as the benchmark value; if the equivalent stress of the target node is higher than the set multiple of the benchmark value, and the number of high-stress nodes in its neighborhood that meet the set support ratio is less than the preset threshold, then the target node is determined to be a false singularity.

8. The fatigue failure location method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The specific process of principal component analysis dimensionality reduction rotation projection in step S6 is as follows: obtain the set of three-dimensional spatial coordinates of effective computing nodes, analyze their spatial distribution characteristics to extract the principal direction parameters of the target section, construct spatial coordinate transformation relationship based on the principal direction parameters, and adaptively rotate and project the three-dimensional spatial coordinates onto a unified two-dimensional feature plane.

9. The fatigue failure location method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The specific process of triangulation interpolation reconstruction in step S6 is as follows: Delaunay triangulation is performed on the projection point set in the two-dimensional feature plane; a maximum side length threshold is set, and triangular cells with side lengths greater than the threshold are automatically traversed and removed from the triangulated mesh to eliminate erroneous mesh connections in the hollow structure of the tire or across the component area; color interpolation rendering is performed on the retained triangular mesh facets using the equivalent stress values ​​of the effective computation nodes.

10. The fatigue failure location method for multi-rubber tires based on equivalent field reconstruction according to claim 8, characterized in that: Step S6 also includes: extracting the lower and upper percentiles of the equivalent stress values ​​of all valid calculation nodes, and performing color saturation truncation on the equivalent stress values ​​below the lower percentile or above the upper percentile to enhance the visual contrast of the cloud map in high-risk fatigue failure hotspot areas.

11. The fatigue failure location method for multi-rubber tires based on equivalent field reconstruction according to claim 1, characterized in that: The step S6 is followed by a closed-loop verification step: obtaining the cross-sectional failure image of the actual tire bench fatigue failure test, and comparing the predicted physical location of fatigue failure with the actual crack initiation and propagation location in the experimental image to verify the spatial location, thereby completing the closed-loop evaluation of the fatigue durability performance of multi-rubber tires.

Images