A tire belt layer bending stiffness decoupling modeling method and system and material parameter calibration method thereof

Abstract

The present application relates to the technical field of tire simulation design, and particularly relates to a tire belt layer bending stiffness decoupling modeling and a material parameter calibration method and system thereof. A basic model of in-plane load bearing is first established by rubber matrix solid elements, film element layers and reinforcing rib layers, then a shell element layer not participating in the assembly of the in-built balance equation is superimposed as a bending stiffness supplement layer, and a bending exclusive shell section is given; by establishing a reference bending force-displacement curve and a reference tensile load-displacement curve, a calibrated shell model and a decoupling strip model are combined to inversely calculate a target material parameter set, and finally a whole tire finite element model is constructed. The present application can accurately supplement the bending stiffness without affecting the in-plane load bearing response of the belt layer, and improve the prediction accuracy of the footprint and the radial stiffness.

Description

Technical Field

[0001] This invention relates to the field of tire simulation design technology, and in particular to a method and system for decoupling modeling of the bending stiffness of tire belt layers and calibrating its material parameters. Background Technology

[0002] Tires, especially radial tires, have belt layers that are essentially layered composite reinforcement structures composed of steel cords and a rubber matrix. This structure needs high in-plane tensile stiffness in the circumferential or cord laying direction to ensure the tire's basic load-bearing capacity under inflation, loading, rolling, and braking conditions. Simultaneously, it needs a bending response consistent with the actual structure to accurately reflect the contact patch, ground pressure distribution, radial stiffness, and local deformation characteristics in the tire crown area. With the development of nonlinear finite element technology and computational resources, using finite element models to replace some physical experiments has become an important technique for tire structural design and performance prediction. In this type of analysis, the choice of finite element modeling method for the belt layer directly affects the accuracy of the whole tire model's prediction of static and dynamic characteristics.

[0003] In existing technologies, the technical approaches related to modeling belt-reinforced or cord-reinforced rubber composites can be broadly categorized into two types. The first type involves establishing a model of the cord-reinforced rubber composite by combining solid rubber matrix elements with planar cord elements or membrane elements. For example, Chinese patent document CN114491812A discloses a finite element modeling method for cord-reinforced rubber composites for aircraft tires. Its basic idea is to first partition the rubber body into rubber matrix elements, then create planar cord elements within each rubber matrix element, subsequently establish embedded constraint relationships between the rubber matrix elements and the planar cord elements, and superimpose the stiffness and load of the planar cord elements onto the corresponding rubber matrix elements to obtain the final equilibrium equation. The key point of this method is to handle the coordinated deformation of the cord and rubber through embedded relationships and improve the efficiency of traditional explicit layered modeling. Therefore, embedding planar cord elements inside the rubber matrix and then achieving in-plane load-bearing of the composite material through constraint relationships is a known solution in this field.

[0004] The second type involves modeling the cord layer and rubber layer in a tire as an equivalent laminated composite structure, using shell elements or composite shell elements to uniformly describe the overall mechanical behavior of the layered structure. For example, US Patent Document US6691566B2 discloses that a single shell element with multiple integration points can be used to model a layered composite unit consisting of at least one cord layer and at least one rubber layer, with each integration point corresponding to one cord layer and one rubber layer, respectively. This document also explicitly states that in the prior art it cites, the cord layer can be modeled using membrane elements, and the rubber layer can be modeled using solid elements; further, it points out that membrane elements only transmit in-plane tension, compression, and shear forces and do not handle out-of-plane mechanical quantities, therefore they cannot handle bending stress and bending stiffness, while shell elements, in contrast, possess bending stiffness.

[0005] While the two aforementioned technical approaches have certain value in terms of modeling efficiency and equivalent representation of layered structures, they still have significant shortcomings in tire belt layer modeling. For the modeling method centered on embedded cord planar elements, its main advantage lies in its ability to intuitively represent the in-plane load-bearing capacity along the cord direction and reflect the coordinated deformation of the composite material through displacement coordination with the rubber matrix. However, the core load-bearing element in this approach is typically a cord planar element or a membrane element, which is inherently more suitable for describing in-plane tension / compression and in-plane shear behavior. It is difficult to directly and accurately reflect the flexural contribution of the belt layer under out-of-plane bending conditions. Especially under conditions of significant tire contact patch, indentation, and localized bending deformation of the tire crown, insufficient description of the belt layer's bending stiffness in the model can lead to deviations in the prediction of contact patch length, shoulder contact patch shape, contact patch pressure gradient, and radial stiffness.

[0006] Regarding the aforementioned technical approach of using a single shell element to uniformly represent the cord layer and rubber layer, although the shell element possesses bending stiffness and can characterize the bending response of the layered structure as a whole, the technical approach typically treats the cord layer and rubber layer as a single composite layer and expresses the overall stiffness of the composite layer through multiple integration points or equivalent parameters. This method helps reduce the number of elements and shorten computation time in engineering, but it also easily introduces another problem: the in-plane tensile response and bending response of the belt layer are often coupled within the same set of shell element material parameters or cross-sectional parameters, making it difficult to control them independently. In reality, the in-plane tensile stiffness of the belt layer is mainly controlled by the direction of the steel cord, the cross-sectional area of ​​the steel wire, the spacing, and the modulus, while its bending response, in addition to being affected by the geometry and material parameters of the steel wire itself, is also closely related to the thickness distribution after the steel wire-rubber composite, interlayer synergy, and local geometric configuration. If these two mechanisms are completely compressed into a single set of unified equivalent parameters, the in-plane stiffness and bending stiffness often cannot be simultaneously matched with the actual structure.

[0007] Furthermore, as can be seen from the published content of the two documents mentioned above, although existing technologies have respectively presented approaches for embedded cord planar elements / membrane elements to bear the in-plane load of composite materials and for using shell elements to uniformly characterize the bending and in-plane behavior of layered composite structures, at least based on their published content, no modeling scheme specifically for tire belt layers has yet been found. This scheme can retain the advantages of membrane elements or cord planar elements in accurately representing in-plane tension / compression while supplementing the belt layer's bending stiffness as an independent structural layer, and ensure that this bending stiffness supplementation layer does not further interfere with the original in-plane load-bearing chain. In other words, existing technologies lack a finite element modeling approach for structurally decoupling the in-plane load and out-of-plane bending of the belt layer.

[0008] Furthermore, existing technologies have not adequately addressed the issue of insufficient accuracy in obtaining bending stiffness parameters. If a unified equivalent shell element approach is used, the orthogonal anisotropy parameters required for the shell element typically need to be obtained through experience, theoretical equivalence, or global fitting. While using embedded planar elements or membrane elements can better reflect in-plane load-bearing capacity, a dedicated parameter inversion and transfer mechanism for bending behavior is lacking. For structures like tire belt layers, which exhibit significant directionality and layered composite characteristics, if the source of bending stiffness parameters is unclear or disconnected from the actual bending response of the composite structure, the stability and reliability of predictions regarding performance such as ground contact marks and radial stiffness in whole-tire simulations will be affected.

[0009] Therefore, in view of the problems in the existing technology, on the one hand, the membrane unit or cord planar unit is difficult to reflect the bending stiffness, and on the other hand, the unified equivalent shell unit is difficult to independently take into account the in-plane tension and bending response. There is an urgent need in the field for a new finite element modeling and material parameter calibration scheme for tire belt layer: the scheme can inherit the advantages of the existing embedded membrane unit / cord planar unit in in-plane load simulation, and can supplement the bending stiffness of the belt layer in an independent and calibrable way, thereby improving the prediction accuracy of the whole tire model for key performance such as ground imprint, pressure distribution and radial stiffness. Summary of the Invention

[0010] The technical objective of this invention is to address the problem that existing finite element modeling methods for tire belt layers struggle to accurately characterize bending stiffness using membrane elements or cord planar elements, while unified equivalent shell models often fail to simultaneously capture the accuracy of in-plane tensile and bending responses. This invention provides a method for decoupling the bending stiffness modeling of tire belt layers and calibrating its material parameters. By separating the in-plane load-bearing behavior and bending load-bearing behavior of the belt layer into separate models, and combining this with a material parameter inversion and transfer mechanism based on the bending reference response, the bending stiffness of the belt layer is accurately supplemented without compromising the accuracy of the original in-plane tensile simulation. This improves the accuracy of simulations of tire contact marks, ground pressure distribution, and radial stiffness. Firstly, to achieve the above objective, this invention employs the following technical solution:

[0011] A method for decoupling modeling of the bending stiffness of a tire belt layer and calibrating its material parameters includes the following steps:

[0012] S1. Establish an in-plane bearing foundation model for the belt layer, including establishing a rubber matrix solid element, establishing a membrane element layer at the geometric position of the belt layer, and setting a reinforcing rib layer in the membrane element layer to characterize the steel wire cord, so that the membrane element layer and the rubber matrix solid element meet the displacement coordination through embedded constraints.

[0013] S2. A shell unit layer is stacked at the corresponding position of the membrane unit layer as a bending stiffness supplement layer. The shell unit layer is registered with the membrane unit layer and does not participate in the assembly of the equilibrium equation of the embedded constraint.

[0014] S3. Define a bending-specific shell section for the shell unit layer, so that its in-plane tensile stiffness and in-plane compressive stiffness are suppressed, the membrane bending coupling stiffness is set to zero, and the bending stiffness is retained.

[0015] S4. Determine the geometric thickness and local material orientation of the shell unit layer based on the diameter and laying direction of the steel wire in the belt layer;

[0016] S5. Establish the reference bending force displacement curve and the reference tensile load displacement curve;

[0017] S6. Establish a calibration shell model and a decoupled strip model. Simultaneously assign the same candidate orthotropic material parameter set to both models and iteratively adjust them so that the bending response of the calibration shell model matches the reference bending force-displacement curve, and the deviation between the tensile response of the decoupled strip model and the reference tensile load-displacement curve is lower than a preset threshold, so as to obtain the target material parameter set. After assigning the target material parameter set to the bending stiffness supplementary layer, integrate and establish the whole tire finite element model.

[0018] The finite element model of the whole tire in this application includes at least the tread, belt layer, carcass, sidewall, bead and inner liner; during simulation, inflation pressure is applied to the inner surface of the tire, vertical load is applied to the rim or axle, and the rigid ground is used as the contact boundary.

[0019] The term "suppressed" refers to the fact that, before and after introducing the shell unit layer, the equivalent axial stiffness deviation of the decoupled strip model under axial tension conditions is no greater than 5%. The preset thresholds include a bending response error threshold and an in-plane isolation error threshold, wherein the bending response error threshold is a maximum load error of no more than 10%, and the in-plane isolation error threshold is an equivalent axial stiffness deviation of no more than 5%.

[0020] As a further improvement, in step S1, the rubber matrix solid unit is used to characterize the rubber matrix in the belt layer, the film unit layer is used to characterize the in-plane load-bearing carrier of the belt layer, and the reinforcing rib layer is used to characterize the in-plane reinforcement effect of the steel wire cord; the reinforcing rib layer includes at least the steel wire elastic modulus, the steel wire cross-sectional area, the steel wire laying angle, and the steel wire spacing, wherein the steel wire elastic modulus characterizes the tensile stiffness of the steel wire material, the steel wire cross-sectional area is the cross-sectional area of ​​a single steel wire, the steel wire laying angle is the angle between the steel wire and the reference direction of the belt layer, and the steel wire spacing is the distance between the center lines of adjacent steel wires.

[0021] As a further improvement, in step S2, the shell unit layer and the membrane unit layer achieve displacement coordination through a common node method, a multi-point constraint method, or a binding constraint method; the displacement coordination is used to ensure that the shell unit layer and the membrane unit layer deform together at the corresponding spatial positions, and the shell unit layer does not write in-plane equivalent stiffness and in-plane equivalent load to the rubber matrix solid unit.

[0022] And / or, in step S3, the bending-specific shell section is achieved through shell section stiffness control, wherein the membrane stiffness term is suppressed, the membrane-bending coupling term is zero, and the bending stiffness term is retained; the membrane stiffness term is the in-plane tensile and in-plane compressive stiffness term corresponding to the shell unit layer, the membrane-bending coupling term is the coupling stiffness term between the in-plane deformation and bending deformation of the shell unit layer, and the bending stiffness term is the stiffness term of the shell unit layer resisting bending deformation;

[0023] And / or, in step S4, the geometric thickness of the shell unit layer is taken as the diameter of the steel wire of the corresponding single steel wire in the belt layer, and the first principal direction in the local material direction is consistent with the laying direction of the steel wire in the corresponding layer; wherein, the steel wire diameter is the outer diameter of the circular cross section of a single steel wire, and the first principal direction is the principal axis direction that defines the principal property direction of the orthogonal anisotropic material.

[0024] As a further improvement, in step S5, the reference bending force-displacement curve is used to characterize the actual bending response of the belt layer, and the reference tensile load-displacement curve is used to characterize the in-plane bearing response without the superimposed bending stiffness supplementary layer; the reference bending force-displacement curve is obtained by performing a three-point bending test on the strip specimen, or by establishing a fine finite element model of the belt layer solid containing steel wire solid elements and rubber solid elements and performing a three-point bending simulation; the reference tensile load-displacement curve is obtained by applying an axial tensile condition to the in-plane bearing foundation model, or by performing a tensile test on the strip specimen.

[0025] As a further improvement, in step S6, the candidate orthotropic material parameter set includes at least the elastic modulus along the wire direction, the elastic modulus perpendicular to the wire direction, Poisson's ratio, the first planar shear modulus, the first thickness shear modulus, and the second thickness shear modulus; wherein, the elastic modulus along the wire direction is the elastic modulus of the local first principal direction of the shell unit layer, the elastic modulus perpendicular to the wire direction is the elastic modulus of the local second principal direction of the shell unit layer, the Poisson's ratio is the Poisson's ratio between the local first principal direction and the local second principal direction, the first planar shear modulus is the shear modulus between the local first principal direction and the local second principal direction, the first thickness shear modulus is the shear modulus between the local first principal direction and the thickness direction, and the second thickness shear modulus is the shear modulus between the local second principal direction and the thickness direction.

[0026] As a further improvement, in step S6, the calibration shell model adopts a conventional shell section to simultaneously possess in-plane stiffness and bending stiffness; the decoupled strip model includes an in-plane load-bearing foundation model and a bending stiffness supplementary layer; the initial values ​​of the candidate orthotropic material parameter set are given by micromechanical theory, historical calibration parameters, or empirical database parameters; the iterative adjustment adopts the least squares method, genetic algorithm, gradient descent method, or a combination thereof; when the error of the bending curve output by the calibration shell model relative to the reference bending force-displacement curve meets the first stopping condition, and the deviation of the tensile curve output by the decoupled strip model relative to the reference tensile load-displacement curve meets the second stopping condition, the iteration stops and the target material parameter set is determined, wherein the first stopping condition is used to limit the bending response fitting accuracy, and the second stopping condition is used to limit the in-plane response isolation accuracy.

[0027] Secondly, the present invention also provides a tire belt layer bending stiffness decoupling modeling and its material parameter calibration system, which is used to implement the method, including:

[0028] The in-plane bearing modeling unit is used to establish the in-plane bearing foundation model of the belt layer, including the rubber matrix solid unit, the membrane unit layer and the reinforcing rib layer in the membrane unit layer, and to establish the embedded constraint between the membrane unit layer and the rubber matrix solid unit.

[0029] The bending supplementary modeling element is used to establish a shell element layer as a bending stiffness supplementary layer at the corresponding position of the membrane element layer, and to define a bending-specific shell section for the shell element layer.

[0030] The geometry and orientation determination unit is used to determine the geometric thickness and local material orientation of the shell unit layer based on the diameter and laying direction of the steel wire in the belt layer;

[0031] The reference curve acquisition unit is used to acquire the reference bending force displacement curve and the reference tensile load displacement curve;

[0032] The parameter inversion unit is used to establish the calibration shell model and the decoupled strip model, and simultaneously assign the same candidate orthogonal anisotropic material parameter set to the calibration shell model and the decoupled strip model to iteratively obtain the target material parameter set;

[0033] The model integration unit is used to assign the target material parameter set to the bending stiffness supplement layer and integrate it with other tire component models to establish a whole tire finite element model.

[0034] Preferably, the bending supplementary modeling unit and the model integration unit are also used to establish the displacement coordination relationship between the shell unit layer and the membrane unit layer through the common node method, multi-point constraint method or binding constraint method, and to ensure that the shell unit layer does not participate in the assembly of the equilibrium equation of the embedded constraint, and does not write the in-plane equivalent stiffness and in-plane equivalent load to the rubber matrix solid unit; the parameter inversion unit is also used to use the error between the bending curve output by the calibration shell model and the reference bending force displacement curve as the bending fitting evaluation index, and the deviation between the tension curve output by the decoupled strip model and the reference tension load displacement curve as the in-plane isolation evaluation index, and output the target material parameter set when the bending fitting evaluation index and the in-plane isolation evaluation index simultaneously meet the preset conditions.

[0035] Thirdly, the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the method.

[0036] Fourthly, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0037] This invention adds a bending stiffness supplement layer that does not participate in the in-plane load-bearing chain, in addition to the original solid units and membrane units / reinforcing ribs in the belt layer. Combined with a material parameter joint inversion based on three-point bending reference response and a same parameter set migration mechanism, it effectively decouples the in-plane tensile behavior and out-of-plane bending behavior of the belt layer. Therefore, it has the following technical effects: First, it retains the high-precision characterization capability of the membrane units and reinforcing ribs for the tensile / compression response in the direction of the steel cord, avoiding contamination of the original in-plane stiffness due to the introduction of the bending supplement structure; second, it uses an independent shell layer to specifically supplement the bending stiffness of the belt layer, enabling the belt layer to withstand grounding, indentation, and local bending of the tire crown. The mechanical response under bending deformation conditions is closer to the real structure, thus significantly improving the prediction accuracy of tire finite element models for ground contact mark shape, shoulder profile, groove edge pressure gradient, and radial stiffness curve. At the same time, this invention does not directly rely on theoretical homogenization formulas to give bending parameters, but uses the bending response of the real composite structure as the calibration benchmark to obtain target material parameters, making the physical meaning of the parameters clearer, the calibration process more controllable, and the model more repeatable. This overcomes the problems of existing methods, such as the difficulty in independently optimizing tension and bending coupling, large deviations in bending stiffness parameters, and insufficient agreement between whole tire simulation results and experiments. It has strong engineering applicability and promotion significance. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the stacked structure for decoupling modeling of the bundled layer in this invention.

[0039] Figure 2 For the bending condition in this invention ( Figure 2 (A) and tensile condition ( Figure 2 (See diagram B)

[0040] Figure 3 This section compares the deflection contour plots of three models under bending conditions in the verification of the cantilever beam principle; among them... Figure 3 In the middle, A is the deflection contour plot of the solid beam of model A. Figure 3 In the middle, B is the deflection contour plot of the membrane element and the stiffened beam in model B. Figure 3 C represents the deflection cloud diagram of the beam in this invention, model C.

[0041] Figure 4 Model B (for the verification of the cantilever beam principle) Figure 4 A) and Model C) Figure 4 Comparison of deformation contour plots under tensile conditions (B)

[0042] Figure 5 For the cross-sectional dimensions of the belt layer ( Figure 5 (A) Three-point bending condition of solid fine model ( Figure 5 (B) and a schematic diagram of the calibration shell model ( Figure 5 (C)

[0043] Figure 6 This is a schematic diagram of the shell material parameter calibration method of the present invention.

[0044] Figure 7 A comparison of force-displacement curves of the solid fine model, the calibration shell model of this invention, and the theoretical parameter shell model under three-point bending conditions.

[0045] Figure 8 Tested under a load of 7252N ( Figure 8 Chinese A), traditional methods ( Figure 8 Comparison diagram of grounding imprints of the method of the present invention (B) and ( ) Figure 8 (C)

[0046] Figure 9 Tested under a load of 10878N ( Figure 9 Chinese A), traditional methods ( Figure 9 Comparison diagram of grounding imprints of the method of the present invention (B) and ( ) Figure 9 (C)

[0047] Figure 10 A comparison chart of radial stiffness curves for experimental, conventional, and present invention methods.

[0048] Figure 11 A comparison chart showing the relative errors of the major axis, minor axis, and shoulder width of grounding imprints under different vertical loads using different methods.

[0049] Figure 12 This is a comparison chart of the relative errors of radial settlement under different vertical loads using different methods.

[0050] Figure 13 A comparison chart of the curve error bands of the solid fine model, the theoretical parameter shell model, and the calibration shell model of this invention under the three-point bending condition. Detailed Implementation

[0051] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0052] I. Terminology Explanation

[0053] To make the technical solution of the present invention easier to understand, the main terms involved in the embodiments are explained in a unified manner below.

[0054] In-plane load-bearing foundation model: refers to a finite element model composed of rubber matrix solid units, membrane unit layers, and reinforcing rib layers in the membrane unit layers. It is mainly used to bear the in-plane tensile and / or compressive response of the belt layer in the cord direction or its combination direction.

[0055] Bending stiffness supplement layer: refers to a structural layer stacked at the corresponding position of the membrane unit layer, composed of shell units, and used to independently supplement the bending stiffness of the belt layer.

[0056] Bending-specific shell section: This refers to a section characteristic that suppresses the in-plane stiffness of the shell element layer, sets the membrane-bending coupling stiffness to zero, and retains the bending stiffness. It is used to ensure that the shell element layer primarily bears bending loads and does not substantially participate in in-plane load bearing. In Abaqus, the ShellGeneralSection can be used and set to bendingonly. In other finite element platforms, a custom shell section stiffness matrix can be used to set the in-plane stiffness component to no more than 5% of the equivalent bending stiffness and set the membrane-bending coupling term to 0. If numerical suppression is used, the verification criteria after suppression should be specified, such as an axial stiffness deviation of no more than 5%.

[0057] Reference bending force-displacement curve: refers to the curve of the relationship between the loading force and the loading displacement obtained by three-point bending test or by solid fine finite element three-point bending simulation, which is used to characterize the bending response of real belt-layer composite structure.

[0058] Reference tensile load-displacement curve: refers to the curve of the relationship between load and displacement obtained by axial tensile simulation of the in-plane bearing foundation model or corresponding strip tensile test, used to characterize the original in-plane bearing response without the superimposed bending stiffness supplement layer.

[0059] Calibration shell model: refers to the shell element model used for bending parameter inversion. This model uses a conventional shell section, so that the parameters of the candidate orthotropic material can be fully involved in the bending response calculation.

[0060] Decoupled strip model: refers to the strip-level decoupled model established according to the present invention, including an in-plane bearing foundation model and a bending stiffness supplementary layer, used to verify whether the candidate parameter set still meets the in-plane response isolation requirements after the introduction of the bending supplementary layer.

[0061] Candidate orthotropic material parameter set: refers to the set of parameters to be optimized assigned to the calibration shell model and the decoupled strip model during the inversion process, including at least the elastic modulus along the wire direction, the elastic modulus perpendicular to the wire direction, Poisson's ratio, the first plane shear modulus, the first thickness shear modulus and the second thickness shear modulus.

[0062] Target material parameter set: refers to the final orthogonal anisotropic material parameter set obtained after double-constraint iterative optimization, which simultaneously meets the requirements of bending fitting accuracy and in-plane isolation accuracy.

[0063] First stopping condition: The maximum load error between the calibration shell model and the reference bending force-displacement curve is not greater than 10%, or the root mean square error of the curve is not greater than 10% of the average load of the reference curve;

[0064] Second stopping condition: The equivalent axial stiffness deviation between the decoupled strip model and the reference tensile load displacement curve is no greater than 5%, preferably no greater than 2%.

[0065] II. System Structure

[0066] This invention can be embodied not only as a modeling and calibration method, but also as a system for performing that method. Referring to the system claims in the claims, the system of this invention may at least include an in-plane load-bearing modeling unit, a bending supplementary modeling unit, a geometry and orientation determination unit, a reference curve acquisition unit, a parameter inversion unit, a model integration unit, and a result output unit.

[0067] The modeling unit comprises several components: an in-plane load-bearing modeling unit, a modeling unit for in-plane load-bearing modeling ... The results output unit is used to output analysis results such as three-point bending curve, tensile response curve, grounding imprint, grounding pressure distribution, and radial stiffness curve.

[0068] Preferably, the system can be deployed on a finite element analysis platform capable of defining solid elements, membrane elements, shell elements, embedded constraints, multi-point constraints, binding constraints, and anisotropic materials, such as the Abaqus platform. The system can be composed of a processor, memory, and display terminal in hardware, and a pre-processing module, a solution module, and a post-processing module in software. Those skilled in the art can write corresponding modeling scripts, material parameter input files, and analysis flow control files according to the steps described in the specification, thereby realizing the technical solution of this invention.

[0069] III. Overall Technical Route

[0070] The overall technical route of this invention is as follows: Figure 1 , Figure 2 and Figure 6 As shown, the process can be summarized as follows: First, establish the in-plane load-bearing foundation model of the belt layer, then stack a shell element layer as a bending stiffness supplementary layer and assign a bending-specific shell section; subsequently, obtain the benchmark bending force-displacement curve characterizing the real bending response and the benchmark tensile load-displacement curve characterizing the original in-plane load-bearing response; then, establish the calibration shell model and the decoupled strip model, and use the bending response matching and in-plane response deviation below a preset threshold as dual constraints for parameter inversion; finally, transfer the obtained target material parameter set to the bending stiffness supplementary layer of the whole tire belt layer, and form a whole tire finite element model together with other tire components to carry out performance analysis such as ground imprint and radial stiffness.

[0071] It should be emphasized that the innovation of this invention is not simply the use of membrane units or shell units, but rather the construction of a complete technical chain through structural path decoupling, cross-sectional stiffness constraints, joint inversion of dual benchmarks and dual models, and migration of the same parameter set.

[0072] The specific implementation method will be explained step by step below, in conjunction with steps S1 to S7.

[0073] IV. Detailed Implementation Step-by-Step

[0074] (I) Step S1: Establish the in-plane bearing foundation model of the belt layer

[0075] The purpose of step S1 is to establish a basic model that can accurately reflect the tensile and / or compressive load-bearing capacity within the belt layer, providing a reference benchmark for subsequent decoupled modeling that only adds bending without altering the in-plane structure.

[0076] In this embodiment, a solid element model of the rubber matrix is ​​first established based on the geometric contour of the region where the target tire belt layer is located. The solid element model of the rubber matrix is ​​used to characterize the volumetric deformation and local strain distribution of the rubber matrix within the belt layer region. Eight-node solid elements are preferred, but are not limited to this. For cases requiring higher accuracy, higher-order solid elements or hybrid elements can also be used.

[0077] Subsequently, membrane unit layers are established at the geometric locations of the belt layer. These membrane unit layers preferably correspond to the geometric surface of the belt layer or the neutral layer, and are used to bear the in-plane tensile and / or compressive response of the belt layer. The membrane unit layers can employ four-node membrane units or equivalent membrane-like units. Unlike shell units, membrane units themselves do not bear bending stiffness; their advantage lies in their ability to directly bear in-plane mechanical forces, making them particularly suitable for use in conjunction with reinforcing rib layers to characterize the cord reinforcement effect.

[0078] A reinforcing rib layer is incorporated into the membrane unit layer to characterize the in-plane reinforcement effect of the steel wire cord. The reinforcing rib layer requires input of at least the steel wire's elastic modulus, cross-sectional area, lay-up angle, and spacing. The steel wire's elastic modulus characterizes the axial stiffness of the steel wire material; the cross-sectional area is the area of ​​a single steel wire; the lay-up angle is the lay-up direction angle of the steel wire relative to the reference direction of the belt layer; and the spacing is the distance between the centerlines of adjacent steel wires. If the steel wire has a circular cross-section, the cross-sectional area can be determined by the steel wire diameter. calculate:

[0079] ;

[0080] in, The cross-sectional area of ​​a single steel wire. The diameter is the wire diameter.

[0081] After establishing the membrane unit layer and the reinforcing rib layer, the membrane unit layer is embedded into the rubber matrix solid unit through internal constraints, ensuring that the membrane unit layer and the rubber matrix solid unit satisfy displacement coordination at their corresponding spatial positions. This displacement coordination means that the displacement of each node in the membrane unit layer is controlled by interpolation constraints from adjacent rubber matrix solid units, thereby ensuring that the steel wire reinforcement layer and the rubber matrix work together during in-plane deformation.

[0082] Step S1 retains the high-precision in-plane modeling advantages of the existing solid element + membrane element + stiffener, and explicitly fixes it as the in-plane load-bearing foundation model in the subsequent decoupled system. Since the bending supplementary layer of the present invention should not substantially change the mechanical response of the foundation model under axial tension, step S1 establishes not only a foundation model, but also the source of the reference tensile load-displacement curve in subsequent steps S5 and S6.

[0083] In practice, an axial tensile load can be applied to the in-plane bearing foundation model formed in step S1, with one end fixed and the other end subjected to axial displacement or axial tension, and the load-displacement curve can be recorded. This curve serves as a source of the reference tensile load-displacement curve and is used to ensure that the introduction of the bending supplementary layer in subsequent inversion does not disrupt the response of the original in-plane bearing chain.

[0084] (ii) Step S2: Establish a bending stiffness supplement layer

[0085] Step S2 involves stacking a shell element layer on top of step S1 to form a bending load-bearing path that is parallel to but functionally different from the in-plane load-bearing foundation model.

[0086] Specifically, a shell element layer is established at the corresponding position of the membrane element layer. Preferably, the shell element layer and the membrane element layer have the same shape in the planar projection, and the same or corresponding mesh partitioning method is used as much as possible. This serves two purposes: first, it facilitates the subsequent establishment of a one-to-one displacement coordination relationship between the shell element layer and the membrane element layer; second, it ensures that the shell element layer coincides geometrically with the original belt layer reinforcement region, so that its bending contribution is consistent with the actual structural position.

[0087] This invention specifically stipulates that the shell unit layer does not participate in the assembly of the equilibrium equations for the embedded constraints in step S1. That is, although the shell unit layer is stacked correspondingly with the membrane unit layer, it does not join the in-plane force equilibrium equations within the rubber entity as an embedded reinforcing layer, does not rewrite its own in-plane equivalent stiffness back to the rubber matrix unit, and does not bear the in-plane tensile / compressive forces originally borne by the membrane unit layer and the reinforcing rib layer. Thus, the shell unit layer established in step S2 is excluded from the original in-plane load-bearing chain from the outset, creating conditions for subsequently defining the bending-specific shell cross-section.

[0088] The technical value of step S2 lies in the fact that it is not simply adding another shell to the traditional model, but rather establishing a bending stiffness supplementary layer that spatially coincides with, functionally separates from, and is isolated in the calculation path of the in-plane load-bearing chain. Therefore, this invention can subsequently control the cross-sectional stiffness to ensure that this shell layer retains only bending resistance, rather than turning it into another in-plane reinforcement layer.

[0089] (III) Step S3: Define the bending-specific shell section

[0090] Step S3 achieves the core mechanism of compensating for bending without altering the in-plane structure. The purpose of this step is to ensure that the shell unit layer established in step S2 has sufficient bending stiffness to compensate for the bending load of the actual structure of the belt layer; at the same time, to suppress its in-plane tensile stiffness and in-plane compressive stiffness to a negligible level, and to set the membrane bending coupling stiffness to zero, so that it does not substantially interfere with the in-plane load-bearing foundation model in step S1.

[0091] 1. Basic principles of bending a dedicated shell cross section

[0092] The cross-sectional stiffness of a shell element can be abstractly divided into membrane stiffness, bending stiffness, and membrane-bending coupling stiffness. Membrane stiffness corresponds to the shell's resistance to in-plane tension and in-plane compression; bending stiffness corresponds to the shell's resistance to curvature changes and bending deformation; and membrane-bending coupling stiffness characterizes the coupling relationship between in-plane deformation and bending deformation.

[0093] The present invention requires that, in the shell unit layer: (1) the membrane stiffness term is suppressed to a negligible level; (2) the membrane bending coupling stiffness term is set to zero; and (3) the bending stiffness term is retained. Thus, the shell unit layer can provide effective resistance under bending conditions, while not significantly changing the original axial stiffness and in-plane load path of the belt layer under in-plane tension conditions.

[0094] 2. Project Implementation Method

[0095] In a preferred embodiment, this characteristic can be achieved by using a general shell section and setting it to a bending-only mode. For example, in a finite element implementation, this can be achieved directly using the bending-only shell section definition method supported by the software. If the software does not have this function, it can also be achieved by explicitly inputting the shell section stiffness matrix, making the membrane stiffness component approximately zero, the membrane bending coupling component zero, and the bending stiffness component effective.

[0096] To facilitate the quantification of the effectiveness of suppressing in-plane stiffness, an in-plane isolation deviation index can be introduced:

[0097] ;

[0098] in, For in-plane isolation deviation, To decouple the equivalent axial stiffness of the strip model under axial tension, This represents the equivalent axial stiffness of the in-plane bearing foundation model under the same working conditions.

[0099] The equivalent axial stiffness It can be calculated as follows:

[0100] ;

[0101] in, For axial load increment, This is the axial displacement increment corresponding to the load increment.

[0102] Preferably, by setting a bend in the specific shell cross-section, so that... Not greater than More preferably not greater than This means that after introducing the bending supplement layer, the axial tensile stiffness of the overall model changes very little compared to the original foundation model, thus confirming that the shell element layer did not cause substantial contamination to the internal load-bearing chain.

[0103] 3. The innovative mechanism of this step

[0104] Existing homogenized shell modeling often assigns both in-plane and bending stiffness to the same shell layer, making it easy to simultaneously affect in-plane stiffness when adjusting bending stiffness. While existing membrane element + stiffener modeling is suitable for in-plane load bearing, it lacks bending stiffness. This invention transforms the shell element layer into a bending-specific component by combining shell layer stacking without entering the embedded equilibrium equation and retaining only bending stiffness in the shell section, thus eliminating the contradiction of both compensating for bending and modifying in-plane stiffness from the source.

[0105] like Figure 3 As shown, in the bending verification of cantilever beams, the traditional solid element + membrane element + stiffener model has a significantly larger deflection due to the lack of bending stiffness; after introducing a bending-specific shell, the model deflection can be restored to the same level as the solid beam reference. Figure 4 This further demonstrates that, under tensile conditions, the elongation of the model before and after introducing the shell is basically the same, indicating that step S3 indeed achieves the goals of effective bending and in-plane isolation.

[0106] (iv) Step S4: Determine the geometric thickness of the shell unit layer and the local material orientation based on the wire diameter and laying direction.

[0107] Step S4 is used to establish a correspondence between the bending stiffness supplement layer and the actual belt layer wire configuration in terms of geometric scale and material direction, thereby ensuring that the target material parameters obtained in subsequent calibration have clear physical meaning.

[0108] First, the geometric thickness of the shell unit layer is preferably taken as the diameter of the corresponding single steel wire in the belt layer. This is because a significant source of the belt layer's bending stiffness is the tensile and compressive resistance generated by the steel wire under bending conditions, and the wire diameter directly affects the bending moment of inertia of a single steel wire section. Therefore, using the wire diameter as the initial value for the shell layer thickness allows for a geometrically established one-to-one correspondence between the shell unit layer and the actual steel wire component.

[0109] Secondly, the first principal direction of the local material orientation of the shell unit layer is preferably consistent with the laying direction of the corresponding steel wire. Therefore, in the orthotropic material model, the elastic modulus along the first principal direction... The equivalent stiffness directly corresponding to the dominant direction of the steel wire, and the elastic modulus perpendicular to it. The anisotropic shear modulus corresponds to the equivalent mechanical characteristics related to the transverse direction and thickness, respectively.

[0110] If it is necessary to further verify the rationality of the thickness selection from the perspective of bending energy consistency, the bending moment-curvature relationship can also be used for verification:

[0111] ;

[0112] in, For equivalent bending stiffness, For bending moment, For curvature.

[0113] Under the same curvature boundary conditions, if the shell model obtained with the wire diameter as the shell thickness is similar to the detailed solid model... Significant differences still exist, and limited corrections can be made without deviating from the actual physical dimensions of the steel wire to obtain a more stable calibration starting point. However, in the preferred embodiment, using the steel wire diameter as the shell thickness is usually sufficient to obtain a good initial fitting basis.

[0114] In step S4: the shell unit layer is not an arbitrarily abstracted patch layer, but an equivalent bending layer that corresponds to the actual steel wire configuration in terms of thickness scale and orientation properties, thus providing a physically oriented carrier for subsequent material parameter calibration.

[0115] (v) Step S5: Establish the reference bending force-displacement curve and the reference tensile load-displacement curve

[0116] Step S5 is used to establish a dual-benchmark system for parameter calibration, which is the basis of the dual-constraint inversion concept of this invention. This step does not simply obtain a target curve, but simultaneously obtains two benchmark curves with different functions: one reflects the bending behavior of the real composite belt layer, and the other reflects the tensile behavior of the original in-plane load-bearing chain.

[0117] 1. Obtaining the reference bending force-displacement curve

[0118] The reference bending force-displacement curve is preferably obtained through one of the following two methods:

[0119] The first method is a physical testing approach, which involves preparing a strip specimen with the same or equivalent structure as the target belt layer, performing a three-point bending test on it, and recording the relationship between the applied force and the applied displacement. Key structural parameters such as wire diameter, wire spacing, wire laying angle, and rubber coating thickness should be preserved in the specimen as much as possible to ensure the test curve is truly representative.

[0120] The second approach is the simulation baseline method, which involves establishing a detailed finite element model of both the steel wire and the rubber matrix, and simulating the three-point bending condition. This method is particularly suitable when experimental conditions are limited or rapid iteration is required.

[0121] In this embodiment, combined with Figure 5 A solid, refined finite element three-point bending model can be preferred for obtaining the reference curve. Specifically, the strip length can be... The span of the fulcrum can be The loading head is located in the middle and is controlled by displacement. The maximum loading displacement is, for example, [missing information]. Record the reaction force and displacement throughout the loading process to obtain the reference bending force-displacement curve.

[0122] 2. Obtaining the reference tensile load-displacement curve

[0123] The reference tensile load-displacement curve reflects the tensile response of the in-plane bearing foundation model itself. This curve can be obtained by directly applying an axial tensile load to the in-plane bearing foundation model established in step S1, or by conducting a tensile test on a corresponding strip specimen. Since the purpose of this invention is not to change the original in-plane bearing characteristics, but to independently supplement the bending stiffness on its basis, the reference tensile load-displacement curve is used as an indestructible constraint target in the subsequent inversion.

[0124] 3. The necessity of dual benchmarks

[0125] If the inversion is performed solely with the bending curve as the target, a set of parameters may be obtained that, while fitting the three-point bending results well, will significantly alter the axial tensile stiffness after integration into the decoupled model. Conversely, if only the tension is kept constant, the shell may not provide sufficient bending resistance. Therefore, this invention establishes dual benchmarks in step S5 to simultaneously control these two types of behavior using a dual-constraint approach in the subsequent step S6.

[0126] Figure 2 The bending and tensile conditions shown correspond to this dual-benchmark acquisition process, demonstrating that the present invention does not employ single-objective fitting, but rather incorporates both correct bending and in-plane invariance into the calibration system.

[0127] (vi) Step S6: Establish the calibration shell model and the decoupled strip model and perform double-constraint inversion.

[0128] 1. The necessity of setting up a dual-model setup

[0129] Traditional homogenization methods typically employ a single shell model or a single composite material model, using theoretical formulas or empirical parameter tuning to approximate a certain type of experimental curve. The problem with this approach is that when parameters are adjusted solely for bending results, the resulting material parameters often have uncontrolled effects on in-surface behavior; and when parameters are adjusted solely for overall tire macroscopic indicators, they easily lose their physical connection with the actual bending mechanism of the local composite structure.

[0130] In step S6 of this invention, two models are established simultaneously:

[0131] The first is the calibration shell model. This model is used to directly load the candidate parameter set under bending conditions and compare it with the reference bending force-displacement curve. The calibration shell model uses a conventional shell section, rather than a bending-specific shell section, in order to ensure that the candidate parameter set... , , , , , These parameters can be fully involved in the mechanical calculation of the shell element, thus fully reflecting the influence of these parameters on the bending response.

[0132] The second is the decoupled strip model. This model is constructed according to the final application method of this invention, that is, it simultaneously includes the in-plane bearing foundation model obtained in step S1 and the bending stiffness supplementary layer formed in steps S2, S3, and S4. This model is used to verify whether the entire decoupled system remains sufficiently close to the original in-plane bearing foundation model under axial tension when the same candidate parameter set is assigned to the bending stiffness supplementary layer.

[0133] Only by introducing both models simultaneously can we ensure that the resulting target parameter set is effective for real bending behavior without disrupting the original in-plane load chain.

[0134] 2. Parameter set of candidate orthotropic materials

[0135] The parameter set of candidate orthotropic materials should include at least:

[0136] : Local first principal direction elastic modulus;

[0137] : Local second principal direction elastic modulus;

[0138] Poisson's ratio between the local first principal direction and the local second principal direction;

[0139] : Shear modulus between the local first principal direction and the local second principal direction;

[0140] : Shear modulus between the local first principal direction and the thickness direction;

[0141] : Shear modulus between the local second principal direction and the thickness direction.

[0142] In this context, the local primary direction coincides with the corresponding wire laying direction. Initial values ​​for the candidate parameter set can be provided by micromechanical formulas, empirical databases, or historical calibration parameters. Using micromechanical formulas as initial values ​​has good engineering applicability because it provides a starting point close to the true directional relationship. However, this invention does not directly use this initial value as the final parameter, but rather uses it as the starting point for the double-constraint inversion.

[0143] 3. Bending Fit Constraints

[0144] The calibration shell model is subjected to the same three-point bending boundary condition as the reference bending condition to obtain the calculated force-displacement curve. This curve is then compared with the reference bending force-displacement curve. Preferably, the root mean square error is used as the bending fitting evaluation index.

[0145] ;

[0146] in, For bending fitting error, The number of sampling points for the curved curve. To calibrate the shell model in the first The computational load for each sampling point The reference bending curve at the 1st Reference load for each sampling point.

[0147] In addition to root mean square error, the degree of bending fit can also be characterized by peak load error, initial stiffness slope error, or a combination of multiple indicators.

[0148] 4. In-plane isolation constraints

[0149] An axial tensile load is applied to the decoupled strip model to obtain its load-displacement curve; this curve is then compared with the reference tensile load-displacement curve obtained in step S5. Preferably, the aforementioned in-plane isolation deviation can be used. The root mean square error of the load-displacement curve can be used to evaluate the degree of in-plane influence. The significance is that if the in-plane response changes significantly after introducing a bending supplementary layer, it indicates that the candidate parameter set or shell section definition has not yet achieved true in-plane isolation.

[0150] 5. Dual-constraint joint inversion process

[0151] During the inversion, the same set of candidate parameters is assigned to both the calibration shell model and the decoupled strip model. Then, the following loop is executed:

[0152] (1) Calculate the three-point bending curve of the calibration shell model;

[0153] (2) Calculate the axial tension curve of the decoupled strip model;

[0154] (3) Calculate the bending fitting error ;

[0155] (4) Calculate the in-plane isolation deviation Or equivalent deviation index;

[0156] (5) Update the candidate parameter set according to the selected optimization algorithm;

[0157] (6) Repeat the above steps until both the bending fitting constraint and the in-plane isolation constraint are satisfied.

[0158] To comprehensively evaluate the two constraints, a comprehensive objective function can be constructed:

[0159] ;

[0160] in, For the comprehensive objective function, These are the bending fitting weight coefficients. This is the in-plane isolation weight coefficient. The reference bending curve is the average value of the reference load. For bending fitting error, This refers to in-plane isolation deviation.

[0161] The optimization algorithm can employ least squares, genetic algorithms, gradient descent, or combinations thereof. For example, using a genetic algorithm for global search followed by gradient descent for local refinement can effectively improve convergence efficiency and final accuracy.

[0162] 6. Determination of the target material parameter set

[0163] The iteration stops and the target material parameter set is output when the following conditions are met:

[0164] (1) The error of the bending curve output by the calibration shell model relative to the reference bending force-displacement curve satisfies the first stopping condition; (2) The deviation of the tension curve output by the decoupled strip model relative to the reference tension load-displacement curve satisfies the second stopping condition.

[0165] Preferably, the first stopping condition can be set to the maximum load error not exceeding a certain value. Or the root mean square error is lower than a predetermined limit; the second stopping condition can be set to the in-plane isolation deviation not exceeding a certain value. More preferably not greater than .

[0166] Unlike single-objective parameter calibration, this invention requires two conditions to be met simultaneously for the parameter set to be recognized as the target material parameter set. This ensures that the final output parameter set is not merely a set that only bends, nor merely a set that does not affect tension, but rather a set that truly combines the realism of local bending with the applicability of overall decoupling.

[0167] 7. The effect of step S6

[0168] Step S6 transforms the bending parameter inversion from a traditional single curve fitting problem into a dual-model consistency constraint problem involving a calibration shell model and a decoupled strip model. This step eliminates the reliance on purely theoretical homogenization formulas or empirical adjustments to the overall tire specifications for determining material parameters. Instead, it establishes a calibration methodology framework that balances local physical realism with the decoupling of system functions.

[0169] Figure 6 The calibration process is clearly shown. Figure 7 and Figure 12 Further evidence shows that when using the target parameter set obtained by inversion using the present invention, the bending curve of the shell model highly overlaps with the fine model of the solid, while the shell model using theoretical initial values ​​has a large deviation.

[0170] (vii) Step S7: Assign the target material parameter set to the bending stiffness supplementary layer and establish the whole tire finite element model.

[0171] Step S7 is used to complete the migration from strip-level calibration to whole-tire application. The target material parameter set obtained in step S6 is directly assigned to the bending stiffness supplementary layer corresponding to each belt layer in the whole-tire model, and integrated with the models of other tire components to establish a whole-tire finite element model.

[0172] Specifically, for each belt layer of the entire tire, a shell unit layer corresponding to the membrane unit layer is established according to steps S2 to S4. This shell layer is assigned a shell thickness corresponding to the diameter of the steel wire in that layer, a local material orientation consistent with the laying direction of the steel wire, and the target material parameter set obtained in step S6 is assigned to that shell layer. If the tire contains multiple belt layers, the target parameter set can be inverted separately for each layer, or a layered shared parameter set can be used when the structure is similar.

[0173] Subsequently, the decoupled models of each belt layer are integrated with components such as the tire carcass, tread, sidewall, tread bead, inner liner, and tire bead to form a complete tire finite element model. By applying inflation pressure, vertical load, and ground contact boundary conditions to this complete tire model, ground imprint analysis and radial stiffness analysis can be performed.

[0174] This invention preferably employs a same parameter set migration, meaning that the bending stiffness supplementary layer in the whole tire model directly adopts the target material parameter set obtained in step S6, without further secondary adjustment of the overall stiffness of the whole tire. This ensures that the parameters remain consistent with the strip-level bending reference and in-plane isolation constraints, avoiding the loss of the physical meaning of the parameters due to readjustment for a certain macroscopic index.

[0175] V. Specific Application Examples

[0176] (I) Application Example 1: Three-point bending calibration and bending response verification of belt layer strip

[0177] To verify the feasibility of the proposed decoupled modeling approach for load-bearing behavior and bending load-bearing behavior within the belt layer, and to obtain a target material parameter set that can be directly used for the whole tire model, strip samples with the same structure as the target tire belt layer were selected. The material parameters of the bending stiffness supplementary layer were calibrated by combining the three-point bending test conditions and the simulation of the solid fine model.

[0178] 1. Sample structure and modeling object

[0179] A belt-layer strip was selected as the test object. The strip was 100 mm long and 15 mm wide. The strip contained several steel wire cords and a rubber matrix. The steel wire diameter was 0.6 mm, the center-to-center spacing was 1.25 mm, and the wire laying angle was 30 degrees. ∘ The thickness of the rubber-coated area is approximately 1 mm. The wire diameter is the outer diameter of a single wire, the wire center-to-center distance is the distance between the centerlines of adjacent wires, and the wire laying angle is the angle between the wire and the reference axis along the strip's length.

[0180] To ensure the reliability of the calibration benchmark, this example uses a two-level model:

[0181] The first type is a fine-grained solid model of the belt layer, which is used as a benchmark for bending response;

[0182] The second type is the shell element calibration model, which is used to invert the parameters of orthogonal anisotropic materials.

[0183] In the detailed solid model, both the steel wire and the rubber matrix are modeled using solid elements. The steel wire material is modeled using a linear elastic model with an elastic modulus of 150,000 MPa; the rubber material is modeled using a linear elastic approximation model with an elastic modulus of 3.5 MPa. In subsequent implementations with higher precision, the rubber can be replaced with a hyperelastic constitutive model, but this will not affect the core concept of the invention.

[0184] 2. Three-point bending condition

[0185] like Figure 5 As shown, two support points are set at both ends of the strip, with a distance of 80 mm between the support points, and the loading head is located in the middle of the sample. A displacement-controlled loading method is used, with a maximum loading displacement of 5 mm. The relationship between the loading head reaction force and displacement during loading is recorded to obtain the reference bending force-displacement curve. In this example, the reference bending force-displacement curve is preferably obtained from a three-point bending simulation using a fine-grained physical model; if a corresponding laboratory sample is available, a physical three-point bending test curve under the same conditions can also be used instead. Regardless of whether an experimental method or a fine-grained physical model is used, it serves as the reference source for the actual bending response of the composite belt layer in this invention.

[0186] 3. Calibration of the shell model and initial parameter values

[0187] A shell element calibration model with the same shape as the strip sample was established. Its initial thickness was set to 0.6 mm (the diameter of the steel wire). The local first principal direction was aligned with the steel wire laying direction, i.e., it was consistent with the 30 mm diameter. ∘ The laying direction corresponds. The shell element material adopts an orthogonal anisotropic elastic model, and its candidate parameter set includes at least:

[0188] : Elastic modulus along the direction of the steel wire;

[0189] : The elastic modulus perpendicular to the direction of the steel wire;

[0190] Poisson's ratio between the local first principal direction and the local second principal direction;

[0191] : Shear modulus between the local first principal direction and the local second principal direction;

[0192] : Shear modulus between the local first principal direction and the thickness direction;

[0193] : Shear modulus between the local second principal direction and the thickness direction.

[0194] The initial values ​​were calculated using micromechanical formulas, and the initial parameters are as follows:

[0195] ;

[0196] ;

[0197] ;

[0198] ;

[0199] ;

[0200] .

[0201] 4. Inversion and Calibration Results

[0202] according to Figure 6 The process shown also establishes:

[0203] A calibration shell model is used to fit a reference bending force-displacement curve.

[0204] The decoupled strip model is used to verify whether the in-plane tensile response remains consistent with the original in-plane bearing foundation model after the same parameter set is applied to the bending stiffness supplement layer.

[0205] Using the baseline bending force-displacement curve as the target, the candidate parameter set is iteratively optimized and adjusted to make the bending curve of the calibration shell model match the baseline curve as closely as possible, while simultaneously ensuring that the axial tensile response deviation of the decoupled strip model is below a preset threshold. The final target material parameter set is as follows:

[0206] ;

[0207] ;

[0208] ;

[0209] ;

[0210] ;

[0211] .

[0212] 5. Technical Effect Analysis

[0213] like Figure 7 As shown, after using the target material parameter set obtained by the inversion of this invention, the three-point bending force-displacement curve of the shell element calibration model highly coincides with the reference curve of the solid fine model, and the maximum load error is controlled within 10. However, when the shell model directly uses the theoretical initial parameters, its force-displacement curve is significantly softer, and the maximum load error is greater than 50. This indicates that simply relying on homogenized theoretical parameters cannot accurately characterize the bending response of the real steel wire-rubber composite structure, while the dual-constraint calibration method described in this invention can significantly improve the bending fitting accuracy.

[0214] Furthermore, such as Figure 13 As shown, the error band of the calibration shell model of the present invention relative to the reference curve is significantly smaller than that of the theoretical parameter shell model, indicating that the target material parameter set determined by the present invention not only matches better at the peak load, but also has a more stable fitting effect throughout the entire loading range.

[0215] Furthermore, after assigning the same parameter set to the decoupled strip model, its axial tensile response is basically the same as that of the original in-plane bearing foundation model, indicating that the target material parameter set improves the bending response without significantly disturbing the original in-plane bearing behavior, thus proving that the dual-constraint calibration idea of ​​bending fitting and in-plane non-contamination in this invention is effective.

[0216] (II) Application Example 2: Verification of Prediction Accuracy of Tire Grounding Imprint

[0217] To verify the application effect of the present invention at the whole tire level, a radial tire with a specification of 255 / 45ZR20 was selected as the test object. Under the same inflation pressure and different vertical loads, the differences between the traditional method and the method of the present invention in predicting ground contact marks were compared.

[0218] 1. Test conditions

[0219] The test tire was mounted on a standard test rim, and the inflation pressure was set to 220 kPa. Before testing, the tire was left at room temperature for at least 24 hours to allow the tire temperature and internal pressure to stabilize. A static ground impression test device was used to apply two sets of typical vertical loads to a rigid plate:

[0220] 7252N, which corresponds to approximately 80% of the rated load of a single tire;

[0221] 10878N, which corresponds to approximately 120 of the rated load of a single tire.

[0222] The grounding imprint profile and grounding pressure distribution were recorded during the experiment, and key geometric parameters such as the major axis, minor axis, and shoulder width of the grounding imprint were extracted. Two whole-tire finite element models were established in the simulation:

[0223] Traditional method model: The belt layer adopts a solid element + membrane element + stiffener + embedded constraint structure, without setting an independent bending stiffness supplement layer;

[0224] The method model of this invention is as follows: Based on the traditional method, a bending-specific shell unit layer is superimposed on each belt layer. The shell layer thickness is taken as the diameter of the corresponding steel wire 0.6mm. The material parameters adopt the target material parameter set obtained by calibration in application example 1, and displacement coordination is established with the membrane unit layer through the common node method.

[0225] 2. Key Dimensions of Grounding Imprint

[0226] The long axis, short axis, and shoulder width of the grounding imprint were extracted under two sets of loads, and the results are shown in Table 1.

[0227] Table 1 Comparison of key dimensions of grounding imprints under different vertical loads.

[0228]

[0229] Among them, the shoulder width is defined as the short axis dimension of the ground imprint approximately The longitudinal dimension at the location.

[0230] 3. Error Analysis

[0231] Based on the data in Table 1, the relative errors are as follows:

[0232] Under 7252N:

[0233] The traditional method results in a major axis error of +9.7, while the present invention results in an error of +4.2.

[0234] The minor axis error of the traditional method is -3.5, while that of this invention is +0.5.

[0235] The traditional method has a shoulder width error of +10.1, while the present invention has an error of -0.8.

[0236] At 10878N:

[0237] The traditional method results in a major axis error of +8.4, while the present invention results in +5.1.

[0238] The minor axis error of the traditional method is -1.9, while that of this invention is +0.5;

[0239] The traditional method has a shoulder width error of +5.0, while the present invention has an error of +1.7.

[0240] The average absolute error of the above six indicators is approximately 6.42 for the traditional method and approximately 2.13 for the method of this invention. This demonstrates that the present invention significantly improves upon the traditional method in predicting the geometry of grounding imprints.

[0241] 4. Technical Effect Analysis

[0242] like Figure 8 As shown, under 7252N conditions, the long axis of the grounding imprint predicted by the traditional method is significantly longer and the shoulder width is significantly larger, indicating that it does not adequately constrain the grounding development in the tire shoulder area. In contrast, the grounding imprint obtained by the method of this invention is closer to the experimental value in both the tire center and the tire shoulder area. In particular, the shoulder width is improved from being 13mm larger than the traditional method to being 1mm smaller, indicating that the belt layer bending stiffness supplement layer has a significant effect on the shape control of the tire shoulder area.

[0243] like Figure 9 As shown, under 10878N operating conditions, the method of the present invention can still maintain good prediction consistency, indicating that its technical effect is not only valid under low load conditions, but also effective under high load grounding extension conditions.

[0244] Furthermore, from Figure 8 , Figure 9 The ground pressure distribution also shows that the traditional method does not produce a significant pressure gradient at the edge of the longitudinal groove, while the method of the present invention forms a local pressure concentration area at the edge of the groove that is closer to the test result. This indicates that the present invention not only improves the size of the imprint outline, but also enhances the ability to characterize the local pressure distribution features of the tire crown.

[0245] Figure 11 Further displaying the relative errors of the major axis, minor axis, and shoulder width in a bar chart makes it more intuitive to see that, regardless of whether it is a 7252N or 10878N operating condition, the error of the method of the present invention in most key dimensions is significantly smaller than that of the traditional method, proving that the present invention has an overall improvement in the accuracy of grounding imprint prediction.

[0246] (III) Application Example 3: Verification of Radial Stiffness Prediction for the Whole Tire

[0247] To further verify the improvement effect of this invention on the overall tire load-bearing characteristics, the radial stiffness of the tire was compared through experiments and simulations under the same tire and inflation conditions as in Application Example 2. This application example mainly corresponds to... Figure 10 and Figure 12 .

[0248] 1. Test conditions

[0249] In the test, the tire was inflated to 220 kPa and mounted on a static load test bench. Vertical loads were applied in stages, and the settlement of the tire crown center relative to the rigid ground was recorded. To facilitate comparison with... Figure 9 Correspondingly, this example selects two typical load points, 7252N and 10878N, for comparison.

[0250] The simulation conditions are the same as in Application Example 2, that is, the radial displacement of the whole tire is extracted under the same inflation pressure and vertical load using both the traditional whole tire model and the whole tire model of the present invention.

[0251] 2. Radial subsidence data

[0252] The results are shown in Table 2.

[0253] Table 2 Comparison of radial settlement under different vertical loads

[0254]

[0255] 3. Error Analysis

[0256] According to Table 2:

[0257] At 7252N, the error of the traditional method is +8.7, while the error of this invention is +2.0.

[0258] At 10878N, the error of the conventional method is +8.7, while the error of the present invention is +2.9.

[0259] The mean absolute error between the two operating conditions was reduced from 8.69 in the traditional method to 2.41 in this invention.

[0260] If the equivalent radial stiffness is approximately characterized by the ratio of load to settlement, then:

[0261] At 7252 N, the experimental equivalent stiffness is approximately 260.6 N / mm, the conventional method is approximately 239.7 N / mm, and the present invention is approximately 255.5 N / mm;

[0262] At 10878 N, the experimental equivalent stiffness is approximately 272.2 N / mm, compared to approximately 250.4 N / mm using the traditional method and approximately 264.6 N / mm using the present invention.

[0263] Therefore, it can be seen that the equivalent radial stiffness of the whole tire obtained by the method of the present invention is significantly closer to the experimental value.

[0264] 4. Technical Effect Analysis

[0265] like Figure 10 As shown, traditional methods, due to the lack of independent supplementation for the bending stiffness of the belt layer, result in insufficient overall bending restraint of the tire under vertical loads, manifested as excessive sinking under the same load, i.e., low radial stiffness. The method of this invention introduces an independent bending stiffness supplementation layer into the belt layer without disrupting the original in-plane load-bearing chain, thereby significantly bringing the overall tire radial stiffness curve closer to the experimental curve.

[0266] Figure 12 Furthermore, it is shown that at two typical load points, the radial settlement error of the present invention is significantly smaller than that of the traditional method, indicating that the present invention not only improves the local grounding geometry prediction capability, but also simultaneously improves the prediction accuracy of the overall load-bearing characteristics of the entire tire, and has a consistent improvement effect from local structure to overall tire performance.

[0267] (iv) Explanation of overall technical effects

[0268] Application Examples 1 to 3 demonstrate that the present invention has at least the following technical effects:

[0269] First, the present invention adds a bending stiffness supplementary layer that does not participate in the assembly of the original embedded equilibrium equation to the original in-plane load-bearing system of solid unit, membrane unit and stiffener, and gives it a bending-specific shell section, thereby realizing the structural decoupling of the in-plane load-bearing behavior and bending load-bearing behavior of the belt layer.

[0270] Second, this invention obtains a target material parameter set that balances bending fitting accuracy and in-plane isolation accuracy by using dual benchmarks of benchmark bending force-displacement curve and benchmark tensile load-displacement curve, as well as dual model joint inversion of calibration shell model + decoupled strip model. This overcomes the defect that traditional homogenized theoretical parameters cannot simultaneously balance real bending response and in-plane bearing stability.

[0271] Third, in whole-tire applications, the present invention significantly outperforms traditional methods in predicting the long axis, short axis, shoulder width, and radial sinking of the ground contact mark. The average absolute error of the six key dimensional indicators of the ground contact mark is reduced from approximately 6.42 to approximately 2.13, and the average absolute error of the radial sinking is reduced from 8.69 to 2.41. This indicates that the present invention can significantly improve the prediction accuracy of the tire finite element model for the ground contact pattern, local pressure distribution, and overall vertical stiffness of the tread area.

[0272] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

[0273] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0274] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0275] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0276] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0277] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0278] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0279] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

Claims

1. A method for decoupling modeling of the bending stiffness of a tire belt layer and calibrating its material parameters, characterized in that, Includes the following steps: S1. Establish an in-plane bearing foundation model for the belt layer, including establishing a rubber matrix solid element, establishing a membrane element layer at the geometric position of the belt layer, and setting a reinforcing rib layer in the membrane element layer to characterize the steel wire cord, so that the membrane element layer and the rubber matrix solid element meet the displacement coordination through embedded constraints. S2. A shell unit layer is stacked at the corresponding position of the membrane unit layer as a bending stiffness supplement layer. The shell unit layer is registered with the membrane unit layer and does not participate in the assembly of the equilibrium equation of the embedded constraint. S3. Define a bending-specific shell section for the shell unit layer, so that its in-plane tensile stiffness and in-plane compressive stiffness are suppressed, the membrane bending coupling stiffness is set to zero, and the bending stiffness is retained. S4. Determine the geometric thickness and local material orientation of the shell unit layer based on the diameter and laying direction of the steel wire in the belt layer; S5. Establish the reference bending force displacement curve and the reference tensile load displacement curve; S6. Establish a calibration shell model and a decoupled strip model. Simultaneously assign the same candidate orthotropic material parameter set to both models and iteratively adjust them so that the bending response of the calibration shell model matches the reference bending force-displacement curve, and the deviation between the tensile response of the decoupled strip model and the reference tensile load-displacement curve is lower than a preset threshold, so as to obtain the target material parameter set. After assigning the target material parameter set to the bending stiffness supplementary layer, integrate and establish the whole tire finite element model.

2. The method according to claim 1, characterized in that, In step S1, the rubber matrix solid unit is used to characterize the rubber matrix in the belt layer, the film unit layer is used to characterize the in-plane load-bearing carrier of the belt layer, and the reinforcing rib layer is used to characterize the in-plane reinforcement effect of the steel wire cord; the reinforcing rib layer includes at least the steel wire elastic modulus, the steel wire cross-sectional area, the steel wire laying angle, and the steel wire spacing, wherein the steel wire elastic modulus characterizes the tensile stiffness of the steel wire material, the steel wire cross-sectional area is the cross-sectional area of ​​a single steel wire, the steel wire laying angle is the angle between the steel wire and the reference direction of the belt layer, and the steel wire spacing is the distance between the center lines of adjacent steel wires.

3. The method according to claim 1, characterized in that, In step S2, the shell unit layer and the membrane unit layer achieve displacement coordination through a common node method, a multi-point constraint method, or a binding constraint method; the displacement coordination is used to ensure that the shell unit layer and the membrane unit layer deform together at the corresponding spatial positions, and the shell unit layer does not write in-plane equivalent stiffness and in-plane equivalent load to the rubber matrix solid unit. And / or, in step S3, the bending-specific shell section is achieved through shell section stiffness control, wherein the membrane stiffness term is suppressed, the membrane-bending coupling term is zero, and the bending stiffness term is retained; the membrane stiffness term is the in-plane tensile and in-plane compressive stiffness term corresponding to the shell unit layer, the membrane-bending coupling term is the coupling stiffness term between the in-plane deformation and bending deformation of the shell unit layer, and the bending stiffness term is the stiffness term of the shell unit layer resisting bending deformation; And / or, in step S4, the geometric thickness of the shell unit layer is taken as the diameter of the steel wire of the corresponding single steel wire in the belt layer, and the first principal direction in the local material direction is consistent with the laying direction of the steel wire in the corresponding layer; wherein, the steel wire diameter is the outer diameter of the circular cross section of a single steel wire, and the first principal direction is the principal axis direction that defines the principal property direction of the orthogonal anisotropic material.

4. The method according to claim 1, characterized in that, In step S5, the reference bending force-displacement curve is used to characterize the actual bending response of the belt layer, and the reference tensile load-displacement curve is used to characterize the in-plane bearing response without the superimposed bending stiffness supplementary layer. The reference bending force-displacement curve is obtained by performing a three-point bending test on the strip specimen, or by establishing a fine finite element model of the belt layer solid containing steel wire solid elements and rubber solid elements and performing a three-point bending simulation. The reference tensile load-displacement curve is obtained by applying an axial tensile condition to the in-plane bearing foundation model, or by performing a tensile test on the strip specimen.

5. The method according to claim 1, characterized in that, In step S6, the candidate orthotropic material parameter set includes at least the elastic modulus along the wire direction, the elastic modulus perpendicular to the wire direction, Poisson's ratio, the first planar shear modulus, the first thickness shear modulus, and the second thickness shear modulus; wherein, the elastic modulus along the wire direction is the elastic modulus of the local first principal direction of the shell unit layer, the elastic modulus perpendicular to the wire direction is the elastic modulus of the local second principal direction of the shell unit layer, the Poisson's ratio is the Poisson's ratio between the local first principal direction and the local second principal direction, the first planar shear modulus is the shear modulus between the local first principal direction and the local second principal direction, the first thickness shear modulus is the shear modulus between the local first principal direction and the thickness direction, and the second thickness shear modulus is the shear modulus between the local second principal direction and the thickness direction.

6. The method according to claim 1, characterized in that, In step S6, the calibration shell model uses a conventional shell section to simultaneously possess in-plane stiffness and bending stiffness; the decoupled strip model includes an in-plane load-bearing foundation model and a bending stiffness supplementary layer; the initial values ​​of the candidate orthotropic material parameter set are given by micromechanical theory, historical calibration parameters, or empirical database parameters; the iterative adjustment uses the least squares method, genetic algorithm, gradient descent method, or a combination thereof; when the error of the bending curve output by the calibration shell model relative to the reference bending force-displacement curve meets the first stopping condition, and the deviation of the tensile curve output by the decoupled strip model relative to the reference tensile load-displacement curve meets the second stopping condition, the iteration stops and the target material parameter set is determined, wherein the first stopping condition is used to limit the bending response fitting accuracy, and the second stopping condition is used to limit the in-plane response isolation accuracy.

7. A decoupled modeling system for the bending stiffness of a tire belt layer and a system for calibrating its material parameters, characterized in that, The system is used to implement the method according to any one of claims 1 to 6, comprising: The in-plane bearing modeling unit is used to establish the in-plane bearing foundation model of the belt layer, including the rubber matrix solid unit, the membrane unit layer and the reinforcing rib layer in the membrane unit layer, and to establish the embedded constraint between the membrane unit layer and the rubber matrix solid unit. The bending supplementary modeling element is used to establish a shell element layer as a bending stiffness supplementary layer at the corresponding position of the membrane element layer, and to define a bending-specific shell section for the shell element layer. The geometry and orientation determination unit is used to determine the geometric thickness and local material orientation of the shell unit layer based on the diameter and laying direction of the steel wire in the belt layer; The reference curve acquisition unit is used to acquire the reference bending force displacement curve and the reference tensile load displacement curve; The parameter inversion unit is used to establish the calibration shell model and the decoupled strip model, and simultaneously assign the same candidate orthogonal anisotropic material parameter set to the calibration shell model and the decoupled strip model to iteratively obtain the target material parameter set; The model integration unit is used to assign the target material parameter set to the bending stiffness supplement layer and integrate it with other tire component models to establish a whole tire finite element model.

8. The system according to claim 7, characterized in that, The bending supplementary modeling unit and model integration unit are also used to establish the displacement coordination relationship between the shell unit layer and the membrane unit layer through common node method, multi-point constraint method or binding constraint method, and to ensure that the shell unit layer does not participate in the assembly of the equilibrium equation of the embedded constraint, and does not write the in-plane equivalent stiffness and in-plane equivalent load to the rubber matrix solid unit; the parameter inversion unit is also used to use the error between the bending curve output by the calibration shell model and the reference bending force displacement curve as the bending fitting evaluation index, and the deviation between the tension curve output by the decoupled strip model and the reference tension load displacement curve as the in-plane isolation evaluation index, and output the target material parameter set when the bending fitting evaluation index and the in-plane isolation evaluation index simultaneously meet the preset conditions.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-6.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-6.

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