Method and system for establishing an electric vehicle tire bead sandwich type rubber-fiber composite simulation model

Abstract

This invention relates to the field of tire simulation design technology, and particularly to a method and system for establishing a simulation model of a sandwich-type rubber-fiber composite tire bead for electric vehicles. The target area is constructed as an equivalent beam / shell sandwich layer, a constrained zone / active zone is defined and coupled with the rim, and a vertical load of P=p·A and a 4-15Hz operating condition are applied. Using the "minimum strain amplitude surface" as the neutral surface criterion, S11 and the interface shear amplitude are extracted; the established empirical relationship is used to inversely calculate Δh, and rapid iteration is performed within the range of 25-40MPa in the constrained zone, 7.5-15MPa in the active zone, and Δh=1-5mm. This allows the compression and shear peak values ​​of the inverted tire carcass to decrease synchronously, the neutral surface to stabilize, and the modeling time to be reduced from weekly to hourly levels, making it suitable for the design and process optimization of inverted bead structures.

Description

Technical Field

[0001] This invention relates to the field of tire simulation design technology, and in particular to a method and system for establishing a simulation model of a sandwich-type rubber-fiber composite tire bead for electric vehicles. Background Technology

[0002] The bead / belly area is a weak point in radial tires, where structure, materials, and manufacturing processes are highly coupled. Figure 1 As shown, its typical components include: an inner liner, a carcass ply, a triangular rubber, a reverse-wrapped sidecar body, sidewall filler, and a bead wire (or wire ring, reinforcing layer), etc. The end of the carcass wraps around the wire ring and cooperates with the triangular rubber to form a reverse-wrapped structure. Common problems in this area include the risk of air accumulation and separation caused by the step and gap at the reverse-wrapped end, stress concentration and shear slip at the end, and fatigue damage caused by cyclical operation. Taking Chinese patent CN102922956A "Tire Bead Structure" as an example, it clearly lists the commonly used bead construction units and the engineering pain point of "the small amount of material between the reverse-wrapped end of the bead reinforcement layer and the reverse-wrapped end of the carcass leading to easy air accumulation and separation", and attempts to improve load-bearing and life performance through structural modification.

[0003] To improve bead durability and assembly quality, some patents alleviate localized stress at the bead wrapping end through structural improvements. For example, Chinese patent CN205059092U introduces a double steel wire ring / auxiliary steel wire ring and a special adhesive to change the wrapping path and eliminate stress concentration and pullback damage at the end points; this solution improves the bead's resistance to deformation and pullback at the structural level. Chinese patent CN104669656A introduces an isolation / gap or elastic buffer design at the bead end, emphasizing the formation of a deformable zone between the cord end, the upper end of the triangular adhesive, and the corresponding cord position to absorb shear energy and reduce the tendency of interlayer peeling, reflecting the engineering community's long-term concern about the "interface shear—end point concentration" problem.

[0004] Besides physical structure optimization, finite element modeling and simulation have become important methods for verifying tire bead designs. For numerical simulation of the forming and tumbling process, Chinese patent CN101923589A divides tire forming into subsystems such as carcass bonding, crown bonding, and triangular rubber tumbling. In numerical implementation, it employs various rubber constitutive models and "REBAR (rib element)" to characterize the cords, combined with boundary conditions such as bonding pressure, inflation internal pressure, rolling load, and interface friction, to reproduce the integrated process of forming, assembly, inflation, and tumbling, used to extract key physical quantities and determine forming quality. Regarding the assessment of post-service or finalized condition, Chinese patent CN105205243A proposes using the positive and negative internal forces of the tire carcass cords after finalization in the vulcanizing machine to determine the cord bending condition of wide-base radial tires, demonstrating the feasibility of identifying structural risks through mechanical field characteristics.

[0005] Regarding the parameterization and optimization of the triangular rubber core, Chinese patent CN111008496 uses "maximum / minimum principal strain and strain energy density cloud map" as evaluation quantities. Based on the finite element method and interpolation / iteration, it determines the boundary and shape of the upper and lower triangular rubber cores, achieving a systematic improvement in the mechanical properties and durability of the triangular rubber core. This method emphasizes directly linking "strain energy / strain amplitude" with structural optimization, providing a path for simulation-driven design of local bead areas. The applicant's Chinese invention patent CN117521249A defines the bead neutral plane as follows: under inflation and loading conditions, the inner bead material is subjected to compressive stress, and the outer bead material is subjected to tensile stress. Therefore, there must be a certain area in the bead where the material is in a state of stress equilibrium, neither under compression nor tension. Placing weak points with large material rigidity differences at the neutral plane can minimize stress concentration. A method to improve bead problems is proposed by placing the tire carcass and steel wire bead ends on the tire bead neutral plane to reduce end rubber stress. Summary of the Invention

[0006] To address the aforementioned technical issues, this invention provides a method for establishing a simulation model of a sandwich-type rubber-fiber composite tire bead for electric vehicles. Under the premise of clearly defining the "constraint zone / active zone" partitioning and rim support coupling, the 4–15Hz grounding loads of the service conditions are equivalently incorporated into the model. Using the "minimum strain amplitude surface, i.e., the neutral surface" as the core criterion, and combining the empirical relationship of Δh-S11, key parameters can be inversely calculated and converged rapidly. This significantly reduces modeling and calculation costs, suppresses the S11 compression of the tire body on the reverse side and the peak value of the interface shear, and provides a directly applicable engineering tool for optimizing the tire bead structure durability and process window.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for establishing a simulation model of a sandwich-type rubber-fiber composite tire bead for electric vehicles, the method comprising the following steps:

[0009] S1) Model the target area hierarchically according to the inner liner rubber, tire carcass, triangular rubber, reverse side tire carcass, sidewall filler rubber and steel wire ring, and determine the design variable set X={Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w}, where Δh is the relative translation distance of the reverse side tire carcass, b1~b3 are the thickness of each rubber layer, σ1~σ3 are the equivalent modulus of each rubber layer, c is the equivalent modulus of the cord, ρ is the cord density, and w is the cord arrangement angle;

[0010] S2) Define the side near the wire ring and the lower triangular end as the constraint zone, and the rest as the active zone. Establish an equivalent beam / shell hybrid model with the tire body, triangular rubber, and reverse-wrapped tire body as the sandwich layer. Apply fixed constraints with zero displacement and rotation to the wire ring and the lower triangular end, and establish a contact-coupling boundary between the active zone and the rim support.

[0011] S3) Determine the vertical load P based on “equivalent load area × air pressure”, and generate a 4-15 Hz periodic load time history by mapping the incoming and outgoing grounding frequencies and apply it to the active area.

[0012] S4) Solve the model to obtain the amplitude distribution of stress and strain along the reverse side of the tire carcass with thickness, and calculate the normal stress S11 in the cord direction and the amplitude of interface shear stress τ; take the plane where the minimum strain amplitude is located as the neutral plane criterion, and output the position of the neutral plane and the tension / compression boundary.

[0013] S5) Iterate and update within the given range of X values ​​until the compressive stress amplitude and interface shear amplitude τ of S11 meet the preset threshold, and the neutral surface position is stable, thereby generating a simulation model for subsequent analysis and design.

[0014] As a preferred embodiment, in step S1, the tire carcass, triangular rubber, and reverse-side tire carcass are abstracted as hyperelastic bodies or anisotropic elastomers, respectively, and the steel wire ring and rim support are equivalent to a beam-spring; the cords are arranged at an angle w, where w is 5° to 25°; and the thickness direction of the sandwich layer is discretized by ≥10 layers to establish amplitude-thickness sampling points.

[0015] Preferably, in step S2, the equivalent elastic modulus of the constrained region is set to 25–40 MPa, and the equivalent elastic modulus of the active region is set to 7.5–15 MPa; and a partitioned modulus transition zone is introduced between the sandwich layer and the adjacent adhesive layer, with a thickness of 0.2–1.5 mm.

[0016] Preferably, in step S2, a fixed constraint with zero displacement and rotation is applied to the wire ring and the lower triangular end. The contact-coupling between the active area and the rim is achieved using a penalty or Lagrange multiplier method, with a normal stiffness of 10. 6 ~10 8 The friction coefficient μ is 0.10 to 0.30 N / mm.

[0017] As a preferred embodiment, the load P in step S3 is determined by P=p·A, where p is the internal pressure in the range of 0.4 to 1.2 MPa and A is the equivalent load area; the periodic load time history adopts a sinusoidal or segmented sinusoidal waveform with a frequency of 4 to 15 Hz, and the load phase is coupled with the rim rotation angle to characterize the grounding input / output.

[0018] As a preferred option, in step S4, S11 and the interface shear stress τ are extracted along the geometric path of the carcass on the reverse side, and an equidistant or adaptively encrypted sampling strategy is adopted in the thickness direction; and a transition window with a length of 0.5 to 2.0 mm is set at the end of the path to suppress false peaks in the boundary values.

[0019] And / or, in step S4, the minimum point of the strain amplitude-thickness curve in the thickness direction is obtained. If there are multiple minimum points, the surface corresponding to the minimum point that intersects with the path of the reverse-wrapped tire body and has the smallest curvature is selected as the neutral surface. The standard deviation of the position of the neutral surface is calculated in adjacent load cycles. Stability is determined when the standard deviation is ≤0.1mm.

[0020] As a preferred option, in step S5, the objective function is set as f1 = compressive stress amplitude of the reverse-side tire body S11, f2 = interface shear stress amplitude, f3 = variance of neutral surface position, and X is updated iteratively using a multi-objective evolutionary algorithm or Bayesian optimization, with Δh limited to the range of 1 to 5 mm.

[0021] And / or, establish an empirical relationship between the translational distance of the reverse-side tire carcass and the amplitude of the S11 compressive stress:

[0022] ,

[0023] In each iteration, the relationship is used to inversely calculate and correct Δh. A, B, C, and D are obtained from calibration experiments or simulation regression and updated online.

[0024] Furthermore, the present invention also provides a simulation modeling system for implementing the method, including: a structural abstraction module, a partition equivalence module, a boundary condition setting module, a load generation and application module, a field quantity extraction module, a neutral surface determination module, and a parameter iteration and convergence module;

[0025] In addition, a processor and a memory, storing programs that run on the processor, enabling the modules to collaboratively complete the establishment of the simulation model.

[0026] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method.

[0027] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0028] By employing the aforementioned technical solution, this invention establishes an equivalent beam / shell hybrid model of the bead / neck sandwich layer as a constrained and active zone, and explicitly introduces the rim support coupling and 4-15Hz grounding load. It utilizes the criterion of "minimum strain amplitude surface = neutral surface" combined with the empirical relationship of Δh-S11 to achieve parameter inversion and rapid convergence. This causes the compression S11 peak value and interface shear amplitude on the reverse-wrapped side of the tire carcass path to decrease synchronously, significantly improving the stability of the neutral surface position. Within an engineering-controllable parameter window, the model can be established and iterated on an hourly basis (reduced from a weekly basis to approximately 2 hours), while maintaining high sensitivity and interpretability to hot spots. This directly supports the durability improvement of the bead wrapping structure and the optimization of the process window (bonding / flipping / vulcanization). Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the tire bead structure involved in the present invention.

[0030] Figure 2 This is a schematic diagram of the sandwich-type rubber-fiber composite structure (equivalent beam / shell) model of the present invention. Arrow P indicates the periodic load applied in the active region.

[0031] Figure 3 This is a diagram showing the strain amplitude distribution and location of LE11.

[0032] Figure 4 This is a contour plot of the strain amplitude for LE23 (shear-related component).

[0033] Figure 5 This is a diagram showing the overall mesh and boundary conditions.

[0034] Figure 6 This is a magnified view of a local area (S12 shear stress). Detailed Implementation

[0035] 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.

[0036] I. Definition of Structure and Symbols

[0037] See Figure 1 (Diagram of tire bead structure) and Figure 2 (Schematic diagram of sandwich model).

[0038] Sandwich layers: tire carcass (including cords), triangle rubber, and reverse-wrapped side tire carcass;

[0039] Adjacent layers: Inner liner rubber, sidewall filler rubber;

[0040] Reinforcing component: steel wire ring;

[0041] Design variable set: X = {Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w}, where:

[0042] Δh: The relative translational distance of the tire body on the reverse side;

[0043] b1, b2, b3: Equivalent thickness of inner lining adhesive, triangular adhesive, and filler adhesive;

[0044] σ1, σ2, σ3: Equivalent modulus (MPa) of the corresponding layer;

[0045] c, ρ, w: Equivalent modulus, density, and arrangement angle of the tire cords (angle with the tire circumferential direction).

[0046] Constraint Area / Active Area: The side closest to the wire loop and the lower triangular end is defined as the constraint area, and the rest is defined as the active area.

[0047] II. Model Building Process

[0048] S1) Structural Abstraction

[0049] The bead area is abstracted into a multi-layered composite, and the sandwich layer is discretized into ≥10 integration points in the thickness direction to obtain sufficient amplitude-thickness resolution. The carcass and the reverse side carcass are described as anisotropic linear elastic or equivalent hyperelastic, and the triangular rubber / filler rubber is described as equivalent elastic. The wire bead and the rim are equivalent to a beam-spring.

[0050] S2) Regional Division and Equivalence

[0051] An equivalent beam / shell hybrid model was established: the sandwich layer used two-dimensional shell / solid elements, and the wire ring and rim support were equivalent to beam / spring elements. Optimal settings: equivalent modulus of the constrained region 25–40 MPa, equivalent modulus of the active region 7.5–15 MPa; a modulus transition zone of 0.2–1.5 mm was set between the triangular adhesive and adjacent layers to weaken numerical pseudo-peaks.

[0052] S3) Boundary conditions coupled with the rim

[0053] Apply fixed constraints with zero displacement and rotation to the wire ring and the lower triangular end; establish contact-coupling between the active area and the rim (normal penalty stiffness 10). 6 ~10 8 N / mm, tangential friction coefficient μ=0.10~0.30), and allows for small-area outward release to fit the rim fillet.

[0054] S4) Load Description and Frequency Mapping

[0055] The load is a vertical force calculated as "equivalent load-bearing area A × internal pressure p". Applied to the active area (tire body and upper triangular end), and mapped to the in / out contact frequency of the vehicle speed v and the tire outer diameter D:

[0056] ,

[0057] The preferred frequency is 4–15 Hz (referencing common operating conditions of 60–180 km / h). The load time history is taken as a sine or piecewise sine, with amplitude and phase coupled to the rim angular displacement.

[0058] S5) Field Volume Acquisition

[0059] Extraction from the geometric path of the reverse-sided tire carcass:

[0060] S11 (curtain direction normal stress) amplitude;

[0061] The amplitude τ of interfacial shear (such as S12 or equivalent shear stress);

[0062] The amplitudes of strain components such as LE11 and LE23.

[0063] Figure 3 Show the minimum / maximum segments (min / max) of LE11. Figure 4 The distribution of LE23 is shown; Figure 5 / 6 is a magnified view of the local mesh and shear distribution, showing the shear hotspot area near the anti-wrap end.

[0064] S6) Neutral surface determination

[0065] A strain amplitude-thickness curve is obtained along the thickness direction of the sandwich layer, and the surface containing the minimum amplitude is taken as the neutral surface. When multiple minimum points appear, the surface corresponding to the minimum point that intersects with the path of the inverted side of the tire carcass and has the smallest curvature is selected. The standard deviation of the neutral surface position is calculated over several cycles, and it is considered stable if it is ≤0.1mm.

[0066] S7) Parameter Convergence and Inverse Calculation

[0067] The search is iteratively performed within an engineering window where Δh∈[1,5]mm and the partition modulus and layer thickness are constrained. The objective is:

[0068] i) The S11 compressive stress amplitude is the smallest on the reverse-wrapping side of the tire carcass path;

[0069] ii) The shear stress amplitude τ at the interface between adjacent adhesive layers is the smallest;

[0070] iii) The neutral plane is stable.

[0071] Preferred introduction of empirical relationships:

[0072] ,

[0073] Δh can be inversely calculated using online regression (or with existing calibration coefficients) to accelerate convergence. Based on this, Δh can be inversely calculated given the target amplitude of S11.

[0074] Application Example: Stress Improvement of Bead Sandwich Structure under Δh Optimization

[0075] 1. Operating conditions and model settings (execute according to S1 to S4)

[0076] Object and Modeling (S1): Select a section of a highway tire bead / nip, and then... Figure 2 Abstractly defined as a sandwich layer consisting of "carcass, triangular rubber, and reverse-wrapped carcass"; adjacent layers include inner liner rubber and sidewall filler rubber; the bead is a steel wire bead. The thickness direction has ≥10 layers with discrete integration points; the initial cord arrangement angle w=15°. Design variable set: X={Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w}.

[0077] Partitioning and Equivalence (S2): The side closest to the wire ring and the lower triangular end is defined as the constrained area, and the rest is the active area. The equivalent modulus of the constrained area is 40MPa, and that of the active area is 10MPa; a 0.5mm modulus transition zone is set between the triangular adhesive and the adjacent layer.

[0078] Boundary and Coupling (S3): Zero displacement / rotation constraints are applied to the wire ring and the lower triangular end; normal penalized contact is established between the active area and the rim (stiffness ≈ 10). 7 N / mm), tangential coulombic friction (μ≈0.2).

[0079] Load and frequency (S4): Inflation internal pressure p = 0.83 MPa; Vertical load applied according to equivalent load area A. To the activity area; vehicle speed 100km / h, outer diameter 1085mm, corresponding to grounding frequency ≈8.15Hz (falling within the range of 4–15Hz); load time history is sinusoidal and synchronized with rim angular displacement.

[0080] 2. Parameter search and criteria (executed according to S5~S7)

[0081] Field quantity extraction (S5): along Figure 3 , Figure 4 The amplitude (positive value) of the normal stress S11 in the cord direction and the interface shear peak τ_max are extracted from the reverse wrapping side of the tire carcass path. At the same time, the thickness strain amplitude curves (such as LE11 and LE23) are output.

[0082] Neutral surface determination (S6): The "surface with the minimum strain amplitude" is the neutral surface; the position standard deviation σ_n is calculated over several load cycles, and σ_n≤0.1mm is judged as stable.

[0083] Δh Iteration and Inverse Calculation (S7): Consider Δh∈{0,0.5,0.8,1.0,1.5,2.5,4.0}mm; and use the fitting relationship to inversely calculate and correct Δh until it satisfies "S11 Minimum compression amplitude, decrease in interface shear peak value + neutral surface stability".

[0084] ,

[0085] in The S11 compressive stress amplitude (positive value); in this example, the fitting values ​​are A=-0.2441, B=1.2051, C=-1.3652, and D=0.4388.

[0086] 3. Comparison and Optimization Results

[0087] Materials and zoning settings are consistent: Nylon is added to the outer side of the reverse-wrapped tire carcass; the constrained area is 40MPa and the active area is 10MPa; the three frequencies × three internal pressures are combined to solve the problem, and the statistics are taken.

[0088] 3.1 Mean results of aggregation with Δh (average of three frequencies × three internal pressures)

[0089] Baseline Δh=0: S11 mean 0.9905; τ mean 0.4924; σ_n mean 0.4267.

[0090] Optimized Δh=1.0mm: S11 mean 0.4387 (↓55.7%), τ mean 0.3001 (↓39.1%), σ_n mean 0.1788 (↓58.1%), and the neutral surface is stable within the period.

[0091] The adverse effects of excessive Δh: Δh=2.5mm (S11=1.6777, τ=0.5917, σ_n=0.5564) and Δh=4.0mm (S11=5.3949, τ=0.8911, σ_n=0.9311) both showed significant deterioration, verifying the existence of "excessive Δh → compression rebound and shear refocusing".

[0092] 3.2 Comparison based on the minimum value of aggregation with Δh

[0093]

[0094] Note: S11 is the compression amplitude (positive value), and the smaller the value, the better; the mean and minimum value conclusions are consistent, both pointing to the optimal window of Δh=1mm. Frequency (4 / 8 / 12Hz) and internal pressure (0.50 / 0.83 / 1.00MPa) have only a small second-order influence on the trend, and the stability is good.

[0095] 4. Summary of Technical Effects

[0096] 1) By using the closed loop of "finding Δh by fitting the curve and verifying with a small matrix", the iteration time is significantly shortened, and the process is changed from blind scanning over a large area to fine scanning of the target interval (≈1mm);

[0097] 2) Under different combinations of frequency and internal pressure, Δh=1.0mm can be achieved simultaneously:

[0098] The S11 compression amplitude decreased by approximately 55–56% (mean).

[0099] The peak shear rate at the interface decreased by approximately 39%.

[0100] The standard deviation of the neutral plane position decreased by approximately 58% and remained stable.

[0101] 3) When Δh is too large (≥2.5mm), compression and shear reconcentration occurs, verifying that "there is a clear engineering optimal Δh window", providing a directly implementable setting basis for the durability and process window optimization of the bead wrapping structure.

[0102] 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.

Claims

1. A method for establishing a simulation model of a sandwich-type rubber-fiber composite tire bead for electric vehicles, characterized in that, This method includes the following: S1) Model the target area hierarchically according to the inner liner rubber, tire carcass, triangular rubber, reverse side tire carcass, sidewall filler rubber and steel wire ring, and determine the design variable set X={Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w}, where Δh is the relative translation distance of the reverse side tire carcass, b1~b3 are the thickness of each rubber layer, σ1~σ3 are the equivalent modulus of each rubber layer, c is the equivalent modulus of the cord, ρ is the cord density, and w is the cord arrangement angle; S2) Define the side near the wire ring and the lower triangular end as the constraint zone, and the rest as the active zone. Establish an equivalent beam / shell hybrid model with the tire body, triangular rubber, and reverse-wrapped tire body as the sandwich layer. Apply fixed constraints with zero displacement and rotation to the wire ring and the lower triangular end, and establish a contact-coupling boundary between the active zone and the rim support. S3) Determine the vertical load P based on "equivalent load area × air pressure", and generate a 4-15Hz periodic load time history by mapping the incoming and outgoing grounding frequencies and apply it to the active area. S4) Solve the model to obtain the amplitude distribution of stress and strain along the reverse side of the tire carcass with thickness, and calculate the normal stress S11 in the cord direction and the amplitude of interface shear stress τ; take the plane where the minimum strain amplitude is located as the neutral plane criterion, and output the position of the neutral plane and the tension / compression boundary. S5) Iterate and update within the given range of X values ​​until the compressive stress amplitude and interface shear amplitude τ of S11 meet the preset threshold, and the neutral surface position is stable, thereby generating a simulation model for subsequent analysis and design.

2. The method as described in claim 1, characterized in that, In step S1, the tire carcass, triangular rubber, and reverse-side tire carcass are abstracted as hyperelastic bodies or anisotropic elastomers, respectively. The steel wire ring and rim support are equivalent to a beam-spring. The cords are arranged at an angle w, where w is 5° to 25°. The thickness direction of the sandwich layer is discretized by ≥10 layers to establish amplitude-thickness sampling points.

3. The method as described in claim 1, characterized in that, In step S2, the equivalent elastic modulus of the constrained region is set to 25–40 MPa, and the equivalent elastic modulus of the active region is set to 7.5–15 MPa; a partitioned modulus transition zone with a thickness of 0.2–1.5 mm is introduced between the sandwich layer and the adjacent adhesive layer.

4. The method as described in claim 1, characterized in that, In step S2, a fixed constraint with zero displacement and rotation is applied to the wire ring and the lower triangular end. The contact-coupling between the active area and the rim is achieved using a penalty or Lagrange multiplier method, with a normal stiffness of 10. 6 ~10 8 The friction coefficient μ is 0.10 to 0.30 N / mm.

5. The method as described in claim 1, characterized in that, In step S3, the load P is determined by P=p·A, where p is the internal pressure in the range of 0.4 to 1.2 MPa and A is the equivalent load area; the periodic load time history adopts a sinusoidal or segmented sinusoidal waveform with a frequency of 4 to 15 Hz, and the load phase is coupled with the rim rotation angle to characterize the grounding input / output.

6. The method as described in claim 1, characterized in that, In step S4, S11 and interface shear stress τ are extracted along the geometric path of the reverse-wrapped tire carcass. An equidistant or adaptively encrypted sampling strategy is adopted in the thickness direction. A transition window with a length of 0.5 to 2.0 mm is set at the end of the path to suppress false peaks in boundary values. And / or, in step S4, the minimum point of the strain amplitude-thickness curve in the thickness direction is obtained. If there are multiple minimum points, the surface corresponding to the minimum point that intersects with the path of the reverse-wrapped tire body and has the smallest curvature is selected as the neutral surface. The standard deviation of the position of the neutral surface is calculated in adjacent load cycles. Stability is determined when the standard deviation is ≤0.1 mm.

7. The method as described in claim 1, characterized in that, In step S5, the objective function is set as f1 = compressive stress amplitude of the reverse-wrapped side body S11, f2 = interface shear stress amplitude, f3 = neutral surface position variance. X is updated iteratively using a multi-objective evolutionary algorithm or Bayesian optimization, and Δh is limited to the range of 1 to 5 mm. And / or, establish an empirical relationship between the translational distance of the reverse-side tire carcass and the amplitude of the S11 compressive stress. lg(Δh)=A·S11³+B·S11²+C·S11+D, In each iteration, the relationship is used to inversely calculate and correct Δh. A, B, C, and D are obtained from calibration experiments or simulation regression and updated online.

8. A simulation modeling system for implementing the method of any one of claims 1-7, characterized in that, include: The module includes a structural abstraction module, a partition equivalence module, a boundary condition setting module, a load generation and application module, a field quantity extraction module, a neutral surface determination module, and a parameter iteration and convergence module. In addition, a processor and a memory, storing programs that run on the processor, enabling the modules to collaboratively complete the establishment of the simulation model.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the method of any one of claims 1–7.

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 1–7.

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