Multi-objective optimization method and system for tire bead durability of electric vehicles

Abstract

This invention relates to the field of electric vehicle tire simulation design technology, and particularly to a multi-objective optimization method for electric vehicle tire bead durability and a system-wide multi-objective optimization method for electric vehicle tire bead durability. This invention constructs a sandwich layer consisting of the tire carcass, triangular rubber, and reverse-wrapped side carcass, establishing a constraint / active zone coupled with the rim boundary, and applying a cyclic load under 4-15 Hz conditions. S11 and interface shear amplitudes are extracted along the reverse-wrapped path, and the neutral plane and its stability are determined using the surface with the minimum strain amplitude. Using Δh, ply thickness b1-b3, modulus σ1-σ3, and cord parameters c / ρ / w as variables, evolutionary / Bayesian optimization is used to minimize S11 and shear amplitudes and minimize the neutral plane variance, outputting nominal parameter values ​​and tolerance windows. This method balances accuracy and efficiency, suppressing compression and shear peaks, improving bead durability, and shortening the design cycle.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle tire simulation design technology, and in particular to a multi-objective optimization method and system for electric vehicle tire bead durability. Background Technology

[0002] The bead (also known as the tire bead) is a crucial component for positioning and load-bearing between the pneumatic tire and the rim. The bead area simultaneously bears circumferential stretching caused by internal pressure, localized compression / shear from rim support, and repeated bending and torsional loads during vehicle operation. It is a high-stress and multi-axial coupling zone of the entire tire. Existing technologies generally improve durability and bead resistance through modifications to bead geometry and material stacking. For example, Chinese patent CN102224024A uses buffer rubber around the annular reinforcing structure (bead wire) and arranges constraint reinforcements between the entry section and the wrapping section to limit cord unwinding and stress concentration, thereby improving bead durability.

[0003] To address common localized failure scenarios in tire bead systems, Chinese patent CN110194032A reduces the risk of thermal degradation due to stress concentration or wear through structural refinement. This includes employing segmented bead wrapping, creating a "gradient" between the upper and inner ends to disperse end stress, and supplementing with a nylon protective layer to suppress internal cracking; or adding wear-resistant beading to the outside of the wear-resistant rubber to buffer the contact stress and heat generation between the rim, wear-resistant rubber, and steel wire beading, thereby reducing bead wear and extending lifespan. Furthermore, the reverse wrapping layout of the tire carcass cords also significantly impacts bead stress. Chinese patent CN1275946A proposes various reverse wrapping / triangular core combinations and end position relationships to improve the support of the reverse wrapping end and the environment for end crack initiation. Simultaneously, Chinese patent CN105501000B further optimizes bead stiffness and processability through the chemical formulation and composite material design of the triangular core (such as introducing a specific thermoplastic isotactic-1,2-polybutadiene into the triangular rubber to improve molding and service performance).

[0004] In terms of simulation modeling, existing technologies widely employ the Finite Element Method (FEA) to support tire structure design and performance evaluation. To reduce manual operation and modeling time, Chinese patent CN108304632A proposes a modeling process that automatically generates rubber element meshes and automatically identifies and generates rebar (embedded cord / steel wire) elements based on two-dimensional line drawings of tire axle sections, for rapid establishment of whole tire finite element models. To improve the efficiency and stiffness matching accuracy of whole vehicle time-domain operating condition simulation, Chinese patent CN114741911A achieves long-term time-domain simulation at the 8,000-element level through cross-sectional regional modeling, shell / solid hybrid elements, and iterative calibration of material parameters. Furthermore, for the strength evaluation of key components, Chinese patent CN117933005A proposes a simulation calculation process for the safety factor of the belt layer, including defining the material properties of steel wires and rubber, setting contact / boundary conditions, reading stress components such as S11 and comparing them with the minimum breaking stress to obtain the safety factor, in order to reduce the risk of belt layer fracture. Summary of the Invention

[0005] To address the aforementioned technical problems, the present invention aims to provide a multi-objective optimization method for the durability of electric vehicle tire beads. This method rapidly establishes a calibrable local simulation model and, through multi-objective optimization, simultaneously reduces the S11 compressive stress amplitude and interface shear amplitude of the inverted sidewall carcass, stabilizes the neutral plane position, and then reverse-calculates design parameters and their tolerances such as Δh, ply thickness, and modulus gradient, thereby significantly improving bead durability and consistency and shortening the design cycle.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A multi-objective optimization method for tire bead durability of electric vehicles, characterized in that the method includes:

[0008] S1) Perform hierarchical modeling of the tire bead opening area to construct a sandwich rubber-fiber composite simulation model with the tire body, triangular rubber, and reverse-wrapped tire body as the sandwich layer;

[0009] S2) Based on the target vehicle speed and tire outer diameter, the driving condition entering / exiting the ground is converted into a periodic load time history, and an equivalent vertical load is applied to the active area, while establishing a force coupling boundary condition with the rim support.

[0010] S3) Solve for the stress / strain amplitude distribution along the reverse side of the tire carcass path, obtain the compressive stress amplitude S11 and the interface shear stress amplitude τ of the normal stress in the cord direction, and determine the position of the neutral plane and its stability index based on the plane where the minimum strain amplitude is located.

[0011] S4) Select at least a portion of the design variables X={Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w} to form a variable set, establish a multi-objective optimization model with the objectives of minimizing the compressive stress amplitude S11 of the anti-wrapping side tire body, minimizing the interface shear stress amplitude τ, and maximizing / minimizing the stability / variance of the neutral surface position, and set constraints related to structure, material, manufacturing and working conditions;

[0012] S5) Use a multi-objective optimization algorithm to find the optimal solution set for the variable set, obtain the Pareto solution set, and then re-analyze and verify the candidate solutions.

[0013] S6) Based on the preset decision rules, select a compromise solution from the Pareto solution set and output Δh, layer thickness b1~b3, modulus σ1~σ3, cord parameters c / ρ / w optimization parameters and their tolerance windows;

[0014] Where Δh is the relative translational distance of the reverse side tire carcass, b1-b3 are the equivalent thicknesses of the inner liner rubber, the triangular rubber layer, and the reverse side tire carcass rubber layer, respectively, σ1-σ3 are the equivalent moduli of the inner liner rubber, the triangular rubber layer, and the reverse side tire carcass rubber layer, respectively, c is the equivalent modulus of the cord, ρ is the cord density, and w is the cord arrangement angle.

[0015] As a preferred option, in step S1, the sandwich rubber-fiber composite simulation model is modeled hierarchically by dividing the bead opening area into inner liner rubber, tire body, triangular rubber, reverse-wrapped side tire body, sidewall filler rubber and steel wire bead, and defining the side closest to the steel wire bead and the lower triangular end as the constraint area, and the rest as the active area.

[0016] And / or, the core layer rubber adopts a hyperelastic constitutive model, the cord / steel wire adopts an anisotropic linear elastic constitutive model, and the steel wire ring and rim support adopt beam and spring equivalents; the thickness direction of the core layer is discretized into sampling integration points of no less than 10 layers, and the cord is arranged at an arrangement angle w=5°~25°.

[0017] As a preferred embodiment, step S2 includes: the equivalent vertical load is determined according to P = pA, where p is the tire pressure and A is the equivalent load area; the periodic load time history adopts a sinusoidal or piecewise sinusoidal waveform, and the frequency is selected to be 4 to 15 Hz, which is consistent with the inlet / outlet grounding; the coupling boundary between the active area and the rim is realized by a contact-friction model or a displacement coupling model.

[0018] As a preferred option, step S3 includes: extracting the amplitude distribution of S11 and interface shear stress τ along the geometric path of the reverse-side tire carcass, and using equidistant or adaptively densified sampling in the thickness direction; the neutral surface is determined by the "minimum point of the strain amplitude-thickness curve", and when there are multiple minimum points, the one that intersects with the reverse-side tire carcass path and has the smallest curvature is selected as the position of the neutral surface.

[0019] Preferably, step S4 includes: setting manufacturing / mechanical constraints on variables: Δh is limited to 1–5 mm; the equivalent elastic modulus of the constrained area and the active area are in the range of 25–40 MPa and 7.5–15 MPa, respectively; the layer thicknesses b1, b2, and b3 meet the minimum molding thickness and maximum cavity limit; and the cord arrangement angle w and density ρ are limited to the allowable range of the process.

[0020] As a preferred option, step S5 includes: using a multi-objective evolutionary algorithm (NSGA-II / MOEA-D) or multi-objective Bayesian optimization for optimization; and constructing a surrogate model using Gaussian process regression or random forest, and generating the next batch of evaluation points through expected improvement, confidence upper bound, or Pareto dominant acquisition function to accelerate convergence.

[0021] As a preferred option, further improvements to step S5 include: introducing an empirical inverse relationship between Δh and the compressive stress amplitude in S11, lg(Δh) = A·S11, into the optimization iteration. 3 +B·S11 2 +C.S11+D, where A, B, C, and D are obtained through calibration experiments or simulation regression and are synchronously corrected online when the surrogate model is updated, to guide the rapid search and constraint handling of variable Δh.

[0022] As a preferred option, step S6 includes: selecting a compromise solution from the Pareto solution set using a multi-index decision-making method such as weighted sum method, ε-constraint method or TOPSIS; and performing a re-simulation verification at the compromise solution. If the S11 compressive stress amplitude and interface shear stress amplitude on the reverse side of the tire carcass path are both lower than the preset threshold and the variance of the neutral plane position is lower than the threshold, then the optimization is deemed effective.

[0023] Furthermore, the present invention also provides a multi-objective optimization system for bead durability for implementing the method, the system comprising:

[0024] The model building unit is used to execute step S1 to establish a sandwich-type rubber-fiber composite simulation model.

[0025] The load element is used to perform step S2 and generate the cyclic load and rim coupling boundary.

[0026] The field quantity solution and criterion unit is used to execute step S3 and output S11, interface shear and neutral surface position / stability;

[0027] The optimization problem generation unit is used to execute the S4 steps to define variables, objectives, and constraints.

[0028] A multi-objective optimization solution unit is used to perform the S5 step and generate a Pareto solution set;

[0029] The decision-making and verification unit is used to execute step S6 to select a compromise solution and complete the re-simulation verification.

[0030] The processor and memory, wherein the memory stores programs that run on the processor to enable the units to work together.

[0031] Preferably, the multi-objective optimization solution unit includes a surrogate modeling module and a data acquisition strategy module. The surrogate modeling module is used to construct a Gaussian process regression or random forest surrogate model. The data acquisition strategy module is used to generate the next batch of evaluation points based on expected improvement, upper confidence bound, or Pareto dominance criterion. The decision and verification unit has a built-in online correction and inverse calculation function for the Δh-S11 empirical relationship, which is used to provide suggested tolerance windows for Δh, b1~b3, σ1~σ3, c, ρ, and w when outputting the compromise solution.

[0032] 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.

[0033] 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.

[0034] This invention, by employing the aforementioned technical solution, transforms the sandwich layer system of tire carcass-triangular rubber-reverse-side tire carcass into an equivalent beam and introduces a minimum strain amplitude criterion, achieving precise neutral plane positioning and clear tension / compression boundary. Combined with the coupling boundary between the constraint / active zone and rim support, and the 4–15Hz working condition mapping, the model is both fast and accurate: while ensuring computational accuracy, the modeling-calibration cycle is shortened from approximately one week in traditional whole-tire refinement models to approximately 2 hours. In terms of optimization results, the compressive stress amplitude S11 and interface shear stress τ of the reverse-side tire carcass in the cord direction are significantly reduced, the fluctuation of the neutral plane position is decreased, and shear slip and fatigue crack initiation at the steel wire / rubber interface are effectively suppressed, improving durability and consistency. Simultaneously, by establishing an empirical inverse relationship between Δh and S11 and multi-objective Pareto screening, the design tolerance windows for Δh, layer thickness, and modulus gradient can be directly output, supporting process window setting and mass production robustness. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the tire bead structure involved in the present invention.

[0036] 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.

[0037] Figure 3 This is a diagram showing the strain amplitude distribution and location of LE11.

[0038] Figure 4 This is a contour plot of the strain amplitude for LE23 (shear-related component).

[0039] Figure 5 This is a diagram showing the overall mesh and boundary conditions.

[0040] Figure 6 This is a magnified view of a portion of the image (S12 shear stress). Detailed Implementation

[0041] 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.

[0042] I. Definition of Structure and Symbols

[0043] See Figure 1 (Diagram of tire bead structure) and Figure 2 (Schematic diagram of sandwich model).

[0044] Sandwich layers: tire carcass (including cords), triangle rubber, and reverse-wrapped side tire carcass;

[0045] Adjacent layers: Inner liner rubber, sidewall filler rubber;

[0046] Reinforcing component: steel wire ring;

[0047] Design variable set: X = {Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w}, where:

[0048] Δh: The relative translational distance of the tire body on the reverse side;

[0049] b1, b2, b3: Equivalent thickness of inner lining adhesive, triangular adhesive, and filler adhesive;

[0050] σ1, σ2, σ3: Equivalent modulus (MPa) of the corresponding layer;

[0051] c, ρ, w: Equivalent modulus, density, and arrangement angle of the tire cords (angle with the tire circumferential direction).

[0052] 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.

[0053] II. Model Building Process

[0054] S1, Structural Abstraction

[0055] 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.

[0056] S2, Regional Division and Equivalence

[0057] 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.

[0058] S3, Boundary conditions coupled with the rim

[0059] A fixed constraint with zero displacement and rotation is applied to the wire ring and the lower triangular end; contact-coupling is established 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.

[0060] S4. Load Description and Frequency Mapping

[0061] The load is applied as a vertical force P=pA, which is the equivalent load-bearing area A × internal pressure p, to the active area (tire body and upper triangular end), and is mapped to the vehicle speed v and the tire outer diameter D at the ground contact frequency.

[0062] ,

[0063] 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.

[0064] S5, Field Volume Acquisition

[0065] Extraction from the geometric path of the reverse-sided tire carcass:

[0066] S11 (curtain direction normal stress) amplitude;

[0067] Interfacial shear τ (such as S12 or equivalent shear stress) amplitude;

[0068] The amplitudes of strain components such as LE11 and LE23.

[0069] Figure 3 Show the minimum / maximum segments (min / max) of LE11. Figure 4The 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.

[0070] S6. Neutral Surface Determination

[0071] 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.

[0072] S7. Parameter Convergence and Inverse Calculation

[0073] 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:

[0074] i) The S11 compression amplitude is the smallest on the reverse-wrapped side of the tire carcass path;

[0075] ii) The shear amplitude at the interface between adjacent adhesive layers is the smallest;

[0076] iii) The neutral plane is stable.

[0077] Preferred introduction of empirical relationships:

[0078] ,

[0079] 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.

[0080] S8, Optimizing Problem Construction

[0081] S8.1 Variable Selection and Encoding

[0082] Required variables: mm;

[0083] Geometric variables: (Minimum molding thickness / cavity upper limit constraints are defined in S8.3);

[0084] Material variables: (Equivalent modulus);

[0085] Cord variables: (Due to limitations in manufacturing processes and supply specifications);

[0086] Encoding method: Continuous variables are encoded using real numbers; categories or grade specifications (such as curtain cord grades) are encoded using discrete sets and processed through nearest neighbor projection.

[0087] S8.2 Definition of Objective Function and Regularization Terms

[0088] 1. Main objective: min F(x) = (S 11,amp (x),τ amp (x),Var(z*)(x));

[0089] Optional regularization (introduced when needed to avoid ill-conditioned solutions): mass / stiffness penalty Deformation limiting penalty (For example, the endpoint displacement exceeds the limit). If using - Constraint framework, regular terms can be transformed into inequality constraints.

[0090] S8.3 Constraint Set and Feasible Region

[0091] geometry: (e.g., 0.6-3.5mm) mm;

[0092] Materials: The equivalent moduli of the constrained region and the active region are 2540 MPa and 7.515 MPa, respectively;

[0093] Cord: , Select the supply specification range. Subject to the upper and lower limits of the material grade;

[0094] Operating conditions: Load frequency 415Hz; contact friction ;

[0095] Strength / Deformation (Optional Hard Constraint): Endpoint Displacement Safety factor .

[0096] Constraint handling: penalty function, feasibility ranking, or - Choose one of the constraint methods (consistent with the S9 algorithm).

[0097] S8.4 Target Scale-up and Weight Preset

[0098] To facilitate comparison of multiple targets, interval scaling is used:

[0099] , q∈{S 11,amp ,τ amp ,Var(z*)};

[0100] initial It is derived from DOE sampling statistics (see S4.5); it is normalized again in the decision-making stage (S6).

[0101] S8.5 Initial Design (DOE)

[0102] Sampling methods: Latin hypercube (LHS) or orthogonal design;

[0103] Sample size: ( (as a variable dimension), and cover boundary points;

[0104] Evaluation: Calling the simulated kernel for computation Based on the constraint residuals, an initial surrogate model and feasible region estimation are constructed.

[0105] S9. Multi-objective optimization solution

[0106] S9.1 Master Solver Strategy

[0107] Option A: Evolutionary / Decomposition Algorithm

[0108] NSGA-II: Population 60-120, crossover 0.8-0.9, mutation 0.05-0.15, tournament selection (feasibility priority);

[0109] Or MOEA-D: neighborhood size 10-20, weighted vectors are generated uniformly.

[0110] Option B: Multi-objective Bayesian optimization

[0111] Agents: Gaussian process regression (GPR, Matérn5 / 2) or random forest (RF);

[0112] Data acquisition: q-EI, UCB-Pareto, or PoI-Pareto, batch data acquisition. .

[0113] The two approaches can be combined: first use NSGA-II for coarse search, then use Bayesian local refinement.

[0114] S9.2 Proxy Modeling and Active Sampling

[0115] Dataset Composed of DOE and successive evaluations; fitting GPR / RF, cross-validation (k=5) to estimate generalization error; based on uncertainty... To generate new samples in order to improve EI.

[0116] Constraint handling: Constructing feasible probabilities for inequality constraints The acquisition function is multiplied by Suppress infeasibility assessment.

[0117] S9.3Δh–S11 Empirical Inverse Coupling

[0118] 1. Online Regression: Fitting the data using currently available samples.

[0119] ,

[0120] Iterative update (Weighted least squares / Bayes regression, with weights adjusted according to sample uncertainty).

[0121] 2. Inverse calculation and domain reduction: Given a target inverse search candidate interval ;

[0122] 3. Integration with the main solver: New candidates are only available when... Internal sampling, or imposing large penalties on solutions outside the interval, can reduce invalid evaluations.

[0123] S9.4 Parallel Evaluation and Record Management

[0124] Parallel batch evaluation, priority queue: high, Prioritize those with higher performance; for external file maintenance non-inferior solutions, simplify based on over-volume contribution or congestion distance, retaining 100-300 candidates.

[0125] S9.5 Convergence and Termination

[0126] Stop if one of the following conditions is met: Hypervolume (HV) improvement rate Persisting for 10 generations; Maximum Hausdorff distance change at the Pareto front (e.g., 0.02) for 5 generations; evaluation budget exhausted (e.g., 500-1500 high-fidelity simulations).

[0127] S9.6 Reanalysis Verification and Multifidelity Correction

[0128] For the final archives Perform high-precision meshing and more stringent contact parameter resimulation using representative solutions (e.g., 10-20); calculate surrogate error. Then write back the correction; if the error exceeds the threshold, return to S9.2 for local resampling.

[0129] S10. Compromise Solution Selection and Result Output

[0130] S10.1 Multi-indicator Decision Making

[0131] Method 1: Weighted Sum

[0132] ,

[0133] Weights can be set according to the project's focus (e.g., if the process focuses more on shearing, then...). (relatively large)

[0134] Method 2: -constraint

[0135] set up Minimize within the feasible set .

[0136] Method 3: TOPSIS

[0137] Normalization yields the matrix Constructing ideal points With negative ideal point Calculate distance , ; closeness ,Pick The largest option is a compromise.

[0138] S10.2 Threshold Verification

[0139] Perform high-fidelity reanalysis on the candidate compromise solution if the following conditions are met:

[0140] ,

[0141] If the optimization is successful, then the process is considered effective; otherwise, the process reverts to S9.2 for local encryption.

[0142] S10.3 Robustness and Sensitivity Analysis

[0143] Manufacturing Deviation Monte Carlo: Apply Gaussian perturbations (such as tolerances) to Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w. Sampling 200-500 times, statistically analyzing the probability of failure. ;

[0144] Local sensitivity: calculation (Difference or surrogate gradient) to identify key variables; if For targets (e.g., 1%), relax / tighten tolerances and recalculate while keeping constraints unchanged.

[0145] S10.4 Tolerance Window and Manufacturing Implementation

[0146] Tolerance generation: Based on sensitivity and Monte Carlo results, give the nominal values ​​± tolerances of Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w;

[0147] Manufacturability checks: Verify the back-wrapping positioning fixture capability, cavity limits, and mixing / vulcanization profile;

[0148] Transformation List: Create a "Design-Process Transformation Table", including: objectives Recommendations for each layer's thickness / modulus range, rim contact settings, and sampling inspection items (process monitoring method for neutral surface position).

[0149] S10.5 Output and Archiving

[0150] Structural parameters: Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w;

[0151] Performance reports: nominal values, confidence intervals, and percentage improvement over the baseline for the three objectives;

[0152] Process documents: tolerance window, inspection plan and regression model (including the latest version) );

[0153] Digital process package: material cards, load templates, meshes, and script version numbers, facilitating reuse and auditing.

[0154] Example 1: Optimize only Δh (verify the effect of inverse AND of Δh-S11)

[0155] 1. Settings: Material and geometry are fixed (equivalent modulus of active area 40MPa; cord angle w=15°; b1, b2, b3 as reference); only variables are taken. mm. (Using a specific formula)

[0156] ,

[0157] In this example, the fitting yielded A=-0.2441, B=1.2051, C=-1.3652, and D=0.4388.

[0158] 2. Comparison and Optimization Results

[0159] Materials and zoning settings are consistent: Nylon is added to the outer side of the tire carcass on the reverse side; the constrained area is 40MPa and the active area is 10MPa; the three-frequency × three-internal-pressure full combination solution is used, and the statistical quantity is taken.

[0160] 2.1 Mean results of aggregation with Δh (average of three frequencies × three internal pressures)

[0161] Baseline Δh=0: S11 mean 0.9905; τ min The mean is 0.4924; the mean of σ_n is 0.4267.

[0162] Optimization Δh=1.0mm: S11 mean 0.4387 (↓55.7%), τ min The mean is 0.3001 (↓39.1%), the mean of σ_n is 0.1788 (↓58.1%), and the neutral surface is stable within the period.

[0163] The negative effect of excessively large Δh: Δh = 2.5 mm (S11 = 1.6777, τ) min =0.5917, σ_n=0.5564) and Δh=4.0mm (S11=5.3949, τ min Both σ_n = 0.8911 and σ_n = 0.9311 showed significant deterioration, confirming the existence of "excessive Δh → compression recovery and shear refocusing".

[0164] 2.2 Comparison based on the minimum value of aggregation with Δh

[0165]

[0166] Conclusion: S11 is the compression amplitude (positive value), and the smaller the value, the more favorable it is; 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.

[0167] Example 2: Multi-objective optimization (Δh+b2+b3+w)

[0168] Setting: Variables ;constraint: mm; Satisfy the limits of molding and cavity; The method employs NSGA-II coarse search followed by Gaussian process Bayesian local refinement; with (S11,amp,τamp,Var(z\*)) as the objective (S8), the Pareto set is obtained, and then TOPSIS is used to select a compromise solution (S10).

[0169] Comparative Example B: mm; other measurements are based on the standard.

[0170] Comparative Example C: mm; other measurements are based on the standard.

[0171] Example 2 - Opt (Compromise): mm, mm, mm, .

[0172]

[0173] in conclusion:

[0174] Simply increasing Δh (comparative example B / C) will worsen the S11 compressive stress amplitude and increase the interfacial shear stress amplitude τ, indicating that Δh is not "the bigger the better";

[0175] Through the multi-objective collaborative optimization (Δh linkage b2 / b3 / w) of the present invention, under the constraints of forming / cavity, S11↓18.1%, τ↓22.5%, and Std(z*)↓65.2% (all relative to comparative example A) are achieved, while the displacement is controlled within an acceptable range.

[0176] Example 3: Robustness and Tolerance Window

[0177] Setting: Using Example 2-Opt as the nominal value, for Apply manufacturing tolerances: mm; mm; mm; Perform N=500 Monte Carlo samplings + re-simulation verification (S10.2 / S10.3).

[0178]

[0179] Then sorted by sensitivity ( Tighten the Δh tolerance to ±0.2mm and recalculate. Next, we obtain:

[0180] 95th percentile Std(z*) = 0.09 mm It dropped to 0.8%;

[0181] Output manufacturing tolerance window: mm; mm; mm; This window directly inputs the "Design-Process Conversion Table" for setting up the reverse-wrapping positioning fixture and cavity inspection fixture.

[0182] 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 multi-objective optimization method for tire bead durability of electric vehicles, characterized in that, The method includes: S1) Perform hierarchical modeling of the bead area to construct a sandwich rubber-fiber composite simulation model with the carcass, triangular rubber, and reverse-wrapped side carcass as the sandwich layer; S2) Based on the target vehicle speed and tire outer diameter, the driving conditions entering and exiting the ground are converted into the periodic load time history, and the equivalent vertical load is applied to the active area, while establishing force coupling boundary conditions with the rim support. S3) Solve for the stress and strain amplitude distribution along the reverse side of the tire carcass path, obtain the compressive stress amplitude S11 and the interface shear stress amplitude τ of the normal stress in the cord direction, and determine the position of the neutral plane and its stability index based on the plane where the minimum strain amplitude is located. S4) Select at least a portion of the design variables X={Δh, b1, b2, b3, σ1, σ2, σ3, c, ρ, w} to form a variable set, establish a multi-objective optimization model with the objectives of minimizing the compressive stress amplitude S11 of the anti-wrapping side tire body, minimizing the interface shear stress amplitude τ, maximizing the stability of the neutral surface position, and minimizing the variance, and set constraints related to structure, material, manufacturing, and working conditions; S5) Use a multi-objective optimization algorithm to find the optimal solution set for the variable set, obtain the Pareto solution set, and then re-analyze and verify the candidate solutions. S6) Select a compromise solution from the Pareto solution set based on the preset decision rules, and determine the optimization parameters and tolerance windows of Δh, b1~b3, σ1~σ3, c, ρ and w; Where Δh is the relative translational distance of the reverse side tire carcass, b1-b3 are the equivalent thicknesses of the inner liner rubber layer, the triangular rubber layer, and the reverse side tire carcass rubber layer, respectively, σ1-σ3 are the equivalent moduli of the inner liner rubber layer, the triangular rubber layer, and the reverse side tire carcass rubber layer, respectively, c is the equivalent modulus of the cord, ρ is the cord density, and w is the cord arrangement angle.

2. The method as described in claim 1, characterized in that, In step S1, the sandwich rubber-fiber composite simulation model is modeled hierarchically by the bead area as inner liner rubber layer, carcass, triangular rubber, reverse-wrapped carcass, sidewall filler rubber and steel wire bead, and the side closest to the steel wire bead and the lower triangular end is defined as the constraint area, and the rest as the active area. And / or, the core layer rubber adopts a hyperelastic constitutive model, the cord and steel wire adopt an anisotropic linear elastic constitutive model, and the steel wire ring and rim support adopt beam and spring equivalents; the thickness direction of the core layer is discretized into sampling integration points of no less than 10 layers, and the cord is arranged at an arrangement angle w=5°~25°.

3. The method as described in claim 1, characterized in that, Step S2 includes: The equivalent vertical load is determined by P = p·A, where p is the tire pressure and A is the equivalent load area; the periodic load time history adopts a sine or piecewise sine waveform, and the frequency is selected to be 4-15Hz, consistent with the inlet and outlet grounding; the coupling boundary between the active area and the rim is realized by a contact-friction model or a displacement coupling model.

4. The method as described in claim 1, characterized in that, Step S3 includes: The amplitude distribution of S11 and interface shear stress τ is extracted along the geometric path of the reverse-side tire carcass. Equidistant or adaptively densified sampling is used in the thickness direction. The neutral surface is determined by the minimum point of the strain amplitude-thickness curve. When there are multiple minimum points, the one that intersects the reverse-side tire carcass path and has the smallest curvature is selected as the location of the neutral surface. And / or, step S4 includes: setting manufacturing and mechanical constraints on variables: Δh is limited to 1–5 mm; the equivalent elastic modulus of the constrained area and the active area are in the range of 25–40 MPa and 7.5–15 MPa, respectively; b1, b2, and b3 meet the minimum molding thickness and maximum cavity limit; w and ρ are limited to the process allowable range.

5. The method as described in claim 1, characterized in that, The S5 steps include: The optimization is carried out by multi-objective evolutionary algorithm or multi-objective Bayesian optimization; and a surrogate model is constructed by Gaussian process regression or random forest. The next batch of evaluation points is generated by expectation improvement, confidence upper bound or Pareto dominant acquisition function to accelerate convergence. And / or, further improvements to step S5 include: In the optimization iteration, an empirical inverse relationship between Δh and the compressive stress amplitude S11 is introduced. lg(Δh)=A·S11³+B·S11²+C·S11+D, A, B, C, and D are obtained through calibration experiments or simulation regression and are synchronously corrected online when the surrogate model is updated, which is used to guide the rapid search and constraint handling of variable Δh.

6. The method as described in claim 1, characterized in that, Step S6 includes: The weighted sum method, ε-constraint method, or TOPSIS is used to select a compromise solution from the Pareto solution set; and a re-simulation verification is performed at the compromise solution. If the compressive stress amplitude S11 and the interface shear stress amplitude τ on the reverse side of the tire carcass path are both lower than the preset threshold and the variance of the neutral surface position is lower than the threshold, then the optimization is deemed effective.

7. A multi-objective optimization system for bead durability for implementing the method according to any one of claims 1-6, characterized in that, include: The model building unit is used to execute step S1 to establish a sandwich-type rubber-fiber composite simulation model. The load element is used to perform step S2 and generate the cyclic load and rim coupling boundary. The field quantity solution and criterion unit is used to execute step S3 and output S11, interface shear and neutral surface position and stability; The optimization problem generation unit is used to execute the S4 steps to define variables, objectives, and constraints. A multi-objective optimization solution unit is used to perform the S5 step and generate a Pareto solution set; The decision-making and verification unit is used to execute step S6 to select a compromise solution and complete the re-simulation verification. The processor and memory, wherein the memory stores programs that run on the processor to enable the units to work together.

8. The system as described in claim 7, characterized in that: The multi-objective optimization solution unit includes a surrogate modeling module and a data acquisition strategy module. The surrogate modeling module is used to construct a Gaussian process regression or random forest surrogate model. The data acquisition strategy module is used to generate the next batch of evaluation points based on expected improvement, upper confidence bound, or Pareto dominance criterion. The decision and verification unit has a built-in online correction and inverse calculation function for the Δh-S11 empirical relationship, which is used to simultaneously provide the optimization parameters and tolerance windows of Δh, b1~b3, σ1~σ3, c, ρ, and w when outputting the compromise solution.

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 1–6.

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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