Air spring burst pressure prediction method fusing finite element and weibull distribution

Abstract

This invention discloses a method for predicting the burst pressure of air springs by fusing finite element analysis and Weibull distribution. The method involves the following steps: Step 1, establishing and simplifying a three-dimensional model based on the actual sample size of the air spring; Step 2, defining the material properties of the rubber matrix, cord layer, cover plate, and piston based on the actual air spring material; Step 3, analyzing the burst damage mechanism of the rubber and cord, defining and embedding damage subroutines for each component (rubber matrix and cord layer) of the rubber airbag; Step 4, extracting the simulated burst pressure and maximum cord stress based on Abaqus simulation results, and introducing Weibull distribution probability to calculate the burst pressure; Step 5, based on the experimental burst pressure and the predicted burst pressure, feedback correction of the Abaqus model parameters to reduce simulation errors. This invention achieves rapid prediction of air spring burst pressure based on a small sample burst test data, providing an intuitive indication of the air spring burst location and burst pressure.

Description

Technical Field

[0001] This invention belongs to the field of mechanical structure strength analysis and computational mechanics, specifically involving a method for predicting the ultimate burst pressure of air springs based on Abaqus finite element simulation and Weibull distribution fitting. It is applicable to the safety assessment and structural optimization of air springs in fields such as automotive suspension and industrial machinery. Background Technology

[0002] As an important vibration isolation element, the burst pressure of air springs is a key indicator for measuring their safety and reliability. Traditional burst testing methods are costly, time-consuming, and risky, and it is difficult to obtain detailed stress and strain distribution information. Although existing finite element simulation methods can simulate the bursting process, most of them rely on idealized assumptions and ignore the dispersion of material properties and the differences in actual processes, resulting in significant deviations between predicted results and experimental values. Verification and correction still require a large number of experiments.

[0003] Therefore, a low-consumption, high-efficiency, and high-precision method for predicting the burst pressure of air springs is needed to meet the requirements of safety assessment and structural optimization in engineering applications. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for predicting the burst pressure of an air spring by combining Abaqus explicit dynamic simulation with Weibull probability distribution. This method can achieve high-precision and high-efficiency burst pressure prediction with the support of limited sample experimental data.

[0005] The technical solution of the present invention includes the following steps: (1) Obtain the geometric parameters, material parameters and burst test data of the air springs, and construct the original database; (2) Establish a refined finite element model of the air spring. The main components include the rubber matrix, cord layer, cover plate and piston. A three-dimensional modeling method is used. (3) Constructing a constitutive model of rubber matrix-cord layer composite material: The rubber matrix adopts the Yeoh hyperelastic model, the cord layer adopts the Rebar embedding technology to simulate anisotropic behavior, and the cover plate and piston are simplified as rigid bodies; (4) Define and embed the damage subroutines for each component of the rubber airbag; (5) Set up surface-to-surface contact, fluid cavity pressure loading and boundary conditions, and perform explicit dynamic analysis using the Abaqus / Explicit module; (6) Apply gradually increasing internal pressure loads to simulate the entire process from inflation to explosion, extract stress and strain data, and identify the failure initiation location and mode; (7) Perform mesh sensitivity analysis to determine the optimal mesh size and ensure computational accuracy and efficiency; (8) Based on the tensile test data of the cord layer, the strength dispersion was fitted using the Weibull distribution, and a burst pressure prediction model was established by combining the tensile-internal pressure relationship of the cord layer obtained from simulation:

[0006] Where P is the burst pressure of the air spring; Let the shape and scale parameters be two-parameter Weibull distributions; there is a nonlinear relationship between the blasting pressure and a certain defect parameter. Mapping this nonlinear problem to a high-dimensional model to achieve linear separability of the data allows us to... For cord tension The parameters related to the linear relationship between the air spring internal pressure P and the parameters are expressed as follows: ; (9) The prediction model is corrected by experimental data, and the material parameters are iteratively optimized to improve the prediction accuracy.

[0007] Furthermore, step (2) employs the Rebar surface embedding three-dimensional solid element technology that comes with the Abaqus program.

[0008] Furthermore, the Yeoh model of the rubber matrix described in step (3) adopts the strain energy function. The model is:

[0009] in, These are material parameters obtained by fitting data from uniaxial tensile tests of rubber. It is the first strain invariant, used to describe the isotropic properties of rubber materials.

[0010] Furthermore, the material damage model in step (4) is implemented through a user-defined subroutine; wherein, the damage subroutine of the rubber matrix is ​​compiled into a dynamic link library based on the Visual Studio platform and then embedded into the Abaqus / Standard solver for use; the damage of the cord layer is simulated by directly calling the built-in damage evolution model of Abaqus.

[0011] Furthermore, in step (5), the contact behavior is set to "hard" contact, frictionless, and the fluid cavity pressure is applied based on the ideal gas law.

[0012] Furthermore, in step (7), three different grid schemes with different densities are compared and analyzed, and convergence verification is performed based on the medium grid.

[0013] Furthermore, the Weibull distribution parameters mentioned in step (8) are obtained by fitting the cord tensile test data and determined using the least squares method. parameter.

[0014] Furthermore, in step (9), a feedback method is used to adaptively adjust the material parameter scaling factor, and the simulated value of the air spring burst pressure is corrected by combining real test data.

[0015] The beneficial effects of this invention are as follows: (1) By combining finite element simulation with probabilistic models, the accuracy and reliability of blast pressure prediction have been significantly improved. (2) It avoids the high cost and high risk of traditional experiments and is suitable for rapid evaluation and optimization in the product development stage; (3) It can be widely used in the safety performance analysis of various air springs and other inflatable structures; (4) Combining mesh sensitivity analysis and material parameter iterative correction improves the engineering applicability and robustness of the model. Attached Figure Description

[0016] Figure 1 This is a method for predicting the burst pressure of an air spring based on finite element simulation and Weibull distribution fitting. Figure 2 This is a schematic diagram of the finite element model of an air spring. Figure 3 Mises stress cloud diagrams of the rubber matrix layers of the front and rear air springs under burst pressure; Figure 4 Mises stress cloud diagrams of the front and rear air spring cord layers under burst pressure; Figure 5 These are stress analysis diagrams of the rubber matrix layer and cord layer of the front and rear air springs; Figure 6 It is the stress-internal pressure fitting curve of the cord layer; Figure 7 This is a graph showing the fitting results of the Weibull distribution. Detailed Implementation

[0017] The present invention will now be described in detail and in its entirety with reference to the accompanying drawings and embodiments. Obviously, the examples described are only a part of the examples; based on the examples described in the present invention, other examples obtained by those skilled in the art without creative effort should all fall within the protection scope of the present invention.

[0018] like Figure 1 The invention shown here is a method for predicting the burst pressure of an air spring based on finite element simulation and Weibull distribution fitting, comprising the following steps: P1. Collect data related to the design and manufacturing dimensions of the air spring and its burst test, specifically including the dimensional parameters of each component of the air spring and the air pressure inside the airbag at the moment of burst; key factors affecting the burst strength of the air spring based on dimensional parameters; and establish a 3D model using Abaqus, such as... Figure 2 As shown, fillets and non-critical features are simplified to improve computational efficiency. The geometric model includes: Rubber matrix: The Yeoh hyperelastic constitutive model was adopted, and the parameters were determined by fitting rubber tensile test data; Cord layer: Embedded in a rubber matrix using Rebar surface unit technology, defined as an anisotropic elastic material; Cover plate and piston: simplified as discrete rigid bodies to avoid unnecessary deformation calculations.

[0019] P2. Collect the material parameters of the components of the rubber airbag and the manufacturing process of the rubber airbag, specifically including the material parameters of the rubber matrix and the cord layer, the laying angle and spacing of the cord layer, and the distance between the cord layer and the center surface of the airbag skin; import the relevant material parameters into the Abaqus 3D model.

[0020] P3. Based on the literature review on the burst test specimens of air spring rubber airbags and the tear damage of related composite materials, a rubber matrix damage subroutine was written using Visual Studio. According to the material and tensile characteristics of the cord layer, the damage was regarded as flexible damage, and the damage parameters were input and corrected based on the cord tensile test data.

[0021] P4. Mesh the rubber matrix to determine the base dimensions and the dimensions of the contact area (bursting area) between the rubber airbag and the cover plate to ensure stress accuracy; use four-node surface elements (SFM3D4R) for the cord layer; contact settings include: surface-to-surface contact and fluid cavity pressure.

[0022] P5. After obtaining the simulated burst pressure and the maximum stress of the cord, as follows: Figure 5 As shown, based on the cord tensile test data, such as Figure 3 , 4 As shown, a two-parameter Weibull distribution is used to fit its strength dispersion; the linear relationship between the cord tension f and the internal pressure P is extracted through simulation data, and relevant parameters are determined by fitting the initial modulus data using Weibull distribution parameters, such as... Figure 6 As shown, the burst pressure is then calculated using the burst pressure prediction formula.

[0023] P6. By comparing the simulated values ​​with the predicted values, the error is analyzed and an iterative correction process is proposed. Example

[0024] A method for predicting the burst pressure of an air spring by fusing finite element analysis and Weibull distribution is described below: P11, the similarity between the finite element 3D model and the actual air spring component should exceed 90%, the error between the internal volume of the finite element 3D model and the actual component should not exceed 5%, and the thickness of the rubber airbag and the position of the cord layer should be the parameters of the actual air spring rubber airbag component. Based on the above conditions, the simplified finite element model is as follows: Figure 2 As shown; the burst pressure of the air spring test is the burst pressure value measured by the water pressure burst test of the air spring.

[0025] P22. The material parameters required for the finite element 3D model include uniaxial tensile test data of rubber matrix material, tensile test data of rubber matrix material, density of rubber matrix material, tensile test data of cord material, elastic modulus of cord material, diameter of cord cross section, number of cord layers and angle, and cord density. The required data are obtained by testing with the required testing machine. The required material parameters are then imported into Abaqus.

[0026] P33, considering the damage mechanisms of the rubber matrix material and the cord layer material, write and set the damage program for the rubber matrix and the cord layer. The required parameters are obtained from step P22. The damage criterion for the rubber matrix adopts the maximum stress damage criterion, and the damage criterion for the cord layer adopts the flexible damage criterion. Specifically, the maximum strain for damage to the rubber matrix is ​​set as follows: The formula for calculating the maximum strain of damage is as follows:

[0027] in, For the strain in the principal directions 1 and 2 of the composite material, The strain values ​​are the shear strains in the 1st and 2nd principal directions; all strain values ​​are determined by the Abaqus internal program.

[0028] P44 uses an eight-node reduced integral element (C3D8R) to mesh the rubber matrix with a base size of 2mm, and refines the mesh to 1mm in the contact area between the airbag and the end cap to ensure stress accuracy; the cord layer uses a four-node surface element (SFM3D4R); the total number of elements in the model is approximately 188,000; the contact settings include: surface-to-surface contact: adopting a "hard" contact criterion, with no tangential friction; fluid cavity pressure: applying an ideal gas pressure load through a reference point, with an initial ambient pressure of 0.1 MPa (1 standard atmosphere), and the pressure increases linearly with inflation time until bursting; Explicit dynamic analysis was performed using the Abaqus / Explicit module; a dynamic explicit analysis step was set, the geometric nonlinearity option was enabled, and automatic incremental step size and mass scaling functions were used; the internal pressure was gradually increased to simulate the entire process of the rubber airbag from inflation to burst.

[0029] P55, based on cord tensile test data, uses a two-parameter Weibull distribution to fit its strength dispersion; cord tension is extracted through simulation data. Linear relationship with internal pressure P: The Weibull distribution parameters are determined by fitting the initial modulus data to determine the scale parameters. Shape parameters ,like Figure 7 As shown; Substitute into the blast pressure prediction formula:

[0030] Where P is the burst pressure of the air spring; Let the shape and scale parameters be two-parameter Weibull distributions; there is a nonlinear relationship between the blasting pressure and a certain defect parameter. Mapping this nonlinear problem to a high-dimensional model to achieve linear separability of the data allows us to... For cord tension The parameters related to the linear relationship between the air spring internal pressure P and the parameters are expressed as follows: ; The predicted burst pressure of the front air spring is calculated.

[0031] P66. By comparing the simulated values ​​with the predicted values, the analysis shows that the errors mainly stem from the simplification of the material constitutive model and the uncertainty of the damage model parameters. An iterative correction process for relevant model parameters based on experimental data is proposed. The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; any modifications, equivalent substitutions or improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the burst pressure of an air spring by fusing finite element analysis and Weibull distribution, characterized in that, Includes the following steps: (1) Obtain the original data of the size parameters, material parameters and burst pressure of each component of the double-layer cord reinforced air spring, and perform data processing to build a database; (2) Based on the air spring size parameters, simplify the external structure that has no impact on the results, and establish a three-dimensional finite element model including the rubber matrix, cord layer, cover plate and piston. (3) Define the material properties of each component of the air spring based on the air spring material parameters; (4) Considering the burst damage mechanism of the rubber matrix and the cord layer, define and embed each damage subroutine; (5) Based on the interrelationships of the components of the air spring, use the Abaqus / Explicit module to set the surface-to-surface contact, fluid cavity pressure loading and boundary conditions; (6) Using the Abaqus / Explicit module, simulate the entire process from inflation to explosion, extract stress and strain data of key parts, and identify the failure initiation location and failure mode; (7) Based on the tensile test data of the cord layer material, and combined with the simulated relationship between the tension and internal pressure of the cord layer, establish and calculate the burst pressure prediction formula; (8) Based on the experimental blast pressure and the predicted blast pressure, the material parameters of the Abaqus model are corrected by feedback to reduce the error between the simulation and experimental values.

2. The method according to claim 1, characterized in that, The finite element model described in step (2) reduces computational costs by simplifying unnecessary structures; the rubber matrix adopts the Yeoh hyperelastic model, the cord layer is simulated by Rebar embedding, and the gas pressure is applied through the fluid cavity unit.

3. The method according to claim 2, characterized in that, The simplified model is based on the actual air spring model. It is necessary to ensure that the volume error of the air spring rubber airbag does not exceed 5%, and the similarity between the three-dimensional model and the actual model exceeds 90%.

4. The method according to claim 1, characterized in that, The cover plate and the piston have a modulus far exceeding that of the rubber airbag, and are assumed to be rigid bodies in Abaqus; the rubber airbag is composed of the rubber matrix and the cord layer disposed in the rubber matrix.

5. The method according to claim 1, characterized in that, The material parameters of the cord layer in step (3) include elastic modulus, Poisson's ratio, and plastic strain-stress curve, and material failure is simulated by writing VUSDFLD, VUMAT subroutines or Abaqus built-in damage models based on Visual Studio.

6. The method according to claim 5, characterized in that, The rubber matrix damage subroutine in step (4) was written using Visual Studio and embedded in Abaqus. The cord layer damage subroutine used the built-in damage program of Abaqus. The parameters required for each damage program were obtained through the processing in step (2).

7. The method according to claim 1, characterized in that, The surface-to-surface contact in step (5) adopts the "hard" contact rule, and the tangential behavior is set to be frictionless; the fluid cavity pressure loading adopts the ideal gas law, and the initial environmental pressure is set to 1 standard atmosphere.

8. The method according to claim 7, characterized in that, It also includes performing a mesh sensitivity analysis after step (5), and determining the optimal mesh size by comparing simulation results under different mesh densities, so as to ensure a balance between computational accuracy and efficiency.

9. The method according to claim 1, characterized in that, The explosion pressure prediction model mentioned in step (7) is as follows: Where P is the burst pressure of the air spring; Let the shape and scale parameters be two-parameter Weibull distributions; there is a nonlinear relationship between the blasting pressure and a certain defect parameter. Mapping this nonlinear problem to a high-dimensional model to achieve linear separability of the data allows us to... For cord tension The parameters related to the linear relationship between the air spring internal pressure P and the parameters are expressed as follows: Furthermore, the correction process described in step (7) is an iterative process. By adjusting the hyperelasticity parameter, damage initialization criterion, or cord-rubber interface properties, the error between the predicted burst pressure and the experimental value is controlled within 20%. The error calculation method adopts relative error. The calculation formula is as follows: in, is the theoretical value, which is the result of finite element simulation; L is the actual value, which is the result of experiment.

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