Finite element stiffness equivalent analysis method of metal-rubber laminated elastic element

Abstract

The present application relates to a kind of metal rubber laminated elastic element finite element stiffness equivalent analysis method.It includes the following steps: determining the stiffness test method of metal rubber laminated elastic element, and the radial stiffness, torsional stiffness, bending stiffness, axial stiffness of metal rubber laminated elastic element are obtained by stiffness test;Using transversely isotropic material characteristics to construct material properties, and the same load as in step one stiffness test is applied, to obtain the equivalent finite element model of metal rubber laminated elastic element;In simulation environment, the initial sample set of material mechanics performance parameters and stiffness results of equivalent finite element model is obtained using Latin hypercube sampling method;Based on bayesian optimization method, with the radial stiffness, torsional stiffness, bending stiffness, axial stiffness obtained by test as target value, train Gaussian process regression model using sample set, to obtain the next sample;The sample set is updated and the new sample is repeatedly obtained until the loss value is less than the threshold or converges, to obtain the material mechanics performance parameters corresponding to target value.

Description

Technical Field

[0001] This invention belongs to the field of strength design technology for helicopter rotor systems, and relates to a finite element stiffness equivalent analysis method for metal-rubber laminated elastic elements. Background Technology

[0002] Metal-rubber laminated elastic elements are elastic components formed by vulcanizing alternating layers of metal and rubber materials. They are widely used in helicopter rotor systems and are a crucial connection method for main structural components. Their elastic properties significantly influence the strength analysis of the connected metal parts. Direct modeling of metal-rubber laminated elastic elements is time-consuming, prone to convergence, and requires substantial computational resources. Furthermore, due to factors such as production and manufacturing processes, the virtual simulation stiffness results differ somewhat from the actual structural stiffness results. Traditional structural analysis often substitutes elastic elements with spring connections, neglecting the effects of deformation and structural displacement of the metal-rubber laminated elastic elements.

[0003] For more complex connection forms of multiple elastic elements in series / parallel multiple-path load transmission and geometric nonlinear cases with large deformation, finite element analysis needs an equivalent analysis method for the stiffness of metal-rubber laminated elastic elements. This method is simple to model and calculate, the virtual simulation stiffness results are highly consistent with the actual structural stiffness test results, and it can reflect the influence of deformation of metal-rubber laminated elastic elements and structural displacement. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a finite element stiffness equivalent analysis method for metal-rubber laminated elastic elements, which can reduce modeling difficulty, reduce computational scale, and improve analysis accuracy.

[0005] To address the aforementioned technical issues, a finite element stiffness equivalent analysis method for metal-rubber laminated elastic elements is proposed. This method is applied to metal-rubber laminated elastic elements, which include rubber layers and metal layers alternately stacked along the main load-bearing direction. The method includes the following steps:

[0006] Step 1: Determine the stiffness test method for the metal-rubber laminated elastic element, and obtain the radial stiffness of the metal-rubber laminated elastic element through stiffness testing. Torsional stiffness Bending stiffness Shaft stiffness ;

[0007] Step 2: Construct material properties using transversely isotropic material characteristics, and apply the same load as the stiffness test in Step 1 to obtain the equivalent finite element model of the metal-rubber laminated elastic element;

[0008] Step 3: In the simulation environment, use the Latin hypercube sampling method to obtain the initial sample set of material mechanical property parameters and stiffness results of the equivalent finite element model;

[0009] Step 4: Based on the Bayesian optimization method, using the radial stiffness from Step 1... Torsional stiffness Bending stiffness Shaft stiffness Using the sample set obtained in step three as the target value, train a Gaussian process regression model to obtain the next sample;

[0010] Step 5: Update the sample set in Step 3 and repeat Step 4 to obtain new samples until the loss value is less than the threshold or convergence is achieved, and obtain the material mechanical property parameters corresponding to the target value.

[0011] In one possible embodiment, for a metal-rubber laminated elastic element, one side of the metal-rubber laminated elastic element is connected to an inner connector, and the other side is connected to an outer connector; in step one, the stiffness testing method includes a radial stiffness testing method, where radial refers to the direction of metal-rubber stacking, and radial stiffness... It is the force required to generate a unit relative displacement in the radial direction of a metal-rubber laminated elastic element; the radial stiffness test method includes:

[0012] Fixed inner joint, radial force F applied to the outer joint of elastic element. R The external connector of the elastic element is under force The displacement produced under the action is Unit: mm. Calculate the radial stiffness of the elastic element using the following formula:

[0013] N / mm.

[0014] In one possible embodiment, for a metal-rubber laminated elastic element, one side of the metal-rubber laminated elastic element is connected to an inner connector, and the other side is connected to an outer connector; in step one, the stiffness testing method includes a torsional stiffness testing method, where the axial direction is perpendicular to the metal-rubber stacking direction, and the torsional stiffness... The torsional stiffness test method includes the torque required to generate a unit relative torsional angle along the axial direction of the elastic element.

[0015] Fix the inner joint and apply an axial torque to the outer joint. Unit: N•m; simultaneously measure the torsion angle of the outer joint relative to the inner joint. The unit is °. The torsional stiffness of the elastic element is calculated using the following formula:

[0016] N•m / °.

[0017] In one possible embodiment, for a metal-rubber laminated elastic element, one side of the metal-rubber laminated elastic element is connected to an inner connector, and the other side is connected to an outer connector; in step one, the stiffness testing method includes a bending stiffness testing method, wherein the bending stiffness... The bending stiffness test method includes the following: The torque required to generate a unit relative torsional angle between the inner and outer joints of the elastic element about the radial direction.

[0018] Fix the inner joint and apply a radial torque to the outer joint. Unit: N•m; simultaneously measure the torsion angle of the outer joint relative to the inner joint. The unit is °. The bending stiffness of the elastic element can be calculated using the following formula:

[0019] N•m / °.

[0020] In one possible embodiment, for the metal-rubber laminated elastic element, one side of the metal-rubber laminated elastic element is connected to the inner connector, and the other side is connected to the outer connector; in step one, the stiffness testing method includes a shaft stiffness testing method, the shaft stiffness... The shaft stiffness test method includes: The force required to generate a unit relative displacement along the axial direction between the inner and outer joints of the elastic element.

[0021] A fixed inner joint is fixed, and an axial force is applied to the outer joint of the elastic element in the negative axial direction, i.e., the direction of tension of the elastic body. Unit: N, elastic element external joint under force The displacement produced under the action is The unit is mm. The axial stiffness of the elastic element is calculated according to the following formula:

[0022] N / mm.

[0023] In one possible embodiment, step two specifically includes the following steps:

[0024] Transversely isotropic materials are a type of orthotropic materials. Transversely isotropic materials are those in which the mechanical properties are the same in a certain plane, but the mechanical properties are different when perpendicular to that plane.

[0025] In the Abaqus finite element model, the mechanical property parameters of transversely isotropic materials are transformed into those of orthotropic materials. Transversely isotropic materials have five mechanical property parameters, namely:

[0026] E1 represents the elastic modulus in the YZ plane;

[0027] E3 represents the elastic modulus in the X direction;

[0028] Represents Poisson's ratio in the YZ plane;

[0029] This represents the Poisson's ratio in the X direction relative to the YZ plane.

[0030] Represents the shear modulus in the XZ direction;

[0031] The YZ plane refers to the plane in which the metal-rubber laminates are stacked, and the X direction refers to the direction perpendicular to the YZ plane.

[0032] Orthotropic materials have nine mechanical property parameters. The conversion formulas for the mechanical property parameters from transversely isotropic materials to orthotropic materials are shown below:

[0033]

[0034] , It is a stress component. It is a strain component. It is a stiffness coefficient that represents the stress-strain relationship.

[0035] The elastic bodies of the metal-rubber laminated elastic element have similar mechanical properties in the YZ plane. Therefore, the outer contour of the elastic body can be closed into a solid, divided into linear hexahedral meshes, and an arbitrary transversely isotropic material can be created. Its mechanical property parameters are converted into stiffness coefficients of orthotropic materials and then assigned to the solid. The stiffness test load in step one is applied to the solid, thereby constructing an equivalent finite element model of the metal-rubber laminated elastic element.

[0036] In one possible embodiment, the specific steps for obtaining the sample set of material mechanical property parameters and stiffness results of the equivalent finite element model using the Latin hypercube sampling method in step three are as follows:

[0037] After inputting the mechanical property parameters of the transversely isotropic material, the radial stiffness is calculated based on the simulation results of the finite element model. Torsional stiffness Bending stiffness Shaft stiffness ; and then establish the independent variable With dependent variable Correspondence ;

[0038] For transversely isotropic materials, five material parameters correspond to four stiffness results, and the correspondence is not unique. To reduce computational complexity, specify... The value is specified based on the material ratio and mechanical properties of the metallic and rubber materials. The domain of definition; based on the calculation results of the equivalent finite element model, the independent variables are established. With dependent variable Correspondence between Each of the independent variables has its own domain.

[0039] A small initial sample set is generated using Latin hypercube sampling. .

[0040] In one possible embodiment, the initial sample set contains 20 to 50 samples.

[0041] In one possible embodiment, the specific steps in step four are as follows:

[0042] Bayesian optimization can solve the problem of quickly finding the optimal output from the input with a small number of samples. Its core idea is to use a probabilistic model to represent the goal and use a sampling function to weigh the exploration and equilibrium between the two to determine the next evaluation point, thereby finding the optimal solution with fewer queries.

[0043] The target value is obtained in step one. The loss function is defined using the weighted sum of squared errors method. ; , These are the weights of the dependent variable. (Regarding the loss function) A Gaussian process regression model is trained using the obtained initial sample set, and independent variables are established. With loss function The relationship between the variables; Gaussian process regression models can provide the relationship for any independent variable. Loss prediction and uncertainty prediction The expected improvement method is used as the acquisition function to find the optimal approach under the current Gaussian process regression model. Largest independent variable The one that will be found Largest independent variable The input is fed into the equivalent finite element model, and a set of independent variables is obtained through calculation. and dependent variable New samples.

[0044] Within the framework of the Gaussian process regression model,

[0045] ,

[0046] It is the value that minimizes the loss function. and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively.

[0047] In one possible embodiment, the specific steps in step five are as follows:

[0048] Combine the sample set obtained in step three with the new sample set obtained in step four to form a new sample set. Retrain the Gaussian process regression model using this sample set, repeating step four to obtain a new sample set; continue this iteration multiple times until... , It is an acceptable error, or in multiple iterations. Convergence; thus, the objective value is obtained. The corresponding dependent variable.

[0049] According to a second aspect of the present invention, a computer-readable storage medium is provided for storing a computer program, wherein when the computer program is executed, the above-described method is performed.

[0050] According to a third aspect of the present invention, a computer program product is provided, the computer program product comprising a computer program, wherein when the computer program is executed, the above-described method is performed.

[0051] In summary, the beneficial effects of the present invention are as follows:

[0052] This invention obtains the correspondence between material mechanical property parameters and stiffness values ​​based on finite element analysis. Through Bayesian optimization, it transforms the exploration of the entire space into directly searching for a set of combinations that make the dependent variable approach the target value using target information. This method avoids the time-consuming, convergence-prone, and computationally resource-intensive process of building precise finite element models for metal-rubber laminated elastic elements by establishing a direct mapping from stiffness values ​​to material mechanical property parameters. Simultaneously, it yields a stiffness-equivalent finite element model for a simplified structure suitable for engineering applications, taking into account the effects of deformation of the metal-rubber laminated elastic element and structural displacement. It has significant advantages in simulating the force transmission path of metal-rubber laminated elastic elements and is of great importance for the refined strength analysis of helicopter rotor systems. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the metal-rubber laminated center elastic bearing structure of a preferred embodiment of the present invention;

[0054] Figure 2 This is a flowchart of a preferred embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of the test connection of the metal-rubber laminated center elastic bearing according to a preferred embodiment of the present invention;

[0056] in:

[0057] 1-Inner connector, 2-Outer connector, 3-Metal-rubber laminated elastic element;

[0058] Figure 4 This is a simplified schematic diagram of the elastomer of the metal-rubber laminated center elastic bearing according to a preferred embodiment of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0060] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0061] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0062] Metal-rubber laminated center elastic bearing is a type of metal-rubber laminated elastic element, as shown in the schematic diagram below. Figure 1 As shown in the figure. The flowchart of the finite element stiffness equivalent analysis method for metal-rubber laminated elastic elements is as follows. Figure 2 As shown. The metal-rubber laminated central elastic bearing comprises rubber layers and metal layers alternately stacked along the main load-bearing direction; the method includes the following steps:

[0063] The inner side of a metal-rubber laminated central elastic bearing is connected to the inner joint, and the outer side is connected to the outer joint, as shown below. Figure 3 As shown. In step one, the inner joint is fixed, and a radial force is applied along the YZ plane to the outer joint of the elastic bearing. The external joint of the elastic bearing is under force The displacement produced under the action is Unit: mm. Calculate the radial stiffness of the elastic element using the following formula:

[0064] N / mm.

[0065] Fix the inner connector and apply a torque along the X-axis to the outer connector. Unit: N•m; simultaneously measure the torsion angle of the outer joint relative to the inner joint. The unit is °. The torsional stiffness of the elastic element is calculated using the following formula:

[0066] N•m / °.

[0067] Fix the inner connector and apply a torque about the YZ plane to the outer connector. Unit: N•m; simultaneously measure the torsion angle of the outer joint relative to the inner joint. The unit is °. The bending stiffness of the elastic element can be calculated using the following formula:

[0068] N•m / °.

[0069] With the inner joint fixed, an axial force is applied to the outer joint of the elastic element along the negative X-axis, i.e., the direction of tension of the elastic body. Unit: N, elastic element external joint under force The displacement produced under the action is The unit is mm. The axial stiffness of the elastic element is calculated according to the following formula:

[0070] N / mm.

[0071] In step two, the mechanical properties of the metal-rubber laminated center elastic bearings are similar in the YZ plane, therefore their elastomer outline can be closed as a solid, and a linear hexahedral mesh can be defined, such as... Figure 4 As shown, the mechanical property parameters of an arbitrary transversely isotropic material are converted into stiffness coefficients for an orthotropic material and then assigned to the solid. The stiffness test load from step one is applied to this solid, thereby constructing an equivalent finite element model of a metal-rubber laminated elastic element.

[0072] In step three, specify The value is specified based on the material ratio and mechanical properties of the metallic and rubber materials. The domain of definition. A domain containing 50 independent variables is generated using Latin hypercube sampling. The independent variable sample set. Input the mechanical property parameters of the transversely isotropic material. The radial stiffness was calculated based on the simulation results of the finite element model. Torsional stiffness Bending stiffness Shaft stiffness Repeat the above steps to obtain a set of 50 independent variables. and dependent variable initial sample set .

[0073] In step four, the result obtained in step one is... The target value is set, and the loss function is defined using the weighted sum of squared errors method. :

[0074] , It is the weight of the dependent variable.

[0075] against Using the obtained initial sample set Train a Gaussian process regression model and establish independent variables. With loss function The relationship between them; using the expected improvement method as the acquisition function, to find the optimal approach under the current Gaussian process regression model. Largest independent variable .Will The input is fed into the equivalent finite element model, and the dependent variable is calculated. .

[0076] In step five, the sample set obtained in step three is combined with the new sample set obtained in step four. To form a new sample set Using sample sets Retrain the Gaussian process regression model and repeat step four to obtain a new sample. and form a new sample set. ; Repeat the iterations multiple times until , It is an acceptable error, or in multiple iterations. Convergence. The last set of samples obtained when convergence occurs. ,think It is the target value The dependent variable within the corresponding error range.

[0077] In this embodiment, the finite element stiffness equivalent analysis method for metal-rubber laminated elastic elements was used to analyze the central elastic bearing of the metal-rubber laminate. The simplified finite element model of the elastic body has approximately 50,000 elements, while the refined finite element model requires more than 500,000 meshes. Compared with the refined finite element model, the simplified finite element model takes about 1 / 100th the modeling time, improving computational efficiency by more than 10 times. Compared with simulation using spring connections, the finite element stiffness equivalent analysis method for metal-rubber laminated elastic elements also considers the effects of deformation and structural displacement of the metal-rubber laminated elastic elements. This method balances the accuracy of the force transmission path with the simplicity of modeling and calculation, and has significant advantages in engineering applications for simulating the force transmission path of metal-rubber laminated elastic elements.

[0078] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0079] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method of finite element stiffness equivalent analysis of a metal rubber laminated elastic element, characterized by, The method includes the following steps: Step 1: Determine the stiffness test method for the metal-rubber laminated elastic element, and obtain the radial stiffness of the metal-rubber laminated elastic element through stiffness testing. Torsional stiffness Bending stiffness Shaft stiffness ; Step 2: Construct material properties using transversely isotropic material characteristics, and apply the same load as the stiffness test in Step 1 to obtain the equivalent finite element model of the metal-rubber laminated elastic element; Step 3: In the simulation environment, use the Latin hypercube sampling method to obtain the initial sample set of material mechanical property parameters and stiffness results of the equivalent finite element model; Step four: Based on the Bayesian optimization method, the radial stiffness , torsional stiffness , bending stiffness , shaft stiffness in step one as the target value, the sample set obtained in step three is used to train the Gaussian process regression model to obtain the next sample; Step 5: Update the sample set in Step 3 and repeat Step 4 to obtain new samples until the loss value is less than the threshold or convergence is achieved, and obtain the material mechanical property parameters corresponding to the target value.

2. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 1, characterized in that, In the step one, the stiffness test method includes a radial stiffness test method, radial refers to the metal rubber stack direction, the radial stiffness is the force required to produce a unit relative displacement of the metal rubber stack elastic element in the radial direction; The radial stiffness test method includes: Fixed inner joint, radial force applied to the outer joint of elastic element The external connector of the elastic element is under force The displacement produced under the action is Unit: mm. Calculate the radial stiffness of the elastic element using the following formula: N / mm.

3. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 1, characterized in that, In the step one, the rigidity test method includes a torsional rigidity test method, the axial direction is perpendicular to the metal rubber stacking direction, and the torsional rigidity is a moment required to produce a unit relative torsional angle of the elastic element along the axial direction, and the torsional rigidity test method comprises: Fix the inner joint and apply an axial torque to the outer joint. Unit: N·m; simultaneously measure the torsion angle of the external joint relative to the internal joint. The unit is degrees. The torsional stiffness of the elastic element is calculated using the following formula: N·m / degree.

4. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 1, characterized in that, In step one, the stiffness testing method includes the bending stiffness testing method, and the bending stiffness... The bending stiffness test method includes the following: The torque required to generate a unit relative torsional angle between the inner and outer joints of the elastic element about the radial direction. Fixing the inner joint, exerting a moment about the radial direction on the outer joint , in N-m, while measuring the torsion angle of the outer joint relative to the inner joint, in degrees, then the bending stiffness of the elastic element is calculated according to the following formula: N-m / degrees.

5. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 1, characterized in that, In step one, the stiffness testing method includes the shaft stiffness testing method, shaft stiffness The axial stiffness test method is the force required to generate a unit relative displacement between the inner and outer joints of the elastic element along the axial direction. It includes: fixing the inner joint and applying an axial force to the outer joint of the elastic element in the negative axial direction, i.e., the direction of tension on the elastic body. Unit: N, elastic element external joint under force The displacement produced under the action is The unit is mm. The axial stiffness of the elastic element is calculated according to the following formula: N / mm.

6. The finite element stiffness equivalent analysis method for a metal-rubber laminated elastic element according to claim 1, characterized in that, Step two specifically includes the following process: The outer contour of the elastic body is enclosed as a solid, a linear hexahedral mesh is divided, and an arbitrary transversely isotropic material is created. Its mechanical property parameters are converted into the stiffness coefficients of orthotropic materials and then assigned to the solid. The formulas for converting mechanical property parameters from transversely isotropic materials to orthotropic materials are shown below: wherein: E1 represents the elastic modulus in the YZ plane; E3 represents the elastic modulus in the X direction; S represents the Poisson's ratio in the YZ plane; represents the Poisson's ratio of the X direction to the YZ plane; Gxz represents a shear modulus in the XZ direction; YZ plane refers to the plane in which the metal rubber stack is stacked, and the X direction refers to the direction perpendicular to the YZ plane; , is a stress component, is a strain component, is a stiffness coefficient representing the stress-strain relationship; Apply the stiffness test load from step one to the entity to obtain the equivalent finite element model of the metal-rubber laminated elastic element.

7. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 6, characterized in that, In step three, the specific steps for obtaining the sample set of material mechanical property parameters and stiffness results for the equivalent finite element model using the Latin hypercube sampling method are as follows: After inputting the mechanical property parameters of the transversely isotropic material, the radial stiffness is calculated based on the simulation results of the finite element model. Torsional stiffness Bending stiffness Shaft stiffness ; and then establish the independent variable With dependent variable Correspondence ; A small initial sample set is generated using Latin hypercube sampling. 。 8. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 7, characterized in that, The initial sample set contains 20 to 50 samples.

9. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 7, characterized in that, In step four, the specific operation steps are as follows: To step one in the obtained As the target value, the weighted sum of squared error method to define the loss function ; wherein, is a weight for the dependent variable; for the loss function a Gaussian process regression model is trained with the obtained initial sample set to establish a relationship between the independent variable and the loss function ​ Loss and uncertainty predictions for arbitrary covariates through Gaussian process regression models ;​​ The expectation improvement method is used as a collection function to find the independent variable that maximizes the Gaussian process regression model under the current ;​ , It is the value that minimizes the loss function. and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. The found Largest independent variable The input is fed into the equivalent finite element model, and a set of independent variables is obtained through calculation. and dependent variable New samples.

10. The finite element stiffness equivalent analysis method of a metal rubber laminated elastic element according to claim 9, characterized in that, In step five, the specific operation steps are as follows: Combine the sample set obtained in step three with the new sample obtained in step four to form a new sample set; use this sample set to retrain the Gaussian process regression model, and repeat the process of step four to obtain a new sample. Repeat the iterations until... , This is an acceptable error, from which the target value is obtained. The corresponding dependent variable.

11. A computer readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program, which, when executed, performs the method according to any one of claims 6-10.

12. A computer program product, characterised in that, The computer program product includes a computer program that, when executed, performs the method according to any one of claims 6-10.

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