CN112507595A - Prediction method for creep property of rubber vibration isolator - Google Patents

Prediction method for creep property of rubber vibration isolator Download PDF

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CN112507595A
CN112507595A CN202011521839.1A CN202011521839A CN112507595A CN 112507595 A CN112507595 A CN 112507595A CN 202011521839 A CN202011521839 A CN 202011521839A CN 112507595 A CN112507595 A CN 112507595A
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creep
vibration isolator
rubber vibration
rubber
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李旻
刘文帅
上官文斌
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South China University of Technology SCUT
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Abstract

The invention discloses a method for predicting creep property performance of a rubber vibration isolator. The method comprises the following steps: establishing a geometric model of the rubber vibration isolator; performing meshing on a rubber part of the rubber vibration isolator; adopting a super-elastic-nonlinear viscoelastic superposition constitutive model, and adopting a constitutive model parameter identification method to complete material attribute setting; the six degrees of freedom of all the nodes of the metal outer pipe of the rubber vibration isolator are restrained; all nodes of the metal inner pipe of the rubber vibration isolator are related to a central node of the rubber vibration isolator, and a force with constant magnitude is applied to the central node to complete the setting of boundary conditions; and (4) carrying out aftertreatment on the result: and recording the change condition of the displacement of the center node of the rubber vibration isolator along with time to obtain a creep curve of the center node, and evaluating the creep characteristic performance of the rubber vibration isolator according to the creep curve of the center node of the rubber vibration isolator. The method can predict the creep characteristics of the rubber vibration isolators with different structures under different load conditions by means of finite elements, and has higher precision.

Description

Prediction method for creep property of rubber vibration isolator
Technical Field
The invention relates to the field of calculation and evaluation of creep characteristic performance of an automobile rubber vibration isolator, in particular to a method for predicting the creep characteristic performance of the rubber vibration isolator.
Background
With the rapid development of national economy and the automobile industry, people have higher and higher requirements on the riding comfort of automobiles. In order to reduce vibration and noise of automobiles, rubber vibration isolators are widely used in automobiles. And the rubber vibration isolator always works under the load condition, so that the creep phenomenon inevitably occurs. The creep characteristic of the rubber vibration isolator has great influence on the dynamic characteristic of the rubber vibration isolator, namely the damping and the dynamic stiffness of the rubber vibration isolator increase along with the creep, which is not beneficial to vibration isolation. The creep phenomenon of the rubber vibration isolator has great influence on the NVH performance of the automobile and the service life of the rubber vibration isolator.
In the early design of the rubber vibration isolator product, the creep allowance of the rubber vibration isolator is generally considered based on experience, and then the product is developed by manufacturing and testing the performance of a sample piece. Therefore, the reliability of the product can be ensured, but the problems of long product development period, waste of manpower and material resources, dependence on subjective experience and the like can be brought. Therefore, the creep characteristic performance of the rubber vibration isolator needs to be calculated and evaluated.
In the prior art, a method for calculating the creep characteristic of the rubber vibration isolator comprises the following steps: (1) luo R K and the like calculate the creep characteristics of the rubber vibration isolator by using a time-dependent superelasticity correction constitutive model (Luo R K, Zhou X L, Tang J F. numerical prediction and experimental on rubber cruise and stress relaxation use time-dependent superelasticity improvement, 2016,52(04): 246-. (2) The creep characteristics of the rubber vibration isolator are calculated by the super-elastic-generalized Maxwell superposition constitutive model (Rongcheng, Huangyoujian, Zhang-Yaxin, and the like. research on the vertical rigidity and the creep characteristics of the spring of the rubber shaft box [ J ]. the special rubber product, 2009,30(02):60-63.), but the method can only accurately describe the creep characteristics of the rubber vibration isolator under a certain load, and has larger calculation error on the creep characteristics of the rubber vibration isolator under different loads. Therefore, a calculation method for calculating the creep characteristic of the rubber vibration isolator in finite element software Abaqus based on a superelastic-nonlinear viscoelastic superposition constitutive model is provided, so that the creep characteristic of the rubber vibration isolator under different loads can be accurately predicted.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: a calculation method for calculating the creep characteristic of the rubber vibration isolator in finite element software Abaqus based on a superelastic-nonlinear viscoelastic superposition constitutive model is provided, so that the creep characteristic of the rubber vibration isolator under different loads can be accurately predicted.
The purpose of the invention is realized by at least one of the following technical solutions.
A method for predicting creep characteristic performance of a rubber vibration isolator comprises the following steps:
s1, establishing a geometric model of the rubber vibration isolator;
s2, performing meshing on the rubber part of the rubber vibration isolator;
s3, adopting a superelastic-nonlinear viscoelastic superposition constitutive model, namely a superposition model of the superelastic constitutive model and the nonlinear viscoelastic constitutive model, and adopting a constitutive model parameter identification method to complete material attribute setting;
s4, restraining six degrees of freedom of all nodes of the metal outer pipe of the rubber vibration isolator to ensure that all nodes of the metal outer pipe do not move; all nodes of the metal inner pipe of the rubber vibration isolator are related to a central node of the rubber vibration isolator, and a force with constant magnitude is applied to the central node to complete the setting of boundary conditions;
s5, result post-processing: and recording the change condition of the displacement of the center node of the rubber vibration isolator along with time to obtain a creep curve of the center node, and evaluating the creep characteristic performance of the rubber vibration isolator according to the creep curve of the center node of the rubber vibration isolator.
Further, in step S1, a geometric model of the rubber vibration isolator is established using the three-dimensional modeling software UG.
Further, in step S2, in order to improve the finite element calculation accuracy, a hexahedral mesh is selected, and the mesh size is controlled within 2 mm.
Further, in step S3, the superelasticity constitutive model is a Mooney-Rivlin model, and the strain potential energy function thereof is expressed as:
Figure BDA0002849263330000025
wherein C is10And C01Is a parameter describing the shear properties of a material; d1Is a parameter describing the compression characteristics of the material; j. the design is a squareelIs the elastic volume ratio;
Figure BDA0002849263330000023
is a first order strain invariant;
Figure BDA0002849263330000024
is a second order strain invariant.
Further, in step S3, the expression of the nonlinear viscoelastic constitutive model with respect to creep strain rate is:
Figure BDA0002849263330000021
wherein A, m, n are material parameters describing creep properties of the material;
Figure BDA0002849263330000022
is the creep strain rate; ε is the creep strain; q is Kirchhoff stress.
Further, in step S3, the constitutive model parameter identification method specifically includes:
for constitutive parameters in the superelasticity constitutive model, performing uniaxial stretching, equibiaxial stretching and plane shearing tests on a rubber sample, processing stress strain data, fitting by a least square method to obtain constitutive parameters of the superelasticity constitutive model, and using the obtained parameters for parameter identification of the nonlinear viscoelastic constitutive model;
for constitutive parameters of a nonlinear viscoelastic constitutive model, firstly, performing shear creep tests on a rubber test piece under different loads, and identifying material parameters of rubber adopting a generalized Maxwell model under a certain load based on test results; then obtaining an initial value of a constitutive parameter of the nonlinear viscoelastic constitutive model through material parameter conversion of the generalized Maxwell model; bringing the initial value of the constitutive parameters of the nonlinear viscoelastic constitutive model into Isight combined with Abaqus to perform parameter identification, and repeating iteration until the constitutive model parameters are identified; after the constitutive model parameters are identified, the setting of the superelastic-nonlinear viscoelastic superposition constitutive model parameters is completed in a mode of modifying an inp file in the finite element software Abaqus.
Further, the specific steps of using Isight in combination with Abaqus to perform parameter identification are as follows:
s3.1, taking the unit grid as a reverse-thrust object, selecting an initial value of a nonlinear viscoelastic constitutive model as a constitutive parameter, and calculating according to the load conditions of the rubber test piece in a shear creep test of different loads in Abaqus respectively to obtain a unit calculation creep variable curve under each load condition;
s3.2, introducing the unit calculated creep curves under each load condition into Isight software, introducing a unit test creep curve obtained by dividing a test creep curve obtained by a rubber test piece test by the thickness of the rubber test piece into Isight software, performing data matching on the unit calculated creep curve and the unit test creep curve in the Isight software, introducing matched errors into an optimization module in the Isight software, and aiming at minimizing the errors between the unit calculated creep curve and the unit test creep curve;
and S3.3, automatically updating constitutive parameters of the nonlinear viscoelastic constitutive model by using a Hooke-Jeeves optimization algorithm in an optimization module in Isight software, automatically restarting the Abaqus software, substituting the updated material parameters into the Abaqus software for recalculation to obtain a new unit calculation creep variable curve, repeating the step S3.1 and the step S3.2 until the error between the unit calculation creep variable curve and the unit test creep variable curve meets the precision requirement, and identifying the constitutive model parameters.
Further, in step S5, the creep amount is the difference between the deformation amount of the rubber in the load direction and the deformation amount immediately after the load is applied under a certain constant load.
Compared with the prior art, the invention has the following advantages:
1) the method can accurately predict the creep characteristics of the rubber vibration isolator under different loads;
2) the creep characteristics of the rubber vibration isolators with different structures can be predicted by a finite element calculation method so as to guide the early-stage design of the rubber vibration isolators;
3) the creep deformation of the center node of the rubber vibration isolator is used for describing the overall creep deformation characteristic of the rubber vibration isolator, and the prediction effect is good.
Drawings
Fig. 1 is a flow chart of a method for predicting creep characteristic performance of a rubber vibration isolator in an embodiment of the invention.
Fig. 2 is a schematic diagram of the rubber vibration isolator in the embodiment of the invention.
FIG. 3 is a schematic diagram of a super-elastic-non-viscous viscoelastic superposition constitutive model in the present invention.
FIG. 4 is a schematic view of a rubber test piece shear creep test tool according to the present invention.
FIG. 5 is a graph showing the results of the shear creep test of rubber test pieces under different loads in the present invention.
FIG. 6 is a graphical representation of the normalized creep compliance and normalized time-domain shear relaxation modulus versus time for a load in accordance with the present invention.
FIG. 7 is a flow chart of the present invention for identifying parameters by Isight in conjunction with Abaqus.
FIG. 8 is a schematic diagram of selected cell grids for identifying parameters of a nonlinear viscoelastic constitutive model according to the present invention.
Fig. 9 is a schematic diagram of a physical model of the rubber vibration isolator for calculating the creep amount in the invention.
Detailed Description
Specific implementations of the present invention are described in further detail below with reference to the accompanying drawings and examples.
Example (b):
a method for predicting creep characteristic performance of a rubber vibration isolator is shown in figure 1 and comprises the following steps:
s1, establishing a geometric model of the rubber vibration isolator by using three-dimensional modeling software UG, wherein the schematic diagram of the rubber vibration isolator is shown in FIG. 2;
s2, performing meshing on the rubber part of the rubber vibration isolator;
in the embodiment, the size of the calculation model is consistent with the physical size of the rubber vibration isolator, and in order to improve the calculation precision of the finite element, a hexahedral mesh is selected, and the size of the mesh is controlled within 2 mm;
s3, as shown in fig. 3, using a superelastic-nonlinear viscoelastic superposition constitutive model, i.e. a superposition model of a superelastic constitutive model and a nonlinear viscoelastic constitutive model;
the superelasticity constitutive model is a Mooney-Rivlin model, and the expression of the strain potential energy function of the superelasticity constitutive model is as follows:
Figure BDA0002849263330000041
wherein C is10And C01Is a parameter describing the shear properties of a material; d1Is a parameter describing the compression characteristics of the material; j. the design is a squareelIs the elastic volume ratio;
Figure BDA0002849263330000042
is a first order strain invariant;
Figure BDA0002849263330000043
is a second order strain invariant.
The expression of the nonlinear viscoelastic constitutive model about creep strain rate is as follows:
Figure BDA0002849263330000044
wherein A, m, n are material parameters describing creep properties of the material;
Figure BDA0002849263330000045
is the creep strain rate; ε is the creep strain; q is Kirchhoff stress. For constitutive parameters of the nonlinear viscoelastic constitutive model, the parameters to be identified are shown in table 1.
TABLE 1 nonlinear viscoelastic constitutive model parameters to be identified
Figure BDA0002849263330000046
The material attribute setting is completed by adopting a constitutive model parameter identification method, which comprises the following steps:
for constitutive parameters in the superelasticity constitutive model, performing uniaxial stretching, equibiaxial stretching and plane shearing tests on a rubber sample, processing stress strain data, fitting by a least square method to obtain constitutive parameters of the superelasticity constitutive model, and using the obtained parameters for parameter identification of the nonlinear viscoelastic constitutive model;
for constitutive parameters of the nonlinear viscoelastic constitutive model, in this embodiment, the rubber test piece shear creep test tool shown in fig. 4a and 4b is designed first, wherein the rubber test piece is vulcanized between the moving block and the fixed block, and the fixed block is fixed on the base through the bolt connection. Performing a shear creep test on the rubber test piece under different loads on an Instron tensile machine, wherein a test creep curve is shown in FIG. 5, and identifying material parameters of the rubber under a certain load by adopting a generalized Maxwell model based on a test result; then, the initial value of the constitutive parameters of the nonlinear viscoelastic constitutive model is obtained through material parameter transformation of the generalized Maxwell model, which in this embodiment is specifically as follows:
converting the shear creep test result under 40N load into normalized creep compliance jS(t) a relationship with time t; normalized creep compliance is the ratio of material strain to stress normalized during creep. Creep compliance JS(t) is the strain per unit stress, and at time t, the creep compliance JS(t) is:
JS(t)=γ(t)/τ0
in the formula, τ0The shear stress constant applied for creep test; γ (t) is the shear strain over time.
At time zero when a load is just applied, creep compliance JS(0) Comprises the following steps:
JS(0)=γ(0)/τ0
in the formula, γ (0) is the strain amount immediately after the load is applied.
For shear experiments, the shear strain γ (t) of the rubber is:
Figure BDA0002849263330000051
in the formula, xtThe deformation is the relation of time, and the unit is mm; delta is the thickness of the test piece in mm.
Normalized creep compliance jS(t) is:
Figure BDA0002849263330000052
in the formula, xtThe unit is mm which is the relation of the shearing deformation along with the time; x is the number of0The amount of shear deformation immediately after application of a load is expressed in mm. Converting creep data into relaxation data by the following convolution integral formula, and converting to obtain normalized time domain shear relaxation modulus gR(t) time dependence. Normalized creep compliance jS(t) and normalized time-domain shear relaxation modulus gRThe results of the conversion of (t) are shown in FIG. 6.
Figure BDA0002849263330000053
Normalized time domain shear relaxation modulus gR(t) satisfies the expression:
Figure BDA0002849263330000054
wherein, gi and tr_i(i ═ 1, 2.., N) are constitutive parameters in the generalized Maxwell model.
Normalized temporal shear relaxation modulus g in FIG. 6RAnd (t) obtaining constitutive parameters of the generalized Maxwell model by least square fitting according to the expression in the relation curve of time and (t).
When the material parameter m in the nonlinear viscoelastic constitutive model is equal to 0 and n is equal to 1, the response of the constitutive model is equal to the response of the generalized Maxwell model, and the parameters of the generalized Maxwell model are converted into the initial values of the parameters of the nonlinear viscoelastic constitutive model based on the following formula:
when m is equal to 0 and n is equal to 1, the stiffness ratio si(i ═ 1, 2., N) satisfies the following relationship:
si=gi
material parameter Ai(i ═ 1, 2., N) satisfies the following relationship:
Ai=1/(3×gi×tr_i×G);
in the formula GIs the quasi-static shear modulus of the material.
Substituting the initial value of the constitutive parameters of the nonlinear viscoelastic constitutive model into Isight combined with Abaqus to perform parameter identification, and repeating iteration until the constitutive model parameters are identified, wherein the identification flow chart is shown in FIG. 7, and the specific steps are as follows:
s3.1, in this embodiment, using a rectangular solid cell grid with a thickness of 1mm as shown in fig. 8 as a reverse-estimation object, selecting an initial value of a non-linear viscoelastic constitutive model for constitutive parameters, and calculating in Abaqus according to the load conditions (stress conditions of the test tool at 40N, 80N, and 120N) of fig. 5, respectively, to obtain a unit calculation creep variable curve under each load condition;
s3.2, leading the three unit calculated creep curves into Isight, leading unit test creep curves obtained by dividing the three test creep curves obtained by the rubber test piece test in FIG. 5 by the thickness of the rubber test piece into Isight, carrying out data matching on the unit calculated creep curves and the unit test creep curves in Isight, leading matched errors into an optimization module in Isight, and aiming at minimizing errors between the unit calculated creep curves and the unit test creep curves;
and S3.3, automatically updating constitutive parameters of the nonlinear viscoelastic constitutive model by using a Hooke-Jeeves optimization algorithm in an optimization module in Isight, automatically restarting the Abaqus, substituting the updated material parameters into the Abaqus for recalculation to obtain a new unit calculation creep variable curve, repeating the steps S3.1 and S3.2 until the error between the calculation creep variable curve and the unit test creep variable curve meets the precision requirement, and identifying the constitutive model parameters.
After the constitutive model parameters are identified, the setting of the superelastic-nonlinear viscoelastic superposition constitutive model parameters is completed in a mode of modifying an inp file in the finite element software Abaqus.
S4 and FIG 9 are physical model schematic diagrams of the calculated creep amount of the rubber vibration isolator. As shown in fig. 9, six degrees of freedom of all nodes of the metal outer tube of the rubber vibration isolator are constrained, so that all nodes of the metal outer tube are ensured not to move; all nodes of the metal inner pipe of the rubber vibration isolator are related to a central node of the rubber vibration isolator, and a force with constant magnitude is applied to the central node to complete the setting of boundary conditions;
s5, result post-processing: recording the change condition of the displacement of the center node of the rubber vibration isolator along with time to obtain a creep curve of the center node, wherein the creep is the difference between the deformation of the rubber along the load direction and the deformation of the rubber after the load is applied under a certain constant load; and evaluating the creep characteristic performance of the rubber vibration isolator according to the creep curve of the central node of the rubber vibration isolator.

Claims (8)

1. A method for predicting creep characteristic performance of a rubber vibration isolator is characterized by comprising the following steps:
s1, establishing a geometric model of the rubber vibration isolator;
s2, performing meshing on the rubber part of the rubber vibration isolator;
s3, adopting a superelastic-nonlinear viscoelastic superposition constitutive model, namely a superposition model of the superelastic constitutive model and the nonlinear viscoelastic constitutive model, and adopting a constitutive model parameter identification method to complete material attribute setting;
s4, restraining six degrees of freedom of all nodes of the metal outer pipe of the rubber vibration isolator to ensure that all nodes of the metal outer pipe do not move; all nodes of the metal inner pipe of the rubber vibration isolator are related to a central node of the rubber vibration isolator, and a force with constant magnitude is applied to the central node to complete the setting of boundary conditions;
s5, result post-processing: and recording the change condition of the displacement of the center node of the rubber vibration isolator along with time to obtain a creep curve of the center node, and evaluating the creep characteristic performance of the rubber vibration isolator according to the creep curve of the center node of the rubber vibration isolator.
2. The method for predicting the creep property of the rubber vibration isolator according to claim 1, wherein in the step S1, the geometric model of the rubber vibration isolator is established by using three-dimensional modeling software UG.
3. The method for predicting the creep property of the rubber vibration isolator according to claim 1, wherein in step S2, in order to improve the finite element calculation accuracy, hexahedral meshes are selected, and the mesh size is controlled within 2 mm.
4. The method for predicting creep property of a rubber vibration isolator according to claim 1, wherein in step S3, the superelastic constitutive model is a Mooney-Rivlin model, and the strain potential energy function thereof is expressed as:
Figure FDA0002849263320000011
wherein C is10And C01Is a parameter describing the shear properties of a material; d1Is a parameter describing the compression characteristics of the material; j. the design is a squareelIs the elastic volume ratio;
Figure FDA0002849263320000012
is a first order strain invariant;
Figure FDA0002849263320000013
is a second order strain invariant.
5. The method for predicting the creep property of the rubber vibration isolator according to claim 1, wherein in the step S3, the expression of the nonlinear viscoelastic constitutive model about the creep strain rate is as follows:
Figure FDA0002849263320000014
wherein A, m, n are material parameters describing creep properties of the material;
Figure FDA0002849263320000015
is the creep strain rate; ε is the creep strain; q is Kirchhoff stress.
6. The method for predicting the creep property of the rubber vibration isolator according to claim 1, wherein in step S3, the constitutive model parameter identification method is as follows:
for constitutive parameters in the superelasticity constitutive model, performing uniaxial stretching, equibiaxial stretching and plane shearing tests on a rubber sample, processing stress strain data, fitting by a least square method to obtain constitutive parameters of the superelasticity constitutive model, and using the obtained parameters for parameter identification of the nonlinear viscoelastic constitutive model;
for constitutive parameters of a nonlinear viscoelastic constitutive model, firstly, performing shear creep tests on a rubber test piece under different loads, and identifying material parameters of rubber adopting a generalized Maxwell model under a certain load based on test results; then obtaining an initial value of a constitutive parameter of the nonlinear viscoelastic constitutive model through material parameter conversion of the generalized Maxwell model; bringing the initial value of the constitutive parameters of the nonlinear viscoelastic constitutive model into Isight combined with Abaqus to perform parameter identification, and repeating iteration until the constitutive model parameters are identified; after the constitutive model parameters are identified, the setting of the superelastic-nonlinear viscoelastic superposition constitutive model parameters is completed in a mode of modifying an inp file in the finite element software Abaqus.
7. The method for predicting the creep property of the rubber vibration isolator according to claim 6, wherein the specific steps of identifying the parameters by combining Isight with Abaqus are as follows:
s3.1, taking the unit grid as a reverse-thrust object, selecting an initial value of a nonlinear viscoelastic constitutive model as a constitutive parameter, and calculating according to the load conditions of the rubber test piece in a shear creep test of different loads in Abaqus respectively to obtain a unit calculation creep variable curve under each load condition;
s3.2, introducing the unit calculated creep curves under each load condition into Isight software, introducing a unit test creep curve obtained by dividing a test creep curve obtained by a rubber test piece test by the thickness of the rubber test piece into Isight software, performing data matching on the unit calculated creep curve and the unit test creep curve in the Isight software, introducing matched errors into an optimization module in the Isight software, and aiming at minimizing the errors between the unit calculated creep curve and the unit test creep curve;
and S3.3, automatically updating constitutive parameters of the nonlinear viscoelastic constitutive model by using a Hooke-Jeeves optimization algorithm in an optimization module in Isight software, automatically restarting the Abaqus software, substituting the updated material parameters into the Abaqus software for recalculation to obtain a new unit calculation creep variable curve, repeating the step S3.1 and the step S3.2 until the error between the unit calculation creep variable curve and the unit test creep variable curve meets the precision requirement, and identifying the constitutive model parameters.
8. The method for predicting the creep property of the rubber vibration isolator according to any one of claims 1 to 7, wherein the creep amount is the difference between the deformation amount of the rubber in the load direction and the deformation amount of the rubber immediately after the load is applied under a certain constant load in step S5.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114088365A (en) * 2021-10-15 2022-02-25 渤海造船厂集团有限公司 Device and method for maintaining and detecting rubber shock absorber after horizontal installation

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* Cited by examiner, † Cited by third party
Title
刘文帅: "橡胶隔振器高频动刚度及蠕变特性研究", 《万方数据知识服务平台》, 14 December 2020 (2020-12-14), pages 9 - 36 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114088365A (en) * 2021-10-15 2022-02-25 渤海造船厂集团有限公司 Device and method for maintaining and detecting rubber shock absorber after horizontal installation
CN114088365B (en) * 2021-10-15 2023-12-19 渤海造船厂集团有限公司 Maintenance and detection device and method for horizontally-arranged and installed rubber shock absorber

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