CN109408969B - Method for identifying viscoelastic parameters of rubber by using finite element software to establish constitutive model - Google Patents
Method for identifying viscoelastic parameters of rubber by using finite element software to establish constitutive model Download PDFInfo
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Abstract
The invention discloses a method for identifying rubber viscoelastic parameters and establishing a constitutive model by using finite element software. And establishing a rubber superelasticity and viscoelastic constitutive model. And identifying viscoelastic parameters by combining experimental data with ANSYS. Inputting parameters of the constitutive model, filling the viscoelastic model according to the results of the three steps, carrying out grid division, setting boundary conditions, setting solving conditions, and carrying out calculation on the dynamic characteristics of the rubber. Compared with the prior method, the method is simple, the result is accurate and reliable, and the deviation of the result obtained by simulation analysis by the method is less than 3%. The method has positive significance for identifying the viscoelastic parameters of the rubber and analyzing the dynamic characteristics of the rubber.
Description
Technical Field
The invention relates to a method for identifying rubber viscoelastic parameters and establishing a constitutive model by using finite element software, in particular to a method for identifying rubber viscoelastic parameters and establishing a constitutive model by using finite element software to calculate the dynamic characteristics of rubber, belonging to the field of solid dynamics calculation.
Background
The rubber has good vibration absorption, vibration reduction and sealing performance, and is widely applied to vibration isolation structures of machines in industries such as automobiles, aviation, precision instruments and the like, for example: vibration isolation sheets of the engine, oil tank sealing rings and the like. The rubber has complex mechanical properties, on one hand, the rubber embodies super elasticity, has very large strain capacity (the ratio of stress to strain is very small), the stress-strain relation of the material is expressed by a strain energy density function, and the material is approximately incompressible; on one hand, the material shows viscoelasticity, and under the action of cyclic force, the response of the material shows rate dependence, and the stress strain has hysteresis effect. Different rubber products with different properties can be produced by different component proportions, and the reflected physical properties are greatly different. Therefore, before the rubber product is really applied to equipment, the rubber is reasonably selected, finite element kinetic analysis is carried out on the rubber, the mechanical property of the rubber is accurately predicted, and the product precision and even the product service life are determined.
The accurate establishment of the rubber constitutive model is the basis for the analysis of rubber dynamic characteristics, and the established constitutive model determines whether the rubber finite element simulation can comprehensively represent the rubber dynamic characteristics. In the previous research, the mechanical property of rubber can not be accurately and comprehensively expressed by only using a superelastic model, when the superelastic and viscoelastic constitutive model is used, the viscoelastic parameters have ambiguous meanings, the identification method is complex and multiple theoretical deductions are applied, and the experimental conditions are limited to static and quasi-static tests such as unidirectional tension, compression, plane shearing and the like. This results in an incomplete analysis of the rubber dynamics, and the predicted rubber dynamics are not realistic, leading to unnecessary losses.
Disclosure of Invention
Aiming at the problems, the invention provides a method for identifying rubber viscoelastic parameters by using finite element software to establish a constitutive model for calculating rubber dynamic characteristics. A new method is provided for identifying parameters of the rubber viscoelastic model, so that the dynamic characteristic analysis of rubber is more comprehensive.
The invention adopts the technical scheme that a method for identifying rubber viscoelastic parameters by using finite element software and establishing a constitutive model to calculate the dynamic characteristics of rubber comprises the following steps:
1) A rubber sample physical model is established in finite element software.
2) The method comprises the steps of establishing a rubber superelasticity and viscoelastic constitutive model, wherein the superelasticity model is represented by using a Mooney-Rivlin two-parameter model, the viscoelastic model is represented by using a generalized Maxwell model, and the generalized Maxwell model is represented as a three-dimensional rheological model in Ansys and is shown as a formula 1:
in the formula: σ is Coxist stress, pa; g (t) is a shear relaxation kernel function; k (t) is a volume relaxation kernel function; e is the shear strain offset; Δ is the bulk strain; t is the current time, s; τ is the process time, s. Wherein:
in the formula: g 0 And K 0 Shear and bulk relaxation moduli at 0 time, pa, respectively; n is G 、n K The number of terms is the PRONY grade number;
is the relative modulus;
is the relaxation time, s. Wherein
Also known as shear response coefficient;
also known as the volume response coefficient.
3) Extracting experimental data of the change of the relaxation modulus of the rubber sample with time
Preparing a rubber sample with the same components as the rubber to be researched according to Dynamic thermal mechanical analysis of DMA (Dynamic thermal mechanical analysis) to be applied, and setting the experimental conditions according to the actual working conditions, wherein the experimental conditions comprise: experiment temperature, experiment frequency sweep range, strain amplitude, etc. And selecting a DMA temperature/frequency scanning experiment to obtain the change curve of the loss modulus and the storage modulus of the rubber along with time, and obtaining the change curve of the relaxation modulus data of the rubber along with time through DMA tester software, wherein the curve fully reflects the viscoelastic property of the rubber under the conditions of frequency and temperature change.
4) Viscoelastic parameter identification in finite element software
Inputting the extracted data of the change of the relaxation modulus of the rubber along with time into prony current fitting of ANSYS, adjusting coeff value initial parameters to be 0,1, and fitting to obtain relative modulus and relaxation time, namely viscoelastic parameters in formulas 2 and 3.
5) Based on finite element ANSYS software, carrying out grid division on simulation projects, establishing boundary conditions, setting solver parameters, and carrying out dynamic characteristic analysis.
The method adopts a mode of combining experiments and software to identify the parameters of the rubber viscoelastic model, compared with the prior method, the method is simple, the result is accurate and reliable, and the deviation of the result obtained by simulation analysis by the method is less than 3 percent. The method has positive significance for identifying the viscoelastic parameters of the rubber and analyzing the dynamic characteristics of the rubber.
Drawings
FIG. 1 is a flow chart of a method according to the present invention.
Fig. 2 is a flow chart of experimental data combined with ANSYS to identify viscoelastic parameters of rubber.
FIG. 3 is a flow chart for obtaining data on the change of the relaxation modulus of rubber with time.
Fig. 4 is a flow chart of ANSYS fitting experimental data to obtain viscoelastic parameters.
Fig. 5 shows viscoelastic parameters of rubber obtained by ANSYS fitting according to an example of application of the present invention.
FIG. 6 is an example of a rubber test specimen and a simulation setup used in an example of the present invention.
FIG. 7 is C 01 /C 10 Curve of the relation with the shore hardness;
Detailed Description
Specific embodiments are given below with reference to the accompanying drawings.
The method is completed by a DMA tester and ANSYS software.
The flow chart of the method of the invention is shown in fig. 1, and specifically comprises the following steps:
the method comprises the following steps: and (4) establishing a physical model of the rubber sample by using ANSYS, wherein the specification is designed according to the specification of the sample used in the experiment.
Step two: and establishing a rubber superelasticity and viscoelastic constitutive model.
Step three: the experimental data was combined with ANSYS for viscoelastic parameter identification, the method is shown in fig. 2.
Step four: inputting constitutive model parameters, wherein the superelastic model parameters are obtained according to the relation of fig. 7, filling the viscoelastic model according to the three results, carrying out grid division, setting boundary conditions (as shown in fig. 6), setting solving conditions, and carrying out calculation on the dynamic characteristics of the rubber.
The method for identifying viscoelastic parameters by combining experimental data with ANSYS is shown in FIG. 2:
the method comprises the following steps: acquiring the change data of the relaxation modulus of the rubber along with time, wherein the method is shown in figure 3;
step two: ANSYS fitting experimental data to obtain viscoelastic parameters, the method is shown in fig. 4;
the change data of the rubber relaxation modulus along with the time is obtained, and the method is shown in figure 3:
the method comprises the following steps: formulating a rubber sample according to the model of the selected DMA experimental instrument
Step two: the range of experimental conditions, including temperature, frequency, strain amplitude, is selected according to the actual working environment in which the rubber is used.
Step three: and selecting a DMA temperature frequency scanning experiment to obtain the rubber loss modulus, the storage modulus and the loss factor.
Step four: and selecting a proper reference temperature, and obtaining the change data of the relaxation modulus of the rubber along with time through DMA analysis software.
ANSYS fitting the experimental data to obtain viscoelastic parameters, the method is shown in figure 4:
the method comprises the following steps: storing the extracted rubber relaxation modulus data into a notebook according to rules, wherein the naming should be performed by English;
step two: entering an ANSYS PRONY CURVE FITTING module, importing named data, adjusting initial parameters, and FITTING data;
step three: checking the fitting result, and adjusting the initial parameters again until the error of the fitting data and the experimental data is in an allowable range;
step four: and storing and applying to obtain the viscoelastic parameters of the rubber.
An example of the calculation of the dynamics of a rubber structure using the present invention is given below.
Fig. 5 gives the experimental relaxation data versus the fitted relaxation data by ANSYS fitting.
Fig. 6 shows an example of a dynamic simulation of a rubber sample according to experimental conditions.
TABLE 1 list of viscoelastic parameters
TABLE 2 comparison of Experimental data with simulation data
Note: HS represents the hardness of the rubber
The viscoelastic parameters of the relaxation modulus data of the rubber obtained by ansys fitting analysis are shown in table 1, and the fitting accuracy can be obtained by combining with fig. 5. The dynamic characteristic analysis is carried out by taking the group of parameters as the viscoelastic parameters of the rubber, and the loss factor of the rubber obtained by analysis and the loss factor obtained by experiment are within 3 percent, as shown in table 2. The process of the present invention is therefore significantly superior to the previous processes.
Claims (4)
1. A method for identifying rubber viscoelastic parameters and establishing a constitutive model by using finite element software is characterized by comprising the following steps: the method specifically comprises the following steps:
the method comprises the following steps: establishing a physical model of the rubber sample by using ANSYS, wherein the specification is designed according to the specification of the sample used in the experiment;
step two: establishing a rubber superelasticity and viscoelasticity constitutive model;
step three: identifying viscoelastic parameters by combining experimental data with ANSYS;
step four: inputting parameters of a constitutive model, filling the viscoelastic model according to the results of the third step, carrying out grid division, setting boundary conditions, setting solving conditions, and carrying out calculation on the dynamic characteristics of the rubber;
the method comprises the following steps of,
1) Establishing a rubber sample physical model in finite element software;
2) Establishing a rubber superelastic and viscoelastic constitutive model, wherein the superelastic model is represented by using a Mooney-Rivlin two-parameter model, the viscoelastic model is characterized by using a generalized Maxwell model, and the generalized Maxwell model is represented as a three-dimensional rheological model in Ansys and is shown as a formula (1):
in the formula: σ is Coxist stress, pa; g (t) is a shear relaxation kernel function; k (t) is a volume relaxation kernel function; e is the shear strain offset; Δ is the bulk strain; t is the current time, s; τ is process time, s; wherein:
in the formula: g 0 And K 0 Shear and bulk relaxation moduli at 0 time, pa, respectively; n is G 、n K The number of terms is the PRONY grade number;
is the relative modulus;
is the relaxation time, s; wherein
Also known as shear response coefficient;
is also known as the volume response coefficient;
3) Extracting experimental data of the change of the relaxation modulus of the rubber sample along with time;
preparing a rubber sample with the same components as the rubber to be researched according to the DMA dynamic thermo-mechanical analysis to be applied, and setting the experimental conditions by combining the actual working conditions, wherein the experimental conditions comprise the following steps: experiment temperature, experiment frequency scanning range and strain amplitude; selecting a DMA temperature/frequency scanning experiment to obtain a change curve of the loss modulus and the storage modulus of the rubber along with time, and obtaining a change curve of the relaxation modulus data of the rubber along with time through DMA tester software, wherein the curve fully embodies the viscoelastic characteristics of the rubber under the conditions of frequency and temperature change;
4) Identifying viscoelastic parameters in finite element software;
inputting the extracted data of the change of the relaxation modulus of the rubber along with time into prony current fitting of ANSYS, adjusting coeffvalue initial parameters to be 0,1, and fitting to obtain relative modulus and relaxation time, namely viscoelastic parameters in formulas (2) and (3);
5) Based on finite element ANSYS software, carrying out grid division on simulation projects, establishing boundary conditions, setting solver parameters, and carrying out dynamic characteristic analysis.
2. The method for establishing the constitutive model by using the finite element software to identify the viscoelastic parameters of the rubber according to claim 1, wherein the method comprises the following steps: the method for identifying viscoelastic parameters by combining experimental data with ANSYS comprises the following steps: acquiring change data of rubber relaxation modulus along with time;
step two: and (5) obtaining viscoelastic parameters by fitting experimental data through ANSYS.
3. The method for establishing the constitutive model by using the finite element software to identify the viscoelastic parameters of the rubber according to claim 1, wherein the method comprises the following steps: obtaining the change data of the rubber relaxation modulus along with time:
the method comprises the following steps: formulating a rubber sample according to the model of the selected DMA experimental instrument
Step two: selecting experimental condition ranges including temperature, frequency and strain amplitude according to the actual working environment of the rubber;
step three: selecting a DMA temperature frequency scanning experiment to obtain rubber loss modulus, storage modulus and loss factor;
step four: and selecting a proper reference temperature, and obtaining the change data of the relaxation modulus of the rubber along with time through DMA analysis software.
4. The method for establishing the constitutive model by using the finite element software to identify the viscoelastic parameters of the rubber as claimed in claim 1, wherein the method comprises the following steps: ANSYS fitting experimental data to obtain viscoelastic parameters,
the method comprises the following steps: storing the extracted rubber relaxation modulus data into a notebook according to rules, wherein the naming should be performed by English;
step two: entering an ANSYS PRONY CURVE FITTING module, importing named data, adjusting initial parameters, and FITTING the data;
step three: checking the fitting result, and adjusting the initial parameters again until the error of the fitting data and the experimental data is in an allowable range;
step four: and storing and applying to obtain the viscoelastic parameters of the rubber.
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| CN112182928B (en) * | 2020-09-17 | 2023-04-07 | 中国海洋大学 | Software system for mechanical property analysis and optimization design of rubber products |
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