CN103884606A - Method for testing precision and stability of parameters of vehicle vibration-damping rubber static nonlinear material - Google Patents
Method for testing precision and stability of parameters of vehicle vibration-damping rubber static nonlinear material Download PDFInfo
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Abstract
The invention discloses a method for testing the precision and the stability of parameters of vehicle vibration-damping rubber static nonlinear material. The method comprises the following steps: acquiring data of force and deformation by virtue of a basic experiment to obtain certain basic experiment data of the vibration-damping rubber, and then fitting a constitutive relation experimental curve according to a least square method; inputting the obtained data of the force and the deformation into finite element software to calculate, and fitting and calculating material constants to obtain a comparative analysis chart of a fitting curve chart and an experiment curve of strain-energy function in various forms; and obtaining a stability evaluation form, an evaluation result and interpretation of the fitting curve by virtue of numerical calculation and analysis functions of a finite element, so that the form of optimal hyperelastic deformation energy density function and homologous material constants are obtained. The method disclosed by the invention has the advantages that the numerical precision, the reliability and the numerical stability analysis of multiple groups of vibration-damping rubber material static characteristic parameters are calculated, and theoretical basis is provided for accurate and reliable practical application of the vibration-damping rubber material static characteristic parameters.
Description
[technical field]
The invention belongs to Element Design and the theoretical research technical field of plant equipment and vehicle, specifically refer to a kind of method of testing of precision and stability of Vehicle damper rubber static non linear material parameter.
[background technology]
Be applied in the rubber shock absorber in Vehicular system, what mainly play oscillation damping and energy dissipating effect is elastomeric polymeric material, and elastomeric polymeric material belongs to elastic material, and its mechanical behavior is presented as a kind of mechanical behavior between solid elastic and liquid viscosity.Its static state and quasistatic mechanical behavior are presented as nonlinearity feature, have strong time and temperature dependency, relevant with load frequency, load amplitude and form of distortion etc.
Because the material parameter of vibration isolation rubber on rubber shock absorber belongs to non-linear force mathematic(al) parameter, the influence factor of such parameter is too complicated, cannot realize for a long time the more accurate experimental study of such parameter and more accurately estimate, the precision of its static non linear material parameter and numerical stability Estimation Study cannot realize all the time.Due to this theoretical calculate and experimental technique on defect, caused that rubber shock absorber design accuracy is low, the insecure present situation of performance.This also just causes the disconnection of rubber shock absorber designing technique and various production technology links.Investigation shows, about theoretical computational accuracy research and numerical stability problem and its application in practice problem of the nonlinear elasticity parameter of vibration isolation rubber, be all the time scientific and technological circle and engineering circles compared with advanced problems.
About many design relevant issues of rubber shock absorber vibration insulating system, now compared with proven technique, the Static Design that can only too simplify, and accuracy computation and the stability analysis that cannot realize more perfect rubber damping material nonlinearity elastic material parameter are calculated, some theories and experimental technique, still only in experimental study and effectiveness in vibration suppression checking.
In engineering design, less to more accurate theoretical calculating and the experimental study of its nonlinear mechanics behavior and mechanics parameters, especially lack experimental technique and theoretical computing technique to its nonlinearity system performance Research on Accuracy.And the design of rubber shock absorber must obtain these theoretical supports of calculating and testing, could realize the design more accurately that meets work condition environment requirement.
Rubber shock absorber is widely used in engineering field, and along with the raising of requirement, instrument and equipment accuracy requirement and the reliability requirement of various work condition environment hommizations, the accuracy requirement of vibration insulating system design is also improving constantly.As, be applied in various Vehicular systems and Marine engineering, be applied in rubber shock absorber in the mechanical systems such as blower fan, comminutor and lathe etc.These data informations and experiment and computing method are to carry out the important support that such rubber shock absorber (and multiple elastomeric polymeric material) is realized accurately design and applied.
[summary of the invention]
Technical matters to be solved by this invention is to provide a kind of rubber vehicle vibration damping nonlinear elasticity parameter static properties method of testing.
The present invention is achieved in that
A kind of rubber vehicle vibration damping nonlinear elasticity parameter static properties method of testing, comprises the steps:
First step: the data that obtain power and distortion by infrastest:
Equivalence about shearing experiment is replaced, and 15 times of above even uniaxial tensile tests that adopt Width size to be greater than height replace, also referred to as limited stretching;
The shearing constitutive equation that can obtain becoming rigidity comprising of shear stress and strain is as formula (1)
τ=G
(γ)γ (1)
τ-shear stress in formula, G
(γ)-shear elasticity is the function of strain; γ-shearing strain;
Its static engineering shear strain numerical value, can videotape the change in size of measuring Width by video, and the size comparison of perpendicular direction, calculate γ, by the relation of shearing strain and shear stress, just can obtain the experimental data that this vibration isolation rubber is sheared, then go out constitutive relation empirical curve according to least square fitting;
Second step: the power that first step is obtained and the data of distortion input finite element software calculate, and the Fitting Calculation goes out material constant:
Obtain the matched curve figure of various forms strain energy function and the comparative analysis figure of empirical curve;
Third step: by numerical evaluation and the analytic function of finite element, utilize computing machine to carry out computational analysis, can obtain the estimation of stability table of matched curve, evaluation result and explanation, the estimation of stability table of Mooney-Rivlin first order modeling material parameter, the estimation of stability table of Polynomial second order material parameter, the estimation of stability table of Yeoh tri-rank material parameters and the estimation of stability table of Arruda-Boyce material parameter, to above-mentioned conclusion relatively and comprehensive analysis, thus obtain form and the corresponding material constant of optimum hyperelastic deformation energy density function.
Further, described infrastest is limited stretching experiment, adopts Width size to be greater than 15 times of above even uniaxial tensile tests of height.
The invention has the advantages that: the present invention mainly describes and stress state analysis by material behavior, from microscopic theory aspect, studied the experimental principle of the vibration isolation rubber material of composition rubber shock absorber.The research and development of loading equipemtn frock are carried out.And carry out installing and tested.Study the expression formula of the multiple elastic material deformation energy density of Vehicle damper elastomeric material, and obtained theory and the experimental technique method of its static materials parameter acquiring.And experimental result has been carried out to statistical study, obtain multiple data informations about vibration isolation rubber nonlinear elasticity parameter.Utilize efficient numerical computation method, in conjunction with the research and development of computer simulation technique and experimental technique, drawn compared with the determine precision method of the vibration isolation rubber elastic material parameter of system, and invented the method for estimating stability of its correlation parameter.Application said method, based on nonlinear FEM (finite element) calculation technology, has calculated many groups vibration isolation rubber material static characterisitic parameter.Application said method, in conjunction with computer numerical analytical technology, has calculated many groups vibration isolation rubber material static characterisitic parameter numerical precision reliability and stability, for the more accurately reliable application in practice of vibration isolation rubber material static characterisitic parameter provides theoretical foundation.
[accompanying drawing explanation]
The invention will be further described in conjunction with the embodiments with reference to the accompanying drawings.
Fig. 1 is limited stretching experiment schematic diagram in the present invention.
Fig. 2 is the limited stretching experiment unit clamp of Vehicle damper rubber in the present invention.
Fig. 3 is the medium biaxial stretch-formed loading figure of the present invention.
Fig. 4 is the superposition principle schematic diagram of compressing stress state in the present invention.
Fig. 5 is Polynomial single order and Polynomial second order uniaxial tension matched curve figure in the present invention.
Fig. 6 is the simple shear stress-strain curve that in the present invention, Polynomial second-order fit goes out.
Fig. 7 is Yeoh tri-rank and Arruda-Boyce matched curve and experimental data curve figure in the present invention.
[embodiment]
A kind of rubber vehicle vibration damping nonlinear elasticity parameter static properties method of testing, comprises the steps:
First step: the data that obtain power and distortion by limited stretching infrastest:
About the compression experiment of vibration isolation rubber, while axially adding uniform pressure, the effect of the friction force on surface of contact will cause the material can not be along vertical movement.And slightly leave the part of surface of contact, and due to incompressibility and the large deformation feature of elastomeric material, when vertical, during without constraint, material is to vertical rapid movement, and transversely deforming is excessive, is out of shape extremely inhomogeneous.Therefore, the Compressing Engineering stress that this compression experiment machine obtains and the relation of engineering strain, can not truly reflect the true constitutive relation of vibration isolation rubber, serious distortion.And rubber shock absorber generally will be through sizing or constraint, limit the mobility of any direction of its material.
Equivalence about shearing experiment is replaced, and 15 times of above even uniaxial tensile tests that can adopt Width size to be greater than height replace, also referred to as limited stretching, as shown in Figure 1.Now, the absolute deformation of Width is far smaller than axial tension distortion, and the absolute deformation of Width can be ignored.
When limited stretching, because Width size is far longer than short transverse, can suppose that Width size remains unchanged, be the axis direction of detrusion.Be that axis of workpiece is constant, and the distortion of xsect generation transverse shifting is exactly detrusion.This experiment, can produce larger shear stress, replaces for the equivalence of shearing experiment.
The shearing constitutive equation that can obtain becoming rigidity comprising of shear stress and strain is as formula (1)
τ=G
(γ)γ (1)
τ-shear stress in formula, G
(γ)-shear elasticity is the function of strain; γ-shearing strain.
According to above-mentioned principle design and made the limited stretching unit clamp of Vehicle damper rubber, as shown in Figure 2.
Comprise upper grip main body 1, lower chuck main body 2; The top of described upper grip main body 1 has the bolt 3 being connected with power sensor; Described lower chuck main body 2 is fixed on the base of electronics stretching experiment machine; Described upper grip main body 1 position corresponding with described lower chuck main body 2 respectively has upper grip 4 and lower chuck 5; The position that described upper grip 4 is corresponding with lower chuck 5 all has rubber sheet gasket 6.
This unit clamp is for material electronics stretching experiment machine, wherein experiment has lower chuck on it to clamp with Vehicle damper rubber, vibration isolation rubber keeps horizontal level, this unit clamp lower chuck main body is fixed on the base of electronics stretching experiment machine, the bolt of unit clamp upper grip directly connects power sensor, and the upper cross-peen of connecting electronic stretching experiment machine.Adopt the directly method of cutting, on the stock of vibration isolation rubber, direct cutting experiment part, is clamped on the upper lower chuck of this fixture, open power supply and the air pump of experimental machine, test according to planning experiment, after having tested, carry out Data Processing in Experiment and analysis of experimental data.And carry out data precision and Calculation of Reliability research.
Designed fixture is material of main part by No. 45 steel, this unit clamp requires to have higher rigidity, and be connected experiment with vibration isolation rubber during at chuck, sliding can not appear in rubber parts, therefore, clamping contact part has been pasted anti-skid rubber cushion, and anti-skid rubber cushion and clamper main body must strong bond be integrated.
This unit clamp is for material electronics stretching experiment machine, wherein Vehicle damper rubber has lower chuck on it to clamp, vibration isolation rubber keeps horizontal level, this unit clamp lower clamp main body is fixed on the base of electronics stretching experiment machine, on unit clamp, the bolt of fixture directly connects power sensor, and the upper cross-peen of connecting electronic stretching experiment machine.First adopt the directly method of cutting, on the stock of vibration isolation rubber, direct cutting experiment part, is clamped on the upper lower chuck of this fixture, open power supply and the air pump of experimental machine, test according to planning experiment, after having tested, carry out Data Processing in Experiment and analysis of experimental data.And carry out data precision and Calculation of Reliability research.
Its static engineering shear strain numerical value, can videotape the change in size of measuring Width by video, and the size comparison of perpendicular direction, calculates γ.By the relation of shearing strain and shear stress, just can obtain the experimental data that this vibration isolation rubber is sheared, then go out constitutive relation empirical curve according to least square fitting.
The equivalence of Normal squeezing experiment is replaced, and can adopt planar stretch the biaxial stretch-formed experiment such as to test, as Fig. 3 replaces.In the time of its constitutive relation of research, the hydrostatic drawing stress state that stress can be by Uniaxial Compression time equates with Three-direction stretching stress superposes, and the result of this stress state stack, just be equivalent to planar stretch stress state etc. biaxial stretch-formed, the biaxial stretch-formed stress state such as this of vibration isolation rubber.Experiment exemplar answers cut-off footpath larger, some even rubber disc test specimens of thinner thickness, as can be cut-off footpath be greater than the even rubber disc test specimen of 12 times of thickness, carry out uniform radial drawing experiment, load schematic diagram as Fig. 3, get near the A point stressed compare Yuan in any distance edge center on it, its stress state such as is at the biaxial stretch-formed stress state.
Rubber shock absorber generally will, through sizing or constraint, limit the mobility of any direction of its material.
If establish etc. biaxial stretch-formed experiment normal stress be σ
l, along σ
lthe strain of direction is ε
l, and the normal stress of establishing uniaxial compression is σ
y, axial strain is ε
y, the superposition principle of stress state as shown in Figure 4, can go out the stress and strain relation of compression by equivalent transformation by these two kinds of stress states.
Can by etc. biaxial stretch-formed experimental data, be converted to the stress and strain data of uniaxial compression experiment, recycling least square fitting goes out the constitutive relation curve of uniaxial compression distortion.
Other infrastest data test method slightly.
Second step: the power that first step is obtained and the data of distortion input finite element software calculate, and the Fitting Calculation goes out material constant: obtain the matched curve figure of various forms strain energy function and the comparative analysis figure of empirical curve;
Can obtain different material constants based on multiple hyperelastic deformation energy density function, the exponent number difference of each deformation energy density function simultaneously, the number of the material constant obtaining is also different, in the time calculating with finite element software, need to be according to the input of static experiment data, the Fitting Calculation goes out material constant.
For the static experiment data of conventional vibration isolation rubber material, carry out data truncation processing, and the Fitting Calculation multiple material constants are gone out.Primary study the multiple material constant of butyronitrile vibration isolation rubber, adopt respectively Mooney-Rivlin, the strain energy function forms such as Neo Hooke and Yeoh, have obtained fitting precision and the error calculated.Result of calculation is as shown in table 1:
In above table,
it is the optimum estimate of population mean.
Standard deviation S is the mean value evolution again of the quadratic sum of each measured value and mean deviation.
Correlation coefficient r
xYit is the statistical study index that represents two curves (referring to empirical curve and matched curve in table) correlationship level of intimate.The computing formula of related coefficient is (2):
Vibration isolation rubber material is according to elastic material static experiment data, statistical error and correlation analysis according to this structure curve of least square fitting show, when the superelastic strain energy density function matching of three times of Polynomial reduction multinomial model Yeoh, error minimum, the constitutive modeling of applicable Vehicle damper elastomeric material.
By the finite element analysis computation of computing machine, can obtain the matched curve figure of various forms strain energy function and the comparative analysis figure of empirical curve, as shown in Fig. 5, Fig. 6 and Fig. 7.
Third step: by numerical evaluation and the analytic function of finite element, utilize computing machine to carry out computational analysis, can obtain the estimation of stability table of matched curve, evaluation result and explanation, the estimation of stability of Mooney-Rivlin first order modeling material parameter is in table 2, the estimation of stability of Polynomial second order material parameter is in table 3, the estimation of stability of Yeoh tri-rank material parameters is shown in Table 5 in the estimation of stability of table 4 and Arruda-Boyce material parameter, above-mentioned conclusion relatively and is comprehensively analyzed, thereby obtain form and the corresponding material constant of optimum hyperelastic deformation energy density function.
Vehicle damper elastomeric material is according to elastic material static experiment data, the data such as statistical error and the correlation analysis computational analysis of this structure curve of matching shows, the superelastic strain energy density function of three reduction multinomial model Yeoh of Polynomial is more suitable for Vehicle damper elastomeric material; The data of the material various deformation form of its matching are all stable; The experimental data statistical study of matching shows, mean value and standard deviation and experimental data are the most approaching; Reach 0.9997 with experimental data related coefficient.Integrated information analysis to above-mentioned result of study shows, the hyperelastic model optimal form of vibration isolation rubber material is that Yeoh constitutive model (also referred to as Reduce-Polynomal third-order model) is more reasonable.
The estimation of stability of table 2Mooney-Rivlin first order modeling material parameter
The estimation of stability of table 3Polynomial second order material parameter
The estimation of stability of table 4Yeoh tri-rank material parameters
The present invention mainly describes and stress state analysis by material behavior, from microscopic theory aspect, has studied the experimental principle of the vibration isolation rubber material of composition rubber shock absorber.The research and development of loading equipemtn frock are carried out.And carry out installing and tested.Study the expression formula of the multiple elastic material deformation energy density of Vehicle damper elastomeric material, and obtained theory and the experimental technique method of its static materials parameter acquiring.And experimental result has been carried out to statistical study, obtain multiple data informations about vibration isolation rubber nonlinear elasticity parameter.Utilize efficient numerical computation method, in conjunction with the research and development of computer simulation technique and experimental technique, drawn compared with the determine precision method of the vibration isolation rubber elastic material parameter of system, and invented the method for estimating stability of its correlation parameter.Application said method, based on nonlinear FEM (finite element) calculation technology, has calculated many groups vibration isolation rubber material static characterisitic parameter.Application said method, in conjunction with computer numerical analytical technology, has calculated many groups vibration isolation rubber material static characterisitic parameter numerical precision reliability and stability, for the more accurately reliable application in practice of vibration isolation rubber material static characterisitic parameter provides theoretical foundation.The present invention is Fujian Province's automotive electronics and electric drive technology key lab open fund project, bullets ZDKB1306.
The foregoing is only better enforcement use-case of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of doing, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.
Claims (2)
1. a method of testing for the precision and stability of Vehicle damper rubber static non linear material parameter, is characterized in that: comprise the steps:
First step: the data that obtain power and distortion by infrastest:
The shearing constitutive equation that can obtain becoming rigidity comprising of shear stress and strain is as formula (1)
τ=G
(γ)γ (1)
τ-shear stress in formula, G
(γ)-shear elasticity is the function of strain; γ-shearing strain;
Its static engineering shear strain numerical value, can videotape the change in size of measuring Width by video, and the size comparison of perpendicular direction, calculate γ, by the relation of shearing strain and shear stress, just can obtain the experimental data that this vibration isolation rubber is sheared, then go out constitutive relation empirical curve according to least square fitting;
Second step: the power that first step is obtained and the data of distortion input finite element software calculate, and the Fitting Calculation goes out material constant:
Obtain the matched curve figure of various forms strain energy function and the comparative analysis figure of empirical curve;
Third step: by numerical evaluation and the analytic function of finite element, utilize computing machine to carry out computational analysis, can obtain the estimation of stability table of matched curve, evaluation result and explanation, the estimation of stability table of Mooney-Rivlin first order modeling material parameter, the estimation of stability table of Polynomial second order material parameter, the estimation of stability table of Yeoh tri-rank material parameters and the estimation of stability table of Arruda-Boyce material parameter, to above-mentioned conclusion relatively and comprehensive analysis, thus obtain form and the corresponding material constant of optimum hyperelastic deformation energy density function.
2. the method for testing of the precision and stability of a kind of Vehicle damper rubber static non linear material parameter as claimed in claim 1, it is characterized in that: described infrastest is limited stretching experiment, adopt Width size to be greater than 15 times of above even uniaxial tensile tests of height, this limited stretching experiment can substitute the rubber shearing experiment that cannot directly carry out on general shear experimental facilities.
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| CN104596843A (en) * | 2015-01-16 | 2015-05-06 | 福建工程学院 | Special fixture for shearing substitution test of rubber material |
| CN105069241A (en) * | 2015-08-19 | 2015-11-18 | 山东大学 | Step-by-step analysis and prediction method for dynamic performances of rubber material structure |
| CN105973834A (en) * | 2016-05-11 | 2016-09-28 | 上海瀚海检测技术股份有限公司 | Comprehensive detection and evaluation method of shock absorber |
| CN106815442A (en) * | 2017-01-22 | 2017-06-09 | 安徽工业大学 | A kind of incompressible hyperelastic body constitutive model of isotropism and its application |
| CN110018072A (en) * | 2019-05-22 | 2019-07-16 | 西南交通大学 | Elastic material Parameters of constitutive model taper is pressed into measuring method |
| CN110823335A (en) * | 2018-08-10 | 2020-02-21 | 张德贤 | Granary detection method and system based on bottom surface single-circle standard deviation polynomial model |
| CN110858255A (en) * | 2018-08-06 | 2020-03-03 | 上海汽车集团股份有限公司 | Method and device for analyzing constitutive performance of vehicle chassis rubber bushing |
| CN111090950A (en) * | 2018-10-08 | 2020-05-01 | 中国石油化工股份有限公司 | Method for solving constitutive model parameters of hydrogenated nitrile rubber in different environments |
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| CN104596843A (en) * | 2015-01-16 | 2015-05-06 | 福建工程学院 | Special fixture for shearing substitution test of rubber material |
| CN105069241A (en) * | 2015-08-19 | 2015-11-18 | 山东大学 | Step-by-step analysis and prediction method for dynamic performances of rubber material structure |
| CN105069241B (en) * | 2015-08-19 | 2018-03-20 | 山东大学 | A kind of multiple step format analysis of elastomeric material structure dynamic and Forecasting Methodology |
| CN105973834A (en) * | 2016-05-11 | 2016-09-28 | 上海瀚海检测技术股份有限公司 | Comprehensive detection and evaluation method of shock absorber |
| CN105973834B (en) * | 2016-05-11 | 2018-07-17 | 上海瀚海检测技术股份有限公司 | The comprehensive detection and appraisal procedure of damper |
| CN106815442A (en) * | 2017-01-22 | 2017-06-09 | 安徽工业大学 | A kind of incompressible hyperelastic body constitutive model of isotropism and its application |
| CN106815442B (en) * | 2017-01-22 | 2020-06-09 | 安徽工业大学 | Method for constructing isotropic incompressible superelastic body constitutive model and application thereof |
| CN110858255B (en) * | 2018-08-06 | 2024-01-30 | 上海汽车集团股份有限公司 | Analysis method and device for constitutive performance of rubber bushing of vehicle chassis |
| CN110858255A (en) * | 2018-08-06 | 2020-03-03 | 上海汽车集团股份有限公司 | Method and device for analyzing constitutive performance of vehicle chassis rubber bushing |
| CN110823335B (en) * | 2018-08-10 | 2021-06-25 | 张德贤 | Granary detection method and system based on bottom surface single-circle standard deviation polynomial model |
| CN110823335A (en) * | 2018-08-10 | 2020-02-21 | 张德贤 | Granary detection method and system based on bottom surface single-circle standard deviation polynomial model |
| CN111090950A (en) * | 2018-10-08 | 2020-05-01 | 中国石油化工股份有限公司 | Method for solving constitutive model parameters of hydrogenated nitrile rubber in different environments |
| CN110018072B (en) * | 2019-05-22 | 2021-04-16 | 西南交通大学 | Hyperelastic material constitutive model parameter conical pressing-in measuring method |
| CN110018072A (en) * | 2019-05-22 | 2019-07-16 | 西南交通大学 | Elastic material Parameters of constitutive model taper is pressed into measuring method |
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Application publication date: 20140625 |