CN110516324A - A kind of method and device obtaining air spring rigidity - Google Patents
A kind of method and device obtaining air spring rigidity Download PDFInfo
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Abstract
The application provides a kind of method and device for obtaining air spring rigidity, this method comprises: experiment obtains air spring static state lag loop, the map maximal friction for determining Coulomb friction model, maximum rigidity；Calculate compressed air rigidity and linear elasticity rigidity；Determine corresponding shift value when maximal friction half；Compare the Static stiffness of calculating and actual measurement and lag loop and meets required precision；Experiment obtains air spring dynamic stiffness, its dynamic stiffness experiment value is subtracted compressed air rigidity value and Coulomb friction model rigidity value obtains viscoelastic models rigidity value；Linear elasticity rigidity value is cut again and obtains the stiffness contribution value of fractional model, is fitted to obtain fractional derivative parameter by least square method；Compare the dynamic stiffness value of calculating and actual measurement and meets required precision.The present invention can effectively recognize rubber pneumatic bag model parameter, establish its parameter database, calculate air spring rigidity and carry out accurate mechanical characteristic matching, be convenient for air bag technological design and optimization, it is horizontal to improve Corporation R & D.
Description
Technical Field
The application relates to the technical field of air springs, in particular to a method and a device for obtaining air spring stiffness.
Background
Air springs, commonly known as air bags, air bag cylinders, bladder cylinders, etc., are springs that are inflated with compressed air in a retractable closed container, utilizing the elastic action of the air. The air spring is formed by filling compressed air into a sealed container and realizing the elastic action by utilizing the compressibility of the air. The air spring has ideal nonlinear elastic characteristics, after the height adjusting device is additionally arranged, the height of a vehicle body does not change along with the increase and decrease of the load, the rigidity of the spring can be designed to be lower, and the riding comfort is good.
An air spring is a fluid-solid coupled system consisting of a fluid (compressed air inside) and a solid (rubber bladder, upper cover, piston, etc.). The rubber air bag mainly adopts a 2-layer cord fabric structure and mainly comprises an outer covering layer rubber, 2 layers of cord fabrics and an inner lining rubber. The nonlinear characteristics of the rubber air bag structure and the composition materials enable the air bag to have strong nonlinear characteristics. The mechanical properties of the rubber air bag have a large influence on the mechanical properties of the air bag and cannot be ignored. However, due to the complexity of the nonlinear mechanical characteristics of the rubber air bag, an effective rubber air bag modeling method and a model parameter identification method thereof are not available.
In the prior art, the nonlinear mechanical characteristic data of the rubber airbag is basically obtained by an experimental method, the time and the labor are consumed, the rubber airbag model cannot be quickly and effectively established and the relevant parameters of the model cannot be obtained, the matching and the optimized design of the air spring are not facilitated, and the design and the optimization of the technological parameters of the rubber airbag are also not facilitated.
Therefore, how to provide a simple, quick, time-saving and labor-saving scheme for parameter information of an air spring is a technical problem to be solved urgently in the field.
Disclosure of Invention
The application aims to provide a method and a device for acquiring the rigidity of an air spring, and the technical problem that in the prior art, no simple, quick, time-saving and labor-saving air spring parameter information exists is solved.
In order to achieve the above object, the present application provides a method for obtaining stiffness of an air spring, including:
carrying out an isothermal transformation characteristic experiment on the air spring at a preset height and a preset internal pressure to obtain a static hysteresis loop of a hysteresis relation between friction force and displacement of the air spring, and obtaining maximum friction force and maximum rigidity by a mapping method;
acquiring the rigidity of compressed air of the air spring, and combining the static hysteresis loop to obtain the linear elastic rigidity of the air spring;
identifying the obtained linear elastic stiffness, and obtaining a corresponding friction displacement value when the maximum friction force is half according to the ratio of the maximum friction force to the maximum stiffness minus the difference value of the compressed air stiffness and the linear elastic stiffness;
comparing the linear elastic stiffness obtained through identification, the identified static stiffness value and the identified hysteresis loop of the air spring obtained through friction model parameter calculation with the experimental static stiffness value and the experimental hysteresis loop obtained through experiments;
when the relative static stiffness error of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the static hysteresis loops of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweeping experiment by using a sinusoidal signal to obtain the dynamic stiffness of the air spring; subtracting the dynamic stiffness value from the compressed air stiffness value in the dynamic state to obtain the stiffness of the rubber air bag, and subtracting the influence of the friction model from the stiffness of the rubber air bag to obtain the stiffness contribution value of the viscoelasticity model; subtracting the linear elastic stiffness value from the viscoelastic model stiffness contribution value to obtain the stiffness value of the standard fractional derivative model; performing fitting calculation by a least square method to obtain a fractional derivative parameter;
comparing the identified dynamic stiffness value and the identified dynamic stiffness curve obtained by identification with the experimental stiffness value and the experimental dynamic stiffness curve obtained by experiment; and when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters.
Optionally, the linear elastic stiffness obtained by identification, the identified static stiffness value of the air spring obtained by calculating friction model parameters, and the identified hysteresis loop are:
passing through the intersection point of the compression section curve and the stretching section curve of the static hysteresis loop, and subtracting the rigidity of the compressed air from the slope of the tangent line of the compression section curve to obtain the linear elastic rigidity;
the frictional force F is obtained by adopting a coulomb friction model describing the amplitude dependence of the nonlinear characteristic of the rubber air bag as a friction modelfThe relationship to the displacement x is:
wherein,
parameter λ ═ Ffs/Ffmax，λ∈[-1,1](ii) a x represents the displacement applied to the air spring; ffmaxRepresenting the maximum friction force, x, in the friction model2To achieve FfmaxFrictional Displacement value at/2, xsFor initial displacement, FfsCalculating to obtain the Coulomb friction model rigidity K for the initial friction forcefAnd lag angle phifThe formula of (1) is as follows:
wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
Optionally, wherein the obtaining of the compressed air stiffness of the air spring is:
respectively acquiring preset heights h0The following air parameters in the air spring: initial absolute pressure P of gasz0Initial volume Vz0And an initial effective area Az0Height of h0Effective rate of change of volume alpha, height h0The effective area change rate β;
obtaining the compressed air rigidity K of the air spring by utilizing the air parametersaThe formula of (1) is as follows:
wherein,
k is a polytropic exponent; patmIs at atmospheric pressure.
Optionally, when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameter of the air spring as the stiffness parameter, where the identification parameter is:
when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters;
and when the relative error of the dynamic stiffness of the identified dynamic stiffness value and the experimental stiffness value is larger than 10%, or the correlation coefficient of the identified dynamic stiffness curve and the experimental dynamic stiffness curve is smaller than 0.85, changing the k value of the polytropic index according to a preset change strategy, and performing refitting calculation to obtain an updated fractional derivative parameter.
Optionally, wherein the identified static stiffness value K of the air spring calculated by the friction model parametersThe method comprises the following steps:
calculating to obtain the rigidity K of the coulomb friction modelfAnd lag angle phifThe formula of (1) is as follows:
wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxA frictional displacement value at/2;
according to said stiffness KfAnd lag angle phifObtaining the static stiffness K of the air springsThe formula of (1) is as follows:
Ks＝Ka+Ke+Kfcosφf+jKfsinφfwherein
Kais the compressed air stiffness of the air spring, KeIs the linear elastic stiffness, and j is the imaginary unit.
Optionally, wherein the visco-elastic model stiffness contribution value is obtained as:
the viscoelastic force F is obtained by adopting a fractional derivative Kelvin-Voigt model of the frequency correlation characteristic representing the nonlinear mechanical characteristic of the rubber air bagvThe relationship between (t) and displacement x is as follows:
Fv(t)＝Kex(t)+bDax (t), wherein,
a. b and KeRespectively representing the order of the fractional derivative, a damping parameter and linear elastic stiffness;
Darepresents a differential of order a, and a is an element (0,1), and x (t) is a variable displacement;
obtaining dynamic stiffness K by utilizing fractional derivative Kelvin-Voigt modelvAnd lag angle phivThe formula of (1) is as follows:
wherein,
ωafor a given circular frequency during the sweep, ω ═ 2 π f, f is the test frequency, a, b, and KeThe order of the fractional derivative, the damping parameter and the linear elastic stiffness are respectively represented.
Optionally, the method for obtaining the dynamic stiffness of the air spring by performing an air spring frequency sweep experiment with a sinusoidal signal includes:
obtaining the compressed air stiffness KaObtaining the dynamic stiffness K of the air spring by utilizing a fractional derivative Kelvin-Voigt model and a coulomb friction modeldThe formula of (1) is as follows:
Kd＝Ka+Kfcosφf+Kvcosφv+j(Kfsinφf+Kvsinφv) Wherein
Kvis dynamic stiffness sum phivLag angle, a, b and KeRespectively representing the order of the fractional derivative, a damping parameter and linear elastic stiffness, wherein j is an imaginary number unit; coulomb friction model stiffness KfAnd lag angle phifThe formula of (1) is as follows:
wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
Optionally, wherein the fractional derivative parameter is calculated by fitting using a least squares method, and is:
the formula for calculating the fractional derivative parameters a and b by fitting with the least squares method is:
wherein,
n represents the number of frequency points of dynamic stiffness experiment, conjugate, Kbvexp(ω) represents the standard fractional derivative model stiffness experimental value.
Optionally, when the relative static stiffness error between the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweep experiment by using a sinusoidal signal to obtain the dynamic stiffness of the air spring, where:
when the relative static stiffness error of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the static hysteresis loops of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweeping experiment by using a sinusoidal signal to obtain the dynamic stiffness of the air spring;
and when the static stiffness relative error between the identification static stiffness value and the experimental static stiffness value is more than 10 percent, or the static hysteresis loop correlation coefficient between the identification hysteresis loop and the experimental hysteresis loop is less than 0.85, re-drawing and identifying the updated maximum friction force and the updated maximum stiffness according to a re-drawing strategy.
In another aspect, the present invention further provides a device for obtaining stiffness of an air spring, including: the device comprises a maximum friction force and maximum rigidity acquisition unit, a linear elastic rigidity acquisition unit, a friction displacement value acquisition unit, a static rigidity value and hysteresis loop processor, a fractional derivative parameter processor and an air spring rigidity parameter acquisition unit; wherein,
the maximum friction force and maximum rigidity acquisition unit is connected with the linear elastic rigidity acquisition unit, and is used for carrying out an isothermal transformation characteristic experiment on the air spring at a preset height and a preset internal pressure to acquire a static hysteresis loop of the hysteresis relationship between the friction force and the displacement of the air spring and obtain the maximum friction force and the maximum rigidity by a mapping method;
the linear elastic stiffness acquisition unit is connected with the maximum friction force and stiffness acquisition unit and the friction displacement value acquisition unit to acquire the compressed air stiffness of the air spring and obtain the linear elastic stiffness of the air spring by combining the static hysteresis loop;
the friction displacement value acquisition unit is connected with the linear elastic stiffness acquisition unit and the static stiffness value and hysteresis loop processor, identifies the obtained linear elastic stiffness, and obtains a corresponding friction displacement value when the maximum friction force is half according to the ratio of the maximum friction force to the maximum stiffness minus the difference between the compressed air stiffness and the linear elastic stiffness;
the static stiffness value and hysteresis loop processor is connected with the friction displacement value acquisition unit and the fractional derivative parameter processor, and compares the linear elastic stiffness obtained through identification, the identified static stiffness value and the identified hysteresis loop of the air spring obtained through friction model parameter calculation with the experimental static stiffness value and the experimental hysteresis loop obtained through experiments;
the fractional derivative parameter processor is connected with the static stiffness value and hysteresis loop processor and the air spring stiffness parameter acquisition unit, and when the static stiffness relative error of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10% and the static hysteresis loop correlation coefficient of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, a sinusoidal signal is adopted to carry out an air spring frequency sweep experiment to acquire the dynamic stiffness of the air spring; subtracting the dynamic stiffness value from the compressed air stiffness value in the dynamic state to obtain the stiffness of the rubber air bag, and subtracting the influence of the friction model from the stiffness of the rubber air bag to obtain the stiffness contribution value of the viscoelasticity model; subtracting the linear elastic stiffness value from the viscoelastic model stiffness contribution value to obtain the stiffness value of the standard fractional derivative model; performing fitting calculation by a least square method to obtain a fractional derivative parameter;
the air spring stiffness parameter acquisition unit is connected with the fractional derivative parameter processor and compares the identified dynamic stiffness value and the identified dynamic stiffness curve obtained by identification with the experimental stiffness value and the experimental dynamic stiffness curve obtained by experiments; and when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters.
The method and the device for acquiring the rigidity of the air spring have the following beneficial effects:
(1) according to the method and the device for acquiring the rigidity of the air spring, the static hysteresis loop of the air spring is acquired through experiments, and the maximum friction force and the maximum rigidity of a coulomb friction model are determined through mapping; calculating the rigidity of compressed air and the linear elastic rigidity; determining a displacement value corresponding to half of the maximum friction force; comparing the static rigidity and the hysteresis loop which are calculated and actually measured, and meeting the precision requirement; the method comprises the steps of obtaining the dynamic stiffness of the air spring through an experiment, and subtracting the stiffness value of compressed air and the stiffness value of a coulomb friction model from the experimental value of the dynamic stiffness to obtain the stiffness value of a viscoelastic model; then subtracting the linear elastic rigidity value to obtain a rigidity contribution value of the fractional derivative model, and fitting by a least square method to obtain a fractional derivative parameter; the dynamic stiffness values of calculation and actual measurement are compared, the precision requirement is met, the rubber air bag model parameters can be quickly and effectively identified, a parameter database is established, the air spring stiffness is calculated, accurate mechanical characteristic matching is carried out, air bag process design and optimization are facilitated, and the research and development level of enterprises is improved.
(2) According to the method and the device for acquiring the rigidity of the air spring, all parameters of the rubber air bag model are identified through two simple experiments, so that the experiment amount required for acquiring the nonlinear mechanical property of the rubber air bag is greatly reduced, and the efficiency is improved; a foundation is provided for establishing a complete and effective air spring parameterized calculation model, and the design and matching of the air spring are facilitated; the scheme enables enterprises to form a rubber air bag model parameter database and lays a foundation for the rapid design of the rubber air bag and the rapid formulation and optimization of the process parameters of the rubber air bag.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a schematic diagram of an air spring according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a rubber air bag of an air spring according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart illustrating a method for obtaining stiffness of an air spring according to an embodiment of the present invention;
FIG. 4 is a schematic flow chart illustrating a second method for determining a stiffness of an air spring according to an embodiment of the present invention;
FIG. 5 is a schematic flow chart illustrating a third method for determining a stiffness of an air spring according to an embodiment of the present invention;
FIG. 6 is a schematic flow chart illustrating a fourth method for determining the stiffness of an air spring according to an embodiment of the present invention;
FIG. 7 is a schematic flow chart illustrating a fifth method for determining a stiffness of an air spring in accordance with an embodiment of the present invention;
FIG. 8 is a schematic flow chart illustrating a sixth method for determining a stiffness of an air spring in accordance with an embodiment of the present invention;
FIG. 9 is a schematic flow chart illustrating a seventh method for determining the stiffness of an air spring in accordance with an embodiment of the present invention;
FIG. 10 is a schematic flow chart illustrating an eighth method for determining the stiffness of an air spring in accordance with an embodiment of the present invention;
FIG. 11 is a schematic flow chart illustrating a ninth method for determining the stiffness of an air spring in accordance with an embodiment of the present invention;
FIG. 12 is a schematic flow chart illustrating a method for obtaining stiffness of an air spring in accordance with an exemplary embodiment of the present invention;
FIG. 13 is a schematic diagram of an air spring static hysteresis loop in a method for obtaining stiffness of an air spring according to an embodiment of the invention;
FIG. 14 is a schematic diagram illustrating a comparison between an identified static hysteresis loop calculation and an experimental static hysteresis loop of an air spring in the method for obtaining the stiffness of an air spring according to the embodiment of the present invention;
FIG. 15 is a schematic diagram illustrating stiffness contribution values of models of an air spring in a method for obtaining stiffness of an air spring according to an embodiment of the present invention;
FIG. 16 is a schematic diagram illustrating identification and experimental comparison of dynamic stiffness of an air spring in a method for obtaining stiffness of an air spring according to an embodiment of the present invention;
FIG. 17 is a schematic diagram illustrating static hysteresis loop identification and experimental result comparison for an air spring at other amplitudes in the method for obtaining stiffness of an air spring according to the embodiment of the present invention;
FIG. 18 is a schematic diagram illustrating comparison of dynamic stiffness identification and experimental results of an air spring at other amplitudes in the method for obtaining stiffness of an air spring according to the embodiment of the present invention;
fig. 19 is a schematic structural diagram of an apparatus for acquiring the stiffness of an air spring according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present application are clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some, but not all, embodiments of the present application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Examples
As shown in fig. 1 and fig. 2, fig. 1 is a schematic structural diagram of an air spring in the present embodiment, and fig. 2 is a schematic structural diagram of a rubber bladder of the air spring in the present embodiment. An air spring is a fluid-solid coupled system consisting of a fluid (compressed air inside) and a solid (rubber bladder, upper cover, piston, etc.). The air spring includes: a stud 101, an upper cover plate 102, a rubber air bag 103, a buffer block 104, a piston 105 and a screw hole 106. The rubber air bag mostly adopts a 2-layer cord fabric layer structure, the structure of which is shown in figure 2 and mainly comprises an outer cover rubber 201, a first cord fabric layer 202, a second cord fabric layer 203 and an inner lining rubber 204, and the nonlinear characteristics of the structure and the composition materials of the rubber air bag enable the air bag to have strong nonlinear characteristics.
Fig. 3 is a schematic flow chart of a method for obtaining stiffness of an air spring in this embodiment, where the method for obtaining stiffness of an air spring includes the following steps:
301, performing an isothermal voltage transformation characteristic experiment on the air spring at a preset height and a preset internal pressure to obtain a static hysteresis loop of a hysteresis relation between friction force and displacement of the air spring, and obtaining a maximum friction force F by a mapping methodfmaxAnd maximum stiffness Kmax。
Optionally, the preset height and the preset internal pressure may be a standard height and a standard internal pressure, and the static hysteresis loop for obtaining the hysteresis relationship between the friction force and the displacement of the air spring may be obtained by performing an isothermal voltage transformation characteristic experiment on the air spring through a triangular wave excitation signal.
Step 302, obtaining the compressed air stiffness K of the air springaCombining with static hysteresis loop to obtain linear elastic rigidity K of air springe。
Optionally, the compressed air stiffness K is subtracted from the slope of the tangent line passing through the intersection point of the compression section curve and the tension section curve of the static hysteresis loop of the air spring and along the compression section curveaTo obtain linear elastic stiffness Ke。
Step 303, identifying the linear elastic stiffness KeAccording to the maximum friction force FfmaxTo maximum stiffness KmaxMinus the stiffness K of the compressed airaAnd linear elastic stiffness KeTo obtain the corresponding friction displacement value x when the maximum friction force is half2. Value of frictional displacement x2The following is determined by the following formula:
step 304, the linear elastic stiffness K obtained by identificationeAnd the identification static stiffness value K of the air spring obtained by calculating the friction model parameterssAnd identifying the hysteresis loop, and comparing the hysteresis loop with the experimental static stiffness value and the experimental hysteresis loop obtained by the experiment.
And 305, when the relative static stiffness error between the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the identified static hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.At 85 hours, a sine signal is adopted to carry out an air spring frequency sweep experiment to obtain the dynamic stiffness K of the air springd(ii) a Dynamic stiffness value KdSubtracting the rigidity value of the compressed air in the dynamic state to obtain the rigidity K of the rubber air bagr(i.e., contribution K of the nonlinear model of the rubber bladderr) And then the rigidity K of the rubber air bagrSubtracting the influence of the friction model to obtain a viscoelasticity model rigidity contribution value Kv(ii) a Stiffness contribution K from viscoelastic modelvMiddle minus fall elastic rigidity value KeObtaining the rigidity value K of the standard fractional derivative modelbv(ii) a And performing fitting calculation by a least square method to obtain fractional derivative parameters a and b.
Step 306, comparing the identified dynamic stiffness value and the identified dynamic stiffness curve obtained by identification with the experimental stiffness value and the experimental dynamic stiffness curve obtained by experiment; and when the relative error of the dynamic stiffness for identifying the dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient of the dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters.
In some optional embodiments, as shown in fig. 4, which is a schematic flow chart of the second method for obtaining the stiffness of the air spring in this embodiment, different from fig. 3, the method includes the steps of calculating the identified linear elastic stiffness, the identified static stiffness value of the air spring obtained through the friction model parameter, and the identified hysteresis loop, and includes:
step 401, passing through the intersection point of the compression section curve and the stretching section curve of the static hysteresis loop, and subtracting the stiffness of the compressed air from the slope of the tangent of the compression section curve to obtain the linear elastic stiffness.
Step 402, adopting a coulomb friction model describing the amplitude dependence of the nonlinear characteristic of the rubber air bag as a friction model to obtain a friction force FfThe relationship to the displacement x is:
wherein,
parameter λ ═ Ffs/Ffmax，λ∈[-1,1](ii) a x represents the displacement applied to the air spring；FfmaxRepresenting the maximum friction force, x, in the friction model2To achieve FfmaxFrictional Displacement value at/2, xsFor initial displacement, FfsAs initial friction, xsAnd FfsGiven initially, may be 0 in each case.
Step 403, calculating the coulomb friction model stiffness K by using the following formulafAnd lag angle phif：
Wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
In some alternative embodiments, as shown in fig. 5, which is a schematic flowchart of a third method for obtaining a stiffness of an air spring in the present embodiment, different from that in fig. 3, the step of obtaining a compressed air stiffness of an air spring is as follows:
step 501, respectively obtaining preset heights h0Air parameters in the lower air spring: initial absolute pressure P of gasz0Initial volume Vz0And an initial effective area Az0Height of h0Effective rate of change of volume alpha, height h0The effective area change rate β.
Step 502, obtaining the compressed air rigidity K of the air spring by using the air parameters according to the following formulaa：
Wherein,
k is a polytropic exponent; patmIs at atmospheric pressure.
In some optional embodiments, as shown in fig. 6, which is a schematic flow chart of a fourth method for obtaining stiffness of an air spring in this embodiment, different from fig. 5, when a relative error between a dynamic stiffness value and an experimental stiffness value is identified to be less than or equal to 10%, and a correlation coefficient between a dynamic stiffness curve and an experimental dynamic stiffness curve is identified to be greater than or equal to 0.85, obtaining an identification parameter of the air spring as a stiffness parameter, where the identification parameter is:
601, when the relative error of the dynamic stiffness of the identified dynamic stiffness value and the experimental stiffness value is smaller than or equal to 10%, and the correlation coefficient of the identified dynamic stiffness curve and the experimental dynamic stiffness curve is larger than or equal to 0.85, acquiring the identification parameter of the air spring as the stiffness parameter.
And step 602, when the relative error of the dynamic stiffness of the identified dynamic stiffness value and the experimental stiffness value is larger than 10%, or the correlation coefficient of the identified dynamic stiffness curve and the experimental dynamic stiffness curve is smaller than 0.85, changing the value of the polytropic exponent k according to a preset change strategy, and performing refitting calculation to obtain an updated fractional derivative parameter.
In some optional embodiments, as shown in fig. 7, which is a schematic flow chart of a fifth method for obtaining stiffness of an air spring in the present embodiment, different from fig. 5, an identified static stiffness value K of the air spring calculated by using friction model parameters is obtainedsThe method comprises the following steps:
step 701, calculating by using the following formula to obtain the coulomb friction model rigidity KfAnd lag angle phif：
Wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
Step 702, calculate the stiffness K from the equationfAnd lag angle phifObtaining static stiffness K of air springs：
Ks＝Ka+Ke+Kfcosφf+jKfsinφfWherein
Kacompressed air stiffness for air spring, KeIs the linear elastic stiffness, and j is the imaginary unit.
In some alternative embodiments, as shown in fig. 8, which is a schematic flow chart of a sixth method for obtaining the stiffness of the air spring in the present embodiment, different from that in fig. 3, the viscoelastic model stiffness contribution value is obtained as:
step 801, obtaining a viscoelastic force F by using a fractional derivative Kelvin-Voigt model of frequency correlation characteristics representing nonlinear mechanical characteristics of the rubber air bagvThe relationship between (t) and displacement x is as follows:
Fv(t)＝Kex(t)+bDax (t), wherein,
a. b and KeRespectively representing the order of the fractional derivative, a damping parameter and linear elastic stiffness;
da represents a differential of order a, and a ∈ (0,1), x (t) represents a varying displacement amount.
Step 802, obtaining the dynamic stiffness K by using the following formula of a fractional derivative Kelvin-Voigt modelvAnd lag angle phiv：
Wherein,
ωafor a given circular frequency during the sweep, ω ═ 2 π f, f is the test frequency, a, b, and KeThe order of the fractional derivative, the damping parameter and the linear elastic stiffness are respectively represented.
In some optional embodiments, as shown in fig. 9, which is a schematic flow chart of a seventh method for obtaining a stiffness of an air spring in this embodiment, different from that in fig. 8, the method for obtaining a dynamic stiffness of an air spring by performing an air spring frequency sweep experiment with a sinusoidal signal includes:
step 901, obtaining the rigidity K of the compressed airaUsing fractional derivatives of Kelvin-VoigA t model and a coulomb friction model, and the dynamic stiffness K of the air spring is obtained by the following formulad：
Kd＝Ka+Kfcosφf+Kvcosφv+j(Kfsinφf+Kvsin phi v), wherein,
Kvis dynamic stiffness sum phivLag angle, a, b and KeRespectively representing the order of the fractional derivative, a damping parameter and linear elastic stiffness, wherein j is an imaginary number unit;
step 902, obtaining the coulomb friction model rigidity K by using the following formulafAnd lag angle phif：
Wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
In some alternative embodiments, as shown in fig. 10, which is a schematic flow chart of an eighth method for obtaining a stiffness of an air spring in the present embodiment, different from that in fig. 3, a fractional derivative parameter is calculated by performing a fitting by a least square method, where the fractional derivative parameter is:
step 1001, acquiring parameters such as the number of experimental frequency points and the rigidity experimental value of the standard fractional derivative model.
Step 1002, calculating fraction derivative parameters a and b by fitting through a least square method by using the following formula:
wherein,
n represents the number of frequency points of dynamic stiffness experiment, conjugate, Kbvexp(ω) represents the standard fractional derivative model stiffness experimental value.
In some optional embodiments, as shown in fig. 11, which is a schematic flow chart of a ninth method for obtaining a stiffness of an air spring in this embodiment, different from fig. 3, when a relative error between a static stiffness value and an experimental static stiffness value is smaller than or equal to 10%, and a correlation coefficient between a hysteresis loop and a static hysteresis loop of the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweep experiment using a sinusoidal signal to obtain a dynamic stiffness of the air spring, where:
and 1101, when the relative error of the static stiffness of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the static hysteresis loop of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweep experiment by using a sinusoidal signal to obtain the dynamic stiffness of the air spring.
And 1102, re-drawing and identifying the updated maximum friction force and the updated maximum stiffness according to a re-drawing strategy when the relative error of the static stiffness of the identified static stiffness value and the experimental static stiffness value is more than 10% or the correlation coefficient of the static hysteresis loop of the identified hysteresis loop and the experimental hysteresis loop is less than 0.85.
In some optional embodiments, as shown in fig. 3 to 18, an application embodiment of a method for obtaining a stiffness of an air spring is provided, and fig. 12 is a schematic general flow chart of the method for obtaining a stiffness of an air spring in the specific application of the embodiment; FIG. 13 is a schematic diagram of an air spring static hysteresis loop in the method for obtaining stiffness of an air spring according to the present embodiment; FIG. 14 is a schematic diagram illustrating a comparison between an identified static hysteresis loop calculation and an experimental static hysteresis loop of an air spring in the method for obtaining stiffness of an air spring in this embodiment; FIG. 15 is a schematic diagram of stiffness contribution values of models of an air spring in the method for obtaining stiffness of an air spring in this embodiment; FIG. 16 is a schematic diagram illustrating identification and experimental comparison of dynamic stiffness of an air spring in the method for obtaining stiffness of an air spring in the present embodiment; FIG. 17 is a schematic diagram illustrating static hysteresis loop identification and experimental result comparison of an air spring at other amplitudes in the method for obtaining stiffness of an air spring in this embodiment; fig. 18 is a schematic diagram illustrating comparison between the dynamic stiffness identification and the experimental result of an air spring at other amplitudes in the method for obtaining the stiffness of an air spring in this embodiment.
The method for acquiring the rigidity of the air spring in the specific application embodiment comprises the following steps:
step 1201, in some optional embodiments, the air spring is at a standard height and a standard internal pressure, the standard height of the air spring in the embodiments is 195mm, and the absolute pressure of the standard internal pressure is 6 × 105Pa. The static hysteresis loop (i.e. the relation curve between the friction force and the displacement hysteresis) of the air spring is obtained by performing an isothermal voltage transformation characteristic experiment on the air spring by using a triangular wave excitation signal with the loading speed of 10mm/min and the amplitude of 10mm, as shown in fig. 13. Determining the maximum friction force F by a mapping method according to the relation curve of the friction force and the displacement hysteresisfmaxMaximum stiffness Kmax。
P is the intersection point of the compression section curve and the stretching section curve of the static hysteresis loop of the air spring, a PD straight line passes through the point P and is a tangent line of the compression section curve, and D is the intersection point of the PD straight line and a vertical coordinate; the PT straight line passes through the point P and is a tangent line of the stretching section curve, and T is an intersection point of the PT straight line and the abscissa. D to the coordinate center O1Is F, the difference in force values represented byfmaxThe slope of the PD line is the linear elastic stiffness KeAnd compressed air stiffness KaSumming; the slope of the PT line being the maximum stiffness Kmax。
Step 1202, calculating the rigidity K of the compressed air according to a formulaaWherein: pz0、Vz0、Az0Respectively, is a standard height h0Initial absolute pressure (P) of air in air spring under 195mmz0＝6×105Pa), initial volume (V)z0＝0.0039m3) And initial effective area (A)z0＝0.0196m2) (ii) a Alpha is a height h0Time effective volume change rate (α ═ 0.0191m3B is a height h0Effective area change rate (β ═ 0 m)2M); k is a polytropic index (k is 1 when the change process of the gas state in the air bag is regarded as an isothermal process in the isothermal transformation characteristic experiment, and k is regarded as an absolute process in the sweep frequency experimentIn the thermal process, k is 1.4; k is equal to [0,1.4]])；PatmIs atmospheric pressure (P)atm＝1×105Pa) is added. Subtracting the compressed air stiffness K from the slope of the PD lineaTo obtain linear elastic stiffness Ke。
Step 1203, calculating and determining a friction displacement value x corresponding to half of the maximum friction force in the friction model according to a formula2。
The parameters associated with the coulomb friction model obtained from the experimental test data and the identification method steps shown in fig. 13 are shown in table 1.
TABLE 1 rubber bladder model parameters
Step 1204, identifying the linear elastic stiffness K obtainedeAnd calculating the static rigidity value and the hysteresis loop of the air spring by using the Coulomb friction model parameters and the like, and comparing the static rigidity value and the hysteresis loop obtained by the experiment, as shown in figure 14.
Step 1205, calculating that the air spring static hysteresis loop has good consistency with an experimental test, wherein the correlation coefficient of the two curves is 0.95, and the correlation is good; the relative error of the static rigidity is about 4 percent, the precision requirement is met, the next step is carried out, if the precision requirement is not met, the maximum friction force F is re-mapped and identifiedfmaxMaximum stiffness KmaxAnd repeating the previous steps until the precision requirement is met.
Under the standard height and the standard internal pressure, the amplitude is 10 mm; and (3) carrying out air spring frequency sweep experiments on sinusoidal signals with excitation frequency interval of 0.5Hz and excitation frequency range of 0.5-10 Hz (frequency points of 0.5Hz, 1Hz, 1.5Hz, 2Hz, 2.5Hz, 3Hz, 3.5Hz, 4Hz, 4.5Hz, 5Hz, 5.5Hz, 6Hz, 6.5Hz, 7Hz, 7.5Hz, 8Hz, 8.5Hz, 9Hz, 9.5Hz and 10Hz) to obtain the dynamic stiffness of the air spring. The pneumatic rigidity of the compressed air is calculated by a formula, and k belongs to [0,1.4 ].
When the isothermal pressure change characteristic experiment of the air spring is carried out as in the embodiment, other loading speeds such as 20mm/min and 30mm/min can be selected by adopting the loading speed; the amplitude can also be 5mm, 15mm and other amplitudes. During the sweep frequency experiment, other amplitudes such as 5mm and 15mm can be selected by adopting the amplitude; the excitation frequency interval is 0.5Hz, the excitation frequency range is 0.5-10 Hz (frequency points are 0.5Hz, 1Hz, 1.5Hz, 2Hz, 2.5Hz, 3Hz, 3.5Hz, 4Hz, 4.5Hz, 5Hz, 5.5Hz, 6Hz, 6.5Hz, 7Hz, 7.5Hz, 8Hz, 8.5Hz, 9Hz, 9.5Hz, 10Hz), the excitation frequency interval or frequency range can also be changed, such as the excitation frequency interval is 1Hz, the excitation frequency range is 1-12 Hz (frequency points are 1Hz, 2Hz, 3Hz, 4Hz, 5Hz, 6Hz, 7Hz, 8Hz, 9Hz, 10Hz, 11Hz, 12 Hz).
Step 1206, subtracting the dynamic air rigidity value of the air spring obtained through the experimental test from the dynamic compressed air rigidity value to obtain a contribution value K of the rubber airbag nonlinear modelr(ii) a The coulomb friction model rigidity K can be calculated according to a formulafAnd lag angle phifAnd then the rigidity K of the rubber air bagrSubtracting Coulomb friction model KfThe influence of (2) to obtain a viscoelastic model stiffness contribution value Kv。
The dynamic stiffness K of the fractional derivative Kelvin-Voigt model can be calculated according to a formulavAnd lag angle phiv. Finally, from the visco-elastic model stiffness contribution KvThe rigidity value K of the standard fractional derivative model can be obtained by subtracting the elastic rigidity value of the drop line from the middlebvThe stiffness contribution values of the models of the air spring are shown in fig. 15.
Fractional derivative parameters a and b were calculated by fitting with the least squares method of the formula, with the order of the fractional derivative parameter a being 0.67 and the damping parameter b being 0.57, as shown in table 1.
The linear elastic stiffness, friction model parameters, visco-elastic model parameters and the like obtained by identification are used for calculating the dynamic stiffness value of the air spring, and the dynamic stiffness value is compared with the dynamic stiffness value obtained by the experiment, as shown in fig. 16.
1207, calculating and testing the air spring dynamic stiffness curve to have good consistency, wherein the relative errors of the dynamic stiffness are less than 5%, the correlation coefficient of the dynamic stiffness curve is 0.95, the correlation is good, the precision requirement is met, all parameters are identified, and if the precision requirement is not met, the multi-variable exponent k value is changed and the previous 2 steps are repeated until the precision requirement is met.
And 1208, calculating the consistency of the dynamic stiffness curve of the air spring tested by the experiment, meeting the precision requirement, completing the identification of all parameters, and identifying all rubber air bag model parameters.
Fig. 17 and 18 show static hysteresis loops and dynamic stiffness curve calculation and experimental curve comparison diagrams of the air spring when the excitation amplitude is 5mm and 15mm, which all meet the accuracy requirement, and strongly prove the effectiveness of the method for acquiring the stiffness of the air spring provided in the embodiment.
Specifically, the friction model is a coulomb friction model, the coulomb friction model describes the amplitude dependence of the nonlinear characteristic of the rubber air bag, and the relation between the force and the displacement is determined by a formula. The coulomb friction model rigidity K can be calculated according to a formulafAnd lag angle phif。
Specifically, in the experiment of the isothermal pressure-changing characteristic of the air spring, because the test speed is low and the frequency is low, the viscoelastic characteristic related to the frequency in the nonlinear mechanical model of the rubber air bag and the static stiffness K of the air spring can be ignoredsThe dependence on the compressed air stiffness, the linear elastic stiffness and the coulomb friction model is determined by the formula.
Specifically, the viscoelasticity model is a fractional derivative Kelvin-Voigt model and is formed by linear elastic stiffness KeAnd a standard fractional derivative model. A fractional derivative Kelvin-Voigt model is adopted to represent the frequency correlation characteristic of the nonlinear mechanical characteristic of the rubber air bag, and the relation between force and displacement is determined by a formula. The dynamic stiffness K of the fractional derivative Kelvin-Voigt model can be calculated according to a formulavAnd lag angle phiv。
Specifically, the dynamic stiffness of the air spring depends on the stiffness of compressed air, a fractional derivative Kelvin-Voigt model and a coulomb friction model, and the dynamic stiffness K of the air springdDetermined by a formula.
In some alternative embodiments, as shown in fig. 19, there is a schematic structural diagram of an apparatus 1900 for obtaining stiffness of an air spring according to the present embodiment, which is used for implementing the method for obtaining stiffness of an air spring. Specifically, the apparatus includes: a maximum friction force and maximum stiffness obtaining unit 1901, a linear elastic stiffness obtaining unit 1902, a friction displacement value obtaining unit 1903, a static stiffness value and hysteresis loop processor 1904, a fractional derivative parameter processor 1905 and an air spring stiffness parameter obtaining unit 1906.
The maximum friction force and maximum stiffness obtaining unit 1901 is connected to the linear elastic stiffness obtaining unit 1902, and performs an isothermal transformation characteristic experiment on the air spring at a preset height and a preset internal pressure to obtain a static hysteresis loop of the hysteresis relationship between the friction force and the displacement of the air spring, and obtains the maximum friction force and the maximum stiffness by a mapping method.
The linear elastic stiffness obtaining unit 1902 is connected to the maximum friction and stiffness obtaining unit 1901 and the friction displacement value obtaining unit 1903, and obtains the compressed air stiffness of the air spring, and obtains the linear elastic stiffness of the air spring by combining the static hysteresis loop.
The friction displacement value obtaining unit 1903 is connected to the linear elastic stiffness obtaining unit 1902 and the static stiffness value and hysteresis loop processor 1904, identifies the obtained linear elastic stiffness, and obtains a friction displacement value corresponding to half of the maximum friction force according to a ratio of the maximum friction force to the maximum stiffness minus a difference between the compressed air stiffness and the linear elastic stiffness.
The static stiffness value and hysteresis loop processor 1904 is connected to the friction displacement value obtaining unit 1903 and the fractional derivative parameter processor 1905, and compares the linear elastic stiffness obtained by identification, the static stiffness value and the hysteresis loop obtained by identification and calculation through friction model parameters with the experimental static stiffness value and the experimental hysteresis loop obtained by experiment.
A fractional derivative parameter processor 1905 connected to the static stiffness value and hysteresis loop processor 1904 and the air spring stiffness parameter obtaining unit 1906, and configured to perform an air spring frequency sweep experiment using a sinusoidal signal to obtain the dynamic stiffness of the air spring when the static stiffness relative error between the static stiffness value and the experimental static stiffness value is less than or equal to 10% and the static stiffness correlation coefficient between the hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85; subtracting the dynamic compressed air stiffness value from the dynamic stiffness value to obtain the stiffness of the rubber air bag, and subtracting the influence of the friction model from the stiffness of the rubber air bag to obtain a stiffness contribution value of the viscoelasticity model; subtracting the linear elastic stiffness value from the viscoelasticity model stiffness contribution value to obtain the stiffness value of the standard fractional derivative model; and performing fitting calculation by a least square method to obtain a fractional derivative parameter.
An air spring stiffness parameter obtaining unit 1906 connected to the fractional derivative parameter processor 1905, for comparing the identified dynamic stiffness value and identified dynamic stiffness curve with the experimental stiffness value and experimental dynamic stiffness curve obtained by the experiment; and when the relative error of the dynamic stiffness for identifying the dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient of the dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters.
The method and the device for acquiring the rigidity of the air spring have the following beneficial effects:
(1) according to the method and the device for acquiring the rigidity of the air spring, the static hysteresis loop of the air spring is acquired through experiments, and the maximum friction force and the maximum rigidity of a coulomb friction model are determined through plotting; calculating the rigidity of compressed air and the linear elastic rigidity; determining a displacement value corresponding to half of the maximum friction force; comparing the static rigidity and the hysteresis loop which are calculated and actually measured, and meeting the precision requirement; the method comprises the steps of obtaining the dynamic stiffness of the air spring through an experiment, and subtracting the stiffness value of compressed air and the stiffness value of a coulomb friction model from the experimental value of the dynamic stiffness to obtain the stiffness value of a viscoelastic model; then subtracting the linear elastic rigidity value to obtain a rigidity contribution value of the fractional derivative model, and fitting by a least square method to obtain a fractional derivative parameter; the dynamic stiffness values of calculation and actual measurement are compared, the precision requirement is met, the rubber air bag model parameters can be quickly and effectively identified, a parameter database is established, the air spring stiffness is calculated, accurate mechanical characteristic matching is carried out, air bag process design and optimization are facilitated, and the research and development level of enterprises is improved.
(2) According to the method and the device for acquiring the rigidity of the air spring, all parameters of the rubber air bag model are identified through two simple experiments, so that the experiment amount required for acquiring the nonlinear mechanical property of the rubber air bag is greatly reduced, and the efficiency is improved; a foundation is provided for establishing a complete and effective air spring parameterized calculation model, and the design and matching of the air spring are facilitated; the scheme enables enterprises to form a rubber air bag model parameter database and lays a foundation for the rapid design of the rubber air bag and the rapid formulation and optimization of the process parameters of the rubber air bag.
While the preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all alterations and modifications as fall within the scope of the application. It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Claims (10)
1. A method of obtaining a stiffness of an air spring, comprising:
carrying out an isothermal transformation characteristic experiment on the air spring at a preset height and a preset internal pressure to obtain a static hysteresis loop of a hysteresis relation between friction force and displacement of the air spring, and obtaining maximum friction force and maximum rigidity by a mapping method;
acquiring the rigidity of compressed air of the air spring, and combining the static hysteresis loop to obtain the linear elastic rigidity of the air spring;
identifying the obtained linear elastic stiffness, and obtaining a corresponding friction displacement value when the maximum friction force is half according to the ratio of the maximum friction force to the maximum stiffness minus the difference value of the compressed air stiffness and the linear elastic stiffness;
comparing the linear elastic stiffness obtained through identification, the identified static stiffness value and the identified hysteresis loop of the air spring obtained through friction model parameter calculation with the experimental static stiffness value and the experimental hysteresis loop obtained through experiments;
when the relative static stiffness error of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the static hysteresis loops of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweeping experiment by using a sinusoidal signal to obtain the dynamic stiffness of the air spring; subtracting the dynamic stiffness value from the compressed air stiffness value in the dynamic state to obtain the stiffness of the rubber air bag, and subtracting the influence of the friction model from the stiffness of the rubber air bag to obtain the stiffness contribution value of the viscoelasticity model; subtracting the linear elastic stiffness value from the viscoelastic model stiffness contribution value to obtain the stiffness value of the standard fractional derivative model; performing fitting calculation by a least square method to obtain a fractional derivative parameter;
comparing the identified dynamic stiffness value and the identified dynamic stiffness curve obtained by identification with the experimental stiffness value and the experimental dynamic stiffness curve obtained by experiment; and when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters.
2. The method for obtaining the stiffness of the air spring according to claim 1, wherein the linear elastic stiffness obtained by identification, the static stiffness value obtained by identification of the air spring calculated by friction model parameters, and the hysteresis loop obtained by identification are as follows:
passing through the intersection point of the compression section curve and the stretching section curve of the static hysteresis loop, and subtracting the rigidity of the compressed air from the slope of the tangent line of the compression section curve to obtain the linear elastic rigidity;
the frictional force F is obtained by adopting a coulomb friction model describing the amplitude dependence of the nonlinear characteristic of the rubber air bag as a friction modelfThe relationship to the displacement x is:
wherein,
parameter λ ═ Ffs/Ffmax，λ∈[-1,1](ii) a x represents the displacement applied to the air spring; ffmaxRepresenting the maximum friction force, x, in the friction model2To achieve FfmaxFrictional Displacement value at/2, xsFor initial displacement, FfsCalculating to obtain the Coulomb friction model rigidity K for the initial friction forcefAnd lag angle phifThe formula of (1) is as follows:
wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
3. The method for obtaining the stiffness of the air spring according to claim 1, wherein the step of obtaining the compressed air stiffness of the air spring comprises the following steps:
respectively acquiring preset heights h0The following air parameters in the air spring: initial absolute pressure P of gasz0Initial volume Vz0And an initial effective area Az0Height of h0Effective rate of change of volume alpha, height h0The effective area change rate β;
obtaining the compressed air rigidity K of the air spring by utilizing the air parametersaThe formula of (1) is as follows:
wherein,
k is a polytropic exponent; patmIs at atmospheric pressure.
4. The method for obtaining the stiffness of the air spring according to claim 3, wherein when the relative error of the dynamic stiffness of the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient of the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, the identification parameter of the air spring is obtained as the stiffness parameter, and the identification parameter is:
when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters;
and when the relative error of the dynamic stiffness of the identified dynamic stiffness value and the experimental stiffness value is larger than 10%, or the correlation coefficient of the identified dynamic stiffness curve and the experimental dynamic stiffness curve is smaller than 0.85, changing the k value of the polytropic index according to a preset change strategy, and performing refitting calculation to obtain an updated fractional derivative parameter.
5. Method for obtaining the stiffness of an air spring according to claim 3, wherein the identified static stiffness value K of the air spring is calculated through friction model parameterssThe method comprises the following steps:
calculating to obtain the rigidity K of the coulomb friction modelfAnd lag angle phifThe formula of (1) is as follows:
wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxA frictional displacement value at/2;
according to said stiffness KfAnd lag angle phifObtaining the static stiffness K of the air springsThe formula of (1) is as follows:
Ks＝Ka+Ke+Kfcosφf+jKfsinφfwhich isIn (1),
Kais the compressed air stiffness of the air spring, KeIs the linear elastic stiffness, and j is the imaginary unit.
6. The method of deriving the stiffness of an air spring of claim 1, wherein the visco-elastic model stiffness contribution is obtained as:
the viscoelastic force F is obtained by adopting a fractional derivative Kelvin-Voigt model of the frequency correlation characteristic representing the nonlinear mechanical characteristic of the rubber air bagvThe relationship between (t) and displacement x is as follows:
Fv(t)＝Kex(t)+bDax (t), wherein,
a. b and KeRespectively representing the order of the fractional derivative, a damping parameter and linear elastic stiffness;
Darepresents a differential of order a, and a is an element (0,1), and x (t) is a variable displacement;
obtaining dynamic stiffness K by utilizing fractional derivative Kelvin-Voigt modelvAnd lag angle phivThe formula of (1) is as follows:
wherein,
ωafor a given circular frequency during the sweep, ω ═ 2 π f, f is the test frequency, a, b, and KeThe order of the fractional derivative, the damping parameter and the linear elastic stiffness are respectively represented.
7. The method for obtaining the stiffness of the air spring according to claim 6, wherein the dynamic stiffness of the air spring is obtained by performing an air spring frequency sweep experiment by using a sine signal, and the method comprises the following steps:
obtaining the compressed air stiffness KaObtaining the dynamic stiffness K of the air spring by utilizing a fractional derivative Kelvin-Voigt model and a coulomb friction modeldThe formula of (1) is as follows:
Kd＝Ka+Kfcosφf+Kvcosφv+j(Kfsinφf+Kvsinφv) Wherein
Kvis dynamic stiffness sum phivLag angle, a, b and KeRespectively representing the order of the fractional derivative, a damping parameter and linear elastic stiffness, wherein j is an imaginary number unit; coulomb friction model stiffness KfAnd lag angle phifThe formula of (1) is as follows:
wherein,
χ＝Ff0/Ffmax，Ffmaxrepresenting the maximum friction force in the friction model, Ff0Amplitude of friction force at steady state, x0For the amplitude of the input excitation, x2To achieve FfmaxFrictional displacement value at/2.
8. The method for obtaining the stiffness of an air spring according to claim 1, wherein the fractional derivative parameter is calculated by performing a fitting calculation using a least squares method, and is:
the formula for calculating the fractional derivative parameters a and b by fitting with the least squares method is:
wherein,
n represents the number of frequency points of dynamic stiffness experiment, conjugate, Kbvexp(ω) represents the standard fractional derivative model stiffness experimental value.
9. The method for obtaining the stiffness of the air spring according to claim 1, wherein when the relative error of the static stiffness of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the static hysteresis loop of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, the method for obtaining the dynamic stiffness of the air spring by performing an air spring frequency sweeping experiment by using a sinusoidal signal comprises:
when the relative static stiffness error of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10%, and the correlation coefficient of the static hysteresis loops of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, performing an air spring frequency sweeping experiment by using a sinusoidal signal to obtain the dynamic stiffness of the air spring;
and when the static stiffness relative error between the identification static stiffness value and the experimental static stiffness value is more than 10 percent, or the static hysteresis loop correlation coefficient between the identification hysteresis loop and the experimental hysteresis loop is less than 0.85, re-drawing and identifying the updated maximum friction force and the updated maximum stiffness according to a re-drawing strategy.
10. An apparatus for obtaining a stiffness of an air spring, comprising: the device comprises a maximum friction force and maximum rigidity acquisition unit, a linear elastic rigidity acquisition unit, a friction displacement value acquisition unit, a static rigidity value and hysteresis loop processor, a fractional derivative parameter processor and an air spring rigidity parameter acquisition unit; wherein,
the maximum friction force and maximum rigidity acquisition unit is connected with the linear elastic rigidity acquisition unit, and is used for carrying out an isothermal transformation characteristic experiment on the air spring at a preset height and a preset internal pressure to acquire a static hysteresis loop of the hysteresis relationship between the friction force and the displacement of the air spring and obtain the maximum friction force and the maximum rigidity by a mapping method;
the linear elastic stiffness acquisition unit is connected with the maximum friction force and stiffness acquisition unit and the friction displacement value acquisition unit to acquire the compressed air stiffness of the air spring and obtain the linear elastic stiffness of the air spring by combining the static hysteresis loop;
the friction displacement value acquisition unit is connected with the linear elastic stiffness acquisition unit and the static stiffness value and hysteresis loop processor, identifies the obtained linear elastic stiffness, and obtains a corresponding friction displacement value when the maximum friction force is half according to the ratio of the maximum friction force to the maximum stiffness minus the difference between the compressed air stiffness and the linear elastic stiffness;
the static stiffness value and hysteresis loop processor is connected with the friction displacement value acquisition unit and the fractional derivative parameter processor, and compares the linear elastic stiffness obtained through identification, the identified static stiffness value and the identified hysteresis loop of the air spring obtained through friction model parameter calculation with the experimental static stiffness value and the experimental hysteresis loop obtained through experiments;
the fractional derivative parameter processor is connected with the static stiffness value and hysteresis loop processor and the air spring stiffness parameter acquisition unit, and when the static stiffness relative error of the identified static stiffness value and the experimental static stiffness value is less than or equal to 10% and the static hysteresis loop correlation coefficient of the identified hysteresis loop and the experimental hysteresis loop is greater than or equal to 0.85, a sinusoidal signal is adopted to carry out an air spring frequency sweep experiment to acquire the dynamic stiffness of the air spring; subtracting the dynamic stiffness value from the compressed air stiffness value in the dynamic state to obtain the stiffness of the rubber air bag, and subtracting the influence of the friction model from the stiffness of the rubber air bag to obtain the stiffness contribution value of the viscoelasticity model; subtracting the linear elastic stiffness value from the viscoelastic model stiffness contribution value to obtain the stiffness value of the standard fractional derivative model; performing fitting calculation by a least square method to obtain a fractional derivative parameter;
the air spring stiffness parameter acquisition unit is connected with the fractional derivative parameter processor and compares the identified dynamic stiffness value and the identified dynamic stiffness curve obtained by identification with the experimental stiffness value and the experimental dynamic stiffness curve obtained by experiments; and when the relative dynamic stiffness error between the identified dynamic stiffness value and the experimental stiffness value is less than or equal to 10%, and the correlation coefficient between the identified dynamic stiffness curve and the experimental dynamic stiffness curve is greater than or equal to 0.85, acquiring the identification parameters of the air spring as stiffness parameters.
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| CN114486131A (en) * | 2022-01-06 | 2022-05-13 | 易瑞博科技（北京）有限公司 | Rigidity measuring method and system for air spring bag skin and storage medium |
| CN114486131B (en) * | 2022-01-06 | 2024-05-17 | 易瑞博科技（北京）有限公司 | Rigidity measuring method, system and storage medium of air spring capsule |
| CN117454695A (en) * | 2023-10-24 | 2024-01-26 | 辰致科技有限公司 | Method for determining design parameters of membrane air spring |
| CN117454695B (en) * | 2023-10-24 | 2024-07-09 | 辰致科技有限公司 | Method for determining design parameters of membrane air spring |
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Application publication date: 20191129 |