Method and system for simulating fatigue life of rubber elastic damping element

Abstract

The invention relates to a method and a system for simulating the fatigue life of a rubber elastic damping element. The method comprises the following steps: acquiring rubber performance parameters; establishing a simulation model in finite element software, wherein the simulation model comprises a rubber surface two-dimensional model and an entity three-dimensional model; the performance parameters are input into the model for simulation calculation, nominal strain of the three-dimensional model is obtained, and an initial simulation fatigue calculation result is calculated; the temperature state of the two-dimensional finite element simulation model is updated based on the result, the nominal strain of the two-dimensional model is calculated, then an intermediate simulation fatigue calculation result is calculated, and meanwhile, simulation data of membrane unit heat transfer of the two-dimensional model is exported based on performance parameters; and obtaining a fatigue life result of the rubber free surface based on an intermediate simulation fatigue calculation result and simulation data of heat transfer of the membrane unit through iterative calculation. According to the method, the possibility that material parameters of the rubber material change along with the fatigue test process is fully considered, the temperature change of the rubber material in the rubber elastic damping element in practical application can be better reflected, and the fatigue simulation precision is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of fatigue life prediction of rubber materials, and in particular relates to a fatigue life simulation method and system for a rubber elastic vibration damping element. Background Art

[0002] Due to its unique nonlinear characteristics, rubber elastic vibration damping components have been widely used in rail transportation and automobiles. With the development of finite element simulation technology, it has become a common method to use finite element simulation software to simulate and predict the fatigue life of rubber elastic vibration damping components.

[0003] However, since rubber materials are poor conductors of heat, when subjected to dynamic loads, as the temperature rises, the material's stress-strain response will change with the temperature. Existing rubber fatigue life calculation methods based on finite element simulation technology usually do not consider the influence of temperature on the stress-strain response and other parameter characteristics of rubber elastic vibration reduction elements, resulting in insufficient fatigue life simulation accuracy and a large difference between the simulation prediction results and the actual test results. Summary of the invention

[0004] The purpose of the present invention is to solve one of the above technical problems and to provide a method and system for simulating the fatigue life of a rubber elastic vibration damping element.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for simulating fatigue life of a rubber elastic vibration damping element comprises the following steps:

[0007] Step 1: Perform performance testing on the rubber material part of the rubber elastic vibration damping element to obtain performance parameters of the rubber material, including constitutive model parameters, Mullins parameters, viscoelastic parameters and fatigue crack growth characteristic parameters;

[0008] Step 2: Establishing a simulation model of the rubber elastic vibration damping element in finite element software, including establishing a three-dimensional finite element simulation model using solid elements and establishing a two-dimensional finite element simulation model using membrane elements;

[0009] Step 3: Input the performance parameters into the finite element software, apply axial cyclic load to the three-dimensional finite element simulation model for simulation calculation, and derive the nominal strain of the three-dimensional finite element simulation model during the loading process;

[0010] Step 4: Perform simulated fatigue calculation based on the performance parameters and the nominal strain of the three-dimensional finite element simulation model to obtain initial simulated fatigue calculation results, which include the simulated temperature of the rubber free surface;

[0011] Step 5: assign the simulated temperature of the rubber free surface to the corresponding membrane unit in the two-dimensional finite element simulation model, update the temperature state of the two-dimensional finite element simulation model, re-perform the simulation calculation, and obtain the nominal strain of the two-dimensional finite element simulation model;

[0012] Step 6: Perform simulation fatigue calculation based on the performance parameters and the nominal strain of the surface two-dimensional finite element simulation model to obtain intermediate simulation fatigue calculation results;

[0013] Step 7: Calculate the simulation data of heat transfer of the membrane unit in the surface two-dimensional finite element simulation model based on the fatigue crack growth characteristic parameters in the finite element software;

[0014] Step 8: Based on the intermediate simulation fatigue calculation results and the simulation data of membrane unit heat transfer, the fatigue life results of the rubber free surface are obtained by iterative calculation.

[0015] In some embodiments of the present invention, the method for obtaining the constitutive model parameters and Mullins parameters of the rubber material in step 1 comprises the following steps:

[0016] Designing a predetermined test temperature, a predetermined stretching rate, and a plurality of predetermined strain levels;

[0017] Using a uniaxial electronic tensile testing machine and an equibiaxial tensile testing machine, uniaxial stretching and equibiaxial stretching are performed at a predetermined temperature and a predetermined stretching rate;

[0018] The tensile test was carried out five times in a cycle for each predetermined strain level. The test curves of the loading section of the first cycle and the unloading section of the fifth cycle were selected. The fitting software was used to fit the Ogden hyperelastic constitutive model and the Ogden-Roxburgh pseudo-elastic model. The constitutive model parameters and Mullins parameters were obtained based on the fitting results.

[0019] The expression of Ogden hyperelastic constitutive model is:

[0020]

[0021] Among them, λ1, λ2, and λ3 are the main stretching ratios in three directions, μ i and α i is the material constitutive constant;

[0022] The expression of the Ogden-Roxburgh pseudoelastic model is:

[0023]

[0024] Where η is the damage variable, W m is the strain energy density of the material from initial loading to unloading, is the strain energy density when the material is unloaded to a certain strain, r, m, β are all material parameters, erf(x) function is the error function, and the expression of erf(x) function is:

[0025]

[0026] Among them, ω is the integral variable and exp(x) function is the natural exponential function.

[0027] In some embodiments of the present invention, the viscoelastic parameters of the rubber material are obtained by fitting the relationship curves of the loss modulus and strain and the loss modulus and frequency of the rubber material at different temperatures. The method for obtaining the relationship curves of the loss modulus and strain, the relationship curves of the loss modulus and frequency, the relationship curves of the hysteresis energy density-strain rate, and the relationship curves of the hysteresis energy density and temperature of the rubber material and fitting the viscoelastic parameters comprises the following steps:

[0028] The method for obtaining the viscoelastic parameters of the rubber material in step 1 comprises the following steps:

[0029] A DMA testing machine is used to perform strain scanning and frequency scanning on the rubber material at different temperatures, and the relationship curves between the loss modulus and strain and the loss modulus and frequency of the rubber material at different temperatures are obtained;

[0030] Data fitting is performed based on the relationship curve between the loss modulus and strain of the rubber material and the functional relationship between the loss modulus and strain of the viscoelasticity to obtain the fitted material parameters at a predetermined temperature.

[0031] The loss modulus of viscoelasticity is related to strain as follows:

[0032]

[0033] Among them, E″ ∞ , E″ p , ε c , m, ΔE″ U are different material parameters, and ΔE″ U =E″0-E″ ∞ ;

[0034] The hysteresis energy density at a predetermined frequency and a predetermined strain amplitude is calculated based on the relationship curve between the loss modulus and the strain of the rubber material and the functional relationship between the hysteresis energy density and the strain;

[0035] The functional relationship between hysteresis energy density and strain is:

[0036] h=πG"ε a 2 ;

[0037] Where, h is the hysteresis energy density, G” is the loss modulus, and εa is the strain amplitude;

[0038] The temperature coefficient is obtained based on the hysteresis energy density and the functional relationship between the hysteresis energy density and the temperature, and then the relationship curve between the hysteresis energy density and the temperature is obtained;

[0039] The functional relationship between hysteresis energy density and temperature is:

[0040]

[0041] Where h(θ) is the hysteresis energy density at a certain temperature, θ0 is the reference temperature, r is the temperature coefficient, and a is the process parameter;

[0042] Calculating a reference strain rate under a predetermined strain amplitude based on a relationship curve between the loss modulus and the frequency of the rubber material and a functional relationship between the strain rate and the loading frequency;

[0043] The functional relationship between strain rate and loading frequency is:

[0044]

[0045] in, is the reference strain rate, ε max is the maximum strain value, ε min is the minimum strain value, f is the loading frequency;

[0046] Based on the reference strain rate and the functional relationship between hysteresis energy density and strain rate, the strain rate coefficient is fitted, and then the relationship curve between hysteresis energy density and strain rate is obtained;

[0047] The functional relationship between hysteresis energy density and strain rate is:

[0048]

[0049] in, is the hysteresis energy density at a predetermined reference strain rate, is the strain rate, is the reference strain rate, a is the process parameter, and a is the coefficient related to strain and loss modulus.

[0050] In some embodiments of the present invention, the method for obtaining the viscoelastic parameters of the rubber material in step 1 further includes the following steps:

[0051] Based on the relationship curve between the loss modulus and strain of rubber materials and the calculation formula of the energy loss rate, the experimental values ​​of the energy loss rate under the reference temperature, reference strain amplitude and reference strain rate are calculated.

[0052] The calculation formula of energy loss rate is:

[0053] Q=π·G”·ε a 2 f;

[0054] Among them, Q is the energy loss rate, G” is the loss modulus, εa is the strain amplitude, and f is the loading frequency;

[0055] Based on experimental values The calculation conditions are used to establish a simple shear finite element calculation model, and the simulation values ​​of the energy loss rate under the reference temperature, reference strain amplitude, and reference strain rate are calculated.

[0056] Based on experimental values and simulation value The proportionality factor C used to enhance the consistency between the calculated results of the dissipated energy and the experimental results is calculated. The calculation formula of the proportionality factor C is:

[0057]

[0058] In some embodiments of the present invention, fatigue crack growth characteristic parameters are obtained by fitting a tear energy-strain curve. The method for obtaining the tear energy-strain curve and fitting the parameters specifically includes the following steps:

[0059] A plane tensile specimen of rubber material is selected, and a crack of a predetermined length is prefabricated on the surface of the plane tensile specimen;

[0060] Using an electromagnetic dynamic testing machine to perform quasi-static and dynamic tensile tests on a plane tensile specimen at different predetermined temperatures, and obtaining test results;

[0061] Based on the test results, the tear energy T of any strain is calculated by combining the tear energy expression, the classical Thomas model and the strain energy density expression, and then the critical tear energy tc at different temperatures is calculated;

[0062] The expression of tearing energy is:

[0063] T = WH;

[0064] Where T is tearing energy, W is strain energy density, and H is the specimen height;

[0065] The expression of the classic Thomas model is:

[0066]

[0067] Among them, r c is the critical crack growth rate, T c is the critical tearing energy, and F is the exponential factor;

[0068] The strain energy density expression is:

[0069]

[0070] Where σ is stress, ε is strain, i is the number of integration points, and ε i is the integration point strain.

[0071] In some embodiments of the present invention, fatigue crack growth characteristic parameters are obtained by fitting a non-full relaxation crack test cycle number-crack length curve. The method of obtaining the non-full relaxation crack test cycle number-crack length curve and fitting the fatigue crack growth characteristic parameters comprises the following steps:

[0072] An electromagnetic dynamic testing machine is used to carry out uniaxial tensile tests on plane tensile specimens at different predetermined temperatures to obtain the relationship between the load ratio R and F(R) of the non-full relaxation crack extension test at different predetermined temperatures; data fitting is performed based on the Mars-Fatemi model to obtain the fitting material parameters, and then the full relaxation crack test cycle number-crack length curve is obtained;

[0073] Among them, the loading conditions of the uniaxial tensile test include:

[0074] Minimum strain ε min The maximum strain increases linearly with time until it reaches the required maximum strain ε max , cyclic stretching for the first predetermined number of times; wherein the minimum strain ε min =0;

[0075] Keep the minimum strain ε min and the maximum strain ε max No change, cycle stretching for a second predetermined number of times;

[0076] Maximum strain ε max Keep unchanged, the minimum strain ε min Increasing with time, cyclically stretching a third predetermined number of times;

[0077] The expression of the Mars-Fatemi model is:

[0078]

[0079] Among them, r c is the critical crack growth rate, T c is the critical tearing energy, F(R) is the exponential factor, R is the ratio of the minimum tearing energy to the maximum tearing energy in the cycle, F0, F1, F2, F3, F exp These are material parameters.

[0080] In some embodiments of the present invention, fatigue crack growth characteristic parameters are obtained by fitting a full relaxation crack test cycle number-crack length curve. The method for obtaining the full relaxation crack test cycle number-crack length curve and fitting the fatigue crack growth characteristic parameters comprises the following steps:

[0081] The uniaxial tensile test was carried out on the plane tensile specimens at different predetermined temperatures using an electromagnetic dynamic testing machine to obtain the relationship between the tear energy and the fatigue crack growth rate under the condition of R = 0. Based on the relationship between the tear energy and the crack growth rate at different temperatures, the critical crack growth rate r at different predetermined temperatures was calculated in combination with the classic Thomas model. c and exponential factor F0, and then the full relaxation crack test cycle number-crack length curve is obtained.

[0082] Among them, the loading conditions of the uniaxial tensile test include:

[0083] The dynamic minimum strain is always 0, and the maximum strain increases linearly with time;

[0084] The initial maximum strain is 15% of the clamping height, and the maximum strain at the end of the test is 60% of the clamping height.

[0085] In some embodiments of the present invention, the fatigue crack growth characteristic parameter also includes uniaxial elongation fatigue, and the method for obtaining uniaxial elongation fatigue includes the following steps:

[0086] The uniaxial tensile test is used to test the number of uniaxial tensile cycle fractures of the rubber material under constant strain conditions to determine the effective size a0 of the initial crack size inside the rubber material;

[0087] The expression of effective size a0 is:

[0088]

[0089] Where N is the number of cycles, i.e. the tensile fatigue life of the specimen, and F is the exponential factor. c is the critical crack growth rate, W is the strain energy under a given strain, T c is the critical tearing energy.

[0090] Some embodiments of the present invention further provide a fatigue life simulation system for a rubber elastic vibration damping element, comprising:

[0091] at least one processor;

[0092] at least one memory for storing at least one program;

[0093] When at least one program is executed by at least one processor, the at least one processor implements the above-mentioned method for simulating fatigue life of rubber elastic vibration damping elements.

[0094] Some embodiments of the present invention further provide a storage medium storing a program executable by a processor. The program executable by the processor is used to implement the above-mentioned method for simulating the fatigue life of a rubber elastic vibration damping element when executed by the processor.

[0095] The beneficial effects of the present invention are:

[0096] The simulation method provided by the present invention fully considers the possibility of changes in material parameters of rubber materials during fatigue testing, and can better reflect the temperature changes of rubber materials in rubber elastic vibration damping elements in actual applications. It is used in the fatigue life simulation calculation of rubber elastic vibration damping elements in the fields of rail transportation and automobiles, and can control the prediction error of fatigue life within 15%, which effectively improves the fatigue simulation accuracy compared with the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the specific embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0098] Figure 1 It is a flow chart of a method for simulating the fatigue life of a rubber elastic vibration damping element;

[0099] Figure 2 It is a schematic diagram of the overall structure of a method for simulating the fatigue life of a rubber elastic vibration damping element;

[0100] Figure 3 A uniaxial tensile stress-strain curve diagram measured in a specific embodiment of the present invention;

[0101] Figure 4 A plane tensile stress-strain curve diagram measured in a specific embodiment of the present invention;

[0102] Figure 5 This is a graph of equibiaxial tensile stress-strain curves measured in a specific embodiment of the present invention;

[0103] Figure 6 is a loss modulus-strain curve diagram measured in a specific embodiment of the present invention;

[0104] Figure 7 A loss modulus-frequency curve diagram measured in a specific embodiment of the present invention;

[0105] Figure 8 The figure is a loss modulus-temperature curve diagram measured in a specific embodiment of the present invention;

[0106] Fig. 9A tear energy-strain curve diagram measured in a specific embodiment of the present invention;

[0107] Fig.10 A curve diagram of the number of cycles of a full relaxation crack test-crack length measured in a specific embodiment of the present invention;

[0108] Fig.11 A curve diagram of the number of cycles of a non-full relaxation crack test-crack length measured in a specific embodiment of the present invention;

[0109] Fig.12 This is a life cloud diagram obtained by simulation calculation according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0110] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is described and illustrated below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0111] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0112] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0113] The technical solution of the present invention is described in detail below in conjunction with specific embodiments and the accompanying drawings.

[0114] As attached Figure 1 -Attached Fig.12 As shown, in an illustrative embodiment of a method for simulating fatigue life of a rubber elastic vibration damping element of the present invention, the simulation method includes the following steps.

[0115] Step 1: Perform performance tests on the rubber material part of the rubber elastic vibration damping element to obtain performance parameters of the rubber material, including constitutive model parameters, Mullins parameters, viscoelastic parameters and fatigue crack growth characteristic parameters.

[0116] In some embodiments of the present invention, constitutive model parameters and Mullins parameters are obtained by fitting a uniaxial tensile stress-strain curve, a planar tensile stress-strain curve, an equibiaxial stress-strain curve, and a bulk modulus.

[0117] The uniaxial tensile stress-strain curve is obtained by performing a uniaxial tensile test on a quasi-static uniaxial tension and compression testing machine. The test loading speed is controlled at 40 mm / min. Since the temperature of the rubber material continues to rise during the dynamic load process, at least 3 to 5 groups of test temperatures are selected for the uniaxial tensile test, and the temperature interval is at least 10°C. The uniaxial tensile stress-strain curve measured under the loading conditions provided in this embodiment is shown in the attached figure. Figure 3 shown.

[0118] The plane tensile stress-strain curve is obtained by performing a uniaxial tensile test on a quasi-static uniaxial tension and compression testing machine. The test loading speed is controlled at 40 mm / min. Since the temperature of the rubber material continues to rise during the dynamic load process, at least 3 to 5 groups of test temperatures are selected for the uniaxial tensile test, and the temperature interval is at least 10°C. The uniaxial tensile stress-strain curve measured under the loading conditions provided in this embodiment is shown in the attached figure. Figure 4 shown.

[0119] The biaxial tensile stress-strain curve is obtained by performing a quasi-static multiaxial tensile test on a multiaxial tensile testing machine. The test loading speed is controlled at 40 mm / min. Since the temperature of the rubber material continues to rise during the dynamic load process, at least 3 to 5 groups of test temperatures are selected for the tensile test, and the temperature interval is at least 10°C. The uniaxial tensile stress-strain curve measured under the loading conditions provided in this embodiment is shown in the attached figure. Figure 5 shown.

[0120] The bulk modulus is measured by a testing mechanism.

[0121] Specifically, the method for obtaining the above constitutive model parameters and Mullins parameters in step 1 includes the following steps.

[0122] Design a predetermined test temperature, a predetermined stretching rate and a plurality of predetermined strain levels. In this embodiment, the predetermined test temperature is room temperature 23°C, the predetermined stretching rate is 40 mm / min, and the predetermined strain levels include four, namely 25%, 50%, 75%, and 100%.

[0123] Using a uniaxial electronic tensile testing machine and an equibiaxial tensile testing machine, at room temperature 23°C and a tensile rate of 40 mm / min, uniaxial tensile (UT) and equibiaxial tensile (ET) tests were performed at four strain levels of 25%, 50%, 75%, and 100%, respectively. Five tensile tests were performed in cycles for each predetermined strain level, and the test curves of the loading section of the first cycle and the unloading section of the fifth cycle were selected. Fitting was performed using fitting software based on the Ogden hyperelastic constitutive model and the Ogden-Roxburgh pseudo-elastic model, and the constitutive model parameters and Mullins parameters were obtained based on the fitting results;

[0124] Among them, the expression of Ogden hyperelastic constitutive model is:

[0125]

[0126] Among them, λ1, λ2, and λ3 are the main stretching ratios in three directions, μ i and α i is the material constitutive constant.

[0127] The expression of the Ogden-Roxburgh pseudoelastic model is:

[0128]

[0129] Where η is the damage variable, W m is the strain energy density of the material from initial loading to unloading, is the strain energy density when the material is unloaded to a certain strain, r, m, β are all material parameters, erf(x) function is the error function, and the expression of erf(x) function is:

[0130]

[0131] Among them, ω is the integral variable, and the exp(x) function is the natural exponential function, that is, the exponential function with e as the base.

[0132] In some embodiments of the present invention, the viscoelastic parameters are obtained by fitting the loss modulus-strain relationship curve, the loss modulus-frequency relationship curve, the hysteresis energy density-temperature relationship curve and the loss modulus-temperature relationship curve, wherein the loss modulus-strain scanning curve and the loss modulus-frequency scanning curve are obtained by performing dynamic tensile tests using a DMA Q800 testing machine, and the hysteresis energy density-temperature relationship curve and the loss modulus-temperature relationship curve are obtained by fitting the loss modulus-strain scanning curve and the loss modulus-frequency scanning curve.

[0133] Specifically, the method for obtaining the loss modulus-strain relationship curve includes the following steps.

[0134] The strain of the rubber material was scanned at 30℃, 40℃, 50℃, 60℃, and 70℃ using a DMA tester, with a scanning range of 0.1% to 5%, to obtain the relationship between the loss modulus and strain of the rubber material at different temperatures. The frequency of the rubber material was scanned at 30℃, 40℃, 50℃, 60℃, and 70℃ using a DMA tester, with a scanning range of 1Hz to 25Hz, to obtain the relationship between the loss modulus and frequency of the rubber material at different temperatures.

[0135] The relationship curve between the loss modulus and strain of the rubber material at different temperatures obtained by the DMA testing machine can be used to obtain the relationship curve between the hysteresis energy density and temperature at a certain frequency and a certain strain amplitude.

[0136] The method for obtaining the hysteresis energy density-temperature relationship curve includes the following steps.

[0137] The relationship between the loss modulus and strain of the rubber material at the same temperature is selected. In this embodiment, 30°C is selected as the reference curve. Data fitting is performed based on the functional relationship between the loss modulus and strain of the viscoelasticity at this temperature to obtain the fitted material parameters.

[0138] The functional relationship between the loss modulus of the viscoelasticity and the strain is:

[0139]

[0140] Among them, E″ ∞ , E″ p , ε c , m, ΔE″ U are the different material parameters obtained from the above fitting, and ΔE″ U =E″0-E″ ∞ .

[0141] Through the functional relationship between hysteresis energy density and strain h=πG”ε a 2 , the hysteresis energy density under a certain strain amplitude is calculated.

[0142] Where, h is the hysteresis energy density, G” is the loss modulus, ε a is the strain amplitude.

[0143] Based on the strain information fed back by fatigue loading of rubber elastic vibration damping elements, the corresponding strain amplitude in the relationship curve between loss modulus and strain of rubber materials at different temperatures is selected, and the functional relationship between hysteresis energy density and temperature is used to calculate the strain amplitude. The temperature coefficient can be fitted and the hysteresis energy density-temperature curve can be obtained.

[0144] Among them, h(θ) is the hysteresis energy density at a certain temperature, θ0 is the reference temperature, r is the temperature coefficient, and a is the process parameter.

[0145] The relationship curve between the loss modulus and the frequency of the rubber material at different temperatures obtained by the DMA testing machine can be used to obtain the hysteresis energy density-strain rate relationship curve at a certain temperature and a certain strain amplitude.

[0146] The method for obtaining the hysteresis energy density-temperature relationship curve includes the following steps.

[0147] Through the functional relationship between strain rate and loading frequency Calculate the reference strain rate under a certain strain amplitude.

[0148] in, is the reference strain rate, ε max is the maximum strain value, ε min is the minimum strain value, and f is the loading frequency.

[0149] Select the loss modulus-frequency curve of the rubber material at a certain temperature, and use the functional relationship between the hysteresis energy density and the strain rate to obtain the The strain rate coefficient can be fitted and the hysteresis energy density-strain rate relationship curve can be obtained.

[0150] in, is the hysteresis energy density at a predetermined reference strain rate, is the strain rate, is the reference strain rate and a is the process parameter.

[0151] In some embodiments of the present invention, the viscoelastic parameters also include a proportionality factor for enhancing the consistency between the calculated results of the dissipated energy and the experimental results.

[0152] The steps to calculate the scale factor include:

[0153] The experimental values ​​of the energy loss rate at the reference temperature, reference strain amplitude and reference strain rate are calculated based on the relationship curve between the loss modulus and strain of the rubber material and the calculation formula of the energy loss rate.

[0154] The calculation formula of energy loss rate is:

[0155] Q=π·G”·ε a 2 ·f.

[0156] Among them, Q is the energy loss rate, G” is the loss modulus, εa is the strain amplitude, and f is the loading frequency;

[0157] Based on the experimental values The calculation conditions are used to establish a simple shear finite element calculation model, and the simulation values ​​of the energy loss rate under the reference temperature, reference strain amplitude, and reference strain rate are calculated.

[0158] Based on the experimental values and the simulation value The proportionality factor C used to enhance the consistency between the calculated results of the dissipated energy and the experimental results is calculated. The calculation formula of the proportionality factor C is:

[0159]

[0160] In this embodiment, the loss modulus-strain scanning curve measured under the above loading conditions is shown in the attached figure. Figure 6 The loss modulus-frequency scanning curve measured under the above loading conditions is shown in the attached figure. Figure 7 The loss modulus-temperature scanning curve measured under the above loading conditions is shown in the attached figure. Figure 8 shown.

[0161] In some embodiments of the present invention, fatigue crack extension characteristic parameters are obtained by fitting the tear energy-strain curve, the full relaxation crack test cycle number-crack length curve, the non-full relaxation crack test cycle number-crack length curve, uniaxial elongation fatigue and thermodynamic performance parameters, wherein the thermodynamic performance parameters include: mass density, specific heat capacity, convection heat transfer coefficient and thermal conductivity.

[0162] Among them, the tear energy-strain curve, i.e. the critical tear energy curve, the full relaxation crack test cycle number-crack length curve and the non-full relaxation crack test cycle number-crack length curve are all obtained by performing quasi-static and dynamic tensile tests on the electromagnetic dynamic testing system. During the test, the tensile deformation rate of the rubber material is 0.01 / sec, and the stretching rate is slow enough to meet the quasi-static tensile state. And during the entire test process, the rubber material is in a pure shear state. Since the temperature of the rubber material continues to rise during the process of bearing dynamic loads, at least 3 to 5 groups of test temperatures are selected for the uniaxial tensile test, and the temperature interval is at least 10°C; in this embodiment, the tear energy-strain curve measured under the above loading conditions is as shown in the attached figure. Fig. 9 The full relaxation crack test cycle number-crack length curve is shown in the attached Fig.10 The non-full relaxation crack test cycle number-crack length curve is shown in the attached Fig.11 Thermodynamic performance parameters are obtained through testing by testing institutions.

[0163] The tear energy-strain curve is the critical tear energy curve. In this embodiment, the method for obtaining the critical tear energy curve specifically includes the following steps.

[0164] A plane tensile specimen of rubber material was selected, the size of which was 146 mm×10 mm×1 mm, a crack with a length of 25 mm was prefabricated on the surface of the plane tensile specimen, and the tensile deformation rate of the plane tensile specimen was 0.01 / sec.

[0165] The electromagnetic dynamic testing machine was used to carry out quasi-static and dynamic tensile tests on the plane tensile specimens at test temperatures of 23°C, 45°C, and 70°C, respectively, to obtain the test results.

[0166] Based on the test results, the tear energy T of any strain can be calculated by combining the tear energy expression, the classical Thomas model and the strain energy density expression, and then the critical tear energy T at different temperatures can be calculated. c , and then obtain the critical tearing energy curve.

[0167] The expression of tearing energy is:

[0168] T = WH;

[0169] Where T is tearing energy, W is strain energy density, and H is the specimen height;

[0170] The expression of the classic Thomas model is:

[0171]

[0172] Among them, r c is the critical crack growth rate, T c is the critical tearing energy, and F is the exponential factor;

[0173] The strain energy density expression is:

[0174]

[0175] Where σ is stress, ε is strain, i is the number of integration points, and ε i is the integration point strain;

[0176] In this embodiment, the method for obtaining a non-full relaxation crack test cycle number-crack length curve specifically includes the following steps.

[0177] An electromagnetic dynamic testing machine was used to carry out uniaxial tensile tests on planar tensile specimens at test temperatures of 23°C, 45°C, and 70°C, respectively, to obtain the relationship between the non-full relaxation crack extension test load ratio R and F(R) at different predetermined temperatures. Data fitting was performed based on the Mars-Fatemi model to obtain the fitting material parameters, and then the non-full relaxation crack test cycle number-crack length curve was obtained.

[0178] Among them, the loading conditions of the uniaxial tensile test are:

[0179] Minimum strain ε min The maximum strain increases linearly with time until it reaches the required maximum strain ε max , cyclic stretching for the first predetermined number of times; wherein the minimum strain ε min =0;

[0180] Keep the minimum strain ε min and the maximum strain ε max No change, cycle stretching for a second predetermined number of times;

[0181] Maximum strain ε max Keep unchanged, the minimum strain ε min Increasing with time, cyclically stretching a third predetermined number of times;

[0182] The expression of the Mars-Fatemi model is:

[0183]

[0184] Among them, r c is the critical crack growth rate, T c is the critical tearing energy, F(R) is the exponential factor, R is the ratio of the minimum tearing energy to the maximum tearing energy in the cycle, and F0, F1, F2, F3, and Fexp are all material parameters.

[0185] In this embodiment, the method for obtaining a full relaxation crack test cycle number-crack length curve specifically includes the following steps.

[0186] The uniaxial tensile test was carried out on the plane tensile specimens at the test temperatures of 23℃, 45℃ and 70℃ respectively using an electromagnetic dynamic testing machine to obtain the relationship between the tear energy and the fatigue crack growth rate under the condition of R=0. Based on the relationship between the tear energy and the crack growth rate at different temperatures, the critical crack growth rate r at different predetermined temperatures was calculated in combination with the classic Thomas model. c and exponential factor F0, and then the full relaxation crack test cycle number-crack length curve is obtained.

[0187] During the test to obtain the full relaxation crack test cycle number-crack length curve, the loading conditions of the test are:

[0188] The dynamic minimum strain is always 0, and the maximum strain increases linearly with time; the initial maximum strain is 15% of the clamping height, and the maximum strain at the end of the test is 60% of the clamping height.

[0189] In this embodiment, the method for obtaining uniaxial elongation fatigue specifically includes the following steps.

[0190] The uniaxial tensile test is used to test the number of uniaxial tensile cycle fractures of the rubber material under constant strain conditions to determine the effective size a0 of the initial crack size inside the rubber material;

[0191] The expression of effective size a0 is:

[0192]

[0193] Where N is the number of cycles, i.e. the tensile fatigue life of the specimen, and F is the exponential factor. c is the critical crack growth rate, W is the strain energy under a given strain, T c is the critical tearing energy.

[0194] Step 2: Based on the geometric structure of the rubber elastic vibration damping element, a simulation model of the rubber elastic vibration damping element is established in the finite element software, including using solid elements to establish a three-dimensional finite element simulation model and using membrane elements to establish a two-dimensional finite element simulation model. Since the fatigue failure of the rubber elastic vibration damping element generally occurs on the free surface of the rubber during actual use, therefore, in this embodiment, during the finite element simulation analysis, a 2D membrane element is established to characterize the free surface of the rubber.

[0195] Step 3: Input the performance parameters obtained in step 1 into the finite element software, apply axial cyclic load to the three-dimensional finite element simulation model for simulation calculation, and derive the nominal strain history NE of the three-dimensional finite element simulation model during the loading process.

[0196] Step 4: Define the calculation conditions of the rubber elastic vibration damping element. Import the constitutive model parameters and Mullins parameters, viscoelastic parameters and fatigue crack growth characteristic parameters obtained in step 1 and the nominal strain NE file of the three-dimensional finite element simulation model into the Endurica software for simulation fatigue calculation. Use the Kraus self-heating model to iteratively calculate the heat generation rate-temperature field of the rubber material on the calculation model until the temperature of the calculation model reaches stability (generally the temperature difference is ≤0.1°C), output the quasi-static temperature results and dissipation results, and obtain the initial simulation fatigue calculation results. The initial simulation fatigue calculation results at least include the simulation temperature of the rubber free surface.

[0197] Step 5: derive the simulated temperature of the rubber free surface obtained in step 4, and assign the simulated temperature of the rubber free surface to the corresponding membrane unit in the two-dimensional finite element simulation model through a self-written program, update the temperature state of the two-dimensional finite element simulation model, and derive the nominal strain NE of the two-dimensional finite element simulation model.

[0198] Step 6: Re-import the constitutive model parameters, Mullins parameters, nominal strain NE of the two-dimensional finite element simulation model and the simulated temperature of the rubber free surface into the Endurica software for simulation calculation, obtain the intermediate simulation fatigue calculation results, and generate them as hfi files.

[0199] Step 7: Input the mass density, convective heat transfer coefficient, specific heat capacity and thermal conductivity of the rubber material obtained in step 1 into the property module of the finite element software, obtain the simulation data of the heat transfer of the membrane unit in the two-dimensional finite element simulation model, and export it as an inp file.

[0200] Step 8: Based on the intermediate simulation fatigue calculation results and the simulation data of membrane unit heat transfer, the hfi file obtained in step 6 and the inp file obtained in step 7 are iteratively calculated through a self-written program to obtain the fatigue life results of the rubber free surface.

[0201] The beneficial effects of the present invention are described below by a specific embodiment:

[0202] In this embodiment, the material parameters of the Ogden model obtained by fitting in step 1 are shown in Table 1, the material parameters of the Mullins model fitting are shown in Table 2, the viscoelastic parameters are shown in Table 3, and the fatigue crack growth characteristic parameters are shown in Table 4. The thermodynamic performance parameters of the rubber material sample and the metal material sample are shown in Table 5.

[0203] Table 1 Material parameters of Ogden model fitting

[0204] <![CDATA[μ1]]> <![CDATA[α1]]> <![CDATA[μ2]]> <![CDATA[α2]]> <![CDATA[μ3]]> <![CDATA[α3]]> 0.005 9.19 0.49 2.12 0.49 0.14

[0205] Table 2 Material parameters of Mullins model fitting

[0206] r m β 2.12 0.36 0.04

[0207] Table 3 Viscoelastic parameters

[0208] <![CDATA[E″ ∞ ]]> <![CDATA[E″ ∞ ]]> <![CDATA[ε c ]]> m <![CDATA[ΔE″ U ]]> r Z C 0.31 0.59 1.34 0.74 0.16 -0.011 0.026 3.03

[0209] Table 4 Fatigue crack growth characteristic parameters

[0210]

[0211] Table 5 Thermodynamic performance parameters

[0212]

[0213] Based on the data in Tables 1 to 5 above, simulation calculations are performed according to the process from step 2 to step 7 to obtain the life cloud diagram of the rubber elastic vibration damping element as shown in the attached figure. Fig.12As shown, the fatigue life result of the rubber free surface is 1.134e5 times, and the average fatigue test life of the three damping elements is 105469 times, with a deviation of +7.5%. The present invention achieves a fatigue life simulation deviation within 15%, and can effectively characterize the fatigue life of the rubber damping element.

[0214] Some embodiments of the present invention further provide a fatigue life simulation system for a rubber elastic vibration damping element, comprising:

[0215] At least one processor.

[0216] At least one memory is used to store at least one program.

[0217] When at least one program is executed by at least one processor, the at least one processor implements the above-mentioned method for simulating fatigue life of rubber elastic vibration damping elements.

[0218] Some embodiments of the present invention further provide a storage medium storing a program executable by a processor. The program executable by the processor is used to implement the above-mentioned method for simulating the fatigue life of a rubber elastic vibration damping element when executed by the processor.

[0219] Finally, it should be noted that: the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0220] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or some technical features can be replaced by equivalents without departing from the spirit of the technical solution of the present invention, which should be included in the scope of the technical solution for protection of the present invention.

Claims

1. A method for simulating fatigue life of a rubber elastic vibration damping element, characterized in that: The following steps are involved: Step 1: Performing a performance test on the rubber material part of the rubber elastic vibration damping element to obtain performance parameters of the rubber material, wherein the performance parameters include constitutive model parameters, Mullins parameters, viscoelastic parameters and fatigue crack growth characteristic parameters; Step 2: Establishing a simulation model of the rubber elastic vibration damping element in finite element software, including establishing a three-dimensional finite element simulation model using solid elements and establishing a two-dimensional finite element simulation model using membrane elements; Step 3: inputting the performance parameters into the finite element software, applying axial cyclic load to the three-dimensional finite element simulation model for simulation calculation, and deriving the nominal strain of the three-dimensional finite element simulation model during the loading process; Step 4: performing a simulated fatigue calculation based on the performance parameter and the nominal strain of the three-dimensional finite element simulation model to obtain an initial simulated fatigue calculation result, wherein the initial simulated fatigue calculation result includes a simulated temperature of the rubber free surface; Step 5: assigning the simulated temperature of the rubber free surface to the corresponding membrane unit in the two-dimensional finite element simulation model, updating the temperature state of the two-dimensional finite element simulation model, re-performing the simulation calculation, and obtaining the nominal strain of the two-dimensional finite element simulation model; Step 6: Perform simulation fatigue calculation based on the performance parameter and the nominal strain of the surface two-dimensional finite element simulation model to obtain an intermediate simulation fatigue calculation result; Step 7: Calculating the simulation data of heat transfer of the membrane unit in the surface two-dimensional finite element simulation model based on the fatigue crack growth characteristic parameters in the finite element software; Step 8: Iteratively calculate the fatigue life result of the rubber free surface based on the intermediate simulation fatigue calculation result and the simulation data of the membrane unit heat transfer.

2. The method for simulating fatigue life of a rubber elastic vibration damping element according to claim 1, characterized in that: The method for obtaining the constitutive model parameters and Mullins parameters of the rubber material in step 1 includes the following steps: Designing a predetermined test temperature, a predetermined stretching rate, and a plurality of predetermined strain levels; Using a uniaxial electronic tensile testing machine and an equibiaxial tensile testing machine, uniaxial stretching and equibiaxial stretching are performed at a predetermined temperature and a predetermined stretching rate; The tensile test was carried out five times in a cycle for each predetermined strain level. The test curves of the loading section of the first cycle and the unloading section of the fifth cycle were selected. The fitting software was used to fit the Ogden hyperelastic constitutive model and the Ogden-Roxburgh pseudo-elastic model. The constitutive model parameters and Mullins parameters were obtained based on the fitting results. The expression of the Ogden hyperelastic constitutive model is: Among them, λ1, λ2, and λ3 are the principal stretching ratios in three directions, μi and αi are the material constitutive constants; The expression of the Ogden-Roxburgh pseudoelastic model is: Where η is the damage variable, W m is the strain energy density of the material from initial loading to unloading, is the strain energy density when the material is unloaded to a certain strain, r, m, β are all material parameters, erf(x) function is the error function, and the expression of erf(x) function is: Among them, ω is the integral variable and exp(x) function is the natural exponential function.

3. The method for simulating fatigue life of a rubber elastic vibration damping element according to claim 1, characterized in that: The method for obtaining the viscoelastic parameters of the rubber material in step 1 comprises the following steps: A DMA testing machine is used to perform strain scanning and frequency scanning on the rubber material at different temperatures, and the relationship curves between the loss modulus and strain and the loss modulus and frequency of the rubber material at different temperatures are obtained; Performing data fitting based on the relationship curve between the loss modulus and strain of the rubber material and the functional relationship between the loss modulus and strain of viscoelasticity to obtain the fitted material parameters at a predetermined temperature; The functional relationship between the loss modulus of the viscoelasticity and the strain is: Among them, E′ ∞ ′、E p ″、ε c , m, ΔE′ U ′ are different material parameters, and ΔE′ U ′=E0″-E′ ∞ ′; Based on the relationship curve between the loss modulus and strain of the rubber material and the functional relationship between the hysteresis energy density and strain, the hysteresis energy density at a predetermined frequency and a predetermined strain amplitude is calculated; The functional relationship between the hysteresis energy density and strain is: h=πG”e a 2 ; Where, h is the hysteresis energy density, G” is the loss modulus, and εa is the strain amplitude; The temperature coefficient is obtained by fitting based on the hysteresis energy density and the functional relationship between the hysteresis energy density and the temperature, and then the relationship curve between the hysteresis energy density and the temperature is obtained; The functional relationship between the hysteresis energy density and temperature is: Where h(θ) is the hysteresis energy density at a certain temperature, θ0 is the reference temperature, r is the temperature coefficient, and a is the process parameter; Calculating a reference strain rate at a predetermined strain amplitude based on a relationship curve between the loss modulus and the frequency of the rubber material and a functional relationship between the strain rate and the loading frequency; The functional relationship between the strain rate and the loading frequency is: in, is the reference strain rate, ε max is the maximum strain value, ε min is the minimum strain value, f is the loading frequency; Based on the reference strain rate and the functional relationship between the hysteresis energy density and the strain rate, the strain rate coefficient is fitted to obtain a hysteresis energy density-strain rate relationship curve; The functional relationship between the hysteresis energy density and the strain rate is: in, is the hysteresis energy density at a predetermined reference strain rate, is the strain rate, is the reference strain rate and a is the process parameter.

4. The method for simulating fatigue life of a rubber elastic vibration damping element according to claim 3, characterized in that: The method for obtaining the viscoelastic parameters of the rubber material in step 1 further includes the following steps: The experimental values ​​of the energy loss rate at the reference temperature, reference strain amplitude and reference strain rate are calculated based on the relationship curve between the loss modulus and strain of the rubber material and the calculation formula of the energy loss rate. The calculation formula of the energy loss rate is: Q=π·G”·e a 2 ·f; Among them, Q is the energy loss rate, G” is the loss modulus, εa is the strain amplitude, and f is the loading frequency; Based on the experimental values The calculation conditions are used to establish a simple shear finite element calculation model, and the simulation values ​​of the energy loss rate under the reference temperature, reference strain amplitude, and reference strain rate are calculated. Based on the experimental values and the simulation value The proportionality factor C used to enhance the consistency between the calculated results of the dissipated energy and the experimental results is calculated. The calculation formula of the proportionality factor C is:

5. The method for simulating fatigue life of a rubber elastic vibration damping element according to claim 1, characterized in that: The method for obtaining the fatigue crack growth characteristic parameter comprises the following steps: Select a plane tensile specimen of a rubber material, and prefabricate a crack of a predetermined length on the surface of the plane tensile specimen; Using an electromagnetic dynamic testing machine to perform quasi-static and dynamic tensile tests on the planar tensile specimen at different predetermined temperatures to obtain test results; Based on the test results, the tear energy T of any strain is calculated by combining the tear energy expression, the classical Thomas model and the strain energy density expression, and then the critical tear energy tc at different temperatures is calculated; The tearing energy is expressed as: T = WH; Where T is tearing energy, W is strain energy density, and H is the specimen height; The expression of the classic Thomas model is: Among them, rc is the critical crack growth rate, Tc is the critical tearing energy, and F is the exponential factor; The strain energy density expression is: Where σ is stress, ε is strain, i is the number of integration points, and ε i is the integration point strain.

6. The method for simulating fatigue life of a rubber elastic vibration damping element according to claim 5, characterized in that: The method for obtaining the fatigue crack growth characteristic parameter further comprises the following steps: Using an electromagnetic dynamic testing machine to perform a uniaxial tensile test on the plane tensile specimen at different predetermined temperatures, obtain the relationship between the non-full relaxation crack extension test load ratio R and F(R) at different predetermined temperatures; performing data fitting based on the Mars-Fatemi model to obtain fitting material parameters, and then obtain a full relaxation crack test cycle number-crack length curve; Among them, the loading conditions of the uniaxial tensile test include: Minimum strain ε min The maximum strain increases linearly with time until it reaches the required maximum strain ε max , cyclic stretching for the first predetermined number of times; wherein the minimum strain ε min =0; Maintain minimum strain ε min and the maximum strain ε max No change, cycle stretching for a second predetermined number of times; Maximum strain ε max remains unchanged, the minimum strain ε min Increasing with time, cyclically stretching a third predetermined number of times; The expression of the Mars-Fatemi model is: Where rc is the critical crack growth rate, Tc is the critical tearing energy, F(R) is the exponential factor, R is the ratio of the minimum tearing energy to the maximum tearing energy in the cycle, and F0, F1, F2, F3, and Fexp are all material parameters.

7. The method for simulating fatigue life of a rubber elastic vibration damping element according to claim 6, characterized in that: The method for obtaining the fatigue crack growth characteristic parameter further comprises the following steps: Using an electromagnetic dynamic testing machine to perform a uniaxial tensile test on the plane tensile specimen at different predetermined temperatures to obtain the relationship between the tear energy and the fatigue crack growth rate under the condition of R=0, and based on the relationship between the tear energy and the crack growth rate at different temperatures, the critical crack growth rate rc and the exponential factor F0 at different predetermined temperatures are calculated in combination with the classical Thomas model, thereby obtaining a full relaxation crack test cycle number-crack length curve; Among them, the loading conditions of the uniaxial tensile test include: The dynamic minimum strain is always 0, and the maximum strain increases linearly with time; The initial maximum strain was 15% of the clamping height, and the maximum strain at the end of the test was 60% of the clamping height.

8. The method for simulating fatigue life of a rubber elastic vibration damping element according to any one of claims 5 to 7, characterized in that: The method for obtaining the fatigue crack growth characteristic parameter further comprises the following steps: The uniaxial tensile test is used to test the number of uniaxial tensile cycle fractures of the rubber material under constant strain conditions to determine the effective size a0 of the initial crack size inside the rubber material; The expression of the effective size a0 is: Where N is the number of cycles, i.e. the tensile fatigue life of the specimen, and F is the exponential factor. c is the critical crack growth rate, W is the strain energy under a given strain, T c is the critical tearing energy.

9. A rubber elastic vibration damping element fatigue life simulation system, used to implement the rubber elastic vibration damping element fatigue life simulation method according to any one of claims 1 to 8, characterized in that: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the fatigue life simulation method of the rubber elastic vibration damping element according to any one of claims 1 to 8.

10. A storage medium storing a program executable by a processor, characterized in that: The program executable by the processor is used to implement the fatigue life simulation method of the rubber elastic vibration damping element as claimed in any one of claims 1 to 8 when executed by the processor.

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