A method and system for simulating the fatigue life of a rubber elastic damping element

Abstract

The application relates to a rubber elastic damping element fatigue life simulation method and system, which comprises the following steps: acquiring rubber performance parameters; establishing a simulation model in finite element software, including a rubber surface two-dimensional model and a solid three-dimensional model; inputting the performance parameters into the model for simulation calculation to obtain the nominal strain of the three-dimensional model and calculate initial simulation fatigue calculation results; updating the temperature state of the two-dimensional finite element simulation model based on the results and calculating the nominal strain of the two-dimensional model, then calculating intermediate simulation fatigue calculation results, meanwhile, simulation data of membrane element heat transfer of the two-dimensional model are derived based on the performance parameters, and the fatigue life results of the rubber free surface are obtained through iterative calculation based on the intermediate simulation fatigue calculation results and the simulation data of the membrane element heat transfer. The application fully considers the possibility that the material parameters of the rubber material change during the fatigue test process, can better reflect the temperature change of the rubber material in the rubber elastic damping element in actual application, and effectively improves the fatigue simulation precision.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rubber material fatigue life prediction, and particularly relates to a rubber elastic damping element fatigue life simulation method and system. BACKGROUND

[0002] The rubber elastic damping element has been widely used in the fields of rail transit and automobiles due to its unique nonlinear characteristics. 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 the rubber elastic damping element.

[0003] However, since the rubber material is a poor conductor of heat, during the process of bearing dynamic load, the stress-strain response of the material will change with the change of temperature. The existing rubber fatigue life calculation method based on finite element simulation technology usually does not consider the influence of temperature on the stress-strain response and other parameter characteristics of the rubber elastic damping element, resulting in insufficient simulation precision of the fatigue life and large differences between the simulation prediction results and the actual test results. SUMMARY

[0004] The application aims to solve one of the above technical problems, and provides a rubber elastic damping element fatigue life simulation method and system.

[0005] To achieve the above-mentioned purpose, the technical solution adopted by the application is:

[0006] A rubber elastic damping element fatigue life simulation method, comprising the following steps:

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

[0008] Step 2: Establish a simulation model of the rubber elastic damping element in 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;

[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 simulation fatigue calculation based on the performance parameters and the nominal strain of the three-dimensional finite element simulation model to obtain initial simulation fatigue calculation results, including the simulation temperature of the rubber free surface;

[0011] Step five: the simulation temperature of the rubber free surface is given to the corresponding membrane unit of the two-dimensional finite element simulation model, the temperature state of the two-dimensional finite element simulation model is updated, the simulation calculation is carried out again, and the nominal strain of the two-dimensional finite element simulation model is obtained;

[0012] Step six: based on the performance parameters and the nominal strain of the surface two-dimensional finite element simulation model, the simulation fatigue calculation is carried out, and the intermediate simulation fatigue calculation result is obtained;

[0013] Step seven: based on the fatigue crack propagation characteristic parameters, the simulation data of the membrane unit heat transfer in the surface two-dimensional finite element simulation model is calculated in the finite element software;

[0014] Step eight: based on the intermediate simulation fatigue calculation result and the simulation data of the membrane unit heat transfer, the fatigue life result of the rubber free surface is obtained through iterative calculation.

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

[0016] Designing predetermined test temperature, predetermined stretching rate and multiple predetermined strain levels;

[0017] Using a uniaxial electronic tensile testing machine and an equi-biaxial tensile testing machine, uniaxial tension and equi-biaxial tension are carried out at the predetermined temperature and the predetermined stretching rate;

[0018] Each predetermined strain level is cycled for five times of stretching test, the test curves of the loading section of the first cycle and the unloading section of the fifth cycle are selected, fitting software is used to carry out fitting based on the Ogden hyperelastic constitutive model and the Ogden-Roxburgh pseudo-elastic model, and the constitutive model parameters and the Mullins parameters are obtained based on the fitting result;

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

[0020]

[0021] Wherein, λ1, λ2 and λ3 are the principal tensile ratios in three directions, μ i and α i are material constitutive constants;

[0022] The expression of the Ogden-Roxburgh pseudo-elastic model is as follows:

[0023]

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

[0025]

[0026] wherein ω is an integral variable, and exp(x) is a natural exponential function.

[0027] In some embodiments of the present application, the viscoelastic parameters of the rubber material are obtained by fitting the curves of loss modulus versus strain and loss modulus versus frequency of the rubber material at different temperatures, and the method for obtaining the curves of loss modulus versus strain and loss modulus versus frequency, the curve of hysteresis energy density versus strain rate, and the curve of hysteresis energy density versus 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 one comprises the following steps:

[0029] The DMA tester is used to perform strain scanning and frequency scanning on the rubber material at different temperatures respectively, so as to obtain the curves of loss modulus versus strain and loss modulus versus frequency of the rubber material at different temperatures;

[0030] Based on the curve of loss modulus versus strain of the rubber material and the functional relationship between the viscoelastic loss modulus and strain, data fitting is performed to obtain the material parameters after fitting at a predetermined temperature.

[0031] The functional relationship between the viscoelastic loss modulus and strain is:

[0032]

[0033] wherein E" ∞ , E" p , ε c , m, and ΔE" U are different material parameters, and ΔE" U =E" ∞ .

[0034] Based on the curve of loss modulus versus 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 and obtained;

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

[0036] h=πG"ε a 2 .

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

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

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

[0040]

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

[0042] The reference strain rate at a predetermined strain amplitude is calculated based on the relationship curve between the loss modulus of the rubber material and the frequency and the functional relationship between the strain rate and the loading frequency.

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

[0044]

[0045] Wherein, 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.

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

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

[0048]

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

[0050] In some embodiments of the present application, the method for obtaining the viscoelastic parameters of the rubber material in step one further comprises the following steps:

[0051] The experimental value of the energy loss rate at the reference temperature, the reference strain amplitude and the reference strain rate is calculated based on the relationship curve between the loss modulus of the rubber material and the strain and the calculation formula of the energy loss rate.

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

[0053] Q = π·G''·εa a 2 ·f;

[0054] Wherein, Q is energy loss rate, G" is loss modulus, εa is strain amplitude, f is loading frequency;

[0055] Based on the experimental value The calculation condition, the simple shear finite element calculation model is established, and the simulation value of energy loss rate under the reference temperature, reference strain amplitude, reference strain rate is obtained

[0056] Based on the experimental value And simulation value The proportional factor C for enhancing the consistency of dissipated energy calculation result and experimental result is calculated, and the calculation formula of the proportional factor C is as follows:

[0057]

[0058] In some embodiments of the application, the fatigue crack propagation characteristic parameter is obtained by fitting the tear energy-strain curve, and the method for obtaining the tear energy-strain curve and fitting the parameter comprises the following steps:

[0059] Selecting a plane tensile sample of rubber material, a crack with a predetermined length is pre-prepared on the surface of the plane tensile sample;

[0060] Using an electromagnetic dynamic testing machine, quasi-static and dynamic tensile tests are carried out on the plane tensile sample at different predetermined temperatures, and test results are obtained;

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

[0062] The expression of tear energy is as follows:

[0063] T = WH;

[0064] Wherein, T is tear energy, W is strain energy density, and H is sample height;

[0065] The expression of the classical Thomas model is as follows:

[0066]

[0067] Wherein, r c Is the critical crack propagation rate, T c Is the critical tear energy, and F is the exponential factor;

[0068] The expression of strain energy density is as follows:

[0069]

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

[0071] In some embodiments of the present application, the fatigue crack propagation characteristic parameter is obtained by fitting the non-full relaxation crack test cycle number-crack length curve, and the method for obtaining the non-full relaxation crack test cycle number-crack length curve and fitting the fatigue crack propagation characteristic parameter comprises the following steps:

[0072] A uniaxial tensile test is performed on a flat tensile sample at different predetermined temperatures using an electromagnetic dynamic testing machine to obtain the relationship between the non-full relaxation crack propagation test load ratio R and F(R) at different predetermined temperatures; data fitting is performed based on the Mars-Fatemi model to obtain fitted material parameters, and then the full relaxation crack test cycle number-crack length curve is obtained;

[0073] wherein the loading conditions of the uniaxial tensile test include:

[0074] the minimum strain ε min remains unchanged, the maximum strain increases linearly with time until it increases to the required maximum strain ε max , and the sample is cyclically stretched for a first predetermined number of times; wherein the minimum strain ε min = 0.

[0075] the minimum strain ε min and the maximum strain ε max remain unchanged, and the sample is cyclically stretched for a second predetermined number of times.

[0076] the maximum strain ε max remains unchanged, and the minimum strain ε min increases with time, and the sample is cyclically stretched for a third predetermined number of times.

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

[0078]

[0079] wherein r c is the critical crack propagation 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 are all material parameters.

[0080] In some embodiments of the present application, the fatigue crack propagation characteristic parameter is obtained by fitting a full relaxation crack test cycle number-crack length curve, and the method for obtaining the full relaxation crack test cycle number-crack length curve and fitting the fatigue crack propagation characteristic parameter comprises the following steps:

[0081] A uniaxial tensile test is performed on a flat tensile sample at different predetermined temperatures using an electromagnetic dynamic testing machine to obtain the relationship between the tear energy and the fatigue crack propagation rate under the condition of R=0, and based on the relationship between the tear energy and the crack propagation rate at different temperatures, the critical crack propagation rate r c and the exponential factor F0 are calculated based on the classical Thomas model to obtain the full relaxation crack test cycle number-crack length curve.

[0082] The loading conditions of the uniaxial tensile test include:

[0083] The dynamic minimum strain is always 0, and the maximum strain linearly increases 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 application, the fatigue crack propagation characteristic parameter further includes uniaxial elongation fatigue, and the method for obtaining the uniaxial elongation fatigue comprises the following steps:

[0086] The uniaxial tensile test is used to test the uniaxial tensile cycle fracture times of the rubber material under a constant strain condition to determine the effective size a0 of the initial crack size inside the rubber material.

[0087] The expression of the effective size a0 is:

[0088]

[0089] Where N is the cycle number, i.e., the tensile fatigue life of the sample, and F is the exponential factor. c is the critical crack propagation rate, W is the strain energy under a given strain, and T c is the critical tear energy.

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

[0091] At least one processor;

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

[0093] When the at least one program is executed by the at least one processor, the at least one processor implements the above-mentioned rubber elastic damping element fatigue life simulation method.

[0094] Some embodiments of the present application further provide a storage medium, wherein a processor-executable program is stored, and the processor-executable program is used to implement the above-mentioned rubber elastic damping element fatigue life simulation method when executed by a processor.

[0095] The present application has the following beneficial effects:

[0096] The simulation method provided by the present application fully considers the possible changes of material parameters of rubber materials during fatigue tests, and can better reflect the temperature changes of rubber materials in rubber elastic damping elements in actual applications. In the fatigue life simulation calculation of rubber elastic damping elements in the fields of rail transit and automobiles, the prediction error of fatigue life can be controlled within 15%, and the fatigue simulation precision is effectively improved compared with the prior art. BRIEF DESCRIPTION OF DRAWINGS

[0097] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, specific embodiments of the present application will be described in detail below with reference to the drawings. For those skilled in the art, other drawings can also be obtained without creative labor on the premise of the drawings.

[0098] Figure 1 A flowchart of a rubber elastic damping element fatigue life simulation method;

[0099] Figure 2 A schematic diagram of the overall architecture of a rubber elastic damping element fatigue life simulation method;

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

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

[0102] Figure 5 An equi-biaxial tensile stress-strain curve measured by a specific embodiment of the present application;

[0103] Figure 6 A loss modulus-strain curve measured by a specific embodiment of the present application;

[0104] Figure 7 A loss modulus-frequency curve measured by a specific embodiment of the present application;

[0105] Figure 8 A loss modulus-temperature curve measured by a specific embodiment of the present application;

[0106] Figure 9A tear energy-strain curve measured for a specific embodiment of the present application;

[0107] Figure 10 A full relaxation crack test cycle number-crack length curve measured for a specific embodiment of the present application;

[0108] Figure 11 A non-full relaxation crack test cycle number-crack length curve measured for a specific embodiment of the present application;

[0109] Figure 12 A life cloud map obtained from simulation calculation for a specific embodiment of the present application. DETAILED DESCRIPTION

[0110] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is described and explained below in connection with the 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 by the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of the present application.

[0111] It should be noted that the terms used herein are only intended to describe specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should be understood that the terms "comprise" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units does not have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to the process, method, product or device.

[0112] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0113] The technical solutions of the present application are described in detail below in connection with specific embodiments and the accompanying drawings.

[0114] As shown in the accompanying Figure 1 - the accompanying Figure 12 In one illustrative embodiment of the simulation method for fatigue life of a rubber elastic damping element according to the present application, the simulation method comprises the following steps.

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

[0116] In some embodiments of the present application, the constitutive model parameters and Mullins parameters are obtained by fitting uniaxial tensile stress-strain curves, plane tensile stress-strain curves, equibiaxial stress-strain curves and bulk modulus.

[0117] The uniaxial tensile stress-strain curves are obtained by uniaxial tensile test using a quasi-static uniaxial tensile testing machine, with a loading speed controlled at 40 mm / min. Since the temperature of the rubber material continuously rises during the dynamic load, at least 3-5 groups of test temperatures are selected for the uniaxial tensile test, with a temperature interval of at least 10°C. The uniaxial tensile stress-strain curves obtained under the loading conditions provided in this embodiment are shown in FIG. 1. Figure 3

[0118] The plane tensile stress-strain curves are obtained by uniaxial tensile test using a quasi-static uniaxial tensile testing machine, with a loading speed controlled at 40 mm / min. Since the temperature of the rubber material continuously rises during the dynamic load, at least 3-5 groups of test temperatures are selected for the uniaxial tensile test, with a temperature interval of at least 10°C. The uniaxial tensile stress-strain curves obtained under the loading conditions provided in this embodiment are shown in FIG. 2. Figure 4

[0119] The biaxial tensile stress-strain curves are obtained by quasi-static biaxial tensile test using a multi-axial tensile testing machine, with a loading speed controlled at 40 mm / min. Since the temperature of the rubber material continuously rises during the dynamic load, at least 3-5 groups of test temperatures are selected for the biaxial tensile test, with a temperature interval of at least 10°C. The uniaxial tensile stress-strain curves obtained under the loading conditions provided in this embodiment are shown in FIG. 3. Figure 5

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

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

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

[0123] ​​​The uniaxial tensile (UT) and equi-biaxial tensile (ET) tests are respectively carried out at four strain levels of 25%, 50%, 75% and 100% at room temperature 23 DEG C and a tensile rate of 40 mm / min using a uniaxial electronic tensile testing machine and an equi-biaxial tensile testing machine. The tensile test is cyclically carried out five times at each predetermined strain level, and the test curves of the loading section of the first cycle and the unloading section of the fifth cycle are selected, fitted based on the Ogden hyperelastic constitutive model and the Ogden-Roxburgh pseudo-elastic model using fitting software, and the constitutive model parameters and Mullins parameters are obtained based on the fitting results;

[0124] The expression of the Ogden hyperelastic constitutive model is as follows:

[0125]

[0126] Wherein, λ1, λ2, λ3 are the principal tensile ratios in three directions, μ i and α i are material constitutive constants.

[0127] The expression of the Ogden-Roxburgh pseudo-elastic model is as follows:

[0128]

[0129] Wherein, η is a damage variable, W m is the strain energy density of the material from initial loading to unloading, is the strain energy density of the material from unloading to a certain strain, r, m, β are material parameters, and erf(x) function is an error function.

[0130]

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

[0132] In some embodiments of the present application, the viscoelastic parameters are obtained based on the fitting of the loss modulus-strain curve, the loss modulus-frequency curve, the hysteresis energy density-temperature curve and the loss modulus-temperature curve, wherein the loss modulus-strain scanning curve and the loss modulus-frequency scanning curve are obtained by dynamic tensile test using a DMA Q800 testing machine, and the hysteresis energy density-temperature curve and the loss modulus-temperature 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 curve comprises the following steps.

[0134] The DMA tester is used to obtain the relationship between the loss modulus of the rubber material and the strain at different temperatures by strain scanning of the rubber material at 30°C, 40°C, 50°C, 60°C and 70°C respectively, with the scanning range being 0.1% to 5%. The DMA tester is used to obtain the relationship between the loss modulus of the rubber material and the frequency at different temperatures by frequency scanning of the rubber material at 30°C, 40°C, 50°C, 60°C and 70°C respectively, with the scanning range being 1 Hz to 25 Hz.

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

[0136] The method for obtaining the relationship curve between the hysteresis energy density and the temperature comprises the following steps.

[0137] The relationship between the loss modulus of the rubber material and the strain at the same temperature is selected, and in this embodiment, 30°C is selected as the reference curve. Based on the function relationship between the viscoelastic loss modulus and the strain at this temperature, data fitting is performed to obtain the material parameters after fitting.

[0138] The function relationship between the viscoelastic loss modulus and the strain is as follows:

[0139]

[0140] wherein E″ ∞ , E″ p , ε c , m and ΔE″ U are different material parameters obtained by fitting, and ΔE″ U =E″0-E″ ∞ .

[0141] The hysteresis energy density at a certain strain amplitude is calculated based on the function relationship h=πG”ε a 2 .

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

[0143] Based on the strain information fed back by the fatigue loading of the rubber elastic damping element, the strain amplitude corresponding to the relationship curve between the loss modulus of the rubber material and the strain at different temperatures is selected, and the temperature coefficient is fitted based on the function relationship h=πG”ε , and the hysteresis energy density-temperature curve is obtained.

[0144] Wherein, 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 hysteresis energy density-strain rate relationship curve at a certain temperature and a certain strain amplitude can be obtained from the relationship curve of the loss modulus of the rubber material and the frequency at different temperatures obtained by the above DMA tester.

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

[0147] The relationship between the strain rate and the loading frequency is The reference strain rate at a certain strain amplitude is calculated.

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

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

[0150] Wherein, 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 application, the viscoelastic parameters further comprise a proportionality factor for enhancing the consistency of the calculation results of dissipated energy and experimental results.

[0152] The calculation steps of the proportionality factor comprise:

[0153] The experimental value of the energy loss rate at the reference temperature, the reference strain amplitude and the reference strain rate is calculated based on the relationship curve of the loss modulus of the rubber material and the strain and the calculation formula of the energy loss rate

[0154] Wherein, the calculation formula of the energy loss rate is:

[0155] Q = π·G''·εa·f. a 2

[0156] Wherein, 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 value ​The simulation values of the energy loss rate under the reference temperature, the reference strain amplitude and the reference strain rate are calculated by establishing a simple shear finite element calculation model under the calculation condition

[0158] Based on the experimental values and the simulation values A proportional factor C is calculated for enhancing the consistency of the dissipated energy calculation results and the experimental results, and the calculation formula of the proportional factor C is:

[0159]

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

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

[0162] The tearing energy-strain curve, i.e., the critical tearing 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 obtained by quasi-static and dynamic tensile tests through an electromagnetic dynamic test system. During the test process, the tensile deformation rate of the rubber material is 0.01 / sec, and the tensile rate is slow enough to meet the quasi-static tensile state. And during the whole test process, the rubber material is in a pure shear state. Since the temperature of the rubber material continuously rises during the dynamic load, at least 3-5 groups of test temperatures are selected for the uniaxial tensile test, and the temperature interval is at least 10℃. In the embodiment, the tearing energy-strain curve measured under the above loading condition is shown in the attached Figure 9 The full relaxation crack test cycle number-crack length curve is shown in the attached Figure 10 The non-full relaxation crack test cycle number-crack length curve is shown in the attached Figure 11 The thermodynamic performance parameters are obtained by detection mechanisms.

[0163] The tearing energy-strain curve, i.e., the critical tearing energy curve, in the embodiment, the method for obtaining the critical tearing energy curve specifically includes the following steps.

[0164] ​A rubber material is selected as a plane tensile sample, the plane tensile sample has a size of 146mm*10mm*1mm, a 25mm long crack is pre-prepared on the surface of the plane tensile sample, and the tensile deformation rate of the plane tensile sample is 0.01 / sec.

[0165] The plane tensile sample is subjected to a quasi-static and dynamic tensile test at a test temperature of 23℃, 45℃ and 70℃ respectively by using an electromagnetic dynamic testing machine, and a test result is obtained.

[0166] Based on the test result, a tear energy expression, a classical Thomas model and a strain energy density expression are combined to calculate a tear energy T at any strain, and then a critical tear energy T at different temperatures is calculated. c , and then a critical tear energy curve is obtained.

[0167] The tear energy expression is as follows:

[0168] T=WH;

[0169] Wherein, T is the tear energy, W is the strain energy density, and H is the sample height;

[0170] The expression of the classical Thomas model is as follows:

[0171]

[0172] Wherein, r c is the critical crack propagation rate, T c is the critical tear energy, and F is an exponential factor;

[0173] The strain energy density expression is as follows:

[0174]

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

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

[0177] The plane tensile sample is subjected to a uniaxial tensile test at a test temperature of 23℃, 45℃ and 70℃ respectively by using an electromagnetic dynamic testing machine, and the relationship between the non-full relaxation crack propagation test load ratio R and F(R) at different predetermined temperatures is obtained; based on the Mars-Fatemi model, the data is fitted to obtain the fitting material parameters, and then the non-full relaxation crack test cycle number-crack length curve is obtained.

[0178] Wherein, the loading condition of the uniaxial tensile test is as follows:

[0179] minimum strain min The maximum strain is kept constant and linearly increases with time until it increases to the required maximum strain max , and the sample is cyclically stretched for a first predetermined number of times; wherein the minimum strain min = 0;

[0180] The minimum strain min and the maximum strain max are kept constant, and the sample is cyclically stretched for a second predetermined number of times;

[0181] The maximum strain max is kept constant, and the minimum strain min increases with time, and the sample is cyclically stretched for a third predetermined number of times;

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

[0183]

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

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

[0186] The uniaxial tensile test is performed on the flat tensile sample at test temperatures of 23°C, 45°C and 70°C respectively using an electromagnetic dynamic testing machine, so as to obtain the relationship between the tearing energy and the fatigue crack growth rate under the condition of R = 0, and based on the relationship between the tearing energy and the crack growth rate at different temperatures, the critical crack growth rate r c and the exponential factor F0 at different predetermined temperatures are calculated based on the classic Thomas model, and then the cycle number-crack length curve of the full relaxation crack test is obtained.

[0187] During the test process of obtaining the cycle number-crack length curve of the full relaxation crack test, the loading conditions of the test are as follows:

[0188] The dynamic minimum strain is constantly 0, and the maximum strain linearly increases 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 the uniaxial elongation fatigue specifically comprises the following steps.

[0190] The uniaxial tensile cyclic fracture times of the rubber material under the condition of constant strain are tested by using a uniaxial tensile test, and the effective size a0 of the initial crack size in the rubber material is determined;

[0191] The expression of the effective size a0 is:

[0192]

[0193] Wherein, N is the cycle number, i.e. the tensile fatigue life of the sample, F is an exponential factor, and r is the crack propagation rate. c is the critical crack propagation rate, W is the strain energy under the given strain, T is the temperature, and D is the critical tearing energy. c is the critical tearing energy.

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

[0195] Step three: the performance parameters obtained in step one are input into the finite element software, the three-dimensional finite element simulation model is subjected to simulation calculation under the action of the axial cyclic load, and the nominal strain history NE of the three-dimensional finite element simulation model during the loading process is derived.

[0196] Step four: define the calculation conditions of the rubber elastic damping element, import the constitutive model parameters, Mullins parameters, viscoelastic parameters, and fatigue crack propagation characteristic parameters obtained in step one and the nominal strain NE file of the three-dimensional finite element simulation model into the Endurica software, perform simulation fatigue calculation, use the Kraus self-generation heat model to iteratively calculate the rubber material heat generation rate-temperature field of the calculation model until the temperature of the calculation model reaches stability (generally, the temperature difference is ≤0.1℃), output the quasi-static temperature results and the dissipation results, and obtain the initial simulation fatigue calculation results. The initial simulation fatigue calculation results at least include the simulation temperature of the free surface of the rubber.

[0197] Step five: derive the simulation temperature of the free surface of the rubber obtained in step four, and assign the simulation temperature of the free surface of the rubber to the corresponding membrane elements in the two-dimensional finite element simulation model through a self-programming 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 six: re-input the constitutive model parameters, Mullins parameters, nominal strain NE of the two-dimensional finite element simulation model and the simulation temperature of the rubber free surface into the Endurica software for simulation calculation, obtain the intermediate simulation fatigue calculation results, and generate hfi files.

[0199] Step seven: input the mass density, convective heat transfer coefficient, specific heat capacity and thermal conductivity of the rubber material obtained in step one into the property module of the finite element software, obtain the simulation data of the membrane element heat transfer in the two-dimensional finite element simulation model, and export as inp files.

[0200] Step eight: based on the intermediate simulation fatigue calculation results and the simulation data of the membrane element heat transfer, the hfi files obtained in step six and the inp files obtained in step seven are iteratively calculated by a self-compiled program to obtain the fatigue life results of the rubber free surface.

[0201] The beneficial effects of the present application are illustrated by a specific embodiment as follows:

[0202] In this embodiment, the Ogden model material parameters obtained by fitting in step one 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 propagation 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 Ogden model fitting material parameters

[0204] [Mu1] [alpha]1 [Mu2] [alpha]2 μ3 [Alpha]3 0.005 9.19 0.49 2.12 0.49 0.14

[0205] Table 2 Mullins model fitting material parameters

[0206] r m β 2.12 0.36 0.04

[0207] Table 3 Viscoelastic parameters

[0208] [E" ∞ ]]> [E" ∞ ]]> e c ]] m 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 propagation characteristic parameters

[0210]

[0211] Table 5 Thermodynamic performance parameters

[0212]

[0213] Based on the data in Tables 1 to 5 above, the simulation calculation is performed according to the procedures of steps two to seven, and the life cloud map of the rubber elastic damping element is shown in FIG. 1. Figure 12As shown, the fatigue life result of the rubber free surface is 1.134e5 times, the average value of the fatigue test life of the three damping elements is 105469 times, and the deviation is +7.5%. The fatigue life simulation deviation of the present application is within 15%, which can effectively represent the fatigue life of the rubber damping element.

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

[0215] At least one processor.

[0216] At least one memory for storing at least one program.

[0217] When the at least one program is executed by the at least one processor, the at least one processor implements the above-mentioned rubber elastic damping element fatigue life simulation method.

[0218] Some embodiments of the present application further provide a storage medium, wherein a processor executable program is stored, and the processor executable program is used to implement the above-mentioned rubber elastic damping element fatigue life simulation method when executed by the processor.

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

[0220] The above embodiments are only used to illustrate the technical solutions of the present application but not to limit it; although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the specific embodiments of the present application can be modified or some technical features can be replaced by equivalent ones; without departing from the spirit of the technical scheme of the present application, they should be covered in the technical scheme range of the present application.

Claims

1. A method for simulating the fatigue life of a rubber elastic vibration damping element, characterized in that, Includes the following steps: Step 1: Perform performance tests on the rubber material component of the rubber elastic damping element to obtain the performance parameters of the rubber material. The performance parameters include constitutive model parameters, Mullins parameters, viscoelastic parameters, and fatigue crack propagation characteristic parameters. Step 2: Establish a simulation model of the rubber elastic damping element in the 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: 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; 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 the initial simulated fatigue calculation results, which include the simulated temperature of the rubber free surface. Step 5: Assign the simulated temperature of the free surface of the rubber to the corresponding membrane element in the two-dimensional finite element simulation model, update the temperature state of the two-dimensional finite element simulation model, and re-perform the simulation calculation to obtain the nominal strain of the two-dimensional finite element simulation model. Step 6: Perform simulated fatigue calculations based on the performance parameters and the nominal strain of the two-dimensional finite element simulation model of the surface to obtain intermediate simulated fatigue calculation results; Step 7: Calculate the simulation data of heat transfer in the membrane unit of the two-dimensional finite element simulation model of the surface based on the fatigue crack propagation characteristic parameters in the finite element software; Step 8: Based on the intermediate simulation fatigue calculation results and the simulation data of heat transfer of the membrane unit, iterative calculation is performed to obtain the fatigue life result of the rubber free surface.

2. The fatigue life simulation method for rubber elastic vibration damping elements according to claim 1, characterized in that, The method for obtaining the constitutive model parameters and Mullins parameters of the rubber material in step one includes the following steps: The design specifies the test temperature, tensile rate, and multiple strain levels. Uniaxial and biaxial tensile tests were performed at predetermined temperatures and tensile rates using a uniaxial electronic tensile testing machine and an equal biaxial tensile testing machine. Five tensile tests were performed for each predetermined strain level. The test curves of the loading segment of the first cycle and the unloading segment of the fifth cycle were selected. The Ogden hyperelastic constitutive model and the Ogden-Roxburgh pseudoelastic model were fitted using fitting software. The constitutive model parameters and Mullins parameters were obtained based on the fitting results. The expression for the Ogden hyperelastic constitutive model is: ； in, , , These are the principal stretch ratios in three directions. and The constitutive constant of the material; The expression for the Ogden-Roxburgh pseudoelasticity model is: ； in, As a damage variable, The strain energy density of the material from initial loading to unloading. The strain energy density is the pressure at which the material is unloaded to a certain strain. , , These are all material parameters. The function is the error function. The function expression is: ； in, For integration variables, The function is a natural exponential function.

3. The fatigue life simulation method for rubber elastic vibration damping elements according to claim 1, characterized in that, The method for obtaining the viscoelastic parameters of the rubber material in step one includes the following steps: The rubber material was subjected to strain scanning and frequency scanning at different temperatures using a DMA testing machine to obtain the relationship curves between the loss modulus and strain and between the loss modulus and frequency of the rubber material at different temperatures. 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, data fitting is performed to obtain the fitted material parameters at a predetermined temperature. The functional relationship between the loss modulus of the viscoelasticity and strain is as follows: ； in, , , , , They are different material parameters, and ; 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 strain of the rubber material and the functional relationship between the hysteresis energy density and strain. The functional relationship between the hysteresis energy density and strain is as follows: ； in, For hysteresis energy density, For loss modulus, This refers to the strain amplitude; Based on the hysteresis energy density and the functional relationship between hysteresis energy density and temperature, the temperature coefficient is obtained, and then the relationship curve between hysteresis energy density and temperature is obtained. The functional relationship between the hysteresis energy density and temperature is as follows: ； in, Let be the hysteresis energy density at a certain temperature. For reference temperature, For temperature coefficient, For process parameters; The reference strain rate at the predetermined strain amplitude is calculated based on the relationship curve between the loss modulus of the rubber material and frequency, and the functional relationship between strain rate and loading frequency. The functional relationship between the strain rate and the loading frequency is as follows: ； in, For reference strain rate, The maximum strain value, The minimum strain value, Loading frequency; Based on the reference strain rate and the functional relationship between hysteresis energy density and strain rate, the strain rate coefficient is fitted to obtain the relationship curve between hysteresis energy density and strain rate. The functional relationship between the hysteresis energy density and the strain rate is as follows: ； in, The hysteresis energy density at a predetermined reference strain rate, For strain rate, For reference strain rate, For process parameters.

4. The fatigue life simulation method for rubber elastic vibration damping elements according to claim 3, characterized in that, The method for obtaining the viscoelastic parameters of rubber materials in step one also includes the following steps: Based on the relationship curve between the loss modulus and strain of the rubber material and the formula for calculating the energy loss rate, experimental values ​​of the energy loss rate at the reference temperature, reference strain amplitude, and reference strain rate were calculated. ; The formula for calculating the energy loss rate is: ； in, Energy loss rate, For loss modulus, For strain amplitude, Loading frequency; Based on the experimental values Under the given computational conditions, a simple shear finite element calculation model was established, and simulated values ​​of the energy loss rate at reference temperature, reference strain amplitude, and reference strain rate were obtained. ; Based on the experimental values and the simulation values Calculate the scaling factor used to improve the agreement between calculated and experimental results for dissipated energy. The scaling factor The calculation formula is: 。 5. The fatigue life simulation method for rubber elastic vibration damping elements according to claim 1, characterized in that, The method for obtaining the fatigue crack propagation characteristic parameters includes the following steps: Select a planar tensile specimen of rubber material and pre-form a crack of a predetermined length on the surface of the planar tensile specimen. The planar tensile specimen was subjected to quasi-static and dynamic tensile tests at different predetermined temperatures using an electromagnetic dynamic testing machine to obtain test results. Based on the experimental results, the tearing energy T for any strain is calculated by combining the expression for tearing energy, the classical Thomas model, and the expression for strain energy density, and then the critical tearing energy tc at different temperatures is calculated. The expression for the tearing energy is: ； in, For tearing energy, For strain energy density, The height of the sample; The expression for the classic Thomas model is: ； in, The critical crack propagation rate. The critical tearing energy, It is an exponential factor; The expression for the strain energy density is: ； in, For stress, In response, The number of integration points. For the integral point strain.

6. The fatigue life simulation method for rubber elastic vibration damping elements according to claim 5, characterized in that, The method for obtaining the fatigue crack propagation characteristic parameters further includes the following steps: The planar tensile specimen was subjected to uniaxial tensile tests at different predetermined temperatures using an electromagnetic dynamic testing machine to obtain the relationship between the load ratio R and F(R) of the non-fully relaxed crack propagation test at different predetermined temperatures; the data was fitted based on the Mars-Fatemi model to obtain the fitted material parameters, and then the fully relaxed crack test cycle number-crack length curve was obtained. The loading conditions for the uniaxial tensile test include: Minimum strain The maximum strain remains constant and increases linearly with time until it reaches the required maximum strain. Cyclic stretching for a first predetermined number of times; where the minimum strain ; Maintain minimum strain and maximum strain The cycle continues for the second predetermined number of times; Maximum strain Remain constant, minimum strain As time increases, the cycle stretches for the third predetermined number of times; The expression for the Mars-Fatemi model is: ； ； in, The critical crack propagation rate. The critical tearing energy, As an exponential factor, It is the ratio of the minimum tearing energy to the maximum tearing energy in the cycle. , , , , All of these are material parameters.

7. The fatigue life simulation method for rubber elastic vibration damping elements according to claim 6, characterized in that, The method for obtaining the fatigue crack propagation characteristic parameters further includes the following steps: The planar tensile specimens were subjected to uniaxial tensile tests at different predetermined temperatures using an electromagnetic dynamic testing machine to obtain the relationship between tear energy and fatigue crack propagation rate under the condition of R=0. Based on the relationship between tear energy and crack propagation rate at different temperatures, the critical crack propagation rate at different predetermined temperatures was calculated using the classical Thomas model. and exponential factors Thus, the number of cycles in the fully relaxed crack test versus the crack length curve is obtained; The loading conditions for the uniaxial tensile test include: The dynamic minimum strain is always 0, while 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 fatigue life simulation method for rubber elastic vibration damping elements according to any one of claims 5-7, characterized in that, The method for obtaining the fatigue crack propagation characteristic parameters further includes the following steps: Uniaxial tensile testing was used to determine the number of cyclic fractures of rubber materials under constant strain conditions, thereby determining the effective size of the initial crack within the rubber material. ; The effective size The expression is: ； in, This refers to the number of cycles, i.e., the tensile fatigue life of the specimen. As an exponential factor, The critical crack propagation rate. The strain energy under a given strain, This is the critical tearing energy.

9. A fatigue life simulation system for rubber elastic vibration damping components, used to implement the fatigue life simulation method for rubber elastic vibration damping components according to any one of claims 1-8, 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 for rubber elastic damping elements as described in any one of claims 1-8.

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

Images