Railway vehicle rubber element service aging prediction method

Abstract

This invention relates to a method for predicting the service aging of rubber components in rail vehicles, comprising: deriving an analytical model of the viscoelastic dynamic characteristics of the rail vehicle rubber components based on the fractional derivative constitutive equation; acquiring the rail vehicle rubber components to be tested, conducting rubber aging tests and dynamic mechanical performance tests, and identifying parameters of the analytical model of the viscoelastic dynamic characteristics of the rail vehicle rubber components based on the test data; constructing a three-dimensional dynamic stiffness model of the rail vehicle rubber components based on the analytical model of the viscoelastic dynamic characteristics of the rail vehicle rubber components after parameter identification; establishing a p-T-t ternary mathematical model based on the relationship between the change of dynamic mechanical properties of the rubber vibration damping components with aging time and the relationship with the change rate of dynamic stiffness, and obtaining a service aging performance model of the rail vehicle rubber components with temperature and time based on the test data. Compared with the prior art, this invention provides a theoretical reference for the prediction of aging performance, life assessment, and parameter design of rail vehicle rubber vibration damping components.

Description

Technical Field

[0001] This invention relates to the field of performance prediction technology for rail transit equipment and facilities, and in particular to a method for predicting the service aging of rubber components in rail vehicles. Background Technology

[0002] With the rapid development of high-speed rail technology, while train speeds have increased significantly, higher demands have been placed on overall performance, including comfort and safety. During operation, external excitations such as track irregularities severely impact train comfort and safety. To improve overall train performance, rubber vibration damping elements are widely used in high-speed train suspension systems. These elements absorb vibrations and store the energy generated, thus mitigating vibrations; simultaneously, their high damping characteristics effectively attenuate vibrations and reduce their transmission to the car body. However, rubber ages over time, causing changes in the damping performance of rubber vibration damping elements, even rendering them unusable. This poses a severe challenge to the comfort and safety of high-speed trains. Rubber vibration damping elements operate under high temperature and high load conditions for extended periods, and the aging of rubber often lacks obvious signs, potentially leading to unpredictable accidents. Therefore, accurate assessment and prediction of the aging performance of rubber vibration damping elements are crucial. To prevent secondary hazards caused by rubber aging, it is essential to accurately understand the aging process of rubber, allowing for timely replacement of aged rubber products. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art by providing a method for predicting the service aging of rubber components in rail vehicles, and to correctly evaluate and predict the aging performance of rubber vibration damping components.

[0004] The objective of this invention can be achieved through the following technical solutions:

[0005] A method for predicting the service aging of rubber components in rail vehicles includes the following steps:

[0006] Based on the fractional derivative constitutive equation, a model for analyzing the viscoelastic dynamics of rubber components in rail vehicles is derived.

[0007] Obtain the rubber components of the rail vehicle to be tested, conduct rubber aging tests and dynamic mechanical property tests, and identify the parameters of the viscoelastic dynamic characteristic analysis model of the rail vehicle rubber components based on the test data;

[0008] Based on the viscoelastic dynamics analysis model of the rubber components of the rail vehicle after parameter identification, a three-dimensional dynamic stiffness model of the rubber components of the rail vehicle is constructed.

[0009] Based on the relationship between the dynamic mechanical properties of rubber vibration damping components and aging time and the relationship between the dynamic stiffness change rate, a pTt ternary mathematical model is established. Based on experimental data, a service aging performance model of railway vehicle rubber components with temperature and time is obtained to predict the aging degree of railway vehicle rubber components.

[0010] Furthermore, the analysis model of the viscoelastic dynamic characteristics of the rubber components of the rail vehicle is a four-parameter three-element fractional derivative model constructed based on the fractional derivative constitutive equation. This four-parameter three-element fractional derivative model includes a linear spring and a fractional derivative model connected in series, which are used to calculate the energy storage modulus and the energy dissipation modulus.

[0011] Furthermore, the expression for the four-parameter, three-element fractional derivative model is:

[0012]

[0013] In the formula, E * (ω) is the complex modulus, E1(ω) is the storage modulus, E2(ω) is the dissipation modulus, p1, α, q0, q1 are unknown material model parameters, and ω is the angular frequency.

[0014] Furthermore, the four-parameter, three-element fractional derivative model also includes calculating a loss factor, which is the tangent of the loss angle used to describe the magnitude of the loss. The expression for calculating the loss factor is as follows:

[0015]

[0016] In the formula, As the loss factor, This is the phase difference caused by the asynchronous changes in strain and stress in rubber.

[0017] Furthermore, the parameter identification process specifically includes:

[0018] Obtain a hot air aging test chamber and, after full preheating, place the rubber components of the rail vehicle under test inside for hot-oxygen aging.

[0019] The temperature scanning range and constant test loading frequency of the dynamic temperature scanning test were set to determine the dynamic mechanical properties of rubber as a function of temperature.

[0020] The frequency scanning range and constant test temperature of the dynamic frequency scanning test were set, and the dynamic mechanical properties of rubber were measured as a function of load frequency under different constant temperatures.

[0021] Based on the experimental data from dynamic temperature scanning and dynamic frequency scanning tests, the parameters of the viscoelastic dynamics analysis model for the rubber components of rail vehicles were identified using the multi-objective nonlinear least squares method.

[0022] Furthermore, when the rubber component of the track vehicle under test is a cuboid rubber component, the expression for the three-dimensional dynamic stiffness model of the track vehicle rubber component is:

[0023]

[0024] In the formula, K x1 K y1 and K z1 Let be the stiffness along the x, y, and z axes in the shear direction, respectively; F be the tensile and compressive external force; Δz be the displacement deformation along the z-axis; S be the cross-sectional area; and a, b, and h be the length, width, and height of the rubber component of the track vehicle under test, respectively, in meters. z The z-axis shape factor is E; E is the elastic modulus, E1 and E2 are the storage modulus and dissipation modulus calculated by the viscoelastic dynamics analysis model of the rubber component of the rail vehicle, respectively; G is the shear modulus, m x and m y denoted by and y, respectively, the shape factors along the x and y axes of the cuboid, μ is the Poisson's ratio of natural rubber, and n is the ratio of the constrained area to the free area.

[0025] Furthermore, when the rubber element of the rail vehicle is a V-shaped rubber vibration damping element, which is composed of two cuboid rubber elements arranged at a specific angle, the expression for the three-dimensional dynamic stiffness model of the rail vehicle rubber element is:

[0026]

[0027] In the formula, K x K y and K z θ represents the stiffness in the x-axis, y-axis, and z-axis directions, respectively, and θ is the angle between the z-axis of the V-shaped rubber damping element and the vertical direction.

[0028] Furthermore, the expression for the relationship between the change in the dynamic mechanical properties of the rubber vibration damping element and aging time is as follows:

[0029]

[0030] In the formula, f(p) represents the change in dynamic mechanical properties of the rubber vibration damping element, A is the experimental constant, t is the aging time, k is the thermo-oxidative aging reaction rate, λ is a constant, 0≤λ≤1, and Δ is a sign factor. When the degree of aging f(p) increases with the aging time t, it is taken as +, otherwise it is taken as -.

[0031] The expression for the relationship between the dynamic mechanical properties of the rubber vibration damping element and the rate of change of dynamic stiffness is as follows:

[0032] f(p) = 1 - ε

[0033]

[0034] In the formula, ε is the rate of change of dynamic stiffness, K is the initial dynamic stiffness of the rubber before aging, and K′ is the dynamic stiffness of the rubber after aging.

[0035] Furthermore, the pTt ternary mathematical model includes the relationship between dynamic stiffness and aging degree, as well as the relationship between the changes in the dynamic mechanical properties of the rubber damping element and aging time. The expression for the relationship between dynamic stiffness and aging degree is as follows:

[0036]

[0037] Furthermore, when the rubber element of the rail vehicle is a V-shaped rubber vibration damping element, the average value of the energy storage modulus and energy dissipation modulus at a certain frequency is used to replace the energy storage modulus and energy dissipation modulus at each temperature in the low-frequency rubber state stage, so as to calculate the initial dynamic stiffness.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (1) This invention analyzes the variation law of the dynamic mechanical property parameters of rubber through accelerated aging test and dynamic mechanical property test; adopts nonlinear least squares method to identify the parameters of the established rubber viscoelastic constitutive model based on the results of rubber dynamic mechanical property test; based on the triaxial dynamic stiffness calculation method of V-type rubber vibration damping element, combined with the Arrhenius equation and the variation law of the viscoelastic dynamic mechanical property parameters of rubber element with time, a thermo-oxidative aging performance evolution model of V-type rubber vibration damping element is established; providing theoretical reference for the aging performance prediction, life assessment and parameter design of rubber vibration damping element of rail vehicle.

[0040] (2) The present invention conducted accelerated thermo-oxidative aging tests and dynamic thermomechanical tests on the rubber part of the vibration damping element to explore the influence of temperature, frequency and aging time on the dynamic mechanical properties of rubber (including: storage modulus, energy dissipation modulus and loss factor).

[0041] (3) This invention establishes a four-parameter, three-element fractional derivative model for rubber components by introducing the Scott-Blair fractional element model. Based on the test results of the dynamic mechanical properties of rubber components, the parameters of the rubber viscoelastic constitutive model are identified with high precision.

[0042] (4) This invention proposes a method for calculating the three-dimensional dynamic stiffness of V-shaped rubber vibration damping elements by introducing a shape factor. Using the dynamic stiffness of the rubber vibration damping element as an aging index parameter, and combining the empirical formula for dynamic performance aging and the Arrhenius equation, a prediction model for the service life of rubber vibration damping elements in the low-frequency range is established.

[0043] (5) This invention establishes a rigid-flexible coupled dynamic model for high-speed trains. The effects of external environment, external excitation frequency, and thermo-oxidative aging on the coupled vibration of the car body and undercarriage equipment, as well as the vertical Sperling stability index, were analyzed and studied. The results show that rubber aging significantly exacerbates the coupled vibration of the car body and undercarriage equipment. Rubber aging mainly affects the dominant frequency peak appearing near the first-order vertical bending frequency. As the rubber gradually ages, changes in vibration energy distribution and a shift in the dominant vibration frequency occur. With increasing service life, the train's vertical Sperling stability index shows a gradually increasing trend. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating a method for predicting the service aging of rubber components in rail vehicles, provided in an embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram of a four-parameter, three-element fractional derivative model provided in an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of the parameter identification process for a viscoelastic constitutive model of a rubber component in a rail vehicle, provided in an embodiment of the present invention.

[0047] Figure 4 This is a schematic diagram of a cuboid rubber element provided in an embodiment of the present invention;

[0048] Figure 5 This is a simplified schematic diagram of a V-shaped rubber vibration damping element provided in an embodiment of the present invention;

[0049] Figure 6 This is a schematic diagram illustrating the relationship between the logarithm lnf(p) of aging degree and time, provided in an embodiment of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0051] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0052] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0053] Example 1

[0054] like Figure 1 As shown, this embodiment provides a method for predicting the service aging of rubber components in rail vehicles. It establishes a viscoelastic constitutive model of the rail vehicle rubber, identifies the parameters of the viscoelastic constitutive model based on experimental data, and combines the relationship between the triaxial dynamic stiffness model of the rail vehicle rubber and the aging temperature and aging time to finally establish a service aging model for the rail vehicle rubber components. This provides a certain reference for the life assessment of rubber vibration damping components and their parameter design. Specifically, it includes the following steps:

[0055] S1: Based on the fractional derivative constitutive equation, the viscoelastic dynamics analysis model of the rubber components of rail vehicles is derived;

[0056] S2: Obtain the rubber components of the rail vehicle to be tested, conduct rubber aging tests and dynamic mechanical property tests, and identify the parameters of the viscoelastic dynamic characteristic analysis model of the rail vehicle rubber components based on the test data;

[0057] S3: Based on the viscoelastic dynamics analysis model of the rubber components of the rail vehicle after parameter identification, construct the triaxial dynamic stiffness model of the rubber components of the rail vehicle.

[0058] S4: Based on the relationship between the dynamic mechanical properties of rubber damping components and aging time and the relationship between the dynamic stiffness change rate, a three-dimensional mathematical model of pTt is established. Based on experimental data, a service aging performance model of the rubber components of rail vehicles with temperature and time is obtained to predict the aging degree of the rubber components of rail vehicles.

[0059] Step S1 above specifically includes the following:

[0060] A viscoelastic dynamics analysis model for rubber components in rail vehicles is derived. The fractional derivative constitutive equation of the general model can be described as equation (1).

[0061]

[0062] In the formula, p k q k , m, and n are all material model parameters for viscoelastic materials, D α The Riemann-Liouville fractional derivative operator; α is the order of the fractional derivative.

[0063] Performing a Fourier transform on both sides of equation (1) yields:

[0064]

[0065] The complex modulus E can be obtained * The expression for (ω) is:

[0066]

[0067] In the formula, E1(ω) is the complex modulus and E2(ω) is the energy-consuming complex modulus.

[0068] When using fractional derivative constitutive models, typically only 3 to 4 parameters are needed to achieve a relatively high-quality fit to the complex modulus of a material over a wide frequency range. Therefore, to describe the dynamic mechanical properties of rubber over a wide frequency range, this invention employs a four-parameter, three-element fractional derivative model (FZM model, e.g.) Figure 2 (As shown) serves as the analytical model for the subsequent analysis of the viscoelastic dynamics of rubber.

[0069] The four-parameter, three-element fractional derivative model is composed of a linear spring and a fractional derivative Kelvin model connected in series. The stress-strain relationship of the four-parameter, three-element fractional derivative model satisfies equation (4):

[0070] σ(t)+p1Dασ(t)=q0ε(t)+q1Dαε(t) (4)

[0071] In the formula, the material model parameters p1, α, q0, and q1 are all unknown parameters.

[0072] Performing a Fourier transform on both sides of equation (4) yields:

[0073] σ(ω)+p1(jω)ασ(ω)=q0ε(ω)+q1(jω)αε(ω) (5)

[0074] The complex modulus E of the four-parameter, three-element fractional derivative model can be obtained. * The expression for (ω) is:

[0075] According to equation j α =cos(απ / 2)+jsin(απ / 2), complex modulus E * (ω) can be decomposed into:

[0076] The energy storage modulus E1, energy dissipation modulus E2, and loss factor of the four-parameter, three-element fractional derivative model are obtained. Equations (8), (9), and (10) are respectively, where E1 is the real part of the complex modulus, reflecting the elastic component of the rubber, mainly manifested as the ability of the rubber to store energy due to elastic deformation under alternating stress, specifically characterized as the stiffness of the material; the energy dissipation modulus E2 is the imaginary part of the complex modulus, reflecting the viscous component of the rubber, mainly manifested as the ability to dissipate energy in the form of heat due to damping, specifically characterized as the damping of the material. The strain and stress changes of the rubber are not synchronized, and there is a phase difference. Also known as the loss angle, it is expressed as the tangent of the loss angle. To describe the magnitude of the loss, It can also be called the loss factor:

[0077]

[0078] From the complex modulus E * The complex flexibility J can be directly calculated from (ω). * The energy storage compliance and energy dissipation compliance of (ω) are given by equations (1.11) and (1.12), respectively.

[0079]

[0080] The above step S2 specifically includes:

[0081] Obtain a hot air aging test chamber and, after full preheating, place the rubber components of the rail vehicle under test inside for hot-oxygen aging.

[0082] The temperature scanning range and constant test loading frequency of the dynamic temperature scanning test were set to determine the dynamic mechanical properties of rubber as a function of temperature.

[0083] The frequency scanning range and constant test temperature of the dynamic frequency scanning test were set, and the dynamic mechanical properties of rubber were measured as a function of load frequency under different constant temperatures.

[0084] Based on the experimental data from dynamic temperature scanning and dynamic frequency scanning tests, the parameters of the viscoelastic dynamics analysis model for the rubber components of rail vehicles were identified using the multi-objective nonlinear least squares method.

[0085] In this embodiment, a service aging model is established using a V-shaped rubber vibration damping element for a certain rail vehicle as an example. The parameter identification process is as follows: Figure 2 As shown, it includes the following steps:

[0086] S201: Cut the rubber part of the V-shaped rubber vibration damping element and make multiple rectangular test strips with a length of 60mm, a width of 10mm, and a thickness of 4mm.

[0087] S202: The temperature of the hot air aging test chamber is set to 70℃. After complete preheating, the test samples are placed in the test chamber for thermo-oxidative aging. In this invention, the rubber aging test simulates the natural oxidation time of rubber, which is approximately 0 to 2000 days. After each test strip reaches the set time, the sample is removed for subsequent dynamic thermomechanical analysis tests.

[0088] S203: This invention studies the vibration characteristics in the frequency range of 0Hz to 20Hz. The dynamic temperature scanning test (temperature spectrum test) has a scanning range of -80℃ to 80℃, and the constant test loading frequencies are set to 2Hz, 10Hz, 15Hz, and 20Hz, respectively, to determine the variation of the dynamic mechanical properties of rubber with temperature. The dynamic frequency scanning test (frequency spectrum test) has a scanning range of 0.1Hz to 20Hz, and the constant test temperatures are set to -10℃, 0℃, 10℃, and 20℃, respectively, to determine the variation of the dynamic mechanical properties of rubber with load frequency at different constant temperatures.

[0089] S204: Select test sample results with an aging test time of 30% of the total test time to characterize the aging results of a certain stage in the aging process of rubber components, and compare and analyze the performance changes of rubber components before and after aging.

[0090] S205: Based on the frequency spectrum test data of storage modulus and dissipation modulus under dynamic thermomechanical analysis frequency scanning, the parameters of the rubber viscoelastic constitutive model considering thermo-oxidative aging at -10℃ to 20℃, identified by the multi-objective nonlinear least squares method, are shown in Table 1. The simulation results obtained using the constitutive model proposed in this paper are compared with the experimentally measured values ​​of the rubber components. Figure 3 As shown in the figure, the results show that the simulation results of the constitutive model have a high degree of consistency with the experimental results, with a relative error of less than 5%. Therefore, the established constitutive model can accurately characterize the viscoelastic dynamic mechanical properties of rubber in the range of 0Hz to 20Hz.

[0091] Table 1. Model parameters identified at different constant temperatures.

[0092]

[0093] In this embodiment, step S3 specifically includes the following steps:

[0094] S301: The strain of rubber vibration damping components in vehicle equipment is usually within the range of 10% to 20% of the rubber thickness, which falls within the scope of the small deformation linear elastic assumption. Therefore, it is considered that the tensile and compressive external forces of the rubber vibration damping components are linearly related to the displacement deformation.

[0095] S302: For a cuboid rubber element with geometric dimensions of a×b×h, such as Figure 4 As shown.

[0096] Based on this, the stiffness in the z-axis direction (i.e., the tensile-compression direction of the rubber) can be expressed as:

[0097]

[0098] In the formula, F is the tensile and compressive external force, Δz is the displacement deformation along the z-axis, S is the cross-sectional area (S=a·b); h is the height of the rubber element; m z Let be the shape factor along the z-axis; E is the elastic modulus, which is related to the storage modulus and dissipation modulus by the following:

[0099]

[0100] For the shear directions x and y, the stiffness expression is:

[0101]

[0102] Where m x and m y Here, are the shape factors along the x and y axes of the cuboid, respectively; G is the shear modulus.

[0103]

[0104] In the formula, μ is the Poisson's ratio of natural rubber.

[0105] m x m y m z Satisfying equation (17),

[0106]

[0107] n is the ratio of the constrained area to the free area.

[0108]

[0109] When the rubber components of a rail vehicle are V-shaped rubber vibration damping components, the V-shaped rubber vibration damping component is composed of two cuboid rubber components arranged at a specific angle, such as... Figure 5 As shown, the x-axis, y-axis, and z-axis directions of the V-shaped rubber damping element are the same as the directions defined in the high-speed train body coordinate system. Based on the V-shaped rubber damping element structure, its triaxial stiffness calculation formula is shown in equation (19).

[0110]

[0111] In step S4 above, the process of establishing the service aging model of the rubber component in rail vehicles, which relates the change p in the dynamic mechanical properties of the rubber component to the aging temperature T and the aging time t, specifically includes the following steps:

[0112] S401: Under thermo-oxidative aging conditions, the viscoelastic dynamic mechanical parameters of rubber components exhibit regular changes with increasing time, and the relationship between the degree of dynamic mechanical property aging f(p) and aging time t satisfies equation (20):

[0113]

[0114] In the formula, A is the experimental constant; t is the aging time (unit: days); k is the thermo-oxidative aging reaction rate; λ is a constant, 0≤λ≤1; Δ is a sign factor, which is "+" when the degree of aging f(p) increases with the aging time t, and "-" otherwise.

[0115] Taking the logarithm of both sides of equation (20), we get:

[0116] lnf(p)=lnA+(Δkt λ ) (twenty one)

[0117] Let ξ = lnA and ζ = Δk in equation (21), then it simplifies to:

[0118] lnf(p)=ε+ζt λ s (22)

[0119] In the formula, ξ, ζ, and λ are all parameters to be determined. Equation (1.22) is a binary mathematical model of pt.

[0120] S402: The Arrhenius equation is introduced to comprehensively reflect the relationship between the thermo-oxidative aging reaction rate of rubber components and temperature, and to establish a ternary mathematical model of the dynamic mechanical performance change p of rubber vibration damping components and the aging temperature T and aging time t, where T is the absolute temperature.

[0121] The degree of aging of rubber is represented by the rate of change of dynamic stiffness ε, i.e.

[0122] f(p)=1-ε (23)

[0123] The rate of change of dynamic stiffness ε over any aging time can be expressed as:

[0124]

[0125] In the formula, K is the initial dynamic stiffness of the rubber before aging; K′ is the dynamic stiffness of the rubber after aging.

[0126] Based on equations (20) to (24), the relationship between dynamic stiffness and aging degree f(p) can be derived as equation (25):

[0127]

[0128] Combining equations (25) and (19), we can see the relationship between triaxial dynamic stiffness and aging degree.

[0129] S403: As can be seen from the dynamic mechanical property test of the V-type rubber used in this invention, the growth rate of storage modulus and dissipation modulus with increasing frequency is relatively slow at higher temperatures. Therefore, in this invention, the average value of storage modulus and dissipation modulus within 0Hz to 20Hz is used to replace the storage modulus and dissipation modulus of the low-frequency rubber state stage at each temperature, and this is used to calculate the initial dynamic stiffness. Based on the results of rubber aging test and dynamic mechanical property test, combined with equations (23) and (24), the logarithm lnf(p) of the degree of aging of rubber dynamic stiffness under accelerated aging at a constant temperature of 70℃, simulating natural aging of rubber at 10℃ for 0 to 2000 days, and the relationship with time are obtained, as follows: Figure 6 As shown in Table 2, the nonlinear least squares method was used to identify the experimental data and obtain the identification coefficients in equations (20) and (22), as well as the experimental constant A and the thermo-oxidative aging reaction rate k.

[0130] Table 2. Calculation results of identification coefficient, experimental constant A, and thermo-oxidative aging reaction rate k.

[0131]

[0132] Based on the above identification results, the expression for the aging degree f(p) of dynamic stiffness is:

[0133]

[0134] The Arrhenius equation then changes to:

[0135]

[0136] Where R is the material parameter value of the rubber element, which is obtained by experiment. In this invention, the R value of the V-type rubber material is 1327. Combined with (23) to (27), the service aging performance model of the rubber element of the rail vehicle with temperature and time can be obtained.

[0137] Ignoring issues such as center of gravity imbalance and uneven mass distribution in the equipment, this article primarily focuses on the vertical coupling vibration of the high-speed train body and its undercarriage equipment. Combining equations (26) and (27), the relationship between the vertical dynamic stiffness K of the rubber and its service life at different temperatures is calculated. Taking 10℃ and 20℃ as examples, the performance evolution is shown in equations (28) and (29).

[0138]

[0139] If the stiffness variation limit of the vibration damping element is set to 25%, then according to equations (28) and (29), the service life of the rubber vibration damping element at 10℃ and 20℃ can be calculated to be 6.5 years and 5.6 years, respectively. In actual engineering practice, the replacement cycle of rubber vibration damping elements for under-vehicle equipment is usually 6 years, which is basically consistent with the above analysis results.

[0140] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for predicting the service aging of rubber components in rail vehicles, characterized in that, Includes the following steps: Based on the fractional derivative constitutive equation, a model for analyzing the viscoelastic dynamics of rubber components in rail vehicles is derived. Obtain the rubber components of the rail vehicle to be tested, conduct rubber aging tests and dynamic mechanical property tests, and identify the parameters of the viscoelastic dynamic characteristic analysis model of the rail vehicle rubber components based on the test data; Based on the viscoelastic dynamics analysis model of the rubber components of the rail vehicle after parameter identification, a three-dimensional dynamic stiffness model of the rubber components of the rail vehicle is constructed. Based on the relationship between the dynamic mechanical properties of rubber vibration damping components and aging time and the relationship between the dynamic stiffness change rate, a system is established... pTt A ternary mathematical model was used, and based on experimental data, a service aging performance model of the rubber components of rail vehicles as a function of temperature and time was obtained to predict the degree of aging of the rubber components of rail vehicles. When the rubber element of the rail vehicle is a V-shaped rubber vibration damping element, which is composed of two cuboid rubber elements arranged at a specific angle, the expression for the three-dimensional dynamic stiffness model of the rail vehicle rubber element is: In the formula, , and They are respectively x axis, y axis, z Stiffness in the axial direction , and Shearing direction x axis, y shaft and z Shaft stiffness, θ V-shaped rubber vibration damping element z The angle between the axis and the vertical direction; The expression for the relationship between the dynamic mechanical properties of the rubber vibration damping element and the rate of change of dynamic stiffness is as follows: In the formula, This refers to the changes in the dynamic mechanical properties of rubber vibration damping components. The rate of change of dynamic stiffness K This represents the initial dynamic stiffness of the rubber before aging. K Ꞌ The dynamic stiffness of rubber after aging; The pTt The ternary mathematical model includes the relationship between dynamic stiffness and aging degree, as well as the relationship between the dynamic mechanical properties of the rubber vibration damping element and aging time. The expression for the relationship between dynamic stiffness and aging degree is as follows:

2. The method for predicting the service aging of rubber components in rail vehicles according to claim 1, characterized in that, The analysis model of the viscoelastic dynamic characteristics of the rubber components of the rail vehicle is a four-parameter three-element fractional derivative model constructed based on the fractional derivative constitutive equation. This four-parameter three-element fractional derivative model includes a linear spring and a fractional derivative model connected in series, which are used to calculate the energy storage modulus and the energy dissipation modulus.

3. The method for predicting the service aging of rubber components in rail vehicles according to claim 2, characterized in that, The expression for the four-parameter, three-element fractional derivative model is: In the formula, For the complex modulus, For energy storage modulus, For energy dissipation modulus, p 1 、α、q 0 、q 1 For unknown material model parameters, ω is the angular frequency.

4. The method for predicting the service aging of rubber components in rail vehicles according to claim 3, characterized in that, The four-parameter, three-element fractional derivative model also includes calculating a loss factor, which describes the magnitude of the loss based on the tangent of the loss angle. The expression for calculating the loss factor is as follows: In the formula, tanφ As the loss factor, φ This is the phase difference caused by the asynchronous changes in strain and stress in rubber.

5. The method for predicting the service aging of rubber components in rail vehicles according to claim 1, characterized in that, The parameter identification process is specifically as follows: Obtain a hot air aging test chamber and, after full preheating, place the rubber components of the rail vehicle under test inside for hot-oxygen aging. The temperature scanning range and constant test loading frequency of the dynamic temperature scanning test were set to determine the dynamic mechanical properties of rubber as a function of temperature. The frequency scanning range and constant test temperature of the dynamic frequency scanning test were set, and the dynamic mechanical properties of rubber were measured as a function of load frequency under different constant temperatures. Based on the experimental data from dynamic temperature scanning and dynamic frequency scanning tests, the parameters of the viscoelastic dynamics analysis model for the rubber components of rail vehicles were identified using the multi-objective nonlinear least squares method.

6. The method for predicting the service aging of rubber components in rail vehicles according to claim 1, characterized in that, When the rubber component of the track vehicle under test is a cuboid rubber component, the expression for the triaxial dynamic stiffness model of the track vehicle rubber component is: In the formula, F For tension and compression, Δz is the external force along the direction of tension and compression. z Axial displacement deformation S For cross-sectional area, a, b, h The length, width, and height of the rubber component of the rail vehicle under test. m z for z The shape factor of the shaft; E For elastic modulus, and These are the storage modulus and dissipation modulus calculated from the viscoelastic dynamics analysis model of rubber components in rail vehicles, respectively. G Shear modulus m x and m y They are cuboids x Axial and y Axial shape factor μ The Poisson's ratio of natural rubber. n This is the ratio of the constrained area to the free area.

7. The method for predicting the service aging of rubber components in rail vehicles according to claim 1, characterized in that, The expression for the relationship between the dynamic mechanical properties of the rubber vibration damping element and aging time is as follows: In the formula, A This is an experimental constant; t This refers to the aging time. k The rate of thermo-oxidative aging reaction; λ It is a constant. 0≤λ≤1 ; As a sign factor, when the degree of aging f(p) With aging time t When an increase occurs, it is represented by a "+" sign; otherwise, it is represented by a "-" sign.

8. The method for predicting the service aging of rubber components in rail vehicles according to claim 1, characterized in that, When the rubber component of the rail vehicle is a V-shaped rubber vibration damping component, the average value of the energy storage modulus and energy dissipation modulus at a certain frequency is used to replace the energy storage modulus and energy dissipation modulus at the low-frequency rubber state stage at each temperature, so as to calculate the initial dynamic stiffness.

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