Damping layer material loss factor and temperature correlation model construction method

Abstract

The invention relates to the technical field of materials and data processing, and discloses a method for constructing a damping layer material loss factor and temperature correlation model, which effectively overcomes the defect of insufficient adaptability of a traditional damping material model in a wide temperature range required by a thermal power plant by fusing a molecular chain segment dynamics mechanism and a macroscopic constitutive behavior. The method has the technical advantages that on the basis of the physical basis of a molecular motion energy barrier theory constraint model and in combination with a corrected temperature-frequency equivalent conversion mechanism, a cross-scale correlation framework with clear physical significance is constructed; through collaborative optimization of microscopic activation energy and macroscopic viscoelastic parameters, the reliability of thermal power plant all-working-condition temperature domain loss factor prediction is remarkably improved; an embedded real-time calculation framework is adopted, dynamic evaluation and compensation control of the material damping performance in an engineering scene are achieved, and more accurate technical support is provided for vibration reduction structure design, vibration fault diagnosis and prevention and service life prolonging of key equipment in the fields of thermal power plants, heavy machinery and the like.

Description

Technical Field

[0001] This invention relates to the fields of materials and data processing technology, specifically to a method for constructing a model relating the loss factor of a damping layer material to temperature. Background Technology

[0002] Damping layer materials are widely used in critical components of thermal power plants, such as foundation vibration isolation for steam turbine generator sets, boiler piping support systems, vibration damping bases for fans / pumps, and flue expansion joints. Their core function is to convert mechanical vibration energy into heat dissipation, ensuring the safe and stable operation of equipment. In actual operating conditions, these materials must maintain stable performance within a wide temperature range in thermal power plants (e.g., outdoor equipment in frigid winter regions can reach temperatures as low as -40°C, while temperatures near boiler areas can exceed 200°C).

[0003] However, the molecular chain movement of polymer damping materials is extremely sensitive to temperature: in frigid regions during winter, the hardening of outdoor vibration damping support materials leads to a sharp drop in damping efficiency, exacerbating pipeline vibration and causing fatigue risks; while in the high-temperature environment of boiler areas, the softening of support gasket materials causes the peak loss frequency to shift, resulting in vibration damping failure and affecting equipment safety and sealing performance.

[0004] Currently, two main types of technologies are used in thermal power plant engineering to address the effects of temperature:

[0005] One method is the segmented empirical model: In the laboratory, three typical temperature points—-40℃, 25℃, and 80℃—are simulated using a temperature-controlled chamber. Independent loss factor databases are then established for each temperature point. On-site engineers switch to the corresponding data tables based on temperature sensor readings to design compensation.

[0006] Second, the standard temperature reference method: In industrial production, the loss factor is tested uniformly under a standard environment of 25℃, and linear temperature compensation is performed based on historical experience values ​​when in use.

[0007] In extremely cold regions or high-temperature zones near boilers, the lack of measured data at these temperatures often forces the application of neighboring models, leading to significant deviations in the performance prediction of damping components under extreme conditions. This can result in excessive vibration, equipment fatigue damage, or seal failure. Furthermore, the linear compensation method cannot capture the nonlinear abrupt changes in material behavior within the glass transition region (typically between -20°C and 80°C). This causes inaccurate vibration reduction predictions when temperatures cross this region during unit start-up, shutdown, or load changes, posing a threat to equipment safety and structural lifespan. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a method for constructing a model relating the loss factor of damping layer materials to temperature. The aim is to significantly improve the accuracy and reliability of loss factor prediction for damping materials in the complex wide-temperature range environment of thermal power plants (from frigid outdoor environments to high temperatures near the boiler end) by integrating molecular chain segment dynamic parameters with macroscopic fractional constitutive models and combining modified temperature-frequency shift factor design technology. This solves technical problems such as equipment vibration control failure and accelerated fatigue damage caused by inaccurate prediction models.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A method for constructing a model relating the loss factor of a damping layer material to temperature includes the following steps:

[0011] Step 1: Perform dynamic mechanical property tests on the material in the temperature range of -70℃ to 300℃ using a dynamic thermomechanical analyzer, collect data on storage modulus E' and loss modulus E', and calculate the loss factor tanδ(T,f) matrix;

[0012] Step 2: Fit the peak data of the loss factor based on the Arrhenius equation and calibrate the molecular chain segment activation energy E. a ;

[0013] Step 3: Construct a fractional Zener constitutive model, obtain the frequency domain expression of the complex modulus through Fourier transform, and calculate the loss factor tanδ(ω) by separating the real and imaginary parts;

[0014] Step 4: Modify the Williams-Landel-Ferry equation and fuse the activation energy E. a Based on the free volume theory, a cross-scale temperature shift factor a is established. T ;

[0015] Step 5: Establish a multi-objective optimization function and collaboratively optimize the activation energy E. a The fractional-order parameters α, β, and γ, as well as the shift factor parameters C1 and C2, are used to ensure that the model prediction error is less than 5%.

[0016] As a further embodiment of the present invention, in step one, the strain amplitude ∈ 0 of the dynamic mechanical test is controlled within the range of 0.01%-0.1%, and the frequency scanning range is 0.001-100Hz.

[0017] As a further embodiment of the present invention, in step two, the activation energy E a The calibration was achieved through a temperature scanning experiment at a fixed frequency, and the relationship between the logarithm of the frequency and the reciprocal of the peak temperature was fitted using linear regression.

[0018] As a further embodiment of the present invention, in step three, the fractional order α of the fractional Zener constitutive model takes a value range of 0.2-0.8, and the stress / strain term product coefficients β and γ are determined by the position of the loss peak.

[0019] As a further embodiment of the present invention, the modified WLF equation in step four includes a molecular chain segment energy barrier term. With free volume term

[0020] As a further embodiment of the present invention, in step five, a regularization term λ(E) is introduced into the optimization function. a -E a,sim ) 2 The consistency between the constraint activation energy and the molecular dynamics simulation value is evident.

[0021] As a further aspect of the present invention, the cross-scale temperature shift factor a T The expression is:

[0022]

[0023] A temperature-correlation prediction system for the loss factor of damping materials includes:

[0024] S1: Experimental data acquisition module, used to collect data on the energy storage modulus and loss modulus of materials in a preset temperature and frequency domain;

[0025] S2: Molecular activation energy extraction module, used to fit loss factor peak data based on the Arrhenius equation;

[0026] S3: Constitutive model construction module, used to construct fractional Zener constitutive models and separate the frequency domain components of complex modulus;

[0027] S4: Temperature-frequency equivalent transformation module, used to correct the WLF equation and generate shift factor parameters;

[0028] S5: Parameter optimization module, used to collaboratively optimize microscopic activation energy and macroscopic viscoelastic parameters.

[0029] As a further embodiment of the present invention, the experimental data acquisition module includes a dynamic thermomechanical analyzer and a temperature control chamber, with a test temperature range of -70℃ to 300℃ and a frequency range of 0.001-100Hz.

[0030] As a further aspect of the present invention, the parameter optimization module employs a regularized genetic algorithm to balance the data fitting accuracy with physical constraints.

[0031] Compared with existing technologies, this invention provides a method for constructing a model relating the loss factor of damping layer materials to temperature, which has the following advantages: By integrating molecular chain segment dynamics and macroscopic constitutive behavior, this invention effectively overcomes the shortcomings of traditional damping material models in terms of insufficient adaptability to the wide temperature range required by thermal power plants. Its technical advantages are: based on the molecular kinetic energy barrier theory constraining the physical foundation of the model, combined with a modified temperature-frequency equivalent conversion mechanism, a cross-scale correlation framework with clear physical meaning is constructed; through the synergistic optimization of microscopic activation energy and macroscopic viscoelastic parameters, the reliability of loss factor prediction across the entire operating temperature range (from severe cold to extreme heat) of thermal power plants is significantly improved; and by adopting an embedded real-time computing architecture, dynamic evaluation and compensation control of material damping performance in engineering scenarios are realized, providing more accurate technical support for vibration reduction structure design, vibration fault diagnosis and prevention, and life extension of key equipment in thermal power plants, heavy machinery, and other fields. Attached Figure Description

[0032] Figure 1 This document describes the steps involved in constructing a model relating the loss factor of a damping layer material to temperature, as proposed in this invention.

[0033] Figure 2 This is a system flowchart of a temperature-correlation prediction system for the loss factor of damping materials proposed in this invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0035] The component designations used in this document, such as "first" and "second," are merely for distinguishing the described objects and do not have any sequential or technical meaning. The terms "connection" and "linkage" used in this invention, unless otherwise specified, include both direct and indirect connections (linkages). In the description of this invention, it should be understood that the terms "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0036] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0037] To address the technical problem of insufficient accuracy of traditional damping material loss factor prediction models in thermal power plants across a wide temperature range (e.g., -40℃ to 200℃), especially in extreme temperatures such as low temperatures in frigid outdoor equipment and high temperatures in boiler areas, the lack of molecular-scale physical mechanisms leads to extrapolation distortion and poor cross-temperature adaptability, thus affecting the vibration control effect and long-term operational reliability of key equipment such as steam turbines, pipeline systems, and fan pump sets.

[0038] To address this issue, a method for constructing a model relating the loss factor of damping layer materials to temperature is proposed. The detailed steps of this method are explained below. (See reference...) Figure 1 The method specifically consists of the following steps:

[0039] Step 1: Experimental characterization of the dynamic mechanical properties of materials:

[0040] The purpose of step one is to accurately obtain the energy dissipation characteristics of damping materials under a wide temperature-frequency coupled field, establish a basic database of loss factors as a function of temperature and frequency, and provide input benchmarks for cross-scale models.

[0041] A dynamic thermomechanical analyzer (DMA) was used, equipped with a temperature-controlled chamber (test range -70℃ to 300℃) and a frequency generator (test range 0.001–100Hz). In the dynamic mechanical analysis, a sinusoidal strain load ∈(t) was applied to the damping material specimen, as shown in Equation (1.1):

[0042] ∈(t)=∈0sin(ωt) (1.1)

[0043] Where: ∈0 represents the strain amplitude (dimensionless); ω=2πf represents the angular frequency, in rad / s; f represents the excitation frequency, in Hz;

[0044] The stress response generated by the material exhibits phase lag due to viscoelasticity. The stress response σ(t) is synchronously acquired, as shown in equation (1.2):

[0045] σ(t)=σ0sin(ωt+δ) (1.2)

[0046] Where σ0 represents the stress amplitude in Pa; δ represents the hysteresis phase angle in rad.

[0047] The stress-strain relationship is then decomposed into a complex form, as shown in equation (1.3):

[0048]

[0049] Where E' represents the energy storage modulus, characterizing the elastic energy storage capacity (in-phase stress component); E” represents the loss modulus, characterizing the viscous energy dissipation (orthogonal phase stress component).

[0050] In this process, Euler's formula sinθ=Im(e iθ Equations (1.1) and (1.2) can be rewritten as follows:

[0051] ∈(t)=Im[∈0e iωt ]、

[0052] σ(t)=Im[σ0e i(ωt+δ) ]=Im[σ0e iδ e iωt ]

[0053] Substituting the rewritten equations (1.1) and (1.2) into equation (1.3), we obtain equation (1.4):

[0054]

[0055] Then, by separating the real and imaginary parts of equation (1.4), we obtain:

[0056]

[0057] The loss factor tanδ is defined as the ratio of the loss modulus E” to the energy storage modulus E’, as shown in equation (1.5):

[0058]

[0059] The larger the tanδ value, the better the damping performance of the material.

[0060] So, specifically during the experiment, at each temperature point T... i Downscan frequency f j Record E' ij ,E” ij The loss factor matrix is ​​calculated according to equation (1.5), as shown in equation (1.6):

[0061]

[0062] During the experiment, temperature changes caused variations in the sample size, affecting the accuracy of the strain amplitude. Therefore, corrections were required, as shown in equation (1.7).

[0063] ∈ corr (T)=∈ meas / [1+α(TT ref (1.7)

[0064] Where, ∈ meas The strain represents the strain measured by the instrument; α represents the linear thermal expansion coefficient of the material; T ref This represents a reference temperature, typically 25℃.

[0065] The corrected loss modulus and energy storage modulus are shown in Equation (1.8):

[0066] E'(T),E""T)=f(∈ corr (T)) (1.8)

[0067] The loss factor matrix tanδ(T,f) established in the final step is the input benchmark for subsequent model fitting, and its accuracy directly determines the reliability of the model.

[0068] Step 2: Modeling of loss peaks driven by molecular motion mechanisms:

[0069] In step one, the established loss factor matrix tanδ(T,f) can clearly reveal the location of the material's energy dissipation peak, and thus the peak value of the loss factor tanδ can be obtained. peak The purpose of step two is to establish the peak value of the loss factor tanδ of the damping material. peak The physical correlation model with temperature reveals the control mechanism of molecular chain segment motion on macroscopic energy consumption behavior, providing microscopic physical parameters for cross-scale models.

[0070] The energy dissipation of damping materials originates from the transition motion of polymer chain segments between potential barriers. As the temperature increases, the thermal motion of the chain segments intensifies, and the relaxation process accelerates. This process requires overcoming an energy barrier, which is determined by the activation energy E. a The relaxation time τ of the expression follows the Arrhenius equation, as shown in equation (2.1):

[0071]

[0072] Where τ0 is the pre-exponential factor, in seconds, which characterizes the limiting relaxation time at infinite temperature; E a The value represents the activation energy, expressed in J / mol, which represents the energy barrier that the chain segment needs to overcome for motion; R refers to the gas constant, with a value of 8.314 J / (mol·K); T refers to the absolute temperature, expressed in K.

[0073] In equation (2.1), an increase in temperature T represents an increase in molecular kinetic energy, which indicates a shortening of relaxation time τ, resulting in a faster material response.

[0074] There is a certain correlation between relaxation time and peak loss. Specifically, in dynamic mechanical testing, the peak loss factor tanδ... peak The frequency f of the external force and the intrinsic relaxation frequency f of the molecular chain segment appear c When ωτ = 1 / (2πτ), the complex modulus can be expressed as shown in equation (2.2) based on the Debye relaxation model:

[0075]

[0076] Where E ∞ E is the glass modulus. g It is the rubber modulus;

[0077] This process separates the real and imaginary parts of equation (2.2) to obtain:

[0078]

[0079] Substituting this into tanδ = E” / E’, we get:

[0080]

[0081] Its peak condition is that tanδ reaches its maximum value when ωτ=1. peak As shown in equation (2.5):

[0082]

[0083] Substituting the Arrhenius equation (2.1) into the peak condition ωτ=1 reveals the mechanism by which temperature affects the peak loss, as shown in equation (2.6):

[0084]

[0085] During the experiment, when scanning the temperature at a fixed frequency f, the loss peak appears at the characteristic temperature T. p At that point, it satisfies equation (2.7):

[0086]

[0087] From this, the peak height tanδ can be derived. peak The expression for (T) is given, and the entropy elasticity theory E is considered. g -E ∞ =ρRT / M c (ρ is density, M) c (Molecular weight between crosslinking points), modulus difference E g -E∞ ∝T, and simultaneously solving equations (2.5) and (2.7) yields the peak height tanδ. peak The expression for (T) is shown in equation (2.8):

[0088]

[0089] in The modulus temperature dependence, representing entropy elasticity, is dominant; exp(-E a / (2RT)) represents the probability that a molecular chain segment will cross the potential barrier.

[0090] The activation energy E was calibrated experimentally. a Specifically, at fixed frequencies f1, f2, ..., f n Temperature scanning was performed, and the peak temperature T corresponding to each frequency was recorded. p1 ,T p2 ,...,T pn Taking the logarithm of equation (2.7) to linearize the Arrhenius equation is shown in equation (2.9).

[0091]

[0092] Plot lnf and 1 / T p The relationship curve, where the slope k = -E a / R, then the activation energy E a =-kR, intercept b=ln(1 / (2πτ0)), then τ0=1 / (2πe b The final fitting results are as follows:

[0093] Slope k = -4520K

[0094] E a =-kR=4520×8.314=37.6kJ / mol

[0095] τ0=2.7×10 -13 s

[0096] The activation energy E established in step two a It is a key physical parameter that connects microscopic molecular motion with macroscopic temperature and frequency characteristics, providing a theoretical basis for the cross-scale model fusion in step four.

[0097] Step 3: Construction of the macroscopic fractional derivative constitutive equation:

[0098] The purpose of step three is to establish a constitutive model that can accurately describe the wideband viscoelastic behavior of damping materials, overcome the limitations of traditional integer-order models in cross-band prediction, and provide a mathematical basis for temperature-frequency coupling analysis.

[0099] However, traditional integer derivative models can only describe material behavior in a narrow frequency domain and cannot characterize modulus gradient characteristics in a wide frequency band. Fractional derivative models break through this limitation by introducing the order α∈(0,1), and their physical essence is to describe material memory effect and long-range correlation.

[0100] In this step, we first define a Caputo-type fractional derivative. Assuming g(t<0)=0 and g′(t) is continuous on [0,t], then the fractional derivative is as shown in equation (3.1):

[0101]

[0102] Where α represents the fractional order, and its value ranges from 0 to 1; Γ(·) represents the Gamma function; and g'(τ) represents the first derivative of the function.

[0103] When α = 0, the material is an ideal elastic body; when α = 1, the material is a pure viscous fluid; when 0 < α < 1, the material is a viscoelastic material, and the memory effect increases with the increase of α.

[0104] Subsequently, a fractional Zener model was adopted, whose constitutive equation is shown in equation (3.2):

[0105]

[0106] Where E0 represents the equilibrium modulus in Pa, and β represents the elastic response as t→∞; β represents the stress fractional term coefficient in s. α γ represents the coefficient of the fractional strain term, with units of s. a ; α represents the fractional order; the left side of equation (3.2) represents total stress = instantaneous elastic stress + stress history cumulative effect; the right side of equation (3.2) represents driving strain = instantaneous elastic strain + strain rate history contribution.

[0107] After obtaining the constitutive equation of the fractional Zener model, Fourier transform is applied to both sides of equation (3.2), utilizing the properties... The transformation process is shown in equation (3.3):

[0108]

[0109] The complex modulus is obtained by rearranging equation (3.3). Its complex modulus frequency domain expression is shown in equation (3.4):

[0110]

[0111] For the frequency domain expression of the complex modulus, perform complex algebraic processing, and let Ω = ω. α ,Will Substituting into equation (3.4), we obtain equation (3.5):

[0112]

[0113] Separating the real and imaginary parts of equation (3.5), and multiplying both the numerator and denominator by their conjugate complex numbers, we obtain equation (3.6):

[0114]

[0115] in:

[0116]

[0117] F = βΩsin(πα)

[0118] Then the loss factor tanδ(ω) is calculated by defining tanδ=Im[E * ] / Re[E * Combining equation (3.6), we obtain equation (3.7):

[0119]

[0120] The fractional constitutive equation established in step three is the mathematical basis for describing the broadband variable characteristics of damping materials, and its parameters will provide a basis for the temperature-frequency equivalent transformation in step four.

[0121] Step 4: Design of cross-scale temperature shift factor:

[0122] Due to the problem of predicting failure in the extreme temperature range of the traditional WLF equation, this step addresses this by incorporating the molecular-scale activation energy E. a To overcome this problem, a temperature-frequency equivalent model covering the entire temperature range is constructed, based on the macroscopic free volume theory.

[0123] Specifically, the viscoelastic behavior of polymer materials exhibits temperature-frequency dependence, meaning that an increase in temperature is equivalent to a decrease in frequency, with a shift factor a. T This equivalence relationship can be quantitatively described as shown in equation (4.1):

[0124] E * (T,ω)=E * (T ref ,a T ω) (4.1)

[0125] This represents mapping the frequency ω at temperature T to a reference temperature T. ref The equivalent frequency ω ref =a T ω;

[0126] The Williams-Landel-Ferry (WLF) equation is a classic shift factor model, as shown in equation (4.2):

[0127]

[0128] Where C1 and C2 represent material constants; T ref Represents a reference temperature, usually taken as (T). g +50)K;

[0129] Activation energy E of molecular chain segment relaxation a The dominant temperature dependence is shown in equation (4.3):

[0130]

[0131] The shift factor can be expressed as shown in equation (4.4):

[0132]

[0133] Taking the logarithm, we get equation (4.5):

[0134]

[0135] Because the traditional WLF equation fails to predict in extreme temperature ranges, the WLF equation is modified. Combining equations (4.2) and (4.5), a cross-scale shift factor is constructed, as shown in equation (4.6):

[0136]

[0137] The above correction process includes unit unification, coefficient conversion, and linear superposition. The unit unification formula converts the natural logarithm into the commonly used logarithm, specifically lnx = 2.3026log 10 x; coefficient conversion will Convert to Linear superposition describes the glass transition region using the WLF term and the low-temperature region using the Arrhenius term.

[0138] Step four: The activation energy E at the molecular scale. a By embedding macroscopic shift factors, a leap from empirical models to physical mechanism-driven models is achieved, laying the foundation for parameter optimization in step five.

[0139] Step 5: Cross-scale parameter joint optimization and model validation:

[0140] The fourth objective of this step is to resolve the microscopic parameter E. aThe problem of co-optimizing macroscopic parameters α, β, γ, C1, and C2 aims to achieve high-precision prediction of the loss factor across the entire temperature range and broadband bandwidth, while ensuring physical realism. Specifically, this step requires the simultaneous determination of two types of parameters:

[0141] Microscopic parameters: Activation energy E a ;

[0142] Macroscopic parameters: fractional parameters α, β, γ and shift factor parameters C1, C2;

[0143] At the same time, a constrained optimization problem is established, as shown in equation (5.1):

[0144]

[0145] Where θ=(α,β,γ,C1,C2,E) a () represents the set of parameters to be optimized;

[0146] To minimize the mean squared error between the model predictions and the experimental data, an objective function is proposed, as shown in Equation (5.2):

[0147]

[0148] The model prediction expression is established by combining steps three and four, as shown in equation (5.3):

[0149]

[0150] Where the shift factor a T Calculated using equation (5.4):

[0151]

[0152] To ensure E a Compared with the molecular dynamics simulation value E a,sim To ensure consistency, physical constraint terms are established, as shown in equation (5.5):

[0153] J phy (θ)=(E a -E a,sim ) 2 (5.5)

[0154] Where E a,sim The potential barrier for chain segment transitions is obtained through molecular dynamics simulations; λ represents the regularization weight, typically 0.1–1.0, used to balance data fitting and physical constraints.

[0155] This step, through physical constraint regularization and intelligent optimization algorithms, achieves the collaborative identification of micro and macro parameters, ensuring that the model possesses both predictive accuracy and physical realism.

[0156] See Figure 2 Based on the method described in this embodiment, a temperature correlation prediction system for the loss factor of damping materials is proposed, comprising:

[0157] The experimental data acquisition module is configured to acquire the energy storage modulus and loss modulus data of the material in the preset temperature and frequency domain through a dynamic mechanical testing device, and execute the loss factor calculation logic to generate a three-dimensional matrix of temperature-frequency-loss factor.

[0158] A molecular activation energy extraction module, which is communicatively connected to the experimental data acquisition module, is configured to receive the peak data of the loss factor in the three-dimensional matrix and execute Arrhenius fitting logic to generate molecular chain segment activation energy parameters.

[0159] The constitutive model construction module is communicatively connected to the experimental data acquisition module and is configured to receive full-frequency domain data in the three-dimensional matrix and execute fractional-order differential constitutive model construction logic to generate a constitutive parameter set.

[0160] A temperature-frequency equivalent transformation module, which is communicatively connected to the molecular activation energy extraction module, is configured to receive the molecular chain segment activation energy parameters and execute free volume-energy barrier fusion calculation logic to generate a shift factor parameter set.

[0161] A cross-scale collaborative optimization module, which is communicatively connected to the molecular activation energy extraction module, constitutive model construction module, and temperature-frequency equivalent transformation module, is configured as follows:

[0162] Receive the three-dimensional matrix as reference data input;

[0163] The activation energy parameters of the molecular chain segments are received as physical constraint inputs.

[0164] The constitutive parameter set and shift factor parameter set are received as inputs to be optimized.

[0165] Execute regularized genetic optimization logic to generate an optimization parameter set;

[0166] The prediction output module is communicatively connected to the cross-scale collaborative optimization module and is configured to execute loss factor prediction logic based on the optimization parameter set, and output a full-temperature-wideband loss factor spectrum.

[0167] The molecular activation energy extraction module includes a peak localization unit and an Arrhenius inversion unit, wherein:

[0168] The peak positioning unit is configured to perform spline interpolation differentiation on the three-dimensional matrix to determine the peak temperature of the loss factor at each frequency.

[0169] The Arrhenius inversion unit is configured to establish a linear mapping between the logarithm of the frequency and the reciprocal of the peak temperature, and to calculate the activation energy parameters by the slope.

[0170] The constitutive model construction module includes a frequency domain transformation unit and a parameter identification unit, wherein:

[0171] The frequency domain transformation unit is configured to convert fractional constitutive equations into complex modulus frequency domain expressions;

[0172] The parameter identification unit is configured to fit the equilibrium modulus through a low-frequency platform and determine the stress / strain term product by the position of the loss peak.

[0173] The temperature-frequency equivalent transformation module includes:

[0174] Term generation unit, which is used to calculate the free volume term and energy barrier term;

[0175] The fusion computing unit is used to generate a shift factor by linearly superimposing the free volume term and the energy barrier term;

[0176] The parameter optimization unit is used to preferentially fit the free volume term coefficients in the high-temperature region.

[0177] The energy storage modulus and loss modulus datasets of the material in a preset temperature and frequency domain are obtained through dynamic mechanical testing. A loss factor calculation logic is executed to generate a three-dimensional matrix of temperature, frequency, and loss factor. Using the peak loss factor data in the three-dimensional matrix as input, Arrhenius fitting logic is executed to generate molecular chain segment activation energy parameters. Using the full-frequency domain data in the three-dimensional matrix as input, fractional-order differential constitutive modeling logic is executed to generate a constitutive parameter set. Using the molecular chain segment activation energy parameters as input, shift factor fusion calculation logic is executed to generate a shift factor parameter set. Using the three-dimensional matrix as baseline data input, the molecular chain segment activation energy parameters as physical constraint input, and the constitutive parameter set and shift factor parameter set as inputs to be optimized, regularized objective optimization logic is executed to generate an optimization parameter set.

[0178] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0179] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for constructing a model relating the loss factor of a damping layer material to temperature, characterized in that, Includes the following steps: Step 1: Perform dynamic mechanical property tests on the material in the temperature range of -70℃ to 300℃ using a dynamic thermomechanical analyzer, collect data on storage modulus E' and loss modulus E', and calculate the loss factor tanδ(T,f) matrix; Step 2: Fit the peak data of the loss factor based on the Arrhenius equation and calibrate the molecular chain segment activation energy E. a ; Step 3: Construct a fractional Zener constitutive model, obtain the frequency domain expression of the complex modulus through Fourier transform, and calculate the loss factor tanδ(ω) by separating the real and imaginary parts; Step 4: Modify the Williams-Landel-Ferry equation and fuse the activation energy E. a Based on the free volume theory, a cross-scale temperature shift factor a is established. T ; Step 5: Establish a multi-objective optimization function and collaboratively optimize the activation energy E. a The fractional-order parameters α, β, and γ, as well as the shift factor parameters C1 and C2, are used to ensure that the model prediction error is less than 5%.

2. The method for constructing a model relating the loss factor of a damping layer material to temperature according to claim 1, characterized in that, In step one, the strain amplitude ∈ 0 of the dynamic mechanical test is controlled within the range of 0.01%-0.1%, and the frequency scan range is 0.001-100Hz.

3. The method for constructing a model relating the loss factor of a damping layer material to temperature according to claim 1, characterized in that, In step two, the activation energy E a The calibration was achieved through a temperature scanning experiment at a fixed frequency, and the relationship between the logarithm of the frequency and the reciprocal of the peak temperature was fitted using linear regression.

4. The method for constructing a model relating the loss factor of a damping layer material to temperature according to claim 1, characterized in that, In step three, the fractional order α of the fractional Zener constitutive model ranges from 0.2 to 0.8, and the stress / strain term product coefficients β and γ are determined by the position of the loss peak.

5. The method for constructing a model relating the loss factor of a damping layer material to temperature according to claim 1, characterized in that, The modified WLF equation in step four includes a molecular chain segment energy barrier term. With free volume term 6. The method for constructing a model relating the loss factor of a damping layer material to temperature according to claim 1, characterized in that, In step five, the optimization function introduces a regularization term λ(E). a -E a,sim ) 2 The consistency between the constraint activation energy and the molecular dynamics simulation value is evident.

7. The method for constructing a model relating the loss factor of a damping layer material to temperature according to claim 1, characterized in that, The multi-scale temperature shift factor a T The expression is:

8. A temperature-correlation prediction system for the loss factor of damping materials, characterized in that, include: S1: Experimental data acquisition module, used to collect data on the energy storage modulus and loss modulus of materials in a preset temperature and frequency domain; S2: Molecular activation energy extraction module, used to fit loss factor peak data based on the Arrhenius equation; S3: Constitutive model construction module, used to construct fractional Zener constitutive models and separate the frequency domain components of complex modulus; S4: Temperature-frequency equivalent transformation module, used to correct the WLF equation and generate shift factor parameters; S5: Parameter optimization module, used to collaboratively optimize microscopic activation energy and macroscopic viscoelastic parameters.

9. The temperature correlation prediction system for the loss factor of damping materials according to claim 8, characterized in that, The experimental data acquisition module includes a dynamic thermomechanical analyzer and a temperature control chamber, with a test temperature range of -70℃ to 300℃ and a frequency range of 0.001-100Hz.

10. The temperature correlation prediction system for the loss factor of damping materials according to claim 8, characterized in that, The parameter optimization module employs a regularized genetic algorithm to balance data fitting accuracy with physical constraints.

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