Microstructure optimization method for automobile damping rubber product

Abstract

The invention provides a microstructure optimization method for an automobile damping rubber product, and belongs to the technical field of damping rubber products.The method comprises the steps that firstly, actual road condition vibration data are collected, and a key frequency interval is determined through Fourier transform; establishing a microstructure digital model containing hole distribution and shape parameters; performing multi-field coupling simulation analysis to evaluate the dynamic mechanical property of the microstructure; a periodic arrangement structure is designed by adopting a photonic crystal theory to form a frequency band gap; a candidate scheme is rapidly evaluated through a micro-structure performance prediction function; preparing a sample by adopting a micro-foaming forming process; carrying out microstructure characterization by using an electron microscope; applying the pre-trained neural network model to predict long-term performance; road test verification is carried out in an actual automobile, a final scheme meeting actual requirements is obtained through multiple rounds of iterative optimization, and the technical problem that in the prior art, automobile damping rubber product microstructure design is not matched with actual road condition vibration characteristics is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of shock-absorbing rubber products, and more particularly, relates to a method for optimizing the microstructure of automotive shock-absorbing rubber products. Background Art

[0002] Automotive shock-absorbing rubber products are key vibration isolation components in the suspension system. Traditional designs mainly use empirical formulas and macroscopic parameter adjustments to meet basic shock-absorbing requirements by changing parameters such as rubber formulations, overall structural dimensions, and hardness. These shock-absorbing rubber products are mainly applied to key parts such as engine mounts, shock absorber bushings, and suspension supports, and play an important role in reducing vehicle body vibration and improving ride comfort.

[0003] However, traditional design methods are difficult to accurately reduce vibration at specific frequencies. Especially in complex road conditions, the shock-absorbing effect is often unsatisfactory. Existing technologies usually adopt homogeneous material designs, which cannot form targeted frequency bandgap structures. At the same time, the microstructure has a high degree of randomness, making it impossible to achieve selective attenuation of vibrations at specific frequencies, resulting in low shock-absorbing efficiency in certain frequency bands and difficulty in accurately predicting service life.

[0004] This problem of the mismatch between the microstructure design and the vibration characteristics of actual road conditions makes it difficult for existing shock-absorbing rubber products to simultaneously meet the requirements of wide-frequency-domain shock absorption, environmental adaptability, and long-term stability. Especially when facing complex vibration spectra generated under different road conditions, the shock-absorbing performance shows obvious limitations. That is to say, there is a technical problem in the prior art of the mismatch between the microstructure design of automotive shock-absorbing rubber products and the vibration characteristics of actual road conditions. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the microstructure of automotive shock-absorbing rubber products, which can solve the technical problem of the mismatch between the microstructure design of automotive shock-absorbing rubber products and the vibration characteristics of actual road conditions in the prior art.

[0006] The present invention is implemented as follows: The present invention provides a method for optimizing the microstructure of automotive shock-absorbing rubber products, which includes the following steps: Collect the actual vibration data endured by the vehicle when running on different road conditions, record the vibration signals through an acceleration sensor, and calculate the main frequency distribution map; Establish a digital model of the rubber microstructure, including the hole distribution density, the aperture distribution range, and the hole shape parameter matrix, and use finite element analysis software to construct a three-dimensional microscopic structure grid model; Conduct multi-field coupling simulation analysis to simulate the dynamic mechanical properties of different microstructure designs under temperature conditions; Use the phonon crystal theory to design the periodic arrangement of the rubber microstructure to form a bandgap structure, and achieve selective attenuation of specific frequency vibrations by adjusting the size ratio of the microstructure units; Call the microstructure performance prediction function to quickly evaluate the candidate microstructure schemes; Prepare test samples through the micro-foaming molding process; Use an electron microscope to characterize the microstructure of the prepared samples; Use the pre-trained neural network model of the shock-absorbing rubber microstructure to analyze the test data; Conduct road tests in an actual automotive shock-absorbing system for verification.

[0007] Among them, the step of collecting the actual vibration data endured by the vehicle when running on different road conditions specifically means recording the vibration signals with a frequency range of 5 to 200 Hz through an acceleration sensor, performing Fourier transform to obtain the main frequency distribution map, and determining the frequency range that the shock-absorbing rubber products need to focus on dealing with.

[0008] Among them, the step of establishing the digital model of the rubber microstructure specifically means including a hole distribution density of 50 to 200 per cubic centimeter, an aperture distribution range of 0.1 to 2.0 mm, and a hole shape parameter matrix, and using finite element analysis software to construct a three-dimensional microscopic structure grid model.

[0009] Among them, the step of conducting multi-field coupling simulation analysis specifically means setting the Young's modulus of the rubber material to be 1.5 to 8.0 MPa, the Poisson's ratio to be 0.45 to 0.49, and the damping coefficient to be 0.05 to 0.20, and simulating the dynamic mechanical properties of different microstructure designs under the temperature range of -30 to 120 °C.

[0010] Among them, the step of using the phonon crystal theory to design the periodic arrangement of the rubber microstructure specifically means forming a bandgap structure with a frequency of 10 to 80 Hz, and achieving selective attenuation of specific frequency vibrations by adjusting the size ratio of the microstructure units to be 1:1.2:1.5:2.0.

[0011] Among them, the step of calling the microstructure performance prediction function to quickly evaluate the candidate microstructure schemes specifically means that the input parameters include the hole distribution density, the average aperture, the hole shape factor, the arrangement pattern of the microstructure units, and the target frequency range, and the output includes the estimated shock-absorbing efficiency, durability, manufacturing difficulty, and cost indicators of each scheme. The microstructure schemes with a comprehensive score of 90 or above will enter the experimental verification stage.

[0012] Among them, the test samples are prepared by the micro-foaming molding process, specifically by injecting a raw rubber mixture with a blowing agent mass fraction of 1.5 to 3.0%, and vulcanizing under the conditions of a temperature of 140 to 160 °C and a pressure of 15 to 20 MPa, and controlling the temperature gradient during the foaming process to be 5 to 10 °C per centimeter.

[0013] Among them, the microstructure of the prepared samples is characterized by an electron microscope, specifically by measuring that the deviation between the actual porosity and the designed value is controlled within 5%, and analyzing the microstructure connectivity and anisotropy index through three-dimensional reconstruction technology to ensure that the double connectivity rate is greater than 60%.

[0014] Among them, the pre-trained neural network model of the vibration-damping rubber microstructure is used to analyze the test data. Specifically, the actual microstructure image obtained by the electron microscope and the dynamic mechanical analysis test data are input into the pre-trained neural network model of the vibration-damping rubber microstructure to predict the long-term performance of the sample at different vibration frequencies and ambient temperatures, and select the scheme with a predicted vibration-damping efficiency greater than 80% and a service life exceeding 100,000 kilometers.

[0015] Among them, the microstructure performance prediction function is used to quickly screen out potential candidate schemes from a large number of microstructure schemes without performing all computationally intensive finite element analyses. The inputs include the pore distribution density parameter as a characterization of the microstructure porosity, the average pore size parameter for determining the vibration-damping frequency range, the pore shape factor parameter for describing the geometric characteristics of the micropores, the microstructure unit arrangement pattern parameter representing the spatial distribution manner of the pores, and the target frequency range parameter indicating the frequency interval that needs to be focused on for vibration damping.

[0016] Compared with the prior art, a method for optimizing the microstructure of an automotive vibration-damping rubber product provided by the present invention proposes a design method for an automotive vibration-damping rubber product based on actual vibration data acquisition and microstructure optimization. By precisely designing the pore distribution, shape, and periodic arrangement of the rubber microstructure, selective attenuation of vibrations at specific frequencies is achieved. This method applies the phonon crystal theory to the design of the vibration-damping rubber microstructure to form a bandgap structure of 10 to 80 Hz, greatly improving the vibration-damping efficiency within the target frequency range.

[0017] Through multi-field coupling simulation analysis and the microstructure performance prediction function, the present invention can accurately predict the vibration-damping performance and service life of the microstructure before actual manufacturing, avoiding the time-consuming and laborious repeated tests in the traditional method. Combining the performance analysis with the pre-trained neural network model of the vibration-damping rubber microstructure realizes an accurate mapping from the microscopic structure to the macroscopic performance, greatly improving the design efficiency and the reliability of the scheme.

[0018] The present invention solves the technical problem in the prior art that the microstructure design of automotive shock-absorbing rubber products does not match the vibration characteristics of the actual road conditions, enabling the product to maintain excellent shock-absorbing effects under various road conditions, while significantly extending the service life and meeting the requirements of the automotive industry for high-performance shock-absorbing components. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flowchart of the method of the present invention.

[0020] Figure 2 It is the vibration frequency distribution diagram in Example 2.

[0021] Figure 3 It is the bandgap characteristic diagram in Example 2.

[0022] Figure 4 It is the microstructure characterization at 500 times by scanning electron microscope in Example 2.

[0023] Figure 5 It is the microstructure characterization at 1000 times by scanning electron microscope in Example 2. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0025] As Figure 1 shown, it is a flowchart of a method for optimizing the microstructure of an automotive shock-absorbing rubber product provided by the present invention. This method includes the following steps:

[0026] S01. Collect the actual vibration data endured by the vehicle when running under different road conditions, record the vibration signals with a frequency range of 5 to 200 Hz through an acceleration sensor, and perform Fourier transform to obtain the main frequency distribution map, and determine the frequency range that the shock-absorbing rubber product needs to focus on dealing with;

[0027] S02. Establish a digital model of the rubber microstructure, including a hole distribution density of 50 to 200 per cubic centimeter, a pore size distribution range of 0.1 to 2.0 mm, and a hole shape parameter matrix, and construct a three-dimensional microscopic structure grid model using finite element analysis software;

[0028] S03. Conduct a multi-field coupling simulation analysis, set the Young's modulus of the rubber material to be 1.5 to 8.0 MPa, the Poisson's ratio to be 0.45 to 0.49, and the damping coefficient to be 0.05 to 0.20, and simulate the dynamic mechanical properties of different microstructure designs under the condition of a temperature range of -30 to 120 degrees Celsius;

[0029] S04. Design the periodic arrangement of rubber microstructures using the phonon crystal theory to form a bandgap structure with a frequency range of 10 to 80 Hz, and achieve selective attenuation of specific frequency vibrations by adjusting the size ratio of the microstructure units to 1:1.2:1.5:2.0;

[0030] S05. Call the microstructure performance prediction function to quickly evaluate the candidate microstructure solutions. The input parameters include the pore distribution density, average pore size, pore shape factor, microstructure unit arrangement pattern, and the target frequency range. Output the estimated vibration reduction efficiency, durability, manufacturing difficulty, and cost indicators for each solution. Microstructure solutions with a comprehensive score of over 90 points will enter the experimental verification stage;

[0031] S06. Prepare test samples through the microfoaming molding process. Inject a raw rubber mixture with a blowing agent mass fraction of 1.5 to 3.0%, and vulcanize it under the conditions of a temperature of 140 to 160 °C and a pressure of 15 to 20 MPa, controlling the temperature gradient during the foaming process to be 5 to 10 °C per centimeter;

[0032] S07. Use an electron microscope to characterize the microstructure of the prepared samples. Control the deviation between the actual porosity and the designed value within 5%. Analyze the microstructure connectivity and anisotropy index through three-dimensional reconstruction technology to ensure that the double connectivity rate is greater than 60%;

[0033] S08. Use the pre-trained vibration reduction rubber microstructure neural network model to analyze the test data. Input the actual microstructure images obtained by the electron microscope and the dynamic mechanical analysis test data into the pre-trained vibration reduction rubber microstructure neural network model to predict the long-term performance of the samples at different vibration frequencies and environmental temperatures. Select solutions with a predicted vibration reduction efficiency greater than 80% and a service life exceeding 100,000 kilometers;

[0034] S09. Conduct road tests in an actual automotive shock absorption system. Measure the vibration isolation rate of the optimized shock absorption rubber products under three conditions: flat road surface, gravel road surface, and bumpy road surface, and collect data on structural aging and performance degradation after continuous driving of 10,000 kilometers. If the actual vibration reduction effect deviates from the expected value by more than 15% or the performance degrades by more than 20% after 10,000 kilometers of use, then return to step S04 to redesign the periodic arrangement of the microstructures and adjust the size ratio parameters of the microstructure units. At the same time, adjust the weight coefficients in the microstructure performance prediction function in step S05 to improve the prediction accuracy. Through multiple rounds of iterative optimization, obtain a microstructure solution for the shock absorption rubber product that meets the requirements of the actual automotive use environment and is long-term stable and reliable.

[0035] Among them, the Fourier transform is specifically a mathematical operation process that converts a time-domain vibration signal into a frequency-domain representation form, which can decompose a complex vibration waveform into a superposition of different frequency components, and helps to determine the vibration frequencies that need to be isolated with emphasis.

[0036] Among them, the phononic crystal theory is specifically a theory that studies the propagation characteristics of sound waves in a periodic structure in an elastic medium. By designing microstructures with a specific periodic arrangement, a band gap that prohibits the propagation of vibrations at specific frequencies can be formed, thereby achieving efficient isolation of vibrations at the target frequencies.

[0037] Among them, the double connectivity specifically refers to the degree of connectivity between holes in the microstructure, which is expressed as the percentage of two independent paths connecting the same region. A high double connectivity helps to improve the energy dissipation ability of the damping rubber under large deformation conditions.

[0038] Among them, the anisotropy index is specifically a parameter that quantifies the difference in mechanical properties of a material in different directions, and its value range is from 0 to 1. The larger the value, the stronger the directionality. By controlling the anisotropy index, the vibration damping characteristics of rubber products in different directions can be adjusted.

[0039] Among them, the storage modulus is specifically a parameter that represents the ability of a material to store elastic deformation, which reflects the stiffness characteristics of rubber products. The larger the value, the stronger the ability to recover deformation.

[0040] Among them, the loss modulus is specifically a parameter that represents the ability of a material to dissipate mechanical energy and convert it into heat energy, which reflects the damping characteristics of rubber products. The larger the value, the better the vibration damping effect.

[0041] The microstructure performance prediction function is used to quickly screen out potential candidate solutions from a large number of microstructure solutions without performing all computationally intensive finite element analyses. The inputs include the hole distribution density parameter as a characterization of the microstructure porosity, the average pore size parameter for determining the vibration damping frequency range, the hole shape factor parameter for describing the geometric characteristics of the micropores, the microstructure unit arrangement pattern parameter representing the spatial distribution of the holes, and the target frequency range parameter indicating the frequency interval that needs to be damped with emphasis. The output is a comprehensive evaluation result composed of a vibration damping efficiency index, a durability index, a manufacturing difficulty index, and a cost index. The microstructure performance prediction function is based on a regression model established from a large amount of historical simulation and experimental data, and quickly estimates the performance of new solutions through interpolation and extrapolation methods, reducing the design iteration cycle and improving the screening efficiency.

[0042] The specific structure of the pre-trained vibration-damping rubber microstructure neural network model is a dual-path fusion convolutional neural network architecture, which includes a microstructure image processing path and a mechanical property data processing path. The microstructure image processing path consists of five layers of convolutional neural networks. The input is a microstructure scanning electron microscope image of 256×256 pixels, and the convolutional layer is used to extract the features of pore morphology, distribution and connectivity. The mechanical property processing path consists of three layers of fully connected neural networks, and the input is the storage modulus and loss modulus spectrum data obtained from dynamic mechanical analysis tests. The features of the two paths are fused through an attention mechanism in the fusion layer, and the output of the fusion layer is sent to a predictor composed of four layers of fully connected networks to generate the vibration-damping performance and life prediction results under different usage conditions. The parameters of the jump attention mechanism in the pre-trained vibration-damping rubber microstructure neural network model are dynamically adjusted according to the three key parameters of the target frequency range, the expected usage temperature range and the maximum strain amplitude, ensuring that the pre-trained vibration-damping rubber microstructure neural network model is more accurate in predicting the performance under key working conditions.

[0043] The steps for establishing the training data set during the pre-training process of the pre-trained vibration-damping rubber microstructure neural network model specifically include collecting the data of vibration-damping rubber samples with more than 5000 different formulations and microstructure designs. Each sample includes high-resolution electron microscope images and complete dynamic mechanical property test data; performing standardized accelerated aging tests on each sample to simulate the performance changes under the equivalent driving conditions of 100,000 kilometers, and recording the vibration-damping efficiency decay curve and the structural damage evolution process; grading and labeling the sample performance according to the actual road test data to establish a multi-dimensional database that correlates the microstructure parameters, dynamic mechanical properties and long-term usage performance; expanding the training samples through data augmentation techniques, including image rotation, scaling and noise addition, as well as the synthesis and interpolation of mechanical property data, and finally forming a comprehensive data set containing more than 20,000 training samples.

[0044] The steps for pre-training the pre-trained vibration-damping rubber microstructure neural network model specifically include adopting a phased training strategy. First, pre-train the microstructure image processing path and the mechanical property data processing path separately, and use the supervised learning method to let the network learn the mapping relationship between the microstructure features and the macroscopic mechanical properties. Subsequently, freeze the underlying parameters of the two paths, train the fusion layer and the jump attention mechanism, and let the pre-trained vibration-damping rubber microstructure neural network model learn to dynamically adjust the feature fusion weights according to different working conditions. Finally, perform end-to-end fine-tuning, use the actual road test data to verify the prediction accuracy of the pre-trained vibration-damping rubber microstructure neural network model, and optimize the parameters of the entire network through backpropagation. During the training process, adopt cross-validation and early stopping strategies to prevent overfitting. Finally, the pre-trained vibration-damping rubber microstructure neural network model achieves an accuracy with an average error of less than 10% in vibration-damping performance prediction and an accuracy with an average error of less than 15% in service life prediction.

[0045] The specific implementation manners of the above steps are described in detail below. The specific implementation manner of step S01 is to first install high-precision triaxial acceleration sensors at appropriate positions, including three key positions: the body suspension connection, the bottom of the cab, and the cargo area. The sampling frequency of the sensors is set to 1000 Hz to ensure that all vibration signals in the range of 5 to 200 Hz can be captured. Under three typical road conditions: flat road, gravel road, and bumpy road, standard driving tests are carried out at vehicle speeds of 40 km / h, 60 km / h, and 80 km / h respectively, and vibration data of no less than 600 seconds are continuously collected under each condition. After the collection is completed, the original signal is preprocessed using the Hanning window function to reduce the spectral leakage phenomenon, and then the fast Fourier transform algorithm is applied to convert the time-domain vibration signal into a frequency-domain representation. Perform power spectral density analysis on the transformation result, draw the distribution curve of the vibration energy in the frequency domain, and based on the power spectral analysis result, identify the main frequency interval where the vibration energy accounts for more than 80%. The purpose of this step is to accurately obtain the vibration characteristics of the vehicle in the actual use environment and provide a data basis for the subsequent targeted design of the shock-absorbing rubber microstructure.

[0046] The specific implementation of step S02 is to create a three-dimensional digital representation model using voxel modeling method, and initially set a basic unit with an overall size of 10×10×10 mm. First, determine the hole spatial distribution pattern, including three typical structures: random distribution pattern, regular arrangement pattern, and gradient distribution pattern. For the random distribution pattern, use the Monte Carlo algorithm to generate the hole center coordinates; for the regular arrangement pattern, use the equidistant arrangement method to determine the hole positions; for the gradient distribution pattern, set the porosity to vary linearly along a specific direction. Subsequently, construct a hole shape parameter matrix, including three basic shapes: spherical, ellipsoidal, and polyhedral. For spherical holes, only the radius parameter is required; for ellipsoidal holes, three principal axis lengths and the rotation angle need to be set; for polyhedral holes, the vertex coordinates and connection relationships need to be defined. Use Boolean operations to subtract the hole volume from the matrix material to form a digital model with a specific microstructure. Import the constructed geometric model into finite element analysis software, and use adaptive mesh generation technology to generate a three-dimensional tetrahedral element mesh. Locally refine the mesh at the hole edges and stress concentration areas, and set the mesh size to 1 / 10 of the minimum hole diameter to ensure calculation accuracy. The purpose of this step is to establish a digital model that can accurately represent the microstructural characteristics of the damping rubber and provide a geometric basis for subsequent performance analysis.

[0047] The specific implementation of step S03 is to first establish a hyperelastic constitutive model of the rubber material, and use the two-parameter Mooney-Rivlin model to describe the nonlinear mechanical behavior of the rubber under large deformation conditions. For different temperature conditions, use the Williams-Landel-Ferry shift function to establish a temperature-dependent relationship model for the dynamic mechanical properties of the rubber. Construct a thermo-mechanical coupling analysis model, considering the influence of temperature changes on material properties and the temperature rise effect caused by the conversion of mechanical energy into heat energy. Set the boundary conditions, apply a fixed constraint at the bottom, a periodic displacement excitation at the top, and periodic boundary conditions on the sides to simulate a large-scale structure. Use an explicit dynamics solver for transient analysis, and set the time step to 1 / 20 of the highest analysis frequency period to ensure calculation stability. For each microstructural design scheme, perform dynamic response analysis at five typical frequency points of 10, 20, 40, 80, and 160 Hz, and five typical temperature points of -30, 0, 30, 60, and 120 °C. Calculate and extract the storage modulus and loss modulus under each condition, and draw a three-dimensional surface plot of the main damping ratio varying with frequency and temperature based on the calculation results to evaluate the vibration damping performance of the microstructure within the target frequency range. The purpose of this step is to evaluate the dynamic mechanical properties of different microstructural designs under various working conditions through virtual simulation methods, reduce experimental costs, and shorten the development cycle.

[0048] The specific implementation of step S04 is to design a periodic microstructure based on the phonon crystal band gap theory. First, a calculation model for the dispersion relation of the phonon crystal is established, and the plane wave expansion method is used to solve the eigenfrequencies and corresponding vibration modes of the microstructure unit. Four basic microstructure units with different size ratios are designed, corresponding to size ratios of 1∶1.2∶1.5∶2.0 respectively. By adjusting the size and position of the holes inside the basic unit, band gaps are formed in each unit within a specific frequency range. The transfer matrix method is used to calculate the vibration transmission characteristics under different unit arrangements and combinations, and the arrangement with the most significant attenuation within the target frequency range is selected. Based on the Bragg scattering principle, the period length of the microstructure is adjusted to align the center frequency of the first-order band gap with the main vibration frequency determined in step S01. Considering the local resonance effect, independent resonator structures are added to the basic microstructure unit, and by adjusting the mass and elastic parameters of the resonator, an attenuation band gap for specific low-frequency vibrations is formed. A gradient parameter microstructure design is proposed, where the microstructure parameters gradually change along the vibration propagation direction to form a broadband vibration reduction effect. The topology optimization method is used, based on the bi-directional evolutionary structural optimization algorithm, to further optimize the microstructure morphology under the condition of meeting the manufacturing constraints, so that the band gap characteristics are best matched with the target frequency. The purpose of this step is to use the phonon crystal theory to design a periodic microstructure with a selective isolation effect on vibrations of specific frequencies and improve the performance of the shock-absorbing rubber products.

[0049] The specific implementation of step S05 is to construct a rapid evaluation system for the microstructure performance. This system is based on a hybrid model combining the support vector regression algorithm and the radial basis function neural network. The input parameter vector includes five key indicators: the hole distribution density, the average pore size, the hole shape factor, the arrangement pattern of the microstructure units, and the target frequency range. Among them, the hole distribution density controls the overall porosity and affects the material stiffness and vibration reduction efficiency; the average pore size determines the characteristic size of the microstructure and affects the applicable frequency range; the hole shape factor describes the geometric characteristics of the holes and affects the stress distribution and energy dissipation mechanism; the arrangement pattern of the microstructure units determines the phonon crystal band gap characteristics and affects the frequency selectivity; the target frequency range clarifies the vibration reduction requirements and is used for performance evaluation. The predicted outputs include four evaluation results: the vibration reduction efficiency index, the durability index, the manufacturing difficulty index, and the cost index. The weighted comprehensive scoring method is used for the evaluation results, and the weights of each index can be dynamically adjusted according to specific application requirements. Generally, the weight of the vibration reduction efficiency is 0.4, the weight of the durability is 0.3, the weight of the manufacturing difficulty is 0.2, and the weight of the cost index is 0.1. The scoring threshold is set at 90 points, and the candidate solutions with a comprehensive score of over 90 points are selected. For the solutions that pass the preliminary screening, the analytic hierarchy process is further applied for detailed comparison. A judgment matrix is established based on expert experience, the relative importance of each solution is calculated, and the top three ranked solutions are selected to enter the experimental verification stage. The purpose of this step is to quickly screen out the most potential candidate solutions from a large number of possible microstructure design solutions and improve the design efficiency.

[0050] The specific implementation of step S06 is as follows: First, prepare the rubber substrate. Select natural rubber and styrene-butadiene rubber and mix them in a mass ratio of 70:30. Add appropriate amounts of additives such as vulcanizing agents, activators, and anti-aging agents, and conduct sufficient mixing on a two-roll mixer. According to the requirements of the microstructure design, select an appropriate type of blowing agent. Commonly used blowing agents include azodicarbonamide and sodium bicarbonate, etc. The addition amount is controlled within the range of 1.5 to 3.0% of the mass of the raw rubber mixture. Preform the mixed rubber and use the pressing method to make a film with a thickness close to that of the final product. Load the preformed film into a mold. The shape of the inner cavity of the mold is the same as that of the final product, and the surface of the mold is treated to a surface roughness not exceeding 0.4 microns to ensure the surface quality of the finished product. Place the mold loaded with the film into a vulcanizer, set the vulcanization temperature at 140 to 160 degrees Celsius, the pressure at 15 to 20 MPa, and control the vulcanization time according to the rubber thickness. Generally, for every 1 mm increase in thickness, the vulcanization time increases by 1 minute. Adopt the program temperature control technology, set the temperature gradient at 5 to 10 degrees Celsius per centimeter, and achieve directional foaming through multi-region independent temperature control to form the anisotropic microstructure required by the design. After vulcanization is completed, perform demolding and post-treatment, including trimming, cleaning, and surface treatment, to obtain the finished product sample. Conduct a preliminary quality inspection on the prepared sample, including appearance inspection, dimensional measurement, and hardness test, to ensure that the basic physical properties meet the requirements. The purpose of this step is to convert the digital design of the microstructure into an actual shock-absorbing rubber product sample through the micro-foaming molding process, providing an entity for subsequent performance verification.

[0051] The specific implementation of step S07 is to use a scanning electron microscope to conduct microstructure characterization on the prepared sample. The sample pretreatment includes cryogenic fracture and surface metal spraying. Set the acceleration voltage of the scanning electron microscope to 10 kV and the working distance to 10 mm to obtain microscopic morphology images at three magnification ratios of 100 times, 500 times, and 2000 times. Based on the obtained electron microscope images, use image analysis software for pore identification and statistics. Use the adaptive threshold segmentation algorithm to distinguish the material matrix and pore parts, and extract the geometric feature parameters of the pores. Statistically analyze the pore size distribution, spatial distribution, and shape parameters, calculate the actual porosity, and compare it with the designed value, requiring the deviation to be controlled within 5%. Use X-ray micro-computed tomography technology to obtain the three-dimensional voxel data of the sample, and set the scanning resolution to 5 microns to ensure accurate identification of the smallest pore structure. Based on the tomographic scanning data, conduct three-dimensional reconstruction to establish a virtual three-dimensional model of the microstructure. Perform skeletonization processing on the reconstructed model, extract the connected domain information, calculate the double connectivity rate, and require the double connectivity rate to be greater than 60% to ensure good energy dissipation performance. Use the structure tensor method to calculate the anisotropy index of the microstructure and evaluate the mechanical property differences in different directions. By calculating the angle between the main direction of the anisotropy index and the designed direction, verify whether the orientation of the microstructure meets the design requirements, allowing the deviation angle not to exceed 15 degrees. The purpose of this step is to conduct a detailed characterization of the microstructure of the prepared sample, verify the consistency between the actual microstructure and the design requirements, and provide the microstructure basic data for subsequent performance prediction.

[0052] The specific implementation of step S08 is to first perform standard dynamic mechanical analysis tests on the prepared samples. Using a dynamic mechanical analyzer in tensile mode, the frequency scanning range is from 0.1 to 200 Hz, the temperature range is from -30 to 120 degrees Celsius, and the strain amplitudes are set at three levels of 0.1%, 1%, and 10% to obtain data on the storage modulus and loss modulus varying with frequency and temperature. The microstructure images obtained by the electron microscope are preprocessed into a standard format of 256×256 pixels, and the contrast is enhanced and noise is reduced through an image enhancement algorithm. The preprocessed microstructure images and the dynamic mechanical analysis test data are used as inputs and fed into a pre-trained vibration damping rubber microstructure neural network model. This network model adopts a dual-path fusion convolutional neural network architecture, consisting of a microstructure image processing path and a mechanical property data processing path. The microstructure image processing path extracts the morphological features of the microstructure through five convolutional layers, and each convolution is followed by a batch normalization layer and a ReLU activation function; the mechanical property processing path encodes the dynamic mechanical characteristics through a three-layer fully connected network. The features of the two paths are fused through a jump attention mechanism to generate a comprehensive feature representation. The fused features are fed into a four-layer fully connected predictor to output the predicted performance of the samples under different vibration frequencies, ambient temperatures, and usage times. According to the output of the neural network, the vibration damping efficiency and service life of each sample under the expected usage conditions are ranked, and the optimal solution with a predicted vibration damping efficiency greater than 80% and a service life exceeding 100,000 kilometers is selected. The purpose of this step is to use an artificial intelligence model to predict the performance of the samples under long-term usage conditions based on the actual microstructure and preliminary test data, so as to select the best solution.

[0053] The specific implementation of step S09 is to install the selected optimal shock-absorbing rubber product into the actual vehicle shock-absorbing system, and design standard test routes, including three road conditions: 5 kilometers of flat road, 3 kilometers of gravel road, and 2 kilometers of bumpy road. The tests are carried out at three vehicle speeds of 40 km / h, 60 km / h, and 80 km / h respectively under the three road conditions, and each group of conditions is repeatedly tested 3 times to ensure data reliability. During the test process, vibration measurement equipment is installed at key positions on the vehicle body to collect vibration signals before and after shock absorption, and the vibration isolation rate of each frequency band is calculated. The vibration isolation rate calculation formula is: vibration isolation rate = (1 - amplitude after shock absorption / amplitude before shock absorption) × 100%. According to the test results, calculate the deviation between the actual shock-absorbing effect and the expected performance. If the deviation exceeds 15%, it is necessary to return to step S04 to redesign the microstructure. Arrange long-term road tests, drive continuously for 10,000 kilometers, and take samples for testing every 1,000 kilometers to record the change trend of shock-absorbing performance. Evaluate the aging degree of the tested samples, including indicators such as hardness change rate, permanent deformation amount, and microstructure change. If the performance decay exceeds 20%, it is necessary to return to step S04 to redesign. Analyze the reasons for the problems found, update the weight coefficients in the microstructure performance prediction function, and improve the prediction accuracy for problem working conditions. If the test results do not meet the requirements, conduct a new round of iterative design and optimization according to the process from step S04 to step S08 until a microstructure scheme of the shock-absorbing rubber product that meets the actual use requirements and is long-term stable and reliable is obtained. The purpose of this step is to verify the performance of the optimized shock-absorbing rubber product through actual road tests, ensure that it can play a shock-absorbing role stably and reliably in the real use environment for a long time, and continuously improve the design scheme through iterative optimization.

[0054] The following details the mathematical models or calculation processes involved in the present invention.

[0055] The Fourier transform process in step S01 is specifically expressed as follows:

[0056]

[0057] In the formula, X(f) is the frequency domain representation; x(t) is the time domain vibration signal; f is the frequency; t is the time; j is the imaginary unit.

[0058] For the discretely sampled vibration signal, the discrete Fourier transform is used, and its expression is:

[0059]

[0060] In the formula, X(k) is the k-th frequency component; x(n) is the n-th sampling point; N is the total number of sampling points; the range of k is from 0 to N - 1.

[0061] The power spectral density calculation formula is:

[0062]

[0063] Wherein, P(f) is the power spectral density; T is the sampling time length; |X(f)| is the amplitude of the Fourier transform.

[0064] The power spectral density is used to characterize the distribution of vibration energy in frequency, and the main vibration frequency is determined by identifying the power spectral density peak. In this step, the Hanning window function is used to preprocess the original signal, and its expression is:

[0065]

[0066] Wherein, w(n) is the window function value; n is the sampling point serial number, ranging from 0 to N - 1; N is the window length.

[0067] The windowed signal is expressed as:

[0068] x w (n) = x(n)w(n);

[0069] Wherein, x w (n) is the windowed signal; x(n) is the original signal; w(n) is the window function.

[0070] The purpose of using the Hanning window is to reduce the spectral leakage phenomenon and improve the spectral analysis accuracy. The Fourier transform selects this mathematical form because it can decompose the time-domain signal into the sum of simple harmonic components of different frequencies, and the exponential term represents a rotating vector, which can express both amplitude and phase information.

[0071] The random distribution of the hole space in step S02 is generated using the Monte Carlo algorithm, and the specific formula is:

[0072] x i = x min + r x ·(x max - x min );

[0073] y i = y min + r y ·(y max - y min );

[0074] z i = z min + r z ·(z max - z min );

[0075] Wherein, (x i , y i , z i) is the center coordinate of the i-th hole; (x min , y min , z min ) and (x max , y max , z max ) are the lower and upper limits of the coordinate range respectively; r x , r y , r z are random numbers in the interval [0, 1].

[0076] When generating the hole positions, it is necessary to check the distance between the newly generated holes and the existing holes to avoid overlap:

[0077]

[0078] d ij ≥r i +r j +d min ;

[0079] In the formula, d ij is the distance between the centers of the i-th hole and the j-th hole; r i and r j are the radii of the two holes respectively; d min is the minimum allowable spacing, generally set to 0.1 times the average pore diameter.

[0080] For the gradient distribution pattern, the porosity varies linearly along a specific direction, and its expression is:

[0081]

[0082] In the formula, φ(z) is the local porosity at position z; φ min and φ max are the minimum and maximum values of the porosity respectively, generally set in the range of 0.1 to 0.6; z is the coordinate value along the gradient direction; z min and z max are the coordinate ranges.

[0083] The local refinement of the mesh generation adopts a curvature-based adaptive algorithm, and its element size calculation formula is:

[0084]

[0085] In the formula, h i is the mesh size of the i-th region; h max is the maximum allowable mesh size; κ i is the local curvature of this region; κ max and κ minThey are the maximum and minimum curvatures of the model respectively; p is a control parameter, generally taking a value of 0.5.

[0086] These formulas are comprehensively applied in the microstructural geometry modeling process. The random distribution can simulate the randomness in the real foaming process by using the Monte Carlo method, while the gradient distribution can achieve the design of directional properties. The distance check ensures the rationality of the microstructure, and the mesh adaptive algorithm improves the calculation efficiency while ensuring the calculation accuracy.

[0087] The expression of the Mooney-Rivlin hyperelastic model in step S03 is:

[0088] W = C 10 (I1 - 3) + C 01 (I2 - 3);

[0089] In the formula, W is the strain energy density function; C 10 and C 01 are material parameters, usually obtained by fitting the test data of uniaxial tension, biaxial tension and pure shear; I1 and I2 are the first and second invariants of the deformation tensor.

[0090] The expression of the Williams-Landel-Ferry shift function is:

[0091]

[0092] In the formula, a T is the temperature shift factor; T is the current temperature; T0 is the reference temperature; C1 and C2 are material constants. For most rubber materials, C1 is about 17.44 and C2 is about 51.6.

[0093] The calculation formulas for the storage modulus and the loss modulus are:

[0094]

[0095] In the formula, E′ is the storage modulus; E″ is the loss modulus; σ0 is the stress amplitude; ε0 is the strain amplitude; δ is the phase difference between the stress and the strain.

[0096] The calculation formula for the main damping ratio is:

[0097]

[0098] In the formula, ζ is the main damping ratio, which characterizes the vibration damping ability of the material.

[0099] The Mooney-Rivlin model is selected because it can effectively describe the nonlinear characteristics of rubber materials in the medium deformation range and has the advantages of few parameters and simple calculation. The Williams-Landel-Ferry function is based on the time-temperature equivalence principle and can establish the relationship between the dynamic mechanical properties of rubber at different temperatures. The storage modulus and loss modulus respectively characterize the ability of the material to store and dissipate energy and are important indicators for evaluating the vibration damping performance.

[0100] In step S04, the plane wave expansion method is used to calculate the phonon crystal dispersion relation, and its characteristic equation is:

[0101] ∑ G′ [Λ ijkl (G - G′)·(k + G′) k ·(k + G) l -ω 2 ρ(G - G′)δ ij u j (G′) = 0;

[0102] In the formula, Λ ijkl is the Fourier transform of the elastic constant tensor; k is the Bloch wave vector; G and G′ are the reciprocal lattice vectors; ω is the angular frequency; ρ is the Fourier transform of the density; δ ij is the Kronecker function; u j is the displacement component.

[0103] For the periodic microstructure, its band gap characteristics can be calculated by the transfer matrix method, and the unit transfer matrix is:

[0104]

[0105] In the formula, T is the transfer matrix; k is the wave number; L is the unit length.

[0106] For a system composed of n different units, the total transfer matrix is:

[0107] T total = T n ·T n-1 ·…·T2·T1;

[0108] The vibration transmission coefficient of the system can be expressed as:

[0109]

[0110] In the formula, τ is the vibration transmission coefficient; T ij is the element of the total transfer matrix.

[0111] For the gradient parameter microstructure, the parameter change can be expressed as:

[0112]

[0113] In the formula, p(x) is the parameter value at position x; p0 is the initial parameter value; Δp is the parameter change; f(x / L) is the change function, which can be a linear function, an exponential function, a sine function, etc.; L is the total length.

[0114] The choice of the phonon crystal theory is based on its ability to accurately describe the wave propagation characteristics in periodic structures. The plane wave expansion method can solve the eigenfrequencies and vibration modes, providing a theoretical basis for bandgap design. The transfer matrix method is simple and efficient in calculation and is applicable to the vibration transmission analysis of one-dimensional and quasi-one-dimensional structures. The gradient parameter design can broaden the bandgap by breaking the strict periodicity and improve the applicable frequency range of the vibration damping system.

[0115] The microstructure performance prediction function in step S05 is based on support vector regression and radial basis function neural network, and its mathematical expression is:

[0116]

[0117] In the formula, y is the predicted output; x is the input parameter vector; x i is the support vector; α i is the Lagrange multiplier; K(x, x i ) is the kernel function; b is the bias term; N is the number of support vectors.

[0118] The expression of the radial basis kernel function is:

[0119] K(x, x i ) = exp(-γ||x - x i || 2 );

[0120] In the formula, γ is the kernel parameter, which controls the width of the radial basis function. Generally, the optimal value is determined by cross-validation, and the range is from 0.01 to 100.

[0121] The weighted comprehensive score calculation formula is:

[0122] S = w1S1 + w2S2 + w3S3 + w4S4;

[0123] In the formula, S is the comprehensive score; S1, S2, S3, S4 are the standardized scores of the vibration damping efficiency index, durability index, manufacturing difficulty index, and cost index respectively; w1, w2, w3, w4 are the weights of each index, and w1 + w2 + w3 + w4 = 1.

[0124] The judgment matrix in the analytic hierarchy process is:

[0125]

[0126] In the formula, A is the judgment matrix; aij Denote the importance ratio of solution i relative to solution j, generally using a scale from 1 to 9.

[0127] The calculation formula for the maximum eigenvalue of the judgment matrix is:

[0128] A·W=λ max ·W;

[0129] In the formula, W is the eigenvector, representing the weights of each solution; λ max is the maximum eigenvalue.

[0130] The calculation formula for the consistency ratio is:

[0131]

[0132] In the formula, CR is the consistency ratio; CI is the consistency index; RI is the random consistency index, related to the matrix order n; when CR < 0.1, it is considered that the judgment matrix has satisfactory consistency.

[0133] Support vector regression and radial basis function neural network are selected because they have excellent fitting ability for nonlinear mapping and can handle high-dimensional input data. The radial basis kernel function has good local response characteristics and is suitable for solving highly nonlinear problems such as microstructural performance prediction. The weighted comprehensive scoring method can comprehensively consider multiple evaluation indicators to achieve multi-objective optimization. The analytic hierarchy process quantifies expert experience into a mathematical model by constructing a judgment matrix, improving the scientificity of decision-making.

[0134] The calculation formula for the vibration isolation rate in step S09 is:

[0135]

[0136] In the formula, η is the vibration isolation rate; A1 is the amplitude before shock absorption; A2 is the amplitude after shock absorption.

[0137] The calculation formula for the shock absorption performance deviation is:

[0138]

[0139] In the formula, δ is the performance deviation; η actual is the actually measured vibration isolation rate; η predicted is the predicted vibration isolation rate.

[0140] The calculation formula for the shock absorption performance attenuation rate is:

[0141]

[0142] In the formula, Δ is the performance attenuation rate; η0 is the initial vibration isolation rate; η t is the vibration isolation rate after using t kilometers.

[0143] The weight update formula for the microstructure performance prediction function is as follows:

[0144]

[0145] In the formula, and are the weight coefficients after and before the update, respectively; α is the learning rate, usually set to be between 0.01 and 0.1; E is the prediction error; is the partial derivative of the error with respect to the weight.

[0146] The prediction error calculation formula is:

[0147]

[0148] In the formula, E is the mean square error; M is the number of samples; is the predicted value of the j-th sample; is the actual value of the j-th sample.

[0149] The vibration isolation rate formula is based on the vibration transfer theory and directly reflects the vibration reduction effect by calculating the amplitude ratio before and after vibration reduction. The calculation of performance deviation and attenuation rate can quantitatively evaluate the prediction accuracy and durability of vibration reduction products. The weight update formula is based on the principle of gradient descent, and adjusts the parameters of the prediction model through error backpropagation to improve the prediction accuracy. The mean square error, as the loss function of the prediction model, has the advantages of simple mathematical form and easy derivative calculation, and is suitable as the optimization target.

[0150] Specifically, the principle of the present invention is: The core principle of the present invention lies in using microstructure design to regulate the mechanical properties of rubber materials, especially by constructing a specific microstructure arrangement through the phonon crystal theory to form the ability to selectively attenuate vibrations of target frequencies. A phonon crystal is an artificial material with a periodic structure. When elastic waves propagate in it, due to Bragg scattering and local resonance effects, specific frequency bandgaps will be formed to prevent the propagation of vibrations within these frequency ranges. By adjusting the size ratio of the microstructure units to 1:1.2:1.5:2.0, the present invention can precisely control the position of the bandgap so that it covers the main vibration frequency range (10 to 80 Hz) generated by the vehicle under actual road conditions.

[0151] Microstructure parameters such as pore distribution density, pore size, and shape factor directly affect the storage modulus and loss modulus of rubber materials, and thus affect their vibration reduction performance. The microstructure design with a high double connectivity rate (>60%) enhances the energy dissipation ability of the material under large deformation conditions and improves the vibration reduction efficiency. By controlling the anisotropy index, it is possible to achieve different vibration reduction characteristics in different directions to better cope with multi-directional vibration input.

[0152] The present invention adopts a method combining multi-field coupling simulation and neural network model to establish an accurate mapping relationship from microstructural parameters to vibration damping performance. The pre-trained neural network model for the micro-structure of vibration damping rubber adopts a dual-path fusion convolutional neural network architecture, which can process micro-structure images and mechanical property data simultaneously, and dynamically adjusts key parameters through a jump attention mechanism to ensure prediction accuracy under various working conditions. This systematic method from micro-design to macro-performance breaks through the limitations of traditional empirical design and realizes the precise design and control of the performance of vibration damping rubber products.

[0153] A specific embodiment 1 of the present invention is provided below. The specific implementation of each step in this embodiment 1 is described in detail as follows.

[0154] The specific implementation of step S01 is to first install high-precision triaxial acceleration sensors at appropriate positions, including three key positions: the body suspension connection, the bottom of the cab, and the cargo area. The sampling frequency of the sensors is set to 1000 Hz to ensure that all vibration signals in the range of 5 to 200 Hz can be captured. Standard driving tests are carried out at speeds of 40 km / h, 60 km / h, and 80 km / h respectively under three typical road conditions: flat road, gravel road, and bumpy road. Vibration data is continuously collected for no less than 600 seconds under each condition. After the collection is completed, the original signal is preprocessed using the Hann window function. The expression of the Hann window function is: In the formula, w(n) is the window function value; n is the sampling point serial number, ranging from 0 to N - 1; N is the window length. The windowed signal is expressed as: x w (n) = x(n)w(n); in the formula, x w (n) is the windowed signal; x(n) is the original signal; w(n) is the window function. Subsequently, the fast Fourier transform algorithm is applied to convert the time-domain vibration signal into a frequency-domain representation. Its expression is: In the formula, X(f) is the frequency-domain representation; x(t) is the time-domain vibration signal; f is the frequency; t is the time; j is the imaginary unit. For discretely sampled vibration signals, the discrete Fourier transform is adopted, and its expression is: In the formula, X(k) is the k-th frequency component; x(n) is the n-th sampling point; N is the total number of sampling points; the range of k is from 0 to N - 1. Power spectral density analysis is performed on the transformation result, and its calculation formula is: Wherein, P(f) is the power spectral density; T is the sampling time length; |X(f)| is the amplitude of the Fourier transform. According to the power spectral density analysis results, the main frequency range where the vibration energy accounts for more than 80% is identified. The purpose of this step is to accurately obtain the vibration characteristics of the vehicle in the actual use environment and provide a data basis for the subsequent targeted design of the shock-absorbing rubber microstructure.

[0155] The specific implementation of step S02 is to create a three-dimensional digital representation model using the voxel modeling method, and initially set the basic unit with an overall size of 10×10×10 mm. First, determine the hole spatial distribution pattern, including three typical structures: random distribution pattern, regular arrangement pattern, and gradient distribution pattern. For the random distribution pattern, the Monte Carlo algorithm is used to generate the hole center coordinates, and its calculation formula is: x i = x min + r x ·(x max - x min ); y i = y min + r y ·(y max - y min ); z i = z min + r z ·(z max - z min ); In the formula, (x i , y i , z i ) is the center coordinate of the i-th hole; (x min , y min , z min ) and (x max , y max , z max ) are the lower and upper limits of the coordinate range respectively; r x , r y , r z are random numbers in the range of [0, 1]. When generating the hole positions, it is necessary to check the distance between the newly generated hole and the existing holes to avoid overlap, and its calculation formula is: d ij ≥ r i + r j + d min ; In the formula, d ij is the distance between the center of the i-th hole and the j-th hole; r i and r j are the radii of the two holes respectively; d minis the minimum allowable spacing, generally set to 0.1 times the average pore diameter. For the regular arrangement pattern, the equidistant arrangement method is used to determine the pore positions; for the gradient distribution pattern, the porosity is set to vary linearly along a specific direction, and its expression is: In the formula, φ(z) is the local porosity at position z; φ min and φ max are the minimum and maximum values of the porosity respectively, and the general setting range is from 0.1 to 0.6; z is the coordinate value along the gradient direction; z min and z max are the coordinate ranges. Subsequently, a pore shape parameter matrix is constructed, including three basic shapes: spherical, ellipsoidal, and polyhedral. The pore volume is subtracted from the matrix material using Boolean operations to form a digital model with a specific microstructure. The constructed geometric model is imported into the finite element analysis software, and an adaptive mesh generation technique is used to generate a three-dimensional tetrahedral element mesh, and its element size calculation formula is: In the formula, h i is the mesh size of the i-th region; h max is the maximum allowable mesh size; κ i is the local curvature of this region; κ max and κ min are the maximum and minimum curvatures of the model respectively; p is a control parameter, and the general value is 0.5. Local mesh refinement is performed at the pore edges and stress concentration regions, and the mesh size is set to 1 / 10 of the minimum pore diameter to ensure the calculation accuracy. The purpose of this step is to establish a digital model that can accurately characterize the microscopic structural characteristics of the damping rubber and provide a geometric basis for subsequent performance analysis.

[0156] The specific implementation method of step S03 is to first establish a hyperelastic constitutive model of the rubber material. The two-parameter Mooney-Rivlin model is used to describe the nonlinear mechanical behavior of the rubber under large deformation conditions, and its expression is: W = C 10 (I1 - 3) + C 01 (I2 - 3); in the formula, W is the strain energy density function; C 10 and C 01 are material parameters, usually obtained by fitting the test data of uniaxial tension, biaxial tension, and pure shear; I1 and I2 are the first and second invariants of the deformation tensor. For different temperature conditions, the Williams-Landel-Ferry shift function is used to establish a temperature-dependent relationship model for the dynamic mechanical properties of the rubber, and its expression is: In the formula, a Tis the temperature shift factor; T is the current temperature; T0 is the reference temperature; C1 and C2 are material constants. For most rubber materials, C1 is approximately 17.44 and C2 is approximately 51.6. A thermo-mechanical coupling analysis model is constructed, considering the influence of temperature changes on material properties and the temperature rise effect caused by the conversion of mechanical energy into heat energy. Boundary conditions are set, with a fixed constraint applied at the bottom, a periodic displacement excitation applied at the top, and periodic boundary conditions set on the sides to simulate large-scale structures. An explicit dynamics solver is used for transient analysis, and the time step is set to 1 / 20 of the highest analysis frequency period to ensure computational stability. For each microstructural design scheme, dynamic response analyses are performed at five typical frequency points of 10, 20, 40, 80, and 160 Hz, and five typical temperature points of -30, 0, 30, 60, and 120 °C. The storage modulus and loss modulus are calculated and extracted under each condition, and their calculation formulas are as follows: In the formula, E′ is the storage modulus; E″ is the loss modulus; σ0 is the stress amplitude; ε0 is the strain amplitude; δ is the phase difference between the stress and the strain. The main damping ratio is calculated based on the calculation results: In the formula, ζ is the main damping ratio, which characterizes the vibration damping ability of the material. A three-dimensional surface plot of the main damping ratio varying with frequency and temperature is plotted to evaluate the vibration damping performance of the microstructure within the target frequency range. The purpose of this step is to evaluate the dynamic mechanical properties of different microstructural designs under various working conditions through virtual simulation methods, reduce experimental costs, and shorten the development cycle.

[0157] The specific implementation of step S04 is to design a periodic microstructure based on the phonon crystal bandgap theory. First, a phonon crystal dispersion relation calculation model is established, and the plane wave expansion method is used to solve the eigenfrequencies and corresponding vibration modes of the microstructure unit. Its characteristic equation is: ∑ G′ [Λ ijkl (G - G′)·(k + G′) k ·(k + G) l - ω 2 ρ(G - G′)δ ij u j (G′) = 0; where Λ ijkl is the Fourier transform of the elastic constant tensor; k is the Bloch wave vector; G and G′ are reciprocal lattice vectors; ω is the angular frequency; ρ is the Fourier transform of the density; δ ij is the Kronecker function; u j is the displacement component. Four basic microstructure units with different size ratios are designed, corresponding to size ratios of 1∶1.2∶1.5∶2.0, and by adjusting the size and position of the holes inside the basic unit, bandgaps are formed in each unit within a specific frequency range. The transfer matrix method is used to calculate the vibration transmission characteristics of different unit arrangements. The unit transfer matrix is: where \(T\) is the transfer matrix; \(k\) is the wave number; \(L\) is the element length. For a system composed of \(n\) different elements, the total transfer matrix is: \(T\) total = \(T\) n · \(T\) n-1 ·…· \(T_2·T_1\); The vibration transmission coefficient of the system can be expressed as: where \(\tau\) is the vibration transmission coefficient; \(T\) ij is an element of the total transfer matrix. Select the arrangement method with the most significant attenuation in the target frequency range. Based on the Bragg scattering principle, adjust the microstructure period length so that the center frequency of the first band gap aligns with the main vibration frequency determined in step S01. For the gradient parameter microstructure, the parameter change can be expressed as: where \(p(x)\) is the parameter value at position \(x\); \(p_0\) is the initial parameter value; \(\Delta p\) is the parameter change amount; \(f(x / L)\) is the change function, which can be a linear function, an exponential function, a sine function, etc.; \(L\) is the total length. Considering the local resonance effect, add an independent harmonic oscillator structure to the basic microstructure unit, and form an attenuation band gap for specific low-frequency vibrations by adjusting the mass and elastic parameters of the harmonic oscillator. Propose a gradient parameter microstructure design, gradually change the microstructure parameters along the vibration propagation direction to form a broadband vibration reduction effect. Use the topology optimization method, based on the bi-directional evolutionary structural optimization algorithm, to further optimize the microstructure morphology under the condition of meeting the manufacturing constraints, so that the band gap characteristics are best matched with the target frequency. The purpose of this step is to use the phonon crystal theory to design a periodic microstructure with a selective isolation effect on vibrations of specific frequencies, and improve the performance of vibration damping rubber products.

[0158] The specific implementation method of step S05 is to construct a rapid evaluation system for microstructure performance. This system is based on a hybrid model combining the support vector regression algorithm and the radial basis function neural network, and its mathematical expression is: where \(y\) is the predicted output; \(x\) is the input parameter vector; \(x\) i is the support vector; \(\alpha\) i is the Lagrange multiplier; \(K(x, x\) i ) is the kernel function; \(b\) is the bias term; \(N\) is the number of support vectors. The expression of the radial basis kernel function is: \(K(x, x\) i ) = \(\exp(-\gamma||x - x\) i || 2) where γ is the kernel parameter that controls the width of the radial basis function. Generally, the optimal value is determined through cross-validation, and its range is from 0.01 to 100. The input parameter vector includes five key indicators: pore distribution density, average pore size, pore shape factor, arrangement pattern of microstructure units, and target frequency range. Among them, the pore distribution density controls the overall porosity and affects the material stiffness and vibration damping efficiency; the average pore size determines the characteristic size of the microstructure and affects the applicable frequency range; the pore shape factor describes the geometric characteristics of the pores and affects the stress distribution and energy dissipation mechanism; the arrangement pattern of microstructure units determines the bandgap characteristics of the phononic crystal and affects the frequency selectivity; the target frequency range clarifies the vibration damping requirements and is used for performance evaluation. The predicted outputs include four evaluation results: vibration damping efficiency index, durability index, manufacturing difficulty index, and cost index. The weighted comprehensive scoring method is used for the evaluation results, and its calculation formula is: S = w1S1 + w2S2 + w3S3 + w4S4; where S is the comprehensive score; S1, S2, S3, and S4 are the standardized scores of the vibration damping efficiency index, durability index, manufacturing difficulty index, and cost index respectively; w1, w2, w3, and w4 are the weights of each index, and w1 + w2 + w3 + w4 = 1. The weights of each index can be dynamically adjusted according to specific application requirements. Generally, the weight of vibration damping efficiency is 0.4, the weight of durability is 0.3, the weight of manufacturing difficulty is 0.2, and the weight of the cost index is 0.1. The scoring threshold is set at 90 points, and the candidate solutions with a comprehensive score of over 90 points are selected. For the solutions that pass the preliminary screening, the analytic hierarchy process is further applied for detailed comparison. According to expert experience, a judgment matrix is established: where A is the judgment matrix; a ij represents the importance ratio of solution i relative to solution j. The calculation formula for the maximum eigenvalue of the judgment matrix is: A·W = λ max ·W; where W is the eigenvector representing the weights of each solution; λ max is the maximum eigenvalue. The calculation formula for the consistency ratio is: where CR is the consistency ratio; CI is the consistency index; RI is the random consistency index, which is related to the matrix order n; when CR < 0.1, the judgment matrix is considered to have satisfactory consistency. Calculate the relative importance of each solution, and select the top three solutions in the final ranking to enter the experimental verification stage. The purpose of this step is to quickly screen out the most potential candidate solutions from a large number of possible microstructure design solutions and improve the design efficiency.

[0159] The specific implementation manners of steps S06 - S08 are the same as those described above and will not be elaborated here.

[0160] The specific implementation of step S09 is to install the selected optimal shock-absorbing rubber product into the actual vehicle shock-absorbing system, and design standard test routes, including three road conditions: 5 kilometers of flat road, 3 kilometers of gravel road, and 2 kilometers of bumpy road. Test is carried out at three vehicle speeds of 40 km / h, 60 km / h, and 80 km / h respectively under the three road conditions, and each group of conditions is tested 3 times to ensure data reliability. During the test, vibration measurement equipment is installed at key positions of the vehicle body to collect vibration signals before and after shock absorption, and the vibration isolation rate of each frequency band is calculated. The formula for calculating the vibration isolation rate is: In the formula, η is the vibration isolation rate; A1 is the amplitude before shock absorption; A2 is the amplitude after shock absorption. According to the test results, calculate the deviation between the actual shock-absorbing effect and the expected performance. The formula for calculating it is: In the formula, δ is the performance deviation; η actual is the vibration isolation rate of actual test; η predicted is the predicted vibration isolation rate. If the deviation exceeds 15%, it is necessary to return to step S04 to redesign the microstructure. Arrange long-term road tests, drive continuously for 10,000 kilometers, and take samples for testing every 1,000 kilometers to record the change trend of shock-absorbing performance. Calculate the shock-absorbing performance attenuation rate. The formula is: In the formula, Δ is the performance attenuation rate; η0 is the initial vibration isolation rate; η t is the vibration isolation rate after using for t kilometers. Evaluate the aging degree of the tested samples, including indicators such as hardness change rate, permanent deformation amount, and microstructure change. If the performance attenuation exceeds 20%, it is necessary to return to step S04 to redesign. Analyze the reasons for the problems found, and update the weight coefficients in the microstructure performance prediction function. The update formula is: In the formula, and are the updated and pre-updated weight coefficients respectively; α is the learning rate, generally set to 0.01 to 0.1; E is the prediction error; is the partial derivative of the error with respect to the weight. The formula for calculating the prediction error is: In the formula, E is the mean square error; M is the number of samples; is the predicted value of the jth sample; is the actual value of the jth sample. Improve the prediction accuracy of problem working conditions. If the test results do not meet the requirements, carry out a new round of iterative design and optimization according to the process from step S04 to step S08 until a microstructure scheme of the shock-absorbing rubber product that meets the actual use requirements and is long-term stable and reliable is obtained. The purpose of this step is to verify the performance of the optimized shock-absorbing rubber product through actual road tests, ensure that it can play a shock-absorbing role stably and reliably in the real use environment for a long time, and continuously improve the design scheme through iterative optimization.

[0161] To better understand and implement the present invention, Example 2 of a specific application scenario of the present invention is provided below: Researchers collected vibration data of a certain mid-sized SUV and found that during high-speed driving, especially on uneven roads, the body vibration significantly affected the riding comfort. To improve this problem, the researchers decided to apply the method of optimizing the microstructure of automotive shock-absorbing rubber products and redesigned the shock-absorbing rubber components of the engine mounts to improve the shock-absorbing effect and service life.

[0162] First, the researchers installed high-precision three-axis acceleration sensors on the engine mounts, body chassis, and seat bottom of the SUV, and set the sampling frequency to 1000 Hz. Under three typical road conditions (smooth highway, urban gravel road, and rural bumpy road), tests were carried out at speeds of 40 km / h, 80 km / h, and 120 km / h respectively, and vibration data was continuously collected for 600 seconds under each condition. Through fast Fourier transform analysis, the main vibration frequency distribution was determined, as shown in Table 1:

[0163] Table 1 Main vibration frequency distribution of SUV under different road conditions

[0164] Road condition type Driving speed (km / h) Main vibration frequency (Hz) Vibration energy proportion (%) Flat highway 40 12-18 35 Flat highway 80 15-25 42 Flat highway 120 18-32 48 Urban gravel road surface 40 18-35 53 Urban gravel road surface 80 25-48 65 Urban gravel road surface 120 30-65 72 Rural bumpy road 40 25-55 68 Rural bumpy road 80 35-78 75 Rural bumpy road 120 45-95 82

[0165] Analyzing the data in Table 1, it can be seen that the vibration of the SUV under different road conditions and speeds mainly concentrates in the range of 12 - 95 Hz, among which the vibration energy in the frequency band of 30 - 65 Hz is the most concentrated, accounting for more than 65% of the total vibration energy. Therefore, the frequency range that the shock-absorbing rubber products need to focus on is determined to be 30 - 65 Hz. Figure 2 The vibration frequency distribution of the SUV under different road conditions and speeds was shown in a visual way.

[0166] Subsequently, the researchers constructed a digital model of the rubber microstructure and generated three hole distribution schemes through the Monte Carlo algorithm, as shown in Table 2:

[0167] Table 2 Design parameters of the hole distribution scheme of the rubber microstructure

[0168]

[0169] For each scheme, the researchers used the finite element analysis software ABAQUS to construct a 10×10×10 mm three-dimensional mesh model, and adopted local mesh refinement technology at the hole edges, with the mesh size set to 1 / 10 of the minimum hole diameter, that is, 0.03 mm.

[0170] Next, a multi-field coupling simulation analysis was carried out, and the rubber material parameters were set as shown in Table 3:

[0171] Table 3 Setting of shock-absorbing rubber material parameters

[0172] Parameter type Numerical range Test temperature condition (°C) Young's modulus (MPa) 3.5-5.2 25 Poisson's ratio 0.48 25 <![CDATA[Mooney-Rivlin parameter C 10 (MPa)]]> 0.82 25 <![CDATA[Mooney-Rivlin parameter C 01 (MPa)]]> 0.15 25 Damping coefficient 0.12 25 <![CDATA[WLF constant C1]]> 17.44 - <![CDATA[WLF constant C2]]> 51.6 -

[0173] Based on the phonon crystal theory, the researchers designed four types of microstructure units with a size ratio of 1:1.2:1.5:2.0 and arranged them into a 2×2×4 three-dimensional array. Through calculations using the plane wave expansion method and the transfer matrix method, the bandgap characteristics of different combinations of microstructure units were obtained, as shown in Table 4:

[0174] Table 4 Bandgap characteristics of different combinations of microstructure units

[0175] Combination method First-order bandgap frequency range (Hz) Second-order bandgap frequency range (Hz) Attenuation peak value within the bandgap (dB) 1-1.2-1.5-2.0 28-45 58-72 32 1-1.5-2.0-1.2 30-48 62-75 35 1.2-1.5-1-2.0 25-42 55-68 30 1.5-2.0-1.2-1 32-50 65-80 38

[0176] According to the data in Table 4, the 1.5-2.0-1.2-1 combination was selected, whose bandgap characteristics match the target frequency range of 30 - 65 Hz most closely, and the attenuation peak is the highest, reaching 38 dB. Figure 3 Intuitively presents the bandgap frequency range and attenuation peak of different combinations of microstructure units, where blue represents the first-order bandgap and green represents the second-order bandgap.

[0177] The microstructure performance prediction function was used to quickly evaluate 30 candidate microstructure schemes, and the results are shown in Table 5:

[0178] Table 5 Comprehensive scoring results of microstructure schemes (partial)

[0179] Scheme Vibration reduction efficiency score Durability score Manufacturing difficulty score Cost index score Comprehensive score C-1.5-2.0-1.2-1 95 88 82 90 91.4 B-1.5-2.0-1.2-1 92 90 85 88 90.0 A-1.5-2.0-1.2-1 88 92 90 85 88.9 C-1-1.2-1.5-2.0 86 85 80 92 85.3 B-1-1.2-1.5-2.0 85 86 83 90 85.2

[0180] According to the comprehensive scores in Table 5, two schemes, C-1.5-2.0-1.2-1 and B-1.5-2.0-1.2-1, were selected to enter the experimental verification stage, and the comprehensive scores of both schemes exceeded 90 points.

[0181] Subsequently, the researchers prepared test samples through the microcellular foaming molding process. When formulating the ingredients, natural rubber and styrene-butadiene rubber were mixed in a ratio of 70:30, and 2.2% of azodicarbonamide blowing agent was added. Vulcanization was carried out at a temperature of 155°C and a pressure of 17.5 MPa, controlling the temperature gradient at 7.5°C per centimeter and the vulcanization time at 12 minutes.

[0182] After preparing the samples, a scanning electron microscope (SEM) was used for microstructure characterization, and microscopic morphology images were obtained at magnification ratios of 500 times and 1000 times, as shown in Figure 4 and as Figure 5 shown, where Figure 4 the red frame part of Figure 5 is the position of

[0183] Table 6 Comparison of the actual microstructure parameters of the two samples with the design values

[0184]

[0185]

[0186] Table 6 shows that the deviations of the actual microstructure parameters of the two samples from the design values are both controlled within 7%, meeting the design requirements.

[0187] The storage modulus and loss modulus data of the two samples under different frequencies and temperatures were obtained through dynamic mechanical analysis tests, and these data, together with the SEM microstructure images, were input into a pre-trained vibration damping rubber microstructure neural network model to predict the long-term performance of the samples. The results are shown in Table 7:

[0188] Table 7 Prediction results of the performance of vibration damping rubber samples

[0189] Performance index C-1.5-2.0-1.2-1 sample B-1.5-2.0-1.2-1 sample Average vibration reduction efficiency in the 30 - 50 Hz frequency band (%) 86.5 83.2 Average vibration reduction efficiency in the 50 - 65 Hz frequency band (%) 82.3 78.5 Vibration reduction efficiency under the condition of -30°C (%) 74.2 70.8 Vibration reduction efficiency under the condition of 120°C (%) 78.5 75.3 Predicted service life (km) 145000 132000 Performance attenuation rate after 100,000 km (%) 12.5 15.2

[0190] According to Table 7, the C-1.5-2.0-1.2-1 sample was selected as the final solution, and its vibration damping efficiency and service life are both better than those of the B-1.5-2.0-1.2-1 sample.

[0191] Finally, the optimized vibration damping rubber products were installed on an SUV for actual road tests. The vibration isolation rates were measured under three road conditions, and the performance data after continuous driving for 10,000 kilometers were collected. The results are shown in Table 8:

[0192] Table 8 Actual road test results

[0193]

[0194] The maximum deviation between the actual test results and the predicted values is 9.3%, which is less than the allowable deviation range of 15%, and the maximum performance attenuation rate after driving for 10,000 kilometers is 7.6%, which is much lower than the allowable limit of 20%. This shows the effectiveness and reliability of the optimized design.

[0195] The design of traditional automotive shock-absorbing rubber products mainly relies on experience and a large number of trial-and-error experiments. Usually, homogeneous rubber materials or simple composite structures are adopted, lacking precise control and optimization of the microstructure. This traditional method has the following problems: First, the shock-absorbing performance has poor frequency selectivity, making it difficult to achieve efficient vibration isolation for specific frequency ranges; second, the environmental adaptability is insufficient, and the performance drops significantly under extreme temperatures; third, the service life is short, and the performance decays severely after long-term use; finally, the development cycle is long and the cost is high. The microstructure optimization method proposed in the present invention designs a bandgap structure through the phonon crystal theory to achieve selective attenuation of vibrations at specific frequencies. Compared with the traditional method, the shock-absorbing efficiency is increased by about 30%; through multi-field coupling simulation analysis and microstructure performance prediction functions, the performance of candidate solutions can be quickly evaluated, and the development cycle is shortened by more than 50%; by adopting the micro-foaming molding process and periodic microstructure arrangement, the environmental adaptability is improved, and stable performance is maintained in the temperature range of -30°C to 120°C; the predicted service life is extended to 145,000 kilometers, which is more than twice that of traditional products. Actual road tests have proved that the shock-absorbing rubber products designed by this method show excellent shock-absorbing effects and durability under various road conditions and speed conditions, providing a new technical path for improving the performance of automotive shock-absorbing systems.

[0196] It should be noted that the detailed explanations of the variables involved in the present invention are shown in Tables 9 and 10 below.

[0197] Table 9 Variable Explanation Table (First Part)

[0198]

[0199] Table 10 Variable Explanation Table (Second Part)

[0200]

[0201]

[0202] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A method for optimizing the microstructure of an automotive shock-absorbing rubber product, characterized in that, It includes the following steps: Collect the actual vibration data borne by the vehicle during operation under different road conditions, record the vibration signals through an acceleration sensor, and calculate the main frequency distribution map; establish a digital model of the rubber microstructure, including the pore distribution density, pore size distribution range, and pore shape parameter matrix, and use finite element analysis software to construct a three-dimensional microstructure grid model; conduct multi-field coupling simulation analysis to simulate the dynamic mechanical properties of different microstructure designs under temperature conditions; adopt the phonon crystal theory to design the periodic arrangement of the rubber microstructure to form a bandgap structure, and achieve selective attenuation of specific frequency vibrations by adjusting the size ratio of the microstructure unit; Call the microstructure performance prediction function to quickly evaluate the candidate microstructure solutions; prepare test samples through the micro-foaming molding process; use an electron microscope to characterize the microstructure of the prepared samples; use the pre-trained neural network model of the vibration-damping rubber microstructure to analyze the test data; Conduct road tests in the actual vehicle shock-absorbing system for verification.

2. The method for optimizing the microstructure of the automotive shock-absorbing rubber product according to claim 1, wherein The actual vibration data collected when the vehicle is running under different road conditions is specifically to record the vibration signals with a frequency range of 5 to 200 Hz through an acceleration sensor, perform Fourier transform to obtain the main frequency distribution map, and determine the frequency range that the vibration-damping rubber product needs to focus on dealing with.

3. The method for optimizing the microstructure of the automotive shock-absorbing rubber product according to claim 2, wherein The establishment of the digital model of the rubber microstructure specifically includes a pore distribution density of 50 to 200 per cubic centimeter, a pore size distribution range of 0.1 to 2.0 mm, and a pore shape parameter matrix, and use finite element analysis software to construct a three-dimensional microstructure grid model.

4. The method for optimizing the microstructure of the automotive shock-absorbing rubber product according to claim 3, characterized in that The multi-field coupling simulation analysis is specifically to set the Young's modulus of the rubber material to be 1.5 to 8.0 MPa, the Poisson's ratio to be 0.45 to 0.49, and the damping coefficient to be 0.05 to 0.20, and simulate the dynamic mechanical properties of different microstructure designs under the temperature range of -30 to 120 °C.

5. The method for optimizing the microstructure of an automotive shock-absorbing rubber product according to claim 4, characterized in that, The adoption of the phonon crystal theory to design the periodic arrangement of the rubber microstructure is specifically to form a bandgap structure with a frequency of 10 to 80 Hz, and achieve selective attenuation of specific frequency vibrations by adjusting the size ratio of the microstructure unit to 1:1.2:1.5:2.

0.

6. The method for optimizing the microstructure of the automotive shock-absorbing rubber product according to claim 5, wherein The call of the microstructure performance prediction function to quickly evaluate the candidate microstructure solutions is specifically that the input parameters include the pore distribution density, average pore size, pore shape factor, microstructure unit arrangement pattern, and target frequency range, and the output includes the estimated vibration-damping efficiency, durability, manufacturing difficulty, and cost indicators of each solution. The microstructure solutions with a comprehensive score of more than 90 points enter the experimental verification stage.

7. The method for optimizing the microstructure of an automotive shock-absorbing rubber product according to claim 6, wherein The preparation of test samples through the micro-foaming molding process is specifically to inject a raw rubber mixture with a blowing agent mass fraction of 1.5 to 3.0%, vulcanize at a temperature of 140 to 160 °C and a pressure of 15 to 20 MPa, and control the temperature gradient during the foaming process to be 5 to 10 °C per centimeter.

8. The method for optimizing the microstructure of an automotive shock-absorbing rubber product according to claim 7, characterized in that, The microstructure characterization of the prepared sample using an electron microscope specifically involves controlling the deviation between the actual porosity and the designed value within 5%, and analyzing the microstructure connectivity and anisotropy index through three-dimensional reconstruction technology to ensure that the double connectivity rate is greater than 60%.

9. The method for optimizing the microstructure of the automotive shock-absorbing rubber product according to claim 8, wherein The analysis of the test data using the pre-trained neural network model for the microstructure of vibration-damping rubber specifically involves inputting the actual microstructure image obtained by the electron microscope and the dynamic mechanical analysis test data into the pre-trained neural network model for the microstructure of vibration-damping rubber to predict the long-term performance of the sample at different vibration frequencies and ambient temperatures, and selecting the scheme with a predicted vibration-damping efficiency greater than 80% and a service life exceeding 100,000 kilometers.

10. The method for optimizing the microstructure of the automotive shock-absorbing rubber product according to claim 9, characterized in that, The microstructure performance prediction function is used to quickly screen out potential candidate schemes from a large number of microstructure schemes without performing all computationally intensive finite element analyses. The inputs include the pore distribution density parameter as a characterization of the microstructure porosity, the average pore size parameter for determining the vibration-damping frequency range, the pore shape factor parameter for describing the geometric characteristics of the micropores, the microstructure unit arrangement pattern parameter representing the spatial distribution pattern of the pores, and the target frequency range parameter indicating the frequency interval that needs to be vibration-damped with emphasis.

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