A method for optimizing microstructure of automobile shock-absorbing rubber products

Abstract

The application provides a microstructure optimization method for automobile shock-absorbing rubber products, and belongs to the technical field of shock-absorbing rubber products.The method first collects actual road vibration data and determines a key frequency interval through Fourier transform; a microstructure digital model containing hole distribution and shape parameters is established; multi-field coupling simulation analysis is performed to evaluate the dynamic mechanical properties of the microstructure; a periodic arrangement structure is designed by using the phonon crystal theory to form a frequency band gap; a microstructure performance prediction function is used to quickly evaluate candidate schemes; a micro-foaming molding process is used to prepare samples; an electron microscope is used for microstructure characterization; a pre-trained neural network model is used to predict long-term performance; road tests are performed in actual automobiles, and multiple rounds of iterative optimization are performed until the final scheme that meets actual requirements is obtained, thereby solving the technical problem that the microstructure design of the automobile shock-absorbing rubber product does not match the actual road vibration characteristics in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of shock-absorbing rubber products, and in particular relates to a microstructure optimization method for automobile shock-absorbing rubber products. BACKGROUND

[0002] Automobile shock-absorbing rubber products are key vibration isolation components in suspension systems. Traditional design mainly uses empirical formulas and macroscopic parameter adjustment to meet basic vibration reduction requirements by changing rubber formula, overall structure size, and hardness and other parameters. These shock-absorbing rubber products are mainly applied to key parts such as engine suspension, shock absorber bushing, and suspension support, and play an important role in reducing vehicle body vibration and improving ride comfort.

[0003] However, the traditional design method is difficult to accurately reduce vibration at a specific frequency, especially in complex road conditions, and the shock-absorbing effect is often not ideal. The existing technology usually uses homogeneous material design, which cannot form a targeted frequency bandgap structure; at the same time, the microstructure randomness is high, and it is difficult to achieve selective attenuation of vibration at a specific frequency, resulting in low vibration reduction efficiency in some frequency bands and difficulty in accurately predicting service life.

[0004] The problem of mismatch between this microstructure design and actual road vibration characteristics makes it difficult for existing shock-absorbing rubber products to simultaneously meet the requirements of wide frequency domain vibration reduction, environmental adaptability, and long-term stability, especially when facing complex vibration frequency spectrum generated under different road conditions, the vibration reduction performance shows obvious limitations. That is, there is a technical problem of mismatch between the microstructure design of the automobile shock-absorbing rubber product and the actual road vibration characteristics in the existing technology. SUMMARY

[0005] Therefore, the application provides a microstructure optimization method for automobile shock-absorbing rubber products, which can solve the technical problem of mismatch between the microstructure design of the automobile shock-absorbing rubber product and the actual road vibration characteristics in the existing technology.

[0006] The application is implemented in the following manner: the application provides a method for optimizing the microstructure of automobile shock-absorbing rubber products, comprising the following steps: collecting actual vibration data of an automobile under different road conditions, recording vibration signals through an acceleration sensor, and calculating a main frequency distribution map; establishing a digital model of rubber microstructure, including hole distribution density, hole diameter distribution range, and hole shape parameter matrix, and using finite element analysis software to construct a three-dimensional microstructure grid model; performing multi-field coupling simulation analysis to simulate the dynamic mechanical properties of different microstructure designs under temperature conditions; using phononic crystal theory to design a periodic arrangement of rubber microstructure to form a bandgap structure, and adjusting the size ratio of the microstructure unit to achieve selective attenuation of specific frequency vibrations; calling a microstructure performance prediction function to quickly evaluate candidate microstructure schemes; preparing test samples through a micro-foaming molding process; using an electron microscope to characterize the microstructure of the prepared samples; using a pre-trained shock-absorbing rubber microstructure neural network model to analyze the test data; and conducting road tests in an actual automobile shock-absorbing system.

[0007] The actual vibration data of the automobile under different road conditions is collected by recording vibration signals with a frequency range of 5 to 200 Hz through an acceleration sensor, and performing Fourier transform to obtain a main frequency distribution map, thereby determining the frequency range that the shock-absorbing rubber product needs to focus on.

[0008] The digital model of rubber microstructure is established by including a hole distribution density of 50 to 200 per cubic centimeter, a hole diameter distribution range of 0.1 to 2.0 millimeters, and a hole shape parameter matrix, and using finite element analysis software to construct a three-dimensional microstructure grid model.

[0009] The multi-field coupling simulation analysis is performed by setting the Young's modulus of the rubber material to 1.5 to 8.0 megapascals, the Poisson's ratio to 0.45 to 0.49, and the damping coefficient to 0.05 to 0.20, and simulating the dynamic mechanical properties of different microstructure designs under temperature conditions ranging from -30 to 120 degrees Celsius.

[0010] The periodic arrangement of rubber microstructure is designed using phononic crystal theory to form a bandgap structure with a frequency of 10 to 80 Hz, and the size ratio of the microstructure unit is adjusted to 1:1.2:1.5:2.0 to achieve selective attenuation of specific frequency vibrations.

[0011] The microstructure performance prediction function is called to quickly evaluate candidate microstructure schemes by inputting parameters including hole distribution density, average hole diameter, hole shape factor, microstructure unit arrangement pattern, and target frequency range, and outputting the estimated shock-absorbing efficiency, durability, manufacturing difficulty, and cost indicators of each scheme. Microstructure schemes with a comprehensive score of 90 points or above enter the experimental verification stage.

[0012] The test sample is prepared by a micro-foaming molding process, specifically, the raw rubber mixture with a foaming agent mass fraction of 1.5 to 3.0% is injected, vulcanization is carried out at a temperature of 140 to 160 degrees Celsius and a pressure of 15 to 20 megapascals, and the temperature gradient during foaming is controlled at 5 to 10 degrees Celsius per centimeter.

[0013] The microstructure of the prepared sample is characterized by an electron microscope, specifically, the actual porosity is measured and the deviation from the design value is controlled within 5%, the microstructure connectivity and anisotropy index are analyzed by three-dimensional reconstruction technology, and the double connectivity rate is ensured to be greater than 60%.

[0014] The test data is analyzed by using a pre-trained vibration damping rubber microstructure neural network model, specifically, the actual microstructure image obtained by an electron microscope and dynamic mechanical analysis test data are input into the pre-trained vibration damping rubber microstructure neural network model, the long-term performance of the sample under different vibration frequencies and environmental temperatures is predicted, and a scheme with a vibration damping efficiency greater than 80% and a service life of more than 100,000 kilometers is selected.

[0015] 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 hole distribution density parameter is input as a representation of the microstructure porosity, the average pore size parameter is used to determine the vibration damping frequency range, the hole shape factor parameter is used to describe the geometric characteristics of the micro-pores, the microstructure unit arrangement mode parameter represents the spatial distribution mode of the holes, and the target frequency range parameter indicates the frequency interval that needs to be focused on for vibration damping.

[0016] Compared with the prior art, the microstructure optimization method for automobile damping rubber products provided by the present application proposes a design method for automobile damping rubber products based on actual vibration data acquisition and microstructure optimization, which realizes selective attenuation of specific frequency vibration by accurately designing the hole distribution, shape and periodic arrangement of the rubber microstructure. The method applies phononic crystal theory to the design of the damping rubber microstructure to form a bandgap structure of 10 to 80 Hz, which greatly improves the vibration damping efficiency in the target frequency range.

[0017] Through multi-field coupling simulation analysis and the microstructure performance prediction function, the present application 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. Combined with the performance analysis of the pre-trained vibration damping rubber microstructure neural network model, the accurate mapping from the microstructure to the macroscopic performance is realized, which greatly improves the design efficiency and the reliability of the scheme.

[0018] The present application solves the technical problem of the mismatch between the microstructure design of automobile shock-absorbing rubber products and the actual road vibration characteristics in the prior art, so that the products can maintain excellent shock-absorbing effect under various road conditions, significantly prolong the service life, and meet the demand of the automobile industry for high-performance shock-absorbing elements. BRIEF DESCRIPTION OF DRAWINGS

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

[0020] Figure 2 is a vibration frequency distribution graph in Example 2.

[0021] Figure 3 is a band gap characteristic graph in Example 2.

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

[0023] Figure 5 is a 1000 times microstructure characterization by scanning electron microscope in Example 2. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0025] As Figure 1 shown, is a flowchart of a microstructure optimization method of automobile shock-absorbing rubber products provided by the present application, and the method comprises the following steps:

[0026] S01, collect the actual vibration data borne by the automobile when running under different road conditions, record the vibration signal with a frequency range of 5 to 200 Hz through an acceleration sensor, and perform Fourier transform to obtain a main frequency distribution graph, so as to determine the frequency interval that needs to be focused on by the shock-absorbing rubber product;

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

[0028] S03, perform multi-field coupling simulation analysis, set the Young's modulus of the rubber material to 1.5 to 8.0 megapascals, the Poisson's ratio to 0.45 to 0.49, and the damping coefficient to 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, adopt phononic crystal theory to design the periodic arrangement of rubber microstructure, form a band gap structure with a frequency of 10 to 80 Hz, and achieve selective attenuation of specific frequency vibration by adjusting the size ratio of microstructure unit to 1:1.2:1.5:2.0;

[0030] S05, call the microstructure performance prediction function to quickly evaluate the candidate microstructure scheme, the input parameters include the hole distribution density, the average hole diameter, the hole shape factor, the microstructure unit arrangement mode and the target frequency range, the output is the estimated vibration reduction efficiency, durability, manufacturing difficulty and cost index of each scheme, the microstructure scheme with comprehensive score of 90 points or more enters the experimental verification stage;

[0031] S06, prepare test samples by micro-foaming molding process, inject raw rubber mixture with foaming agent mass fraction of 1.5 to 3.0%, vulcanize at temperature of 140 to 160 degrees Celsius and pressure of 15 to 20 megapascals, control the temperature gradient during foaming process to be 5 to 10 degrees Celsius per centimeter;

[0032] S07, use electron microscope to characterize the microstructure of the prepared sample, measure the actual porosity deviation from the design value within 5%, analyze the microstructure connectivity and anisotropy index by three-dimensional reconstruction technology, 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 image obtained by electron microscope and dynamic mechanical analysis test data into the pre-trained vibration reduction rubber microstructure neural network model, predict the long-term performance of the sample under different vibration frequencies and environmental temperatures, select the scheme with vibration reduction efficiency greater than 80% and service life more than 100,000 kilometers;

[0034] S09, perform road test verification in actual automobile damping system, measure the vibration isolation rate of optimized damping rubber products under three conditions of flat road, gravel road and bumpy road, and collect structure aging and performance attenuation data after continuous driving for 10,000 kilometers, if the actual vibration reduction effect deviates from the expected value by more than 15% or the performance attenuation is more than 20% after 10,000 kilometers of use, return to step S04 to redesign the periodic arrangement of microstructure and adjust the size ratio parameters of microstructure unit, at the same time adjust the weight coefficient in the microstructure performance prediction function in step S05 to improve the prediction accuracy, through multiple rounds of iteration optimization until the microstructure scheme of damping rubber products that meets the requirements of actual use environment of automobile and is stable and reliable in long term is obtained.

[0035] The Fourier transform is a mathematical operation process of converting a time-domain vibration signal into a frequency-domain representation, which can decompose a complex vibration waveform into superposition of different frequency components, and helps to determine the vibration frequency that needs to be isolated.

[0036] The phononic crystal theory is a theory for studying the propagation characteristics of acoustic waves in periodic structures in elastic media. By designing a specific periodic microstructure, a band gap that prohibits the propagation of vibrations at a specific frequency can be formed, thereby achieving efficient isolation of vibrations at the target frequency.

[0037] The dual connectivity rate is a measure of the degree of interconnection between holes in the microstructure, expressed as the percentage of two independent paths connecting the same area. A high dual connectivity rate helps to improve the energy dissipation capacity of the shock-absorbing rubber under large deformation conditions.

[0038] The anisotropy index is a parameter that quantifies the difference in mechanical properties of a material in different directions, with a value ranging from 0 to 1. A larger value indicates stronger directionality. By controlling the anisotropy index, the vibration damping characteristics of the rubber product in different directions can be adjusted.

[0039] The storage modulus is a parameter that represents the ability of a material to store elastic deformation, reflecting the stiffness characteristics of the rubber product. A larger value indicates a stronger ability to recover deformation.

[0040] The loss modulus is a parameter that represents the ability of a material to dissipate mechanical energy into heat, reflecting the damping characteristics of the rubber product. A larger value indicates better vibration damping effect.

[0041] The microstructure performance prediction function is used to quickly screen potential candidate schemes from a large number of microstructure schemes without performing full computational intensive finite element analysis. The input includes the hole distribution density parameter as a representation 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 micro-pores, the microstructure unit arrangement mode parameter representing the spatial distribution of the holes, and the target frequency range parameter indicating the frequency interval that needs to be focused on for vibration damping. The output is a comprehensive evaluation result composed of vibration damping efficiency index, durability index, manufacturing difficulty index, and cost index. The microstructure performance prediction function is a regression model established based on a large amount of historical simulation and experimental data, which quickly estimates the performance of new schemes 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, including a microstructure image processing path and a mechanical property data processing path. The microstructure image processing path is composed of five layers of convolutional neural networks, with an input of 256x256 pixel microstructure scanning electron microscope images. The convolutional layers extract hole morphology, distribution, and connectivity features. The mechanical property processing path is composed of three layers of fully connected neural networks, with an input of dynamic mechanical analysis test obtained storage modulus and loss modulus frequency spectrum data. The features of the two paths are fused through an attention mechanism in the fusion layer. The fusion layer output is fed into a predictor composed of four layers of fully connected networks to generate vibration damping performance and life prediction results under different use conditions. The skip attention mechanism parameters in the pre-trained vibration damping rubber microstructure neural network model are dynamically adjusted according to the target frequency range, expected use temperature range, and maximum strain amplitude, ensuring more accurate performance prediction of the pre-trained vibration damping rubber microstructure neural network model under key working conditions.

[0043] The training data set establishment step in the pre-training process of the pre-trained vibration damping rubber microstructure neural network model specifically includes collecting more than 5000 different formula and microstructure design vibration damping rubber sample data, each sample containing high-resolution electron microscope images and complete dynamic mechanical property test data. Each sample is subjected to standardized accelerated aging test to simulate performance changes under equivalent 100,000 km driving conditions, record vibration damping efficiency attenuation curve and structure damage evolution process. The sample performance is graded according to actual road test data to establish a multi-dimensional database containing microstructure parameters, dynamic mechanical properties, and long-term use performance. The training samples are expanded through data enhancement techniques, including image rotation, scaling, and noise addition, as well as mechanical property data synthesis and interpolation, finally forming a comprehensive data set containing more than 20,000 training samples.

[0044] The pre-training step of the pre-trained damping rubber microstructure neural network model specifically includes adopting a phased training strategy, first pre-training the microstructure image processing path and the mechanical property data processing path respectively, using a supervised learning method to let the network learn the mapping relationship between microstructure features and macroscopic mechanical properties; then freeze the bottom layer parameters of the two paths, train the fusion layer and the jump attention mechanism, let the pre-trained damping rubber microstructure neural network model learn to dynamically adjust the feature fusion weight according to different working conditions; finally, fine-tune end-to-end, use actual road test data to verify the prediction accuracy of the pre-trained damping rubber microstructure neural network model, and optimize the whole network parameters through back propagation; cross-validation and early stopping strategy are adopted in the training process to prevent overfitting, and finally the pre-trained damping rubber microstructure neural network model reaches an average error of less than 10% in damping performance prediction and an average error of less than 15% in service life prediction.

[0045] The specific implementation of the above steps is described in detail below. The specific implementation of step S01 is to first select appropriate positions to install high-precision three-axis acceleration sensors, including the body suspension connection, the bottom of the cab, and the three key positions of the cargo area. The sensor sampling frequency is set to 1000 Hz to ensure that all vibration signals in the range of 5 to 200 Hz can be captured. On flat road, gravel road and bumpy road, standard driving tests are carried out at speeds of 40 km / h, 60 km / h and 80 km / h respectively. Under each condition, vibration data is continuously collected for not less than 600 seconds. After collection, the original signal is preprocessed using the Hanning window function to reduce spectral leakage, and then the fast Fourier transform algorithm is applied to convert the time-domain vibration signal to frequency-domain representation. The transformed result is analyzed for power spectral density, and the distribution curve of vibration energy in the frequency domain is drawn. Based on the power spectrum analysis result, the main frequency interval with vibration energy exceeding 80% is identified. The purpose of this step is to accurately obtain the vibration characteristics of the vehicle in the actual use environment, providing a data basis for subsequent targeted design of damping rubber microstructure.

[0046] The specific implementation of step S02 is to create a three-dimensional digital representation model using a voxel modeling method, and initially set the basic unit size to 10x10x10 mm. First, determine the hole space distribution pattern, including three typical structures of 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 position; for the gradient distribution pattern, set the porosity to vary linearly along a specific direction. Then build a hole shape parameter matrix, including three basic shapes of spherical, ellipsoidal, and polyhedral. For spherical holes, only the radius parameter is needed; for ellipsoidal holes, three principal axis lengths and rotation angles need to be set; for polyhedral holes, vertex coordinates and connection relationships need to be defined. Use Boolean operations to subtract the hole volume from the base material to form a digital model with a specific microstructure. Import the completed geometric model into the finite element analysis software, and use adaptive meshing technology to generate a three-dimensional tetrahedral element mesh. The mesh size is set to 1 / 10 of the minimum pore size to ensure calculation accuracy. The purpose of this step is to establish a digital model that accurately represents the microstructure characteristics of the shock-absorbing rubber, providing a geometric basis for subsequent performance analysis.

[0047] The specific implementation of step S03 is to first establish an elastic constitutive model for rubber materials, and use the two-parameter Mooney-Rivlin model to describe the nonlinear mechanical behavior of rubber under large deformation conditions. For different temperature conditions, use the Williams-Landel-Ferry shift function to establish a temperature-dependent model of the dynamic mechanical properties of rubber. Build a thermal-mechanical coupling analysis model, considering the effect of temperature change on material properties and the temperature rise effect caused by mechanical energy conversion to heat energy. Set the boundary conditions, apply fixed constraints at the bottom, periodic displacement excitation at the top, and periodic boundary conditions on the sides to simulate large-size structures. Use the explicit dynamic solver for transient analysis, and set the time step to 1 / 20 of the highest analysis frequency period to ensure calculation stability. For each microstructure 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 negative 30, 0, 30, 60, and 120 degrees Celsius. Calculate and extract the storage modulus and loss modulus under each condition, and based on the calculation results, draw a three-dimensional surface plot of the main damping ratio versus frequency and temperature, to evaluate the damping performance of the microstructure in the target frequency range. The purpose of this step is to evaluate the dynamic mechanical properties of different microstructure designs under various working conditions through virtual simulation methods, reducing experimental costs and shortening development cycles.

[0048] The specific implementation of step S04 is to design a periodic microstructure based on the phononic crystal band gap theory. First, a phononic crystal dispersion relation calculation model is established, and the plane wave expansion method is used to solve the intrinsic frequency and corresponding vibration mode 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 in the basic unit, each unit forms a band gap in a specific frequency range. The transfer matrix method is used to calculate the vibration transmission characteristics of different unit arrangements, and the arrangement with the most significant attenuation in the target frequency interval is selected. Based on the Bragg scattering principle, the periodic length of the microstructure is adjusted to align the first-order band gap center frequency with the main vibration frequency determined in step S01. Considering the local resonance effect, independent resonator structures are added to the basic microstructure unit. By adjusting the mass and elastic parameters of the resonator, an attenuation band gap is formed for specific low-frequency vibrations. A gradient parameter microstructure design is proposed, which gradually changes the microstructure parameters along the vibration propagation direction to achieve a wideband vibration reduction effect. Using the topology optimization method based on the bidirectional evolutionary structure optimization algorithm, the microstructure morphology is further optimized under the condition of meeting the manufacturing constraints, so that the band gap characteristics and the target frequency are best matched. The purpose of this step is to use the phononic crystal theory to design a periodic microstructure that selectively isolates specific frequency vibrations, improving the performance of shock-absorbing rubber products.

[0049] The specific implementation of step S05 is to build a microstructure performance rapid evaluation system based on a hybrid model combining support vector regression algorithm and radial basis function neural network. The input parameter vector includes five key indicators: hole distribution density, average hole diameter, hole shape factor, microstructure unit arrangement mode, and target frequency range. The hole distribution density controls the overall porosity, affecting the material stiffness and vibration reduction efficiency; the average hole diameter determines the microstructure feature size, affecting the applicable frequency range; the hole shape factor describes the hole geometry, affecting the stress distribution and energy dissipation mechanism; the microstructure unit arrangement mode determines the phononic crystal band gap characteristics, affecting the frequency selectivity; the target frequency range specifies the vibration reduction requirements for performance evaluation. The prediction output includes four evaluation results: vibration reduction efficiency indicator, durability indicator, manufacturing difficulty indicator, and cost indicator. The weighted comprehensive scoring method is used for evaluation results, and the weight of each indicator can be dynamically adjusted according to specific application requirements. Generally, the vibration reduction efficiency weight is 0.4, the durability weight is 0.3, the manufacturing difficulty weight is 0.2, and the cost indicator weight is 0.1. Set the score threshold to 90 points, and select the candidate schemes with a comprehensive score of 90 points or more. For the schemes that pass the preliminary screening, further apply the analytic hierarchy process for detailed comparison. According to expert experience, a judgment matrix is established to calculate the relative importance of each scheme, and the top three schemes are selected for experimental verification. The purpose of this step is to quickly select the most promising candidate scheme from a large number of possible microstructure design schemes, improving the design efficiency.

[0050] The specific implementation of step S06 is to first prepare the rubber base material, select natural rubber and styrene-butadiene rubber mixed according to a mass ratio of 70:30, add appropriate amount of vulcanizing agent, active agent, antioxidant and other additives, and fully mix on a double roller mixer. According to the microstructure design requirements, select appropriate types of foaming agent, commonly used foaming agents include azodicarbonamide and sodium bicarbonate, and the addition amount is controlled within 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 rubber sheet with a thickness similar to that of the final product. Put the preformed rubber sheet into the mold, the shape of the inner cavity of the mold is consistent with that of the final product, and the surface treatment of the mold is to ensure that the surface roughness is not more than 0.4 microns, so as to ensure the surface quality of the finished product. Put the mold with the rubber sheet into the vulcanizing machine, set the vulcanizing temperature to 140 to 160 degrees Celsius, the pressure to 15 to 20 megapascals, and control the vulcanizing time according to the thickness of the rubber, generally increase 1 minute for every 1 millimeter increase in thickness. Use the program temperature control technology, set the temperature gradient to 5 to 10 degrees Celsius per centimeter, realize directional foaming through multi-region independent temperature control, and form the anisotropic microstructure required by the design. After vulcanization, demold and post-treat, including trimming, cleaning and surface treatment, to obtain the finished product sample. Preliminary quality inspection is performed on the prepared sample, including appearance inspection, size 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, and to provide an entity for subsequent performance verification.

[0051] The specific implementation of step S07 is to perform microstructure characterization on the prepared sample using a scanning electron microscope. The sample pretreatment includes freeze fracture and surface metal spraying. The scanning electron microscope is set to an acceleration voltage of 10 kilovolts and a working distance of 10 millimeters. Microscopic morphology images are obtained at three magnification ratios of 100x, 500x, and 2000x. Based on the obtained electron microscope images, image analysis software is used for hole identification and statistics. The adaptive threshold segmentation algorithm is used to distinguish the material matrix and the hole part, and the hole geometric feature parameters are extracted. The hole size distribution, spatial distribution, and shape parameters are statistically analyzed, the actual porosity is calculated, and compared with the design value, and the deviation is required to be controlled within 5%. Using X-ray micro-computed tomography technology, three-dimensional voxel data of the sample is obtained, and the scanning resolution is set to 5 microns to ensure accurate identification of the smallest hole structure. Based on the tomographic data, three-dimensional reconstruction is performed to establish a virtual three-dimensional model of the microstructure. Skeletonization processing is performed on the reconstructed model to 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. The structural tensor method is used to calculate the anisotropy index of the microstructure to evaluate the mechanical performance difference in different directions. By calculating the angle between the principal direction of the anisotropy index and the design direction, it is verified whether the orientation of the microstructure meets the design requirements, and the allowed deviation angle is not more than 15 degrees. The purpose of this step is to characterize the microstructure of the prepared sample in detail, verify the consistency of the actual microstructure with the design requirements, and provide microstructure basic data for subsequent performance prediction.

[0052] The specific implementation of step S08 is to first perform a standard dynamic mechanical analysis test on the prepared sample, using a dynamic mechanical analyzer in tension mode, with a frequency scanning range of 0.1 to 200 Hz, a temperature range of -30 to 120 degrees Celsius, and a strain amplitude set to three levels of 0.1%, 1%, and 10%. The data of the storage modulus and loss modulus changing with frequency and temperature are obtained. The microstructure image obtained by the electron microscope is preprocessed into a standard format of 256x256 pixels, and the contrast is improved and the noise is reduced through an image enhancement algorithm. The preprocessed microstructure image and the dynamic mechanical analysis test data are input into the pre-trained vibration damping rubber microstructure neural network model. The network model uses 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 morphological features of the microstructure through five convolutional layers, and each convolutional layer is followed by a batch normalization layer and a ReLU activation function; the mechanical property processing path encodes the dynamic mechanical properties through a three-layer fully connected network. The features of the two paths are fused through a skip attention mechanism to generate a comprehensive feature representation. The fused features are input into a four-layer fully connected predictor to output the predicted performance of the sample under different vibration frequencies, environmental temperatures, and service times. According to the neural network output, the vibration damping efficiency and service life of each sample under the expected use conditions are sorted, 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 sample under long-term use 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 an actual automobile shock-absorbing system, design a standard test route including three road conditions of 5 kilometers of flat road, 3 kilometers of gravel road, and 2 kilometers of bumpy road. Test is performed at three vehicle speeds of 40 km / h, 60 km / h, and 80 km / h under the three road conditions, respectively, and each group of conditions is repeatedly tested 3 times to ensure data reliability. During the test, vibration measurement devices are 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 vibration isolation rate calculation formula is vibration isolation rate = (1 - amplitude after shock absorption / amplitude before shock absorption) x 100%. According to the test results, the deviation of the actual shock-absorbing effect from the expected performance is calculated. If the deviation exceeds 15%, return to step S04 to redesign the microstructure. Arrange for long-term road testing, continuously drive 10,000 kilometers, and sample test every 1,000 kilometers to record the trend of shock-absorbing performance. Perform aging degree evaluation on the tested samples, including hardness change rate, permanent deformation, microstructure change, etc. If the performance attenuation exceeds 20%, return to step S04 to redesign. Analyze the causes of the problems found, update the weight coefficients in the microstructure performance prediction function, and improve the prediction accuracy of the problem working conditions. If the test results do not meet the requirements, perform a new round of iterative design and optimization according to the steps S04 to 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 testing, ensure that it can play a long-term stable and reliable shock-absorbing role in real use environment, and continuously improve the design scheme through iterative optimization.

[0054] The mathematical models or calculation processes involved in the present application are described in detail below.

[0055] The Fourier transform process in step S01 is specifically represented 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; and j is the imaginary unit.

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

[0059]

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

[0061] The power spectral density calculation formula is:

[0062]

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

[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 original signal is preprocessed using the Hanning window function, whose expression is:

[0065]

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

[0067] The windowed signal is represented as:

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

[0069] where 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 accuracy of spectral analysis. The Fourier transform selects this mathematical form because it can decompose the time-domain signal into the sum of different frequency harmonic components, and the exponential term represents the rotation vector, which can express the amplitude and phase information at the same time.

[0071] The random distribution of 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] where (x i , y i , z i) is the center coordinate of the ith hole; (x min , y min , z min ) and (x max , y max , z max ) are the lower and upper limits of the coordinate range; r x , r y , r z are random numbers in the interval [0, 1].

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

[0077]

[0078] d ij ≥ r i + r j + d min ;

[0079] In the formula, d ij is the distance between the ith hole and the jth hole center; r i and r j are the radii of the two holes; d min is the minimum allowed distance, generally set to 0.1 times the average pore size.

[0080] For the gradient distribution mode, the porosity changes linearly along a certain 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, 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 encryption of grid division uses a curvature-based adaptive algorithm, and the cell size calculation formula is:

[0084]

[0085] In the formula, h i is the grid size of the ith region; h max is the maximum allowed grid size; κ i is the local curvature of the region; κ max and κ minare the maximum and minimum curvatures of the model respectively; p is a control parameter, generally taking the value of 0.5.

[0086] These formulas are applied to the microstructure geometry modeling process, the random distribution uses the Monte Carlo method to simulate the randomness in the real foaming process, and the gradient distribution can realize the directional performance design. Distance checking ensures the rationality of the microstructure, and the adaptive mesh algorithm improves the calculation efficiency while ensuring the calculation accuracy.

[0087] The Mooney-Rivlin hyperelastic model expression 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 uniaxial tension, biaxial tension and pure shear test data; I1 and I2 are the first and second invariants of the deformation tensor.

[0090] The Williams-Landel-Ferry shift function expression 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 formula of storage modulus and loss modulus is:

[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 stress and strain.

[0096] The main damping ratio calculation formula is:

[0097]

[0098] In the formula, ζ is the main damping ratio, representing the damping capacity of the material.

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

[0100] The calculation of the phononic crystal dispersion relation in step S04 uses the plane wave expansion method, and the 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 inverse lattice vectors; ω is the angular frequency; ρ is the Fourier transform of the density; δ ij is the Kronecker function; and u j is the displacement component.

[0103] For a periodic microstructure, the bandgap 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; and 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; and T ij is the element of the total transfer matrix.

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

[0112]

[0113] where p(x) is the parameter value at position x; p0 is the initial parameter value; Δp is the parameter variation; f(x / L) is the variation function, which can be linear, exponential or sinusoidal function, etc.; L is the total length.

[0114] The phononic crystal theory is chosen based on its ability to accurately describe the wave propagation characteristics in periodic structures. The plane wave expansion method can solve the eigenfrequencies and modes, providing a theoretical basis for bandgap design. The transfer matrix method is simple and efficient, suitable for vibration transmission analysis of one-dimensional and quasi-one-dimensional structures. Gradient parameter design achieves bandgap widening by breaking strict periodicity, improving the applicable frequency range of the vibration reduction 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] where 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] where γ is the kernel parameter, which controls the width of the radial basis function, and is generally determined by cross-validation to determine the optimal value, ranging from 0.01 to 100.

[0121] The weighted comprehensive score calculation formula is:

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

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

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

[0125]

[0126] where A is the judgment matrix; aij The importance ratio of scheme i to scheme j is generally represented by a scale of 1 to 9.

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

[0128] A·W=λ max ·W;

[0129] In the formula, W is the eigenvector, indicating the weight of each scheme; λ max is the maximum eigenvalue.

[0130] The calculation formula of 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, which is related to the order n of the matrix; 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 process high-dimensional input data. Radial basis kernel function has good local response characteristics and is suitable for solving highly nonlinear problems such as microstructure performance prediction. Weighted comprehensive score method can consider multiple evaluation indexes and realize multi-objective optimization. Analytic hierarchy process can improve the scientificity of decision-making by quantifying expert experience into mathematical model through the construction of judgment matrix.

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

[0135]

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

[0137] The damping performance deviation calculation formula is:

[0138]

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

[0140] The damping performance attenuation rate calculation formula 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 t kilometers of use.

[0143] The microstructure performance prediction function weight update formula is:

[0144]

[0145] In the formula, and are the weight coefficients after and before updating respectively; alpha 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.

[0146] The prediction error calculation formula is:

[0147]

[0148] In the formula, E is the mean square error; M is the sample size; is the predicted value of the jth sample; is the actual value of the jth sample.

[0149] The vibration isolation rate formula is based on the vibration transmission theory, and directly reflects the damping effect by calculating the amplitude ratio before and after damping. The performance deviation and attenuation rate calculation can quantitatively evaluate the prediction accuracy and durability of the damping product. The weight update formula is based on the gradient descent principle, and adjusts the prediction model parameters through error back propagation 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 an optimization target.

[0150] Specifically, the principle of the present application is: the core principle of the present application is to use microstructure design to regulate the mechanical properties of rubber materials, especially by constructing a specific microstructure arrangement method through phononic crystal theory to form selective attenuation ability for target frequency vibration. Phononic crystal is a kind of artificial material with periodic structure, when elastic wave propagates in it, due to Bragg scattering and local resonance effect, specific frequency band gap will be formed, which prevents the propagation of vibration in this frequency range. By adjusting the size ratio of the microstructure unit to 1:1.2:1.5:2.0, the present application can accurately control the band gap position to cover the main vibration frequency interval (10 to 80 Hz) generated by the car in the actual road conditions.

[0151] The microstructure parameters such as hole distribution density, hole size and shape factor directly affect the storage modulus and loss modulus of the rubber material, and then affect its damping performance. The microstructure design with high dual connectivity rate (> 60%) enhances the energy dissipation ability of the material under large deformation conditions, and improves the damping efficiency. By controlling the anisotropy index, differential damping characteristics in different directions can be realized, better responding to multi-directional vibration input.

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

[0153] A specific embodiment 1 of the present application is provided below, and the specific implementation of each step in embodiment 1 is described in detail as follows.

[0154] The specific implementation of step S01 is to first select appropriate positions to install high-precision three-axis acceleration sensors, including three key positions of the vehicle body suspension connection, the bottom of the cab, and the cargo area. The sensor sampling frequency 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 of 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. Under each condition, vibration data is continuously collected for not less than 600 seconds. After collection is completed, the original signal is preprocessed using the Hanning window function, and the expression of the Hanning 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; and N is the window length. The windowed signal is represented as: x w (n)=x(n)w(n); in the formula, x w (n) is the windowed signal; x(n) is the original signal; and w(n) is the window function. Then, the fast Fourier transform algorithm is applied to convert the time-domain vibration signal into a frequency-domain representation, and the 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; and j is the imaginary unit. For a discrete sampled vibration signal, the discrete Fourier transform is used, and the expression is: In the formula, X(k) is the kth frequency component; x(n) is the nth sampling point; N is the total number of sampling points; and k ranges from 0 to N-1. The transform result is analyzed for power spectral density, and the calculation formula is: In the formula, P(f) is the power spectral density; T is the sampling time length; and |X(f)| is the amplitude of Fourier transform. According to the power spectral density analysis result, the main frequency interval with vibration energy ratio exceeding 80% is identified. The purpose of this step is to accurately obtain the vibration characteristics of the automobile in the actual use environment, and to provide a data basis for the subsequent targeted design of the damping rubber microstructure.

[0155] The specific implementation of step S02 is to create a three-dimensional digital representation model by using a voxel modeling method, and an initial basic unit with an overall size of 10*10*10 mm is set. First, the hole space distribution mode is determined, including three typical structures of random distribution mode, regular arrangement mode and gradient distribution mode. For the random distribution mode, the Monte Carlo algorithm is used to generate the hole center coordinates, and the calculation formula is as follows: 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 i-th hole center coordinate; (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]. When generating the hole position, it is necessary to check the distance between the newly generated hole and the existing hole to avoid overlap, and the calculation formula is as follows: d ij ≥r i +r j +d min ; In the formula, d ij is the distance between the i-th hole and the j-th hole center; r i and r j are the radii of the two holes respectively; d minThe minimum allowable spacing is generally set to 0.1 times the average pore size. For a regular arrangement pattern, the hole positions are determined by equidistant arrangement. For a gradient distribution pattern, the porosity is set to vary linearly along a specific direction, and the expression is: where 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 are generally set to be 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. Subsequently, a hole shape parameter matrix is constructed, including three basic shapes of spherical, ellipsoidal, and polyhedral. The hole volume is subtracted from the base material using Boolean operations to form a digital model with a specific microstructure. The completed geometric model is imported into a finite element analysis software, and an adaptive meshing technique is used to generate a three-dimensional tetrahedral element mesh, with the element size calculation formula being: where 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 the region; κ max and κ min are the maximum and minimum curvatures of the model, respectively; p is a control parameter, generally taking a value of 0.5. The mesh is locally refined at the hole edges and stress concentration regions, with the mesh size set to 1 / 10 of the minimum pore size to ensure calculation accuracy. The purpose of this step is to establish a digital model that can accurately characterize the microstructure characteristics of the shock-absorbing rubber, providing a geometric basis for subsequent performance analysis.

[0156] The specific implementation of step S03 is to first establish an elastic constitutive model of the rubber material, and a two-parameter Mooney-Rivlin model is used to describe the nonlinear mechanical behavior of the rubber under large deformation conditions, with the expression being: W = C 10 (I1-3) + C 01 (I2-3); where W is the strain energy density function; C 10 and C 01 are material parameters, usually obtained by fitting uniaxial tension, biaxial tension, and pure shear test data; I1 and I2 are the first and second invariants of the deformation tensor. For different temperature conditions, a Williams-Landel-Ferry shift function is used to establish a temperature-dependent model of the dynamic mechanical properties of the rubber, with the expression being: where a THere, T is the temperature shift factor; T0 is the current temperature; and 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: a fixed constraint is applied at the bottom, a periodic displacement excitation is applied at the top, and periodic boundary conditions are set on the sides to simulate large-scale structures. Transient analysis is performed using an explicit dynamic solver, with the time step set to 1 / 20 of the period of the highest analysis frequency to ensure computational stability. For each microstructure design scheme, dynamic response analysis is 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 degrees Celsius. The storage modulus and loss modulus under each condition are calculated and extracted using the following formulas: In the formula, E′ is the storage modulus; E″ is the loss modulus; σ0 is the stress amplitude; ε0 is the strain amplitude; and δ is the phase difference between stress and strain. The principal damping ratio is calculated based on the results: In the formula, ζ is the principal damping ratio, characterizing the material's vibration reduction capability. A three-dimensional surface plot of the principal damping ratio as a function of frequency and temperature is plotted to evaluate the vibration reduction performance of the microstructure within the target frequency range. The purpose of this step is to evaluate the dynamic mechanical performance of different microstructure designs under various operating conditions using virtual simulation methods, thereby reducing experimental costs and shortening the development cycle.

[0157] The specific implementation of step S04 is based on the design of periodic microstructures according to the phononic crystal bandgap theory. First, a calculation model of the phononic crystal dispersion relationship is established, and the plane wave expansion method is used to solve for the eigenfrequency and corresponding mode shape of the microstructure unit. Its characteristic equation is: ∑ G′ [Λ ijkl (GG′)·(k+G′) k ·(k+G) l -ω 2 ρ(GG′)δ ij ]u j (G′)=0; where Λ ijkl ρ 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 U is the Kronecker function; j The displacement component is represented by four basic microstructure elements with different size ratios, corresponding to a ratio of 1:1.2:1.5:2.0. By adjusting the size and position of the internal holes of the basic elements, band gaps are formed in each element within a specific frequency range. The vibration transmission characteristics under different element arrangements are calculated using the transfer matrix method. The element transfer matrix is ​​as follows: where T is the transfer matrix; k is the wave number; and L is the unit length. For a system consisting of n different units, the total transfer matrix is: T total = T n · T n-1 ·…·T2·T1; and the vibration transmission coefficient of the system can be expressed as: where τ is the vibration transmission coefficient; T ij is an element of the total transfer matrix. The arrangement mode with the most significant attenuation in the target frequency range is preferably selected. Based on the Bragg scattering principle, the period length of the microstructure is adjusted so that the center frequency of the first-order band gap is aligned with the main vibration frequency determined in step S01. For a gradient parameter microstructure, the parameter variation can be expressed as: where p(x) is the parameter value at position x; p0 is the initial parameter value; Δp is the parameter variation; f(x / L) is a variation function, which can be a linear function, an exponential function, or a sinusoidal function, etc.; and L is the total length. Considering the local resonance effect, independent resonator structures are added to the basic microstructure unit, and by adjusting the resonator mass and elastic parameters, an attenuation band gap for specific low-frequency vibrations is formed. A gradient parameter microstructure design is proposed, which gradually changes the microstructure parameters along the vibration propagation direction to form a wideband vibration reduction effect. A topology optimization method is used to further optimize the microstructure morphology based on a bidirectional evolutionary structure optimization algorithm to meet the manufacturing constraint conditions, so that the band gap characteristics are best matched with the target frequency. The purpose of this step is to use the phononic crystal theory to design a periodic microstructure that selectively isolates specific frequency vibrations, thereby improving the performance of the shock-absorbing rubber product.

[0158] The specific implementation of step S05 is to construct a microstructure performance rapid evaluation system based on a hybrid model combining a support vector regression algorithm and a radial basis function neural network, which has the mathematical expression: where 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; and N is the number of support vectors. The expression of the radial basis kernel function is: K(x, x i ) = exp(-γ||x-x i || 2where y is a kernel parameter that controls the width of the radial basis function, and is generally determined by cross-validation with a range of 0.01 to 100. The input parameter vector includes five key indicators, i.e., the void distribution density, the average pore size, the void shape factor, the microstructure unit arrangement pattern, and the target frequency range. The void distribution density controls the overall porosity and affects the material stiffness and damping efficiency; the average pore size determines the microstructure characteristic size and affects the applicable frequency range; the void shape factor describes the geometric characteristics of the voids and affects the stress distribution and energy dissipation mechanism; the microstructure unit arrangement pattern determines the phononic crystal bandgap characteristics and affects the frequency selectivity; and the target frequency range specifies the damping requirement and is used for performance evaluation. The prediction output includes four evaluation results, i.e., the damping efficiency indicator, the durability indicator, the manufacturing difficulty indicator, and the cost indicator. The evaluation results are evaluated by using a weighted comprehensive scoring method, and the calculation formula is S = w1S1 + w2S2 + w3S3 + w4S4; in the formula, S is the comprehensive score; S1, S2, S3, and S4 are the standardized scores of the damping efficiency indicator, the durability indicator, the manufacturing difficulty indicator, and the cost indicator, respectively; w1, w2, w3, and w4 are the weights of the indicators, and satisfy w1 + w2 + w3 + w4 = 1. The weights of the indicators can be dynamically adjusted according to the specific application requirements. Generally, the weight of the damping 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 indicator is 0.1. The score threshold is set to 90 points, and the candidate schemes with a comprehensive score of more than 90 points are selected. For the schemes that pass the preliminary screening, the analytic hierarchy process is further used for detailed comparison, and the judgment matrix is established according to the expert experience: where A is the judgment matrix; a ij represents the importance ratio of scheme i relative to scheme j. The calculation formula of the maximum eigenvalue of the judgment matrix is A·W = l max ·W; in the formula, W is the eigenvector, indicating the weight of each scheme; l max is the maximum eigenvalue. The calculation formula of 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 order n of the matrix; when CR < 0.1, it is considered that the judgment matrix has satisfactory consistency. The relative importance of each scheme is calculated, and the top three schemes are selected for the experimental verification stage. The purpose of this step is to quickly select the most potential candidate schemes from a large number of possible microstructure design schemes, thereby improving the design efficiency.

[0159] The specific implementation of steps S06-S08 is the same as the foregoing, and will not be described here again.

[0160] The specific implementation of step S09 is to install the selected optimal shock-absorbing rubber product into an actual automobile shock-absorbing system, design a standard test route including three road conditions of 5 kilometers of flat road, 3 kilometers of gravel road, and 2 kilometers of bumpy road. Test is performed at three vehicle speeds of 40 kilometers / hour, 60 kilometers / hour, and 80 kilometers / hour under the three road conditions, respectively, and each group of conditions is repeatedly tested 3 times to ensure data reliability. During the test, vibration measuring devices are 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 vibration isolation rate calculation formula is: In the formula, η is the vibration isolation rate; A1 is the amplitude before shock absorption; and A2 is the amplitude after shock absorption. According to the test results, the deviation of the actual shock-absorbing effect from the expected performance is calculated, and the calculation formula is: In the formula, δ is the performance deviation; η actual is the actual test vibration isolation rate; and η predicted is the predicted vibration isolation rate. If the deviation exceeds 15%, the microstructure needs to be redesigned from step S04. Long-term road tests are arranged, and the vehicle is continuously driven for 10,000 kilometers. Every 1,000 kilometers, a sample test is taken to record the trend of shock-absorbing performance. The shock-absorbing performance attenuation rate is calculated, and 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 t kilometers of use. The aging degree of the tested sample is evaluated, including hardness change rate, permanent deformation amount, microstructure change, etc. If the performance attenuation exceeds 20%, the microstructure needs to be redesigned from step S04. The reasons for the problems found are analyzed, and the weight coefficients in the microstructure performance prediction function are updated. 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 to the weight. The prediction error calculation formula is: In the formula, E is the mean square error; M is the sample number; is the predicted value of the jth sample; is the actual value of the jth sample. The prediction accuracy of the problem working condition is improved. If the test results do not meet the requirements, a new round of iterative design and optimization is performed according to the process of steps S04 to 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, to ensure that it can play a long-term stable and reliable shock-absorbing role in the real use environment, and to continuously improve the design scheme through iterative optimization.

[0161] For a better understanding and implementation of the present application, the following provides an embodiment 2 of a specific application scenario of the present application: researchers collect vibration data of a certain medium-sized SUV, and find that during high-speed driving, especially on uneven road surfaces, the body vibration significantly affects the ride comfort. In order to improve this problem, the researchers decide to apply the microstructure optimization method of automobile damping rubber products to redesign the damping rubber components of the engine support to improve the damping effect and service life.

[0162] Firstly, the researchers installed high-precision three-axis acceleration sensors on the engine support, body chassis and seat bottom of the SUV, and set the sampling frequency to 1000Hz. Under three typical road conditions (smooth highway, urban gravel road and rural bumpy road), tests were conducted at speeds of 40km / h, 80km / h and 120km / h respectively, and 600 seconds of vibration data were continuously collected 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 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 40 18-35 53 Urban gravel road 80 25-48 65 Urban gravel road 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 is mainly concentrated in the range of 12-95Hz, and the vibration energy in the frequency band of 30-65Hz is the most concentrated, accounting for more than 65% of the total vibration energy. Therefore, it is determined that the frequency interval that damping rubber products need to focus on is 30-65Hz. Figure 2 The vibration frequency distribution of the SUV under different road conditions and speeds is shown in a visual manner.

[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 rubber microstructure hole distribution scheme

[0168]

[0169] For each scheme, the researchers used the finite element analysis software ABAQUS to construct a 10x10x10mm three-dimensional grid model, and used local grid refinement technology at the hole edge, with a grid size of 1 / 10 of the smallest pore size, i.e. 0.03mm.

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

[0171] Table 3 Damping rubber material parameter settings

[0172] Parameter type Value range Test temperature condition (℃) Young's modulus (MPa) 3.5-5.2 25 Poisson's ratio 0.48 25 Munro-Rivlin parameters C 10 (MPa) 0.82 25 Munro-Rivlin parameters C 01 (MPa) 0.15 25 Damping coefficient 0.12 25 [WLF constant C1] 17.44 - [WLF constant C2] 51.6 -

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

[0174] Table 4 Band gap characteristics of different microstructure unit combinations

[0175] Combination mode Primary band gap frequency range (Hz) Secondary band gap frequency range (Hz) In-band attenuation peak value (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 is selected, which has the best matching band gap characteristics with the target frequency range of 30-65 Hz and the highest attenuation peak of 38 dB. Figure 3 The band gap frequency range and attenuation peak of different microstructure unit combinations are intuitively presented, with blue representing the first-order band gap and green representing the second-order band gap.

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

[0178] Table 5 Microstructure scheme comprehensive score results (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 score in Table 5, the C-1.5-2.0-1.2-1 and B-1.5-2.0-1.2-1 schemes are selected for experimental verification, both of which have a comprehensive score of more than 90 points.

[0181] Subsequently, the researchers prepared test samples through micro-foaming molding process. When batching, natural rubber and styrene-butadiene rubber were mixed in a ratio of 70:30, and azodicarbonamide foaming agent was added at 2.2%. Sulfurization was carried out at a temperature of 155℃ and a pressure of 17.5MPa, with a temperature gradient of 7.5℃ per centimeter and a sulfurization time of 12 minutes.

[0182] After preparing the samples, scanning electron microscopy (SEM) was used for microstructure characterization, and microstructure images were obtained at 500x and 1000x magnification, as shown in Figure 4 and Figure 5 , respectively, where Figure 4 The red box part of Figure 5 is the position. The actual microstructure parameters were measured by image analysis software, as shown in Table 6:

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

[0184]

[0185]

[0186] Table 6 shows that the actual microstructure parameters of the two samples deviate from the design values by less than 7%, meeting the design requirements.

[0187] The dynamic mechanical analysis test obtains the storage modulus and loss modulus data of the two samples under different frequency and temperature conditions, and inputs these data together with the SEM microstructure images into the pre-trained vibration damping rubber microstructure neural network model to predict the long-term performance of the samples, and the results are shown in Table 7:

[0188] Table 7 Performance prediction results 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 30-50 Hz frequency band average vibration reduction efficiency (%) 86.5 83.2 50-65 Hz frequency band average vibration reduction efficiency (%) 82.3 78.5 Vibration reduction efficiency under -30 ℃ condition (%) 74.2 70.8 Vibration reduction efficiency under 120 ℃ condition (%) 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 is selected as the final scheme, and its vibration damping efficiency and service life are better than those of the B-1.5-2.0-1.2-1 sample.

[0191] Finally, the optimized shock absorbing rubber products are installed on the SUV for actual road testing, and the vibration isolation rate is measured under three road conditions, and the performance data after 10000 kilometers of continuous driving are collected, as 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 allowed deviation range of 15%, and the performance attenuation rate after driving 10000 kilometers is at most 7.6%, which is far below the limit value of 20%, indicating the effectiveness and reliability of the optimized design.

[0195] The traditional design of automobile damping rubber products mainly relies on experience and a large number of trial and error experiments, usually uses homogeneous rubber materials or simple composite structures, and lacks precise control and optimization of microstructure. Such traditional methods have the following problems: first, the frequency selectivity of the damping performance is poor, and it is difficult to achieve efficient vibration isolation for a specific frequency range; second, the environmental adaptability is poor, and the performance decreases significantly at extreme temperatures; third, the service life is short, and the performance decays seriously after long-term use; finally, the development cycle is long and the cost is high. The microstructure optimization method proposed in the present application designs a bandgap structure through phononic crystal theory to achieve selective attenuation of specific frequency vibrations, which improves the damping efficiency by about 30% compared with traditional methods; through multi-field coupling simulation analysis and microstructure performance prediction function, the performance of the candidate scheme is quickly evaluated, and the development cycle is shortened by more than 50%; the micro-foaming molding process and periodic microstructure arrangement are adopted to improve the environmental adaptability and maintain stable performance in the temperature range of-30℃ to 120℃; 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 damping rubber products designed by this method have excellent damping effect and durability under various road conditions and speed conditions, providing a new technical path for the performance improvement of automobile damping systems.

[0196] It should be noted that the variables involved in the present application are explained in detail as shown in Tables 9 and 10.

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

[0198]

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

[0200]

[0201]

[0202] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for microstructure optimization of an automotive shock absorbing rubber article, characterized by, The method comprises the following steps: Collecting actual vibration data of the automobile under different road conditions, recording vibration signals through an acceleration sensor, and calculating a main frequency distribution map; establishing a digital model of the rubber microstructure, including a hole distribution density, a pore size distribution range, and a hole shape parameter matrix, and using a finite element analysis software to construct a three-dimensional microstructure grid model; performing multi-field coupling simulation analysis to simulate the dynamic mechanical properties of different microstructure designs under temperature conditions; using phononic crystal theory to design a periodic arrangement of the rubber microstructure to form a bandgap structure, and adjusting the size ratio of the microstructure unit to selectively attenuate specific frequency vibrations; Calling a microstructure performance prediction function to quickly evaluate candidate microstructure schemes; preparing test samples through a micro-foaming molding process; using an electron microscope to characterize the microstructure of the prepared samples; using a pre-trained neural network model of the damping rubber microstructure to analyze the test data; and performing road test verification in an actual automobile damping system; The periodic arrangement of the rubber microstructure is designed using phononic crystal theory, specifically forming a bandgap structure with a frequency of 10 to 80 Hz, and adjusting the size ratio of the microstructure unit to 1:1.2:1.5:2.0 to selectively attenuate specific frequency vibrations. The microstructure performance prediction function is called to quickly evaluate candidate microstructure schemes based on a hybrid model combining support vector regression algorithm and radial basis function neural network, specifically input parameters including hole distribution density, average pore size, hole shape factor, microstructure unit arrangement mode, and target frequency range, outputting estimated damping efficiency, durability, manufacturing difficulty, and cost indicators for each scheme, and using a weighted comprehensive scoring method to set a score threshold of 90 points, and microstructure schemes with a comprehensive score of 90 points or more are entered into the experimental verification stage. The test samples are prepared through a micro-foaming molding process, specifically by injecting a raw rubber mixture with a foaming agent mass fraction of 1.5 to 3.0%, vulcanizing at a temperature of 140 to 160 degrees Celsius and a pressure of 15 to 20 megapascals, and controlling the temperature gradient during the foaming process to be 5 to 10 degrees Celsius per centimeter.

2. The method of microstructure optimization of automotive shock absorbing rubber articles according to claim 1, characterized in that, The actual vibration data of the automobile under different road conditions is collected, specifically by recording vibration signals with a frequency range of 5 to 200 Hz through an acceleration sensor, and performing Fourier transform to obtain a main frequency distribution map to determine the frequency range that the damping rubber product needs to cope with.

3. The method of microstructure optimization of automotive shock absorbing rubber articles according to claim 2, characterized in that, The digital model of the rubber microstructure is established, specifically including a hole distribution density of 50 to 200 per cubic centimeter, a pore size distribution range of 0.1 to 2.0 millimeters, and a hole shape parameter matrix, and a three-dimensional microstructure grid model is constructed using a finite element analysis software.

4. The method of microstructure optimization of automotive shock absorbing rubber articles according to claim 3, characterized in that, The multi-field coupling simulation analysis is performed, specifically by setting the Young's modulus of the rubber material to 1.5 to 8.0 megapascals, the Poisson's ratio to 0.45 to 0.49, and the damping coefficient to 0.05 to 0.20, and simulating the dynamic mechanical properties of different microstructure designs under temperature conditions ranging from negative 30 to 120 degrees Celsius.

5. The method of microstructure optimization of automotive shock absorbing rubber articles according to claim 4, characterized in that, The microstructure of the prepared sample is characterized by using an electron microscope, specifically, the deviation of the actual porosity from the design value is controlled within 5%, the microstructure connectivity and anisotropy index are analyzed by a three-dimensional reconstruction technology, and it is ensured that the double connectivity rate is greater than 60%.

6. The method of microstructure optimization of automotive shock absorbing rubber articles according to claim 5, characterized in that, The pre-trained microstructure neural network model of the damping rubber is used for analyzing 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 microstructure neural network model of the damping rubber, the long-term performance of the sample under different vibration frequencies and environmental temperatures is predicted, and a scheme with a damping efficiency greater than 80% and a service life of more than 100,000 kilometers is selected.

7. The method of microstructure optimization of automotive shock absorbing rubber articles according to claim 6, characterized in that, The microstructure performance prediction function is used for quickly screening out potential candidate schemes from a large number of microstructure schemes without performing full calculation-intensive finite element analysis, and the input includes the hole distribution density parameter as the characterization of the microstructure porosity, the average pore size parameter for determining the damping frequency range, the hole shape factor parameter for describing the geometric characteristics of the micro-pores, the microstructure unit arrangement mode parameter representing the spatial distribution mode of the holes, and the target frequency range parameter indicating the frequency interval that needs to be damped.

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