Brake friction squeal inhibition method considering surface topography

Abstract

The invention relates to a brake friction squeal inhibition method considering surface topography. The method comprises the following steps: carrying out a brake friction squeal test; carrying out a surface topography measurement test, and obtaining complemented surface topography data in combination with MATLAB pretreatment; establishing a friction squeal finite element model, applying a rotation effect of a brake disc and a nonlinear friction contact condition, performing complex mode simulation to obtain a complex mode analysis result, and establishing a friction squeal prediction model in combination with a kriging method; generating a new surface topography parameter combination through a parameterization method; inputting the new surface topography parameter combination into a friction scream prediction model, outputting a corresponding complex feature value, quantifying the parameter sensitivity based on a Sobol method, and obtaining a sensitivity analysis result; and according to a sensitivity analysis result, the friction scream of the brake is inhibited by modifying and optimizing the surface topography parameters of the brake. Compared with the prior art, the method not only can improve the prediction precision of the friction scream, but also can effectively inhibit the friction scream from the perspective of surface topography optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of brake squeal suppression, and in particular to a brake friction squeal suppression method taking surface topography into consideration. Background Art

[0002] As a core component of the vehicle's safety system, brake vibration and noise issues directly impact driving comfort and environmental friendliness. Statistics show that user complaints caused by brake squeal account for over 23% of vehicle NVH (Noise, Vibration, Harshness) issues, resulting in over $1.5 billion in after-sales costs to the global automotive industry annually, and has become a key technical bottleneck restricting the development of high-end automotive brands. In research on the mechanism of brake squeal, the dynamic characteristics of the friction interface are considered to be the core factor inducing system instability. The dynamic evolution of the friction coefficient with surface topography determines the prediction accuracy of complex eigenvalue analysis (CEA).

[0003] Brake squeal, a dynamic bifurcation behavior, is closely related to the friction coefficient and plays a central role in brake squeal analysis and suppression strategies. The SAE J2521 standard also clearly defines the requirements for the measurement and analysis of the friction coefficient. However, in the field of brake squeal mechanism research and prediction, traditional complex eigenvalue analysis simplifies the friction coefficient to a global constant value, ignoring the spatial distribution of the friction coefficient caused by the elastic-plastic deformation of micro-asperities in actual contact. Surface micro-pits can cause local fluctuations in the friction coefficient. This nonlinear distribution can significantly alter the singularity of the pressure distribution matrix, thereby affecting the calculation accuracy of the system stability boundary.

[0004] Traditional methods for controlling brake squeal often focus on mechanical vibrations, suppressing it by adjusting the modal vibration characteristics of component structures. For example, by modifying the weight or structure of the brake disc or caliper, natural frequencies prone to resonance can be shifted. Furthermore, the introduction of silencers with specific structures and materials can effectively reduce the tendency and intensity of brake squeal. However, most of these methods fail to consider contact characteristics, and research into the influence of surface topography on brake squeal and its suppression strategies remains insufficient.

[0005] Although patents such as CN117787041A have proposed a brake squeal suppression method based on the improvement of the non-uniform characteristics of the friction coefficient, this method uses the macroscopic continuous medium hypothesis to describe the friction interface to establish a friction coefficient spatial distribution model, introduces the gradient change characteristics of the friction coefficient to perform system stability analysis, and optimizes the brake pad stiffness distribution based on the non-uniform friction characteristics to reduce the unstable modal energy at a specific frequency, but its core is still focused on optimizing the brake structure with friction characteristics, and does not touch on the influence of the microscopic real surface morphology of the brake on the brake squeal, nor does it propose a corresponding suppression strategy, and cannot accurately and effectively suppress the friction squeal of the brake. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a brake friction squeal suppression method taking into account the surface morphology, which can not only improve the prediction accuracy of friction squeal, but also effectively suppress friction squeal from the perspective of surface morphology optimization.

[0007] The object of the present invention can be achieved by the following technical solution: A method for suppressing brake friction squeal considering surface morphology, comprising the following steps:

[0008] S1. Conduct brake friction squeal tests to obtain key information about brake squeal, including characteristic frequency, amplitude, and temporal variation.

[0009] S2. Perform surface topography measurement tests to obtain surface topography data of the brake disc and friction pad, and use MATLAB for preprocessing to obtain completed surface topography data;

[0010] S3. Based on the completed surface morphology data, a friction squeal finite element model is established;

[0011] S4. For the friction squeal finite element model, apply the rotation effect of the brake disc and nonlinear friction contact conditions to perform complex modal simulation and obtain complex modal analysis results;

[0012] S5. Based on the complex modal analysis results, a friction squeal prediction model is established based on the Kriging method, wherein the input of the friction squeal prediction model is the surface topography parameters and the operating condition parameters, and the output is the complex eigenvalue;

[0013] S6. Generate a new surface topography parameter combination through a parametric method;

[0014] S7. Input the new surface topography parameter combination into the friction squeal prediction model, output the corresponding complex eigenvalue, and quantify the parameter sensitivity based on the Sobol method to obtain the sensitivity analysis results;

[0015] S8. Based on the sensitivity analysis results, the surface morphology parameters of the brake are modified and optimized to suppress the friction squeal of the brake.

[0016] Furthermore, the specific process of step S1 is as follows: preparing a standard brake test sample to simulate actual braking conditions;

[0017] Use acoustic and vibration testing equipment to collect acoustic and vibration characteristic information during braking, including sound pressure level and acceleration of key components, and record operating condition information, including brake disc speed, brake pressure, and braking torque;

[0018] After data collection is completed, time domain analysis, frequency domain analysis, and phase diagram analysis are performed to extract key information about brake squeal, including characteristic frequency, amplitude, and changes over time.

[0019] Furthermore, the specific process of step S2 is as follows: for a standard brake test sample, a profilometer is used to perform high-precision topography scanning on the surfaces of the brake disc and the friction pad. During the measurement process, the test sample is fixed with a special fixture to ensure the installation flatness error, and the surface topography data of the brake disc and the friction pad are measured;

[0020] The measurement data are preprocessed by MATLAB, including the removal of abnormal noise points, interpolation and completion of missing areas, and the extraction of key morphological parameters, including surface roughness Ra, waviness WT and end face runout SRO.

[0021] Furthermore, the specific process of step S3 is: reconstructing a three-dimensional surface model based on the completed surface topography data and fractal geometry theory;

[0022] For the three-dimensional surface model, mesh division is performed in the unit division software to obtain a disk-block contact model with complex surface morphology. Adaptive mesh encryption technology is used at the contact interface to accurately characterize the elastic-plastic deformation and friction behavior of the micro-convex body, and a friction scream finite element model with surface morphology is established.

[0023] Furthermore, the specific process of step S4 is as follows: importing the friction squeal finite element model into the finite element software, applying the actual braking conditions and thermal boundary conditions, simulating the rotation effect of the brake disc and the nonlinear friction contact conditions;

[0024] Perform complex modal analysis to extract complex eigenvalues ​​and mode shapes, where the real part of the complex eigenvalue represents system stability and the imaginary part corresponds to the squeal frequency;

[0025] The simulated modal frequency is compared with the characteristic frequency obtained in step S1. If the deviation between the two exceeds the threshold, the friction coefficient curve and contact stiffness parameters are adjusted through the inverse optimization algorithm, and the complex modal analysis is performed again.

[0026] Furthermore, the specific process of step S5 is as follows: using the surface topography parameters obtained in step S2 and the brake disc speed and brake pressure obtained in step S1 as model inputs, using the real and imaginary parts of the complex eigenvalues ​​obtained in step S4 as model outputs, generating a training data set based on a parameterized method, where the sample size in the training data set is equal to the parameter dimension × 10;

[0027] The Kriging Gaussian process regression algorithm is used to establish an input-output mapping model. The training dataset is used for model training. The nonlinear relationship between parameters is captured by the covariance function. The goodness of fit is ensured through cross-validation. An active learning strategy is introduced to dynamically optimize the sample space to construct a friction squeal prediction model.

[0028] Furthermore, the specific process of step S6 is as follows: first, the design space of each morphological parameter is defined based on the preliminary test data, and each parameter dimension is equally divided into non-overlapping intervals in the three-dimensional parameter space, that is, the number of layers in each dimension is equal to the sample size, ensuring that each interval contains only one sample point;

[0029] The stratified intervals of each parameter dimension were then randomly permuted independently to avoid artificial correlations between variables;

[0030] Then, the sampling points of the three parameters were randomly paired through matrix combination to generate morphological parameter combinations. In this process, an orthogonal optimization strategy was introduced, and the Levenberg-Marquardt algorithm was used to minimize the Pearson correlation coefficient between the parameters, so that the absolute values ​​of the correlation coefficients of Ra-WT, Ra-SRO, and WT-SRO were all lower than 0.1.

[0031] Furthermore, the specific process of step S7 is as follows: inputting the new surface topography parameter combination into the friction squeal prediction model, outputting the corresponding complex eigenvalue, and using the Sobol method to quantify the contribution of each surface topography parameter and their interaction to the complex eigenvalue;

[0032] Then the first-order sensitivity index (S i ) and the total sensitivity index (S Ti ), filter out the dominant parameters;

[0033] Through main effect analysis, the synergistic effect among surface morphology parameters was obtained;

[0034] Generate sensitivity heat maps and prioritize surface topography parameters.

[0035] Furthermore, the specific process of step S8 is: designing an optimized morphology scheme based on the sensitivity analysis result of step S7;

[0036] Bench tests were carried out to verify the optimized morphology scheme, and an inhibitory morphology database including Ra, WT, SRO and their combinations was established. The surface self-similar characteristics were described by fractal dimension to guide the batch production process of brake discs.

[0037] Furthermore, the optimization scheme includes:

[0038] Laser texturing, grinding or sandblasting processes are used to control surface roughness Ra, reduce microscopic contact stress fluctuations, and achieve sound pressure level noise reduction;

[0039] Adjust the end face runout (SRO) through CNC grinding process to suppress the modal coupling caused by rotational imbalance;

[0040] Optimize the hot rolling process parameters to make the surface waviness WT distribution fluctuation amplitude within the preset range.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] The present invention first conducts a brake friction squeal test, followed by a surface topography measurement test to obtain surface topography data for the brake disc and friction pad. This data is then preprocessed using MATLAB to obtain completed surface topography data. A friction squeal finite element model is then established based on the completed surface topography data. Complex modal simulation is then performed to obtain complex modal analysis results, which are then combined with the kriging method to establish a friction squeal prediction model. A new surface topography parameter combination is then generated using a parameterization method, input into the friction squeal prediction model, and the corresponding complex eigenvalues ​​are output. The parameter sensitivity is quantified using the Sobol method to obtain sensitivity analysis results. Finally, based on the sensitivity analysis results, the brake surface topography parameters are modified and optimized to suppress brake friction squeal. This method, by accurately measuring the brake surface topography, then performing complex modal analysis and constructing a prediction model, and generating a simulated brake surface topography, then using the Sobol method to analyze the effect of surface topography on friction squeal, effectively suppresses friction squeal by modifying the surface topography. This method not only improves the prediction accuracy of friction squeal but also effectively suppresses friction squeal from the perspective of surface topography optimization.

[0043] Through meticulous experimental simulations (brake friction squeal tests, surface topography measurements, and complex modal simulations), this invention accurately quantifies the mapping between surface topography parameters and the system's dynamic instability threshold. This precise data is then used to analyze the mechanism of brake squeal, guiding the development of brakes that suppress it. This approach transcends the limitations of traditional methods that only consider the macroscopic continuum assumption and uniform friction coefficient, achieving precise prediction of brake squeal.

[0044] This paper establishes a joint framework combining the Kriging surrogate model and Sobol global sensitivity analysis. This framework can analyze the nonlinear contribution of topographic parameters (Ra / WT / SRO) to system stability with only a small number of training samples. It also incorporates an active learning strategy to dynamically optimize the sample space, improving topographic optimization efficiency and shortening the optimization cycle. Furthermore, through a fractal dimension database and online SPC process control, it enables the mass production of low-noise brakes. This strategy not only accelerates the development of low-noise brakes but also significantly enhances vehicle ride comfort.

[0045] When establishing the friction scream finite element model, the present invention adopts a non-uniform grid division strategy and implements an adaptive grid encryption technology at the contact interface to accurately characterize the deformation behavior of the micro-convex body and ensure the physical fidelity of the friction scream finite element model.

[0046] The present invention generates new surface topography parameter combinations through a parametric method. First, the design space of each topography parameter is defined based on the preliminary experimental data. Each parameter dimension is divided into non-overlapping intervals in the three-dimensional parameter space (that is, the number of layers in each dimension is equal to the sample size), ensuring that each interval contains only one sample point, thereby achieving full coverage of the parameter space. Subsequently, the layered intervals of each parameter dimension are independently and randomly arranged to avoid artificial correlation between variables. Then, the sampling points of the three parameters are randomly paired through matrix combination to generate a topography parameter combination (Ra i WT j 、SRO k ), and in this process, an orthogonal optimization strategy was introduced, and the Levenberg-Marquardt algorithm was used to minimize the Pearson correlation coefficient between parameters, so that the absolute values ​​of the correlation coefficients of Ra-WT, Ra-SRO, and WT-SRO were all lower than 0.1, thereby ensuring the uniform distribution and statistical independence of the parameter combination in three-dimensional space.

[0047] Based on the results of sensitivity analysis, the present invention designs a morphology optimization scheme and conducts bench tests to verify the scheme after optimizing the morphology parameters to ensure that the squeal sound pressure level is reduced. In addition, an inhibitory morphology database constrained by fractal dimension is established. The self-similar characteristics of the surface are described by fractal dimension, which is conducive to integration into the brake disc production line, thereby realizing the mass production of low-noise brakes. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the method flow of the present invention;

[0049] Figure 2a and 2b Standard test specimens (brake discs and friction pads) prepared for the brake bench test in the examples;

[0050] Figure 3 This is a schematic diagram of the brake friction squeal test bench system in the embodiment;

[0051] Figure 4a and 4b This is a time-frequency analysis diagram of bench test noise data in the embodiment;

[0052] Figure 5 This is a real picture of the surface morphology measurement in the embodiment;

[0053] Figure 6a and 6b Schematic diagram of the surface topography measurement of the brake disc and friction pad in the embodiment;

[0054] Figure 7a and 7b Surface topography of the brake disc and friction pad in the embodiment;

[0055] Figure 8 Schematic diagram of the finite element model of the hub angle system in the embodiment;

[0056] Figure 9 Schematic diagram of complex modal analysis results in the embodiment;

[0057] Figure 10a and 10b Schematic diagram of the prediction results of the proxy model in the embodiment;

[0058] Figure 11 Schematic diagram of the impact analysis results in the embodiment. DETAILED DESCRIPTION

[0059] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Example

[0061] This solution aims to solve the problem that traditional methods fail to fully consider the influence of surface morphology on brake squeal. In order to solve the shortcomings of existing brake squeal suppression methods, this solution integrates surface morphology parameter modeling, friction dynamics coupling analysis and morphology optimization design technology to break through the limitation of existing technology that only relies on the assumption of uniform macro friction coefficient. This solution takes the construction of a quantitative mapping relationship between surface morphology parameters and system dynamic instability threshold as the starting point, aiming to achieve accurate prediction and control of brake squeal. A brake friction squeal suppression method considering surface morphology is proposed, such as Figure 1 As shown, the following steps are included:

[0062] S1. Conduct brake friction squeal tests to obtain key information about brake squeal, including characteristic frequency, amplitude, and temporal variation.

[0063] Specifically, standard brake test specimens are prepared, with a jack applying vertical force, a driving force device providing driving force, and a hydraulic system providing braking pressure to simulate actual braking conditions. High-precision acoustic and vibration testing equipment, such as microphone arrays and accelerometers, is used to collect acoustic and vibration characteristic information such as the sound pressure level and acceleration of key components during braking. In addition, operating condition information such as brake disc speed, brake pressure, and braking torque must be recorded to provide basic data for subsequent analysis. After data collection is completed, time domain analysis, frequency domain analysis, and phase diagram analysis are performed to extract key information such as the characteristic frequency, amplitude, and time-varying patterns of brake squeal, which will be used for subsequent verification and optimization of the finite element model.

[0064] S2. Perform surface topography measurement tests to obtain surface topography data of the brake disc and friction pad, and use MATLAB for preprocessing to obtain completed surface topography data;

[0065] Specifically, after preparing standard brake test specimens, surface topography measurements were performed using a profilometer. Based on the test results, the surfaces of the brake disc and friction pad were visualized and preprocessed using MATLAB, enabling data cleaning and interpolation to complete missing points. Furthermore, a dedicated fixture was designed to secure the specimens, ensuring accurate flatness measurement and providing high-precision input for finite element modeling.

[0066] S3. Based on the completed surface morphology data, a friction squeal finite element model is established;

[0067] Specifically, the surface topography data obtained after MATLAB processing in the previous step is meshed in the unit partitioning software to obtain a disc-block contact model with complex surface topography (i.e., a brake disc-friction pad contact model). Adaptive mesh encryption technology is used at the contact interface to accurately characterize the elastic-plastic deformation and friction behavior of the micro-asperities, providing a high-precision and fidelity model for subsequent complex modal analysis.

[0068] S4. For the friction squeal finite element model, apply the rotation effect of the brake disc and nonlinear friction contact conditions to perform complex modal simulation and obtain complex modal analysis results;

[0069] Specifically, the rotation effect of the brake disc and nonlinear friction contact conditions are applied to the disc-block contact model established in step S3, and the finite element method is used to perform complex modal simulation and analysis of the friction squeal finite element model with surface morphology. This operation provides a physically driven data foundation and dynamic characteristic targets for the subsequent construction of the proxy model;

[0070] S5. Based on the complex modal analysis results, a friction squeal prediction model is established based on the Kriging method, wherein the input of the friction squeal prediction model is the surface topography parameters and the operating condition parameters, and the output is the complex eigenvalue;

[0071] Specifically, based on the analysis results obtained from the complex modal analysis in step S4, a rapid prediction model of input (surface topography parameters, operating condition parameters) and output (complex eigenvalues) is established based on the kriging method. The proxy model can be used to quickly predict the tendency of friction squeal, while avoiding repeated and costly finite element simulations. It can also reveal the intrinsic relationship between surface topography parameters and system stability.

[0072] S6. Generate a new surface topography parameter combination through a parametric method;

[0073] Specifically, a large number of new surface topography parameter combinations are generated through parametric methods (such as Latin hypercube sampling, optimized Latin hypercube, or physical rule-based parametric modeling) to cover a wider parameter space, provide sufficient input samples for subsequent sensitivity analysis, and ensure the statistical significance of the analysis results;

[0074] S7. Input the new surface topography parameter combination into the friction squeal prediction model, output the corresponding complex eigenvalues, and quantify the parameter sensitivity based on the Sobol method to obtain sensitivity analysis results. This step reveals the mechanism of friction squeal and provides a statistical basis for the subsequent proposal of a method based on surface topography modification to suppress friction squeal.

[0075] S8. Based on the sensitivity analysis results, the surface topography parameters of the brake are modified and optimized to suppress the friction squeal of the brake;

[0076] Specifically, according to the sensitivity analysis results of step S7, an optimization scheme is designed for the dominant parameters (such as surface roughness Ra, waviness WT, and end face runout SRO, etc.):

[0077] Through processes such as laser texturing, grinding, or sandblasting, Ra is controlled to reduce microscopic contact stress fluctuations and thus suppress squeal. Based on thermal-mechanical coupling analysis, the ripple distribution on the brake disc surface is optimized to suppress end face runout caused by thermal deformation to suppress squeal. Through precision machining processes (such as CNC grinding), end face runout is controlled to reduce vibration mode coupling caused by rotational imbalance to suppress squeal.

[0078] The optimized parameter combination was then verified by bench testing to ensure that the squeal sound pressure level was reduced;

[0079] In addition, an inhibitory morphology database including Ra, WT, SRO and their combination is established, and the surface self-similar characteristics are described by fractal dimension to guide the batch production process of brake discs.

[0080] This embodiment applies the above solution, and its main contents are:

[0081] 1. Brake friction squeal test

[0082] First, this embodiment prepares Figure 2a and 2b Brake test specimens of the standard shown ( Figure 2a For the brake disc, Figure 2b These samples need to strictly simulate the actual vehicle braking conditions. Figure 3 The high-precision brake test bench and acoustic vibration test equipment shown in the figure comprehensively collect acoustic and vibration characteristic information such as sound pressure level and acceleration of key components during braking. At the same time, detailed information on working conditions such as brake disc speed, brake pressure, and brake torque are recorded. After data collection is completed, this embodiment uses professional analysis software to perform time domain analysis, frequency domain analysis, and phase diagram analysis to extract key information such as the characteristic frequency, amplitude, and time-varying patterns of brake squeal. Typical results are shown in Figure 4a and Figure 4b This information provides solid basic data for subsequent analysis.

[0083] It should be noted that brake pad samples should be test samples from the same batch and should have a high degree of consistency, including size, weight, material composition, etc., to reduce test errors and improve the repeatability and comparability of the test; they should have high durability and be able to withstand multiple braking tests without obvious wear or deformation, so as to ensure the stability and reliability of the test results.

[0084] To ensure high consistency of brake pad samples, this embodiment, in addition to strict control of parameters such as size, weight, and material composition, should also increase unified management of brake pad surface roughness, hardness, and heat treatment processes. Slight differences in these parameters may affect the friction performance and vibration characteristics during braking, thereby affecting the accuracy of brake squeal prediction. At the same time, a strict batch inspection process is established to ensure that each batch of brake pad samples meets the preset test standards. In addition, in this embodiment, to ensure that the surface morphology of the friction plate does not change much during the entire friction squeal bench test, a pre-running-in test is performed on the friction plate before the formal test: a certain loading pressure is applied, and a drag wear test is performed on the friction plate, with a cumulative drag travel of approximately 3.75 km to complete the friction plate pre-running-in test.

[0085] 2. Disk-block surface topography measurement

[0086] This embodiment uses Figure 5 Toyota CV-2000 profile measuring instrument Figure 2a and 2b The surface topography of the standard brake disc / friction pad sample shown is scanned. Before measurement, the specimen is fixed with a special fixture and the contact surface is cleaned to remove oil. Figure 6a and 6bThe obtained measurement data is preprocessed by MATLAB, including abnormal noise removal and bicubic spline interpolation of missing areas, to generate Figure 7a and 7b Extract key surface parameters: roughness Ra, waviness WT, and end runout SRO.

[0087] During this process, before measurement, it is necessary to ensure that the contact surface between the fixture and the caliper is free of rust and oil, and the horizontality of the fixture surface should be adjusted to eliminate the influence of installation errors on the morphology measurement; during measurement, ensure that the contact surface of the caliper and the fixture is tightly combined, and use roughness Ra and straightness as indicators to measure the consistency of the two measurement results. If the relative error of the above two indicators of the two measurement results is less than 5%, the measurement data is considered valid, otherwise a third measurement and data comparison analysis are carried out; after completing the installation operation, the caliper should be locked to prevent the fixture and specimen from falling; until it is parallel to the base surface.

[0088] In addition to pre-running-in tests, this example also monitors surface topography stability after run-in using a laser confocal microscope (Keyence VK-X1000) to ensure Ra fluctuations and microcrack density. Before measurement, the fixture is cleaned and calibrated with a laser level. Data consistency is verified by performing two repeated measurements. If the relative error in Ra or straightness is significant, a third measurement is performed, using a median filter algorithm to process the data. The average of these three measurements is used as the valid result.

[0089] 3. Establishment of finite element model of friction squeal with surface topography

[0090] Based on the measured surface morphology data, this embodiment constructs a three-dimensional non-uniform grid model (such as Figure 8 The digitized surface topography was imported into HyperMesh / Abaqus software, and a non-uniform meshing strategy was adopted. Adaptive mesh refinement technology was implemented at the contact interface to accurately characterize the deformation behavior of the micro-asperities. Specifically, a non-uniform mesh model was generated in HyperMesh / Abaqus based on the three-dimensional surface topography data (including roughness Ra, waviness WT, and end face runout SRO) preprocessed by MATLAB. The adaptive mesh refinement technology was used to set the local element size at the contact interface to accurately characterize the elastic-plastic deformation and frictional contact behavior of the micro-asperities.

[0091] Then, the elastic-plastic constitutive model of the micro-asperity and the speed-dependent Stribeck friction curve are defined, and the thermal-mechanical load boundary conditions are coupled to simulate the material performance degradation and dynamic evolution of the surface morphology caused by temperature rise during braking. That is, the penalty function method is used to define the disk-block contact pair, set the pressure-penetration relationship and the Stribeck friction curve, and ensure the physical authenticity of the dynamic response of the model.

[0092] Finally, the macroscopic braking pressure and microscopic topographic stress gradient are coupled through sub-model technology to ensure the physical authenticity of the model and provide a high-fidelity model basis for complex modal analysis.

[0093] It should be noted that when constructing the finite element model, in addition to generating a non-uniform mesh based on 3D topography data (Ra, WT, SRO) preprocessed using MATLAB, this example incorporates GPU parallel computing technology to improve meshing efficiency. An adaptive mesh refinement is employed at the contact interface, and a strain-rate-sensitive constitutive model for asperities and a temperature-dependent friction coefficient are defined. Furthermore, an Archard wear model is coupled to simulate the dynamic evolution of surface topography, ensuring the model's physical fidelity under multiple operating conditions.

[0094] 4. Complex modal analysis of friction squeal

[0095] In this example, a friction squeal finite element model is imported into Abaqus, and actual working conditions are applied to simulate the brake disc rotation effect. Complex modal analysis is performed to extract complex eigenvalues: the real part represents the system stability, and the imaginary part corresponds to the squeal frequency (see Figure 9 The simulation results are compared with the modal frequencies obtained from the friction squeal test, and the mode shape consistency is verified using the MAC value. If the deviation exceeds the threshold, the friction coefficient curve and contact stiffness parameters are adjusted through an inverse optimization algorithm, and complex modal analysis is repeated until the model accuracy meets engineering requirements, providing a reliable data foundation for subsequent proxy model construction.

[0096] That is, the friction squeal finite element model is imported into the finite element software, and the actual braking conditions (brake pressure P, speed ω) and thermal boundary conditions (ambient temperature T) are applied; the rotation effect of the brake disc and the nonlinear friction contact conditions are simulated; then, complex modal analysis is performed to extract the real part, imaginary part and modal vibration shape of the complex eigenvalue; the simulated modal frequency is compared with the friction squeal test data to verify the reliability of the model and provide a dynamic stability data set for the construction of the proxy model.

[0097] When conducting complex modal analysis, experimental modal analysis algorithms include time-domain methods, such as the Ibrahim Time Domain (ITD) method and the State Space Time Domain (STD) method. These methods directly analyze the system's time-domain response to extract modal parameters, offering unique advantages for processing non-stationary signals and transient responses. Combining frequency-domain decomposition with the least-squares complex frequency-domain method creates a comprehensive modal parameter identification system, improving the comprehensiveness and accuracy of brake squeal prediction.

[0098] 5. Construction of friction squeal proxy model based on Kriging method

[0099] Based on the measured surface morphology parameters and combined with the complex mode simulation results ( Figure 10a and 10b As shown in Figure 2, a Kriging surrogate model is established for the input (morphological parameters)-output (real and imaginary parts of complex eigenvalues). The model uses a Gaussian kernel function as the covariance function, ensures goodness of fit through cross-validation, and introduces an active learning strategy to dynamically optimize the sample space.

[0100] This embodiment uses surface morphology parameters (Ra, WT, SRO) and operating condition parameters (P, ω) as input, and the real and imaginary parts of complex eigenvalues ​​as output. A training data set (sample size = parameter dimension × 10) is generated based on Latin hypercube sampling (LHS) or other parameterization methods. The Kriging Gaussian process regression algorithm is used to establish an input-output mapping model, and the nonlinear relationship between parameters is captured through the covariance function. The proxy model is improved through cross-validation and active learning strategies (based on prediction variance optimization samples) to improve the model generalization ability. It can replace high-cost complex modal simulation and quickly predict the scream risk of different morphology combinations.

[0101] When constructing the Kriging surrogate model, in addition to generating a training data set based on LHS, the Bayesian optimization algorithm (Expected Improvement criterion) can be introduced to dynamically adjust the hyperparameters of the Gaussian kernel function and ensure R through cross-validation. 2 For highly sensitive areas, an active learning strategy is used to add new samples to reduce the prediction error of the model in the critical instability zone.

[0102] 6. Surface topography generation

[0103] Using parametric methods (such as Latin hypercube sampling, optimized Latin hypercube, or physical-rule-based parametric modeling), we generate combinations of topographic parameters covering the design space of Ra, WT, and SRO. We also simulate the ripple topography deviation at a 200°C temperature rise (using fractal geometry theory to generate self-similar surfaces and using thermo-mechanical coupling simulation to predict the topographic distortion at a 200°C temperature rise). The dataset includes samples from some extreme operating conditions to enhance the generalization capabilities of the surrogate model.

[0104] This embodiment also combines the thermal-mechanical coupling rules to define the wave temperature distribution and generate a corrugated morphology with thermal deformation characteristics; uses the proxy model to batch predict the complex eigenvalues ​​of new parameters to form a large-scale data set containing input-output mapping, providing a statistical basis for global sensitivity analysis.

[0105] 7. Surface morphology influence analysis based on Sobol method

[0106] Using the newly generated topography parameter combinations, a global sensitivity analysis of the real and imaginary parts of the complex eigenvalues ​​output by the surrogate model is performed using the Sobol method to quantify the independent contributions and interactive effects of the topography parameters. The main effect curves identify critical thresholds: when the topography parameters exceed the threshold, the risk of system instability increases dramatically, providing a quantitative basis for topography optimization.

[0107] This embodiment uses the Sobol method to quantify the contribution of morphological parameters (such as Figure 11 The interaction effect analysis shows that the risk of system instability increases significantly when the contribution rate of the Ra-WT combination is greater than a certain value.

[0108] It should be noted that when performing Sobol sensitivity analysis in practical applications, in addition to calculating the first-order sensitivity index and the total sensitivity index, the confidence interval (95% confidence level) of the parameter interaction effect can also be quantified through Monte Carlo sampling, and a three-dimensional main effect surface plot can be drawn to reveal the nonlinear law of the sudden increase in the real part of the complex eigenvalue caused by the Ra-WT combination.

[0109] 8. Friction Squeal Suppression Based on Surface Topography Modification

[0110] Based on the results of the sensitivity analysis, a morphology optimization plan was formulated (laser texturing to control Ra, hot rolling process to limit WT fluctuations, and CNC grinding to adjust SRO): the laser texturing process was used to control the surface roughness Ra, reduce the micro-contact stress fluctuations, and achieve sound pressure level noise reduction; the end face runout SRO was adjusted through the CNC grinding process to suppress the modal coupling caused by rotational imbalance; and the hot rolling process parameters were optimized to keep the fluctuation amplitude of the surface waviness WT distribution within a certain range.

[0111] At the same time, an inhibitory morphology database of fractal dimension is established to correlate process parameters with noise reduction effects to guide mass production.

[0112] That is to say, when implementing morphology optimization, in addition to controlling Ra through laser texturing and adjusting SRO through CNC grinding, it is also necessary to optimize the WT distribution in combination with the hot rolling process, and simultaneously monitor the temperature-noise correlation in the bench test, and finally establish a morphology database of fractal dimension.

[0113] Through the implementation of the above process, this embodiment can fully and deeply understand the vibration characteristics and brake squeal problems of the brake, establish a brake friction squeal suppression method considering the surface morphology, and provide a reliable technical basis for subsequent structural optimization design and improvement.

[0114] In summary, this solution can comprehensively analyze and suppress brake squeal, contributing to the low-cost, low-noise development of brakes and improving vehicle braking NVH performance. The core of this solution lies in establishing a quantitative mapping relationship between surface topography parameters and the system's dynamic instability threshold. This, combined with process control techniques, allows for targeted optimization of friction interface characteristics. This not only significantly improves brake squeal prediction accuracy but also proposes effective suppression strategies from the perspective of surface topography optimization, providing strong support for the development of low-noise brakes and the improvement of vehicle comfort.

Claims

1. A brake friction squeal suppression method considering surface topography, characterized in that: The following steps are involved: S1. Conduct brake friction squeal tests to obtain key information about brake squeal, including characteristic frequency, amplitude, and temporal variation. S2. Perform surface topography measurement tests to obtain surface topography data of the brake disc and friction pad, and use MATLAB for preprocessing to obtain completed surface topography data; S3. Based on the completed surface morphology data, a friction squeal finite element model is established; S4. For the friction squeal finite element model, apply the rotation effect of the brake disc and nonlinear friction contact conditions to perform complex modal simulation and obtain complex modal analysis results; S5. Based on the complex modal analysis results, a friction squeal prediction model is established based on the Kriging method, wherein the input of the friction squeal prediction model is the surface topography parameters and the operating condition parameters, and the output is the complex eigenvalue; S6. Generate a new surface topography parameter combination through a parametric method; S7. Input the new surface topography parameter combination into the friction squeal prediction model, output the corresponding complex eigenvalue, and quantify the parameter sensitivity based on the Sobol method to obtain the sensitivity analysis results; S8. Based on the sensitivity analysis results, the surface morphology parameters of the brake are modified and optimized to suppress the friction squeal of the brake.

2. The brake friction squeal suppression method considering surface topography according to claim 1, characterized in that: The specific process of step S1 is as follows: preparing a standard brake test sample to simulate actual braking conditions; Use acoustic and vibration testing equipment to collect acoustic and vibration characteristic information during braking, including sound pressure level and acceleration of key components, and record operating condition information, including brake disc speed, brake pressure, and braking torque; After data collection is completed, time domain analysis, frequency domain analysis, and phase diagram analysis are performed to extract key information about brake squeal, including characteristic frequency, amplitude, and its change pattern over time.

3. The brake friction squeal suppression method considering surface topography according to claim 2, characterized in that: The specific process of step S2 is as follows: for a standard brake test sample, a profilometer is used to perform high-precision topography scanning on the surfaces of the brake disc and the friction pad. During the measurement process, the test sample is fixed with a special fixture to ensure the installation flatness error, and the surface topography data of the brake disc and the friction pad are measured; The measurement data are preprocessed by MATLAB, including the removal of abnormal noise points, interpolation and completion of missing areas, and the extraction of key morphological parameters, including surface roughness Ra, waviness WT and end face runout SRO.

4. The method for suppressing brake friction squeal considering surface topography according to claim 3, characterized in that: The specific process of step S3 is: reconstructing a three-dimensional surface model based on the completed surface topography data and fractal geometry theory; For the three-dimensional surface model, mesh division is performed in the unit division software to obtain a disk-block contact model with complex surface morphology. Adaptive mesh encryption technology is used at the contact interface to accurately characterize the elastic-plastic deformation and friction behavior of the micro-convex body, and a friction scream finite element model with surface morphology is established.

5. The method for suppressing brake friction squeal considering surface topography according to claim 3, characterized in that: The specific process of step S4 is: importing the friction squeal finite element model into the finite element software, applying the actual braking conditions and thermal boundary conditions, simulating the rotation effect of the brake disc and the nonlinear friction contact conditions; Perform complex modal analysis to extract complex eigenvalues ​​and mode shapes, where the real part of the complex eigenvalue represents system stability and the imaginary part corresponds to the squeal frequency; The simulated modal frequency is compared with the characteristic frequency obtained in step S1. If the deviation between the two exceeds the threshold, the friction coefficient curve and contact stiffness parameters are adjusted through the inverse optimization algorithm, and the complex modal analysis is performed again.

6. The method for suppressing brake friction squeal considering surface topography according to claim 5, characterized in that: The specific process of step S5 is: using the surface topography parameters obtained in step S2 and the brake disc speed and brake pressure obtained in step S1 as model inputs, and using the real and imaginary parts of the complex eigenvalues ​​obtained in step S4 as model outputs, to generate a training data set based on a parameterized method; The Kriging Gaussian process regression algorithm is used to establish an input-output mapping model. The training dataset is used for model training. The nonlinear relationship between parameters is captured by the covariance function. The goodness of fit is ensured through cross-validation. An active learning strategy is introduced to dynamically optimize the sample space to construct a friction squeal prediction model.

7. The method for suppressing brake friction squeal considering surface topography according to claim 6, characterized in that: The specific process of step S6 is as follows: first, the design space of each morphological parameter is defined based on the preliminary test data, and each parameter dimension is equally divided into non-overlapping intervals in the three-dimensional parameter space, that is, the number of layers in each dimension is equal to the sample size, ensuring that each interval contains only one sample point; The stratified intervals of each parameter dimension were then randomly permuted independently to avoid artificial correlations between variables; Then, the sampling points of the three parameters were randomly paired through matrix combination to generate a combination of morphological parameters. In this process, an orthogonal optimization strategy was introduced, and the Levenberg-Marquardt algorithm was used to minimize the Pearson correlation coefficient between the parameters, so that the absolute values ​​of the correlation coefficients of Ra-WT, Ra-SRO, and WT-SRO were all lower than the preset threshold.

8. The method for suppressing brake friction squeal considering surface topography according to claim 3, characterized in that: The specific process of step S7 is as follows: inputting the new surface topography parameter combination into the friction squeal prediction model, outputting the corresponding complex eigenvalue, and using the Sobol method to quantify the contribution of each surface topography parameter and their interaction to the complex eigenvalue; Then calculate the first-order sensitivity index S i and total sensitivity index S Ti , filter out the dominant parameters; Through main effect analysis, the synergistic effect among surface morphology parameters was obtained; Generate sensitivity heat maps and prioritize surface topography parameters.

9. The method for suppressing brake friction squeal considering surface topography according to claim 3, characterized in that: The specific process of step S8 is: designing an optimized morphology scheme based on the sensitivity analysis results of step S7; Bench tests were carried out to verify the optimized morphology scheme, and an inhibitory morphology database including Ra, WT, SRO and their combinations was established. The surface self-similar characteristics were described by fractal dimension to guide the batch production process of brake discs.

10. The method for suppressing brake friction squeal considering surface topography according to claim 9, characterized in that: The optimized morphology scheme includes: Laser texturing, grinding or sandblasting processes are used to control surface roughness Ra, reduce microscopic contact stress fluctuations, and achieve sound pressure level noise reduction; Adjust the end face runout (SRO) through CNC grinding process to suppress the modal coupling caused by rotational imbalance; Optimize the hot rolling process parameters to make the surface waviness WT distribution fluctuation amplitude within the preset range.

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