A brake disc fatigue crack rapid prediction method based on modal stress field

Abstract

The application discloses a kind of brake disc fatigue crack fast prediction method based on modal stress field, the method comprises: establishing the three-dimensional assembly model of brake disc and friction block, the whole braking process is simulated by complete thermal coupling transient analysis, and the original residual stress field after brake cooling is extracted;Brake disc structure is carried out free modal analysis, and the modal stress field base is extracted and constructed;Residual stress field is projected on modal stress field base, and linear equation set is assembled based on Gauss numerical integration method, and modal participation coefficient vector is solved;Modal participation coefficient vector and modal stress field base are linearly superposed to reconstruct reduced-order residual stress field;Reconstruction residual stress field is applied to brake disc model, preset initial crack, and crack is simulated under the driving of residual stress by extended finite element method, and the predicted fatigue life of brake disc is calculated.The application realizes the efficient, precision controllable fatigue crack fast simulation prediction based on physical reduction.

Description

Technical Field

[0001] This invention belongs to the field of mechanical structure fatigue life simulation and prediction technology, and in particular relates to a rapid prediction method for brake disc fatigue cracks based on modal stress field. Background Technology

[0002] In the field of fatigue life simulation and prediction of mechanical structures, brake discs are subjected to severe thermo-mechanical coupled loads during friction braking, and the resulting complex residual stress field is the main cause of the initiation and propagation of thermal fatigue cracks on their surface. To predict their fatigue life, current advanced methods typically employ a two-stage analysis framework with clear physical meaning: first, a fully thermo-mechanical coupled analysis is performed to obtain the residual stress field of the brake disc; then, this stress field is used as a load condition to drive the second-stage crack propagation analysis. However, this framework faces a significant bottleneck in engineering practice: the residual stress field calculated in the first stage is a massive spatial dataset containing hundreds of thousands or even millions of nodal stress components. Completely and accurately transferring and applying this massive amount of data to the second-stage crack propagation model is not only cumbersome but also results in low computational efficiency due to the enormous initial data size. This often leads to unacceptable time costs in scenarios requiring multi-parameter optimization or rapid design iteration.

[0003] To improve computational efficiency, existing technologies employ several simplification methods. For example, ideal loads such as uniform pressure and simplified temperature gradients are used to replace the actual residual stress field, but these methods severely sacrifice the physical accuracy of the prediction results. Another approach is to use sub-modeling techniques, analyzing local regions to reduce the model size. However, the selection of sub-regions and the transfer of boundary conditions still heavily rely on engineering experience and fail to fundamentally address the problem of excessively large residual stress datasets in the core analysis region (i.e., the potential crack initiation and propagation region). Therefore, there is an urgent need to develop a novel residual stress field processing method. This method should achieve significant compression of the original data size while fully preserving its key mechanical characteristics affecting fatigue life, thereby constructing an efficient and accurate load input for subsequent crack propagation analysis and breaking through the efficiency bottleneck of current engineering simulations. Summary of the Invention

[0004] The purpose of this invention is to provide a rapid prediction method for brake disc fatigue cracks based on modal stress fields, which solves the problems in the prior art where the large scale of residual stress field data leads to low efficiency in subsequent crack propagation analysis, and the difficulty in balancing accuracy and efficiency in existing simplified methods. This invention achieves efficient and accurate rapid simulation prediction of fatigue cracks based on physical order reduction.

[0005] The technical solution adopted in this invention is a method for rapid prediction of fatigue cracks in brake discs based on modal stress fields, comprising the following steps: S1: Establish a three-dimensional assembly model of the brake disc and friction block, define material parameters and contact properties, apply braking load and natural cooling boundary conditions, simulate the entire braking process through fully thermomechanical coupled transient analysis, and extract the original residual stress field on the element Gaussian integration point after the brake disc is cooled to room temperature. S2: Extract the brake disc unit structure from the three-dimensional assembly model, and perform modal analysis on the unit structure in a free state to extract its front end... The first mode shape and the corresponding modal stress field are used to construct the modal stress field basis; S3: Based on the consistency of the brake disc mesh in steps S1 and S2, the original residual stress field is projected onto the modal stress field basis, and numerical integration is performed based on the Gaussian numerical integration method to assemble a linear equation system. The modal participation coefficient vector is obtained by solving the linear equation system. S4: Based on the modal participation coefficient vector and the modal stress field basis, the reduced-order residual stress field is reconstructed by linear superposition, and point-by-point weighted summation is performed at the unit Gaussian integration points of the brake disc single structure to generate the reconstructed residual stress field. S5: Apply the reconstructed residual stress field to the finite element model containing only the brake disc structure, and perform static analysis to verify the stress field balance; if the stress field balance does not meet the preset conditions, adjust the modal order and return to step S2; after the stress field balance meets the preset conditions, preset an initial crack, use the extended finite element method to simulate the crack propagation under residual stress, and obtain the predicted fatigue life of the brake disc based on the crack propagation model integral.

[0006] Furthermore, in S2, The single structure of the brake disc directly uses the finite element mesh of the brake disc part in step S1. The modal order is determined by a convergence criterion strategy. Starting from a preset initial order, the modal order is gradually increased. The original residual stress field is reconstructed using the extracted modal stress field basis. When the root mean square error between the reconstructed stress field and the original residual stress field in the key region satisfies the preset convergence condition twice consecutively, the current modal order is changed. It is determined to be the final order.

[0007] Furthermore, S3 specifically includes: The original residual stress field and the modal stress fields of each order are transformed to the same set of Gaussian integration points of the elements. Based on the Gaussian numerical integration method, all elements of the brake disc structure and their internal Gaussian integration points are traversed. At each integration point, the double dot product of the stress tensor is calculated and multiplied by the weight of that integration point and the Jacobian determinant. The calculation results of all elements and integration points are summed to obtain the coefficient matrix and the right-hand side vector, and a system of linear equations is constructed. The system of linear equations is solved to obtain the modal participation coefficient vector.

[0008] Further, S5 includes: A new finite element model of the brake disc is established based on the brake disc unit structure in step S2, and the reconstructed residual stress field is applied as a predefined initial stress field to the Gaussian integration points of the unit of the model. The static analysis, under the condition of applying only the reconstructed residual stress field without applying any other external loads or constraints, checks whether the nodal residual force norm of the brake disc model is less than an allowable threshold; if the nodal residual force norm is greater than the allowable threshold, then return to step S2 to increase the modal order. .

[0009] Furthermore, S5 also includes: An initial crack is pre-set in the region of maximum principal stress in the reconstructed residual stress field, and the quasi-static propagation of the crack under residual stress is simulated by the extended finite element method. During crack propagation, the stress intensity factor at the crack tip is calculated using the interaction integral method, and the crack propagation rate is calculated based on the Paris fatigue crack propagation formula. By numerically integrating the entire propagation process, the number of cycles from the initial crack length to the critical length is accumulated, and this number of cycles is used as the predicted fatigue life of the brake disc.

[0010] The beneficial effects of this invention are: 1. This invention significantly reduces the initial data size, memory usage, and single-run solution time of crack propagation analysis by compressing the residual stress field to be transmitted from a large amount of nodal stress data into a small number of modal coefficients and a fixed set of modal bases. This significantly shortens the overall prediction time of brake disc fatigue cracks and improves computational efficiency by more than an order of magnitude, effectively supporting multi-parameter optimization and rapid design iteration.

[0011] 2. This invention uses physical mode reduction based on the principle of structural dynamics to characterize the main stress and deformation modes of the structure using low-order modes. By selecting an appropriate modal order, an optimal balance can be achieved between computational efficiency and prediction accuracy, ensuring that the reconstructed stress field has sufficient fidelity in key mechanical characteristics such as maximum stress value and stress gradient, thus overcoming the defect of large accuracy loss in simplified load methods.

[0012] 3. The modal extraction, stress field projection into modal space, and stress field reconstruction steps in crack analysis involved in this invention can all be automated through scripts. They can be effectively connected with mainstream commercial finite element software and are easy to integrate into automated simulation analysis and design processes, thereby improving the engineering practicality and repeatability of the method.

[0013] 4. This invention is applicable as a set of efficient and reliable simulation prediction methods for implementation and application; its effectiveness and superiority can be verified by comparing the core results such as crack propagation path, fatigue life and calculation time with the traditional full data transfer method under the same conditions. This verification process is completed entirely at the numerical simulation level and does not depend on physical experiments. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is the overall flowchart of the method of the present invention.

[0016] Figure 2 This is a schematic diagram of the finite element model setup for the thermo-mechanical coupling analysis of the brake disc in an embodiment of the present invention, wherein (a) is a three-dimensional finite element model and (b) is a schematic diagram of mesh generation and boundary conditions.

[0017] Figure 3 This is a schematic diagram of the four modes of the brake disc in an embodiment of the present invention, wherein (a) is the first breathing mode, (b) is the second bending mode, (c) is the third bending mode, and (d) is the fourth bending mode.

[0018] Figure 4 This is a comparison diagram of the original residual stress field and the reconstructed residual stress field in an embodiment of the present invention.

[0019] Figure 5 The images show a comparison of crack propagation paths between the traditional full data transmission method and the method of this invention under different modal orders. (a) is a schematic diagram of the crack propagation path and friction contact ring distribution in the three-dimensional space of the brake disc, (b) is a top view of the brake disc, and (c) is a detailed comparison of the crack propagation path under a magnified view.

[0020] Figure 6 This is a schematic diagram of the crack propagation path of the brake disc predicted using the traditional full data transfer method.

[0021] Figure 7 This is a schematic diagram comparing the brake disc crack propagation path predicted by the traditional full data transmission method and the method of this invention.

[0022] Figure 8 This is a bar chart comparing the total computation time of the traditional full data transfer method and the method of this invention at different modal orders.

[0023] Figure 9 The diagram shows the variation of the reconstructed stress field and fatigue life prediction accuracy with modal order in the embodiments of the present invention. (a) is the curve of the maximum principal stress error of the reconstructed stress field, and (b) is the curve of the fatigue life prediction error. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] like Figure 1 As shown in the embodiment, a method for rapid prediction of brake disc fatigue cracks based on modal stress field is provided, including the following steps: Step S1: Obtaining the residual stress field: A three-dimensional assembly model of the brake disc and friction block is established, material parameters and contact properties are defined, braking load and natural cooling boundary conditions are applied, and the entire braking process is simulated through fully thermomechanical coupled transient analysis. The full-field nodal residual stress tensor after the brake disc cools to room temperature is extracted to obtain the original residual stress field. This analysis comprehensively considers the coupling effects of multiple physical fields, such as frictional heat generation, heat conduction, and thermal stress. In this embodiment of the invention, the above process is implemented using the finite element software ANSYS, and the specific process is as follows: Establish a three-dimensional assembly model of the brake disc and friction block, such as... Figure 2 As shown in (a), the brake disc material is defined as gray cast iron, and the friction block material is defined as composite material, and they are respectively assigned material parameters such as elastic modulus, Poisson's ratio, density, coefficient of thermal expansion, thermal conductivity, specific heat capacity and friction coefficient; hexahedral elements are used for meshing; in this embodiment, the mesh side length of non-critical areas (such as the inner ring of the brake disc and non-friction surfaces) is set to 2 mm; the friction contact ring area (i.e. the annular area where the brake disc surface contacts the friction block) is locally densified, the mesh side length is set to 0.5 mm, and no less than 4 layers of calculation units are divided along the thickness direction of the brake disc to accurately analyze the temperature gradient and stress gradient.

[0026] Define the surface-to-surface contact between the brake disc and the friction block; apply contact constraints using the penalty function method or the augmented Lagrange method; define the normal contact behavior as hard contact, allowing contact separation; employ the Coulomb friction model for tangential behavior, setting the friction coefficient as a function of temperature; in this embodiment, the friction coefficient... With temperature The relationship is approximated by a linear function: Among them, reference temperature coefficient of friction at time Temperature coefficient This means that the coefficient of friction decreases as temperature increases; the function is calibrated based on typical experimental data of gray cast iron / composite friction pairs.

[0027] In practical applications, the aforementioned friction coefficient-temperature function can be replaced with a polynomial, exponential, or other form based on the experimental results of specific materials, and is not limited to the linear expression given in this embodiment; the contact algorithm selects symmetrical contact pairs, with the brake disc friction surface as the master surface and the friction block surface as the slave surface; to improve convergence, contact stability damping is set in the initial analysis step, and an asymmetric solver is used to handle highly nonlinear friction contact problems; such as Figure 2 As shown in (b), to simulate braking conditions, a normal pressure is applied to the friction block, which is 1 MPa in this embodiment; and the brake disc is set to have a rotational speed, which is 100 rad / s in this embodiment; the specific values ​​of the pressure and speed can be determined according to the actual braking conditions; convective heat transfer boundary conditions are set on the surface of the brake disc to simulate air cooling, and then natural cooling analysis is performed until the temperature field tends to stabilize; the calculation time in this embodiment is 300 seconds.

[0028] Submit transient thermal-structural coupling calculations; after convergence, extract the full-field nodal residual stress data of the brake disc under room temperature conditions, i.e., 6 independent stress components: normal stress. , , With shear stress , , Thus, the original residual stress field is obtained. The output is saved as a CSV data file, with each line containing the node / integral point number, spatial coordinates, and six stress components, for direct reading and use in subsequent steps.

[0029] Step S2: Modal stress field basis construction: Modal analysis in a free state was performed on the individual brake disc structure extracted from the assembly to extract its front end characteristics. First-order mode shape and the corresponding modal stress field The modal stress field It is the first First-order mode shape Stress distribution field calculated using material constitutive relations; stress field based on each modal stress field. Constructing modal stress field basis .

[0030] In this embodiment of the invention, the finite element model for modal analysis retains only the brake disc structure, removes the friction block, and directly uses the finite element mesh of the brake disc portion from step S1; the material properties of this model remain consistent with those defined in step S1; free boundary conditions are applied to the model, i.e., no displacement constraints are applied to the model, and modal analysis is performed; its preceding... First-order mode shape Its first four vibration modes are as follows Figure 3 As shown; and derive the corresponding modal stress field (containing six stress components); modal order. The accuracy requirement is determined automatically or manually. To balance computational efficiency and accuracy, for the brake disc structure described in this embodiment, a low-order mode of 10 to 50 is usually selected to effectively characterize the main distribution characteristics of its residual stress field. The specific value needs to be determined according to the specific geometric complexity of the brake disc. The stress field data is stored at the element integration point (i.e., Gaussian point), and this storage location is the calculation location for the subsequent reconstruction step.

[0031] Modal order The convergence is determined using the following strategy: starting from a preset initial order (e.g., 10 orders), the modal order is gradually increased (e.g., by 5 orders each time); each time it is increased, the original residual stress field obtained in step S1 is applied using the currently extracted modal stress field basis. Reconstruction is performed in critical regions (such as the friction contact ring), and the root mean square error (RMSE) between the reconstructed stress field and the original stress field in that region is calculated. To prevent premature termination due to non-monotonic fluctuations in error, a continuous judgment criterion is adopted: when the calculation error falls below a preset convergence threshold (e.g., 5%) twice consecutively, the order increase is stopped, and the order at this point is determined as the final order. .

[0032] Figure 3 The first four typical mode shapes of the brake disc in this embodiment of the invention are shown; (a) is the first breathing mode, which is characterized by uniform expansion and contraction of the annular contour; (b) is the second bending mode, in which the annular shape is concave on both sides (point P); (c) is the third bending mode, in which the annular shape is concave at the top and bottom (point V) and on both sides (point P); (d) is the fourth bending mode, which presents a more complex asymmetric torsion shape; in (a)-(d), the dashed line represents the original contour of the brake disc, and the solid line represents the magnified mode shape; P represents the peak and V represents the trough.

[0033] Step S3: Solving for modal projection coefficients: This step aims to solve a least-squares problem to obtain the original residual stress field obtained in step S1. Projected onto the modal stress field basis constructed in step S2 This allows us to obtain a set of optimal modal participation coefficients. The essence of this problem is to find a set of coefficients. This minimizes the error between the linear combination of the original residual stress field and the modal basis under the energy norm, i.e., solving the following optimization problem: This least squares problem is equivalent to solving the following system of linear equations: ; where the matrix ,vector The elements of are defined over a continuous field by the following integrals: , ;in, The total modal order involved in the calculation is given; the integration domain V is the volume of the entire brake disc. Let be the coefficient matrix constructed by numerical integration, whose elements It represents the weighted inner product of the stress fields of the i-th and j-th modes over the entire domain; Let be the vector of right-hand side terms constructed by numerical integration, whose elements It represents the weighted inner product of the original stress field and the i-th order modal stress field over the entire domain; Let i be the stress tensor field of the i-th modal; Let be the vector of modal participation coefficients to be determined; the symbol ":" represents the double dot product of tensors; in the actual numerical implementation, the above volume integral is efficiently calculated by discretizing and summing over all elements and Gaussian integration points of the finite element model; the specific process is as follows: Data export and alignment: The modal analysis model in step S2 is obtained by directly using the finite element mesh of the brake disc portion of the thermomechanical coupling model in step S1 after removing the friction block; therefore, the two models share the exact same node coordinates and element connection relationships, which is a prerequisite for strict correspondence of spatial points; in order to achieve unified calculation in the numerical integration of subsequent steps, it is necessary to export and align the original residual stress field originally stored in the nodes in step S1. The modal stress fields stored at the Gaussian integration points in step S2 All data are converted and exported to the same set of Gaussian integration points. Specifically, in the post-processing of the finite element software, shape function interpolation is applied to the original nodal stress results to interpolate them from the nodes to the Gaussian integration points. After completing this step, two sets of data located in the same set of Gaussian integration points, each containing all six stress components, can be obtained for direct use in subsequent steps.

[0034] Based on the Gaussian numerical integration method, the integrals in the above equation are discretized and calculated to assemble the linear equation system. Iterate through all elements of the brake disc structure and their internal Gaussian integration points, calculate the double dot product of the stress tensor at each integration point, and multiply it by the weight of that integration point. Jacobian determinant This is used for volumetric infinitesimal element transformation; finally, the calculation results of all elements and integration points are summed to obtain... × coefficient matrix and ×1 right-hand side vector Its mathematical expression is as follows:

[0035]

[0036] in, The modal order determines the size of the system of equations; For the original residual stress tensor field; Let i be the stress tensor field of the i-th modal; Let be the coefficient matrix constructed by numerical integration, whose elements It represents the weighted inner product of the stress fields of the i-th and j-th modes over the entire domain; Let be the vector of right-hand side terms constructed by numerical integration, whose elements It represents the weighted inner product of the original stress field and the i-th order modal stress field over the entire domain; Let be the vector of modal participation coefficients to be determined; e represents the cell index; g represents the index of the Gaussian point within the cell; , These are the Gaussian point weights and the Jacobian determinant, respectively. The double dot product operation ":" represents the sum of the products of the two second-order stress tensors over all corresponding components. In the numerical implementation of this step, this means performing point-to-point multiplication and summation on the six components of the two sets of stress data at each Gaussian point.

[0037] Finally, solving this system of linear equations yields the modal participation coefficient vector. Due to the matrix For symmetric positive definite solutions, the Cholesky decomposition method can be used for efficient and stable solutions.

[0038] In an embodiment of the present invention, the above process is automated through programming: after ensuring data alignment, a script is written in the MATLAB environment to execute the numerical integration to construct the coefficient matrix. and the right-hand term vector Then, the built-in linear solver (such as a solver based on Choreski decomposition) is invoked to solve the problem. Thus, the modal participation coefficient vector is obtained. .

[0039] Step S4: Residual stress field reconstruction: The modal participation coefficient vector obtained by solving step S3 (its weight is) The modal stress field basis constructed in step S2 The reduced-order representation of the reconstructed residual stress field is reconstructed through linear superposition. Its mathematical expression is:

[0040] in, The modal order is determined in step S2 according to the accuracy convergence criterion, and represents the dimension of the modal basis used for reconstruction. For the first First-order modal participation coefficients; For the first First-order modal stress tensor field; reconstructing the residual stress field It is uniquely determined by the following two sets of data: one set is scalar coefficients The other set is pre-calculated and stored. First-order modal stress field basis In specific calculations, to achieve the above reconstruction in the discrete finite element model, a point-by-point weighted summation needs to be performed at the element Gaussian integration points of the brake disc unit structure: that is, the modal stress tensor components stored at each point are multiplied by the corresponding coefficients. Subsequent superposition generates a complete reconstructed residual stress field point by point. .

[0041] Reconstructing the residual stress field This will serve as the input load for subsequent crack propagation analysis; during data storage and transfer, it is not necessary to save the complete stress tensor at all nodes / integration points, only the load that is saved is required. coefficients The method provides the corresponding modal stress field base data file (which stores the tensor data of all orders of modal stress fields at the Gaussian integration points of the elements in a compressed format). This method reduces the size of the core data to be processed from the original stress field to the GB level. After order reduction using the method of this invention, assuming 20 modes are used for reconstruction, only 20 modal participation coefficients and their corresponding modal stress field base files need to be transmitted, and the total data size can be controlled within 10MB. The compression ratio exceeds two orders of magnitude, thus achieving a significant reduction in the size of the massive node dataset to coefficients and base files in the few MB level, greatly improving the efficiency of data transmission and subsequent analysis.

[0042] To verify the accuracy of the reconstructed residual stress field using this method, Figure 4 The original residual stress field along the critical region (friction contact ring) of the brake disc was compared with the reconstructed stress field at different modal orders (N=20, 30). The horizontal axis in the figure represents the path coordinates, and the vertical axis represents the maximum principal stress. The results show that the stress field reconstructed by the method of this invention (red dashed line, blue dotted line) can effectively approximate the distribution trend and peak value of the original residual stress field (black solid line). On the critical path of the friction contact ring, the stress curve reconstructed using the N=20 modal order is highly consistent with the original full-field stress curve, and the deviation of the maximum principal stress is minimal. When the modal order is increased to N=30, the fit between the reconstructed curve and the original curve is further improved, and there is no obvious visual distinction. The above comparison results clearly show that the reconstructed stress field has a significant approximation effect on the original stress field, and the reconstruction accuracy increases monotonically with the increase of the modal order. This indicates that the reduced-order model constructed in steps S2 to S4 can efficiently characterize the complex original stress field with controllable accuracy.

[0043] Step S5: Crack propagation and fatigue life prediction: Based on the brake disc geometry and mesh used for modal analysis in step S2, a new finite element model specifically for crack propagation analysis is established; this model requires the removal of the friction block, retaining only the brake disc structure.

[0044] The reconstructed reduced-order stress field obtained in step S4 As a predefined initial stress field, it is applied to the Gaussian integration points of the elements in the model via script mapping; this process only requires loading. Each modal coefficient and modal stress field basis is used without transferring complete nodal stress data; subsequently, a static analysis is performed to verify stress field equilibrium; only the reconstructed stress field is applied. Without applying any other external loads or constraints, verify whether the nodal residual force norm of the brake disc model is less than the allowable threshold (e.g., ...). If the residual force norm is greater than the allowable value, it indicates poor self-equilibrium of the reconstructed stress field, usually due to the modal order. Insufficient precision leads to inadequate reconstruction accuracy; in this case, we should return to step S2 to increase the precision. This is to improve the accuracy of reconstruction.

[0045] Reconstructing the stress field The maximum principal stress region (usually located in the friction contact ring) is pre-set with an initial crack; in the embodiments of the present invention, an initial surface crack with a length of 2 mm and a direction along the circumference is set to simulate a typical thermal fatigue crack initiation mode.

[0046] Numerical methods such as the Extended Finite Element Method (XFEM) are used to simulate the quasi-static propagation of cracks driven by residual stress. This method introduces enrichment functions to describe the discontinuous displacement field, eliminating the need for mesh re-division during crack propagation. Crack propagation criteria (such as the maximum circumferential stress criterion) are set, driving crack propagation when the equivalent stress intensity factor amplitude reaches the material threshold, and the propagation step size is set. (For example, fixed at 0.5 mm or adaptively adjusted according to the rate of change of stress intensity factor).

[0047] At each step of crack propagation, the following fatigue life prediction calculations are performed: the Type I, Type II, and Type III stress intensity factors at the crack tip are calculated using the interaction integral method. , , And equivalent to the magnitude of the equivalent stress intensity factor. Used for fatigue calculations; the crack propagation rate for each propagation step is calculated using the Paris fatigue crack propagation formula:

[0048] in, Indicates the crack length; , The fatigue characteristic parameters of the material are determined based on experimental calibration data of the brake disc material (such as gray cast iron) used in the embodiments of the present invention; in the embodiments of the present invention, the following parameters are taken: , .

[0049] From the initial crack length Initially, numerical integration is performed on the entire crack propagation process, and the summation is used to obtain the crack propagation to the critical length. (Based on the fracture toughness of the material) (Determination) Number of loops required This value represents the predicted fatigue life of the brake disc. When the crack length reaches... Or stress intensity factor exceeds The simulation will automatically terminate at that time.

[0050] To systematically verify the comprehensive performance of the method of this invention, a comprehensive evaluation was conducted from three dimensions: the accuracy of prediction results, the advantage of computational efficiency, and the influence of key parameters. The verification results are as follows: Figures 5 to 9 As shown.

[0051] To evaluate the prediction accuracy of the method of the present invention, the simulation results of the traditional full data transfer method are used as a benchmark; Figure 6 This demonstrates the complete crack propagation path (red trajectory) predicted by the method from crack initiation to critical length; based on this, Figure 7The predicted paths of the traditional method (red line) and the method of this invention (blue line) were directly compared; the results show that the two paths highly overlap in geometric shape and expansion trend; to further examine the parameter stability of the method of this invention, Figure 5 In the middle, (a)-(c) compare the modal orders at different times ( =20 and Under the setting of =30), the path predicted by the method of the present invention; the results show that the paths are almost identical and unaffected by... The significant effect of small changes in value; Figure 5 , Figure 6 and Figure 7 Comprehensive comparisons demonstrate that the method of this invention achieves prediction accuracy comparable to traditional high-fidelity models, and its prediction results are accurate for key parameters. It exhibits good stability, thus verifying the reliability and robustness of the reduced-order model.

[0052] While ensuring consistent prediction accuracy, the efficiency advantage of the method of this invention is highlighted; Figure 8 The two methods were quantitatively compared from the perspective of total computation time. The traditional full data transfer method has a relatively high and essentially constant computation time (approximately 12 hours). In contrast, the method of this invention significantly reduces computation time (only 1.2 to 1.7 hours), and this reduction increases with modal order. With the increase in time, the time consumption only shows a gradual growth trend; this directly proves from the perspective of time cost that the "modal coefficient and modal stress field basis" data compression and transmission mode adopted in this invention brings about an order of magnitude efficiency improvement.

[0053] Modal order This is the core parameter of this method, and its selection directly affects the balance between accuracy and efficiency; Figure 9 The system revealed The influence of the value on the model accuracy provides a quantitative basis for parameter selection in step S2; among them, (a) shows that the maximum principal stress error of the reconstructed stress field increases with... The value increases and decreases monotonically, when (a) When ≥20, the engineering tolerance can be stably below 4%; (b) shows that the final fatigue life prediction error decreases synchronously, when A value of ≥30 can meet the accuracy requirement of 6%; Figure 9 The quantitative relationships revealed above clearly indicate the requirements for achieving different levels of precision. The range of values ​​provides direct and clear guidance for balancing computational accuracy and efficiency in practical applications.

[0054] The embodiments of this invention are implemented using the following commercial software and programming environment. Specific tools used are as follows: finite element modeling and preprocessing are completed in ANSYS Mechanical; thermo-mechanical coupled transient analysis (corresponding to step S1) is achieved through the coupling of the ANSYS Transient Thermal and Structural modules; modal analysis and crack propagation analysis framework (corresponding to steps S2 and S5) are performed in ANSYS Mechanical, with crack propagation simulation calling its XFEM module; data export and post-processing are completed using a combination of ANSYS APDL command flow and MATLAB; core numerical calculations and automation scripts (corresponding to steps S3-S5) are implemented using MATLAB programming to solve for modal projection coefficients, reconstruct stress fields, integrate fatigue life, and automate the process. The above tools are merely an optional software combination for implementing the method of this invention.

[0055] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0056] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A rapid prediction method for fatigue cracks in brake discs based on modal stress fields, characterized in that, Includes the following steps: S1: Establish a three-dimensional assembly model of the brake disc and friction block, define material parameters and contact properties, apply braking load and natural cooling boundary conditions, simulate the entire braking process through fully thermomechanical coupled transient analysis, and extract the original residual stress field on the element Gaussian integration point after the brake disc is cooled to room temperature. S2: Extract the brake disc unit structure from the three-dimensional assembly model, and perform modal analysis on the unit structure in a free state to extract its front... The first mode shape and the corresponding modal stress field are used to construct the modal stress field basis; S3: Based on the consistency of the brake disc mesh in steps S1 and S2, the original residual stress field is projected onto the modal stress field basis, and numerical integration is performed based on the Gaussian numerical integration method to assemble a linear equation system. The modal participation coefficient vector is obtained by solving the linear equation system. S4: Based on the modal participation coefficient vector and the modal stress field basis, the reduced-order residual stress field is reconstructed by linear superposition, and point-by-point weighted summation is performed at the unit Gaussian integration points of the brake disc single structure to generate the reconstructed residual stress field. S5: Apply the reconstructed residual stress field to the finite element model containing only the brake disc structure, and perform static analysis to verify the stress field balance; if the stress field balance does not meet the preset conditions, adjust the modal order and return to step S2; after the stress field balance meets the preset conditions, preset an initial crack, use the extended finite element method to simulate the crack propagation under residual stress, and obtain the predicted fatigue life of the brake disc based on the crack propagation model integral.

2. The method for rapid prediction of brake disc fatigue cracks based on modal stress field according to claim 1, characterized in that, In S2, The single structure of the brake disc directly uses the finite element mesh of the brake disc part in step S1. The modal order is determined by a convergence criterion strategy. Starting from a preset initial order, the modal order is gradually increased. The original residual stress field is reconstructed using the extracted modal stress field basis. When the root mean square error between the reconstructed stress field and the original residual stress field in the key region satisfies the preset convergence condition twice consecutively, the current modal order is changed. It is determined to be the final order.

3. The method for rapid prediction of brake disc fatigue cracks based on modal stress field according to claim 1, characterized in that, S3 specifically includes: The original residual stress field and the modal stress fields of each order are transformed to the same set of Gaussian integration points of the elements. Based on the Gaussian numerical integration method, all elements of the brake disc structure and their internal Gaussian integration points are traversed. At each integration point, the double dot product of the stress tensor is calculated and multiplied by the weight of that integration point and the Jacobian determinant. The calculation results of all elements and integration points are summed to obtain the coefficient matrix and the right-hand side vector, and a system of linear equations is constructed. The system of linear equations is solved to obtain the modal participation coefficient vector.

4. The method for rapid prediction of brake disc fatigue cracks based on modal stress field according to claim 1, characterized in that, S5 includes: A new finite element model of the brake disc is established based on the brake disc unit structure in step S2, and the reconstructed residual stress field is applied as a predefined initial stress field to the Gaussian integration points of the unit of the model. The static analysis, under the condition of applying only the reconstructed residual stress field without applying any other external loads or constraints, checks whether the nodal residual force norm of the brake disc model is less than an allowable threshold; if the nodal residual force norm is greater than the allowable threshold, then return to step S2 to increase the modal order. .

5. The method for rapid prediction of brake disc fatigue cracks based on modal stress field according to claim 4, characterized in that, The S5 also includes: An initial crack is pre-set in the region of maximum principal stress in the reconstructed residual stress field, and the extended finite element method is used to simulate the quasi-static propagation of the crack under residual stress. During crack propagation, the stress intensity factor at the crack tip is calculated using the interaction integral method, and the crack propagation rate is calculated based on the Paris fatigue crack propagation formula. By numerically integrating the entire propagation process, the number of cycles from the initial crack length to the critical length is accumulated, and this number of cycles is used as the predicted fatigue life of the brake disc.

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