A method for measuring and predicting springback deformation of an automobile stamping part

Abstract

The application provides a kind of automobile stamping part forming springback deformation measurement and prediction method, belong to automobile stamping part production technical field, the application is established by collecting the finite element grid model of embedded crystal plastic micro-unit of stamping part surface point cloud coordinates and material stress strain curve, set adaptive friction coefficient function and mixed contact solution strategy to carry out springback simulation calculation, the model after simulation is abstracted as stress propagation analysis chart structure and using the algorithm based on graph theory shortest path identifies stress release leading channel and stress concentration key node, adopts the springback prediction fusion model based on multi-head cross attention output springback deformation prediction value, according to the deviation of prediction value and threshold value adjustment stamping process parameters and according to the model training data set of prediction error update, solve the technical problem of automobile stamping part forming springback deformation prediction precision insufficient.

Description

Technical Field

[0001] This invention belongs to the field of automotive stamping parts manufacturing technology, and specifically relates to a method for measuring and predicting the springback deformation of automotive stamping parts. Background Technology

[0002] In the automotive stamping manufacturing industry, accurate prediction of springback deformation is a key technical aspect to ensure the quality of part forming. Traditional springback prediction methods mainly employ simplified calculations based on empirical formulas or finite element simulation analysis using a single physics field. These methods obtain the deformation state of the stamped part after unloading by numerically solving a constitutive model of the sheet metal and contact boundary conditions. However, in current automotive stamping production, due to the complex geometry of stamped parts and significant material anisotropy, traditional methods only consider macroscopic deformation characteristics while ignoring the influence of microscopic crystal structure on plastic behavior, leading to significant deviations between predicted results and actual measurements. Furthermore, existing technologies lack in-depth analysis of stress propagation patterns within the stamped part, failing to identify the dominant stress release path and key stress concentration locations, and making it difficult to establish a correlation mechanism between geometric features, material properties, contact states, and stress propagation topology. In other words, existing technologies suffer from insufficient accuracy in predicting springback deformation in automotive stamping parts. Summary of the Invention

[0003] In view of this, the present invention provides a method for measuring and predicting the springback deformation of automotive stamping parts, which can solve the technical problem of insufficient prediction accuracy of springback deformation of automotive stamping parts in the prior art.

[0004] This invention is implemented as follows: It provides a method for measuring and predicting the springback deformation of automotive stamping parts. A 3D scanner is used to collect the surface point cloud coordinates and thickness distribution of the stamping part as geometric data. A tensile testing machine is used to test the sheet metal to obtain stress-strain curves and Lankford coefficients as material property data. A finite element mesh model of the stamping part is established based on the surface point cloud coordinates and thickness distribution. Crystalline plastic micro-units are embedded at each integration point of the finite element mesh model. Homogenization theory is used to establish the scale transfer relationship between the finite element mesh model and the crystalline plastic micro-units. The contact interface between the die and the sheet metal is set in the finite element mesh model. A hybrid contact solution strategy is used to handle changes in contact state. An adaptive friction coefficient function is established based on contact pressure and sliding velocity. Initial blank holder force and initial stamping speed are set as stamping process parameters. Springback simulation calculations are performed on the finite element mesh model. The finite element mesh model after springback simulation calculation is abstracted into a stress propagation analysis graph structure. A stress propagation analysis algorithm based on graph theory shortest path is used to identify the dominant stress release channel and key stress concentration nodes to obtain stress propagation path characteristic data. Geometric shape data, material property data, contact pressure distribution data, and stress propagation path characteristic data are input into the springback prediction fusion model to output the predicted values ​​of springback deformation of each node of the stamped part.

[0005] The stress-strain curves are obtained through uniaxial tensile tests, recording the true stress and true strain data points of the sheet metal at different strain rates. The stress-strain curves are used for parameter calibration of the material constitutive model in the finite element mesh model.

[0006] The Lankford coefficient includes the rolling direction Lankford coefficient, the transverse Lankford coefficient, and the 45-degree direction Lankford coefficient. It is obtained by measuring the ratio of width strain to thickness strain through sheet tensile testing. The Lankford coefficient is used to characterize the degree of anisotropy of the sheet.

[0007] Among them, the crystal plastic micro-unit is the representative volume element structure, which contains several grains, each grain having random orientation and slip system.

[0008] The process of establishing scale transfer relationships using homogenization theory involves obtaining the macroscopic strain tensor at each integration point of the finite element mesh model, using the macroscopic strain tensor as the boundary condition input for the crystal plastic micro-unit, solving the microscopic stress tensor for the crystal plastic micro-unit at the microscale, averaging the microscopic stress tensor within the representative volume element structure to obtain the macroscopic stress tensor, and feeding the macroscopic stress tensor back to the integration points of the finite element mesh model.

[0009] Among them, the hybrid contact solution strategy adopts a combination of the penalty function method and the Lagrange multiplier method. The penalty function method is used to handle contact penetration constraints, while the Lagrange multiplier method is used to handle the accurate solution of contact forces.

[0010] The adaptive friction coefficient function calculates the current friction coefficient value based on the normal contact pressure, tangential sliding velocity, and contact temperature of the contact interface. The adaptive friction coefficient function adopts a smooth approximation of the Coulomb friction model.

[0011] The rebound simulation calculation uses an implicit dynamic solver in conjunction with a mass scaling factor and an adaptive time step control strategy to dynamically adjust the calculation step based on the energy error estimate to obtain the contact pressure distribution data at the contact interface.

[0012] In this structure, the nodes of the stress propagation analysis graph represent the center points of the elements in the finite element mesh model, the edges of the stress propagation analysis graph represent the connection relationships between adjacent elements, and the weight of the edge is defined as the reciprocal of the stress transfer efficiency between adjacent elements.

[0013] Among them, the stress propagation analysis algorithm based on graph theory shortest path identifies the peak nodes of residual stress and the boundary free end nodes in the finite element mesh model. The Dijkstra algorithm is used to calculate the shortest path from the residual stress peak node to each boundary free end node. The shortest path with the smallest path weight is selected as the dominant channel for stress release. The Floyd-Warshall algorithm is used to calculate the shortest path distance matrix between any two nodes in the stress propagation analysis graph structure. The betweenness centrality index is calculated for each node in the stress propagation analysis graph structure. Nodes with betweenness centrality indices exceeding the centrality threshold are marked as key nodes of stress concentration.

[0014] The betweenness centrality index represents the proportion of the number of shortest paths through a node to the total number of shortest paths. The centrality threshold is set to 1.5 times the average betweenness centrality index of all nodes in the stress propagation analysis graph structure.

[0015] Among them, the stress propagation path characteristic data includes the path length of the dominant stress release channel, the average stress value of the nodes on the path, the spatial coordinates of the key nodes of stress concentration, and the betweenness centrality index value.

[0016] The springback prediction fusion model adopts a feature fusion calculation framework based on multi-head cross-attention. The input layer receives geometric shape data, material property data, contact pressure distribution data, and stress propagation path feature data, and encodes them into geometric feature vectors, material feature vectors, contact feature vectors, and topological feature vectors, respectively. The multi-head cross-attention layer contains four attention heads that calculate the attention weight matrix between different feature vectors. The feature fusion layer concatenates the weighted feature vectors output by the four attention heads and maps them to a fused feature vector through a fully connected layer. The decoding layer maps the fused feature vector to the predicted springback deformation value of each node in the finite element mesh model of the stamping part through a fully connected network and activation function.

[0017] Among them, the deviation rate between the predicted value of springback deformation and the springback deformation threshold is calculated. When the deviation rate is greater than 15%, the blank holder force and stamping speed in the stamping process parameters are adjusted and the springback simulation calculation is performed again.

[0018] The actual geometric coordinates of the stamped part after forming are measured using a coordinate measuring machine. The difference between the actual geometric coordinates and the design geometric coordinates is calculated as the actual springback deformation. The prediction error between the predicted value of the springback deformation and the actual springback deformation is calculated. When the prediction error is greater than 10%, the geometric shape data, material property data, contact pressure distribution data, stress propagation path characteristic data and the actual springback deformation are added to the training dataset and the springback prediction fusion model is retrained.

[0019] Furthermore, the number of attention heads in the multi-head cross-attention layer is determined jointly based on the spatial resolution of the contact pressure distribution data, the node density of the stress propagation path characteristic data, and the number of dimensions of the material property data.

[0020] This invention addresses the technical problem of insufficient prediction accuracy for springback deformation in automotive stamping parts by establishing a cross-scale finite element model and integrating stress propagation topology analysis and multimodal feature learning into a prediction framework. The invention embeds crystalline plastic micro-units at the integration points of the finite element mesh model, employing homogenization theory to achieve bidirectional coupling between macroscopic deformation and microstructure behavior, capturing the essential influence of material anisotropy on springback. By abstracting the springback-simulated finite element model into a stress propagation analysis graph structure, a graph-based shortest path algorithm identifies the dominant stress release channels and key stress concentration nodes, revealing the stress transmission mechanism and energy dissipation law within the material, overcoming the limitation of traditional methods that only focus on surface deformation while neglecting internal stress topology. A springback prediction fusion model based on multi-head cross-attention dynamically integrates four types of heterogeneous data sources: geometry, material properties, contact pressure distribution, and stress propagation path characteristics, establishing cross-modal implicit dependencies and enabling the model to adaptively adjust the contribution of different information sources. In summary, this invention solves the technical problem of insufficient prediction accuracy for springback deformation in automotive stamping parts mentioned in the background art. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 A schematic diagram of embedding finite element integration points into crystalline plastic micro-units.

[0023] Figure 3 This is a graph showing the evolution of energy error under adaptive time step control.

[0024] Figure 4 This is a diagram showing the distribution of betweenness centrality of the structure in the stress propagation analysis diagram.

[0025] Figure 5 This is a comparison chart of the distribution of measuring points on a coordinate measuring machine and the amount of springback deformation. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0027] like Figure 1 The diagram shown is a flowchart of a method for measuring and predicting springback deformation in automotive stamping parts provided by this invention. The method includes the following steps:

[0028] S01. Use a 3D scanner to collect the surface point cloud coordinates and thickness distribution of the stamping part to be analyzed as geometric shape data, and use a tensile testing machine to test the sheet metal to obtain stress-strain curves and Lankford coefficients as material property data.

[0029] S02. Based on the surface point cloud coordinates and thickness distribution, a finite element mesh model of the stamping part is established. Crystalline plastic micro-units are embedded at each integration point of the finite element mesh model. The scale transfer relationship between the finite element mesh model and the crystalline plastic micro-units is established using the homogenization theory.

[0030] S03. Set the contact interface between the mold and the sheet in the finite element mesh model, adopt a hybrid contact solution strategy to handle the contact state change, establish an adaptive friction coefficient function based on the contact pressure and sliding speed, and set the initial blank holder force and initial stamping speed as stamping process parameters.

[0031] S04. Perform rebound simulation calculations on the finite element mesh model. Use an implicit dynamic solver in conjunction with a mass scaling factor and an adaptive time step control strategy to dynamically adjust the calculation step size based on the energy error estimate to obtain the contact pressure distribution data of the contact interface.

[0032] S05. The finite element mesh model obtained after the springback simulation calculation is abstracted into a stress propagation analysis graph structure. The stress propagation analysis algorithm based on graph theory shortest path is used to identify the dominant stress release channel and key stress concentration nodes to obtain stress propagation path characteristic data.

[0033] S06. Input the geometric shape data, the material property data, the contact pressure distribution data and the stress propagation path characteristic data into the springback prediction fusion model, and the springback prediction fusion model outputs the predicted value of springback deformation of each node of the stamping part.

[0034] S07. Calculate the deviation rate between the predicted value of springback deformation and the threshold value of springback deformation. When the deviation rate is greater than 15%, adjust the blank holder force and stamping speed in the stamping process parameters and return to step S04 to recalculate.

[0035] S08. Use a coordinate measuring machine to measure the actual geometric coordinates of the stamped part after forming, and calculate the difference between the actual geometric coordinates and the design geometric coordinates as the actual springback deformation.

[0036] S09. Calculate the prediction error between the predicted value of the springback deformation and the actual springback deformation. When the prediction error is greater than 10%, add the geometric data, the material property data, the contact pressure distribution data, the stress propagation path characteristic data and the actual springback deformation to the training dataset and retrain the springback prediction fusion model.

[0037] The stress-strain curve is obtained through a uniaxial tensile test, recording the true stress and true strain data points of the sheet material at different strain rates. The stress-strain curve is used for parameter calibration of the material constitutive model in the finite element mesh model.

[0038] The Lankford coefficient includes the rolling direction Lankford coefficient, the transverse Lankford coefficient, and the 45-degree direction Lankford coefficient, which is obtained by measuring the ratio of width strain to thickness strain through sheet tensile testing. The Lankford coefficient is used to characterize the anisotropy of the sheet and is input into the finite element mesh model.

[0039] The crystal plastic micro-unit is a representative volume element structure, which contains several grains, each grain having a random orientation and a slip system.

[0040] Specifically, the steps for establishing the scale transfer relationship using the homogenization theory include: obtaining the macroscopic strain tensor at each integration point of the finite element mesh model; using the macroscopic strain tensor as the boundary condition input for the crystal plastic micro-unit; solving the microscopic stress tensor for the crystal plastic micro-unit at the microscale; averaging the microscopic stress tensor within the representative volume element structure to obtain the macroscopic stress tensor; and feeding the macroscopic stress tensor back to the integration points of the finite element mesh model.

[0041] The hybrid contact solution strategy employs a combination of the penalty function method and the Lagrange multiplier method. The penalty function method is used to handle contact penetration constraints, while the Lagrange multiplier method is used to handle the accurate solution of contact forces.

[0042] The adaptive friction coefficient function calculates the current friction coefficient value based on the normal contact pressure, tangential sliding velocity, and contact temperature of the contact interface. The adaptive friction coefficient function adopts a smooth approximation of the Coulomb friction model to avoid discontinuities in the tangential stiffness matrix.

[0043] The mass scaling factor is used to increase the critical time step by artificially increasing the material density. The mass scaling factor ranges from 100 to 1000, and its value is determined based on a balance between computational efficiency and accuracy.

[0044] The energy error estimate is calculated by comparing the relative change between the total system energy and the initial total energy. When the energy error estimate exceeds 5%, the time step is reduced; when the energy error estimate is less than 1%, the time step is increased.

[0045] In this structure, the nodes of the stress propagation analysis graph represent the center points of the elements in the finite element mesh model, the edges of the stress propagation analysis graph represent the connection relationships between adjacent elements, and the weight of the edge is defined as the reciprocal of the stress transfer efficiency between adjacent elements.

[0046] The stress transfer efficiency is calculated based on the stress gradient and stiffness of adjacent elements. The stress transfer efficiency is expressed as follows: the stress transfer efficiency between element i and element j is equal to the absolute value of the stress difference between the two elements divided by the standard value of the sum of the equivalent stiffness of the two elements, and then divided by the ratio of the center distance between the two elements to the characteristic length. The standard value of the equivalent stiffness is the product of the material elastic modulus and the characteristic size of the element.

[0047] The steps of the stress propagation analysis algorithm based on graph theory shortest path specifically include: identifying the peak nodes and free-end nodes of residual stress in the finite element mesh model; calculating the shortest path from the peak nodes of residual stress to each of the free-end nodes of the boundary using the Dijkstra algorithm; selecting the shortest path with the smallest path weight as the dominant channel for stress release; calculating the shortest path distance matrix between any two nodes in the stress propagation analysis graph structure using the Floyd-Warshall algorithm; calculating the betweenness centrality index for each node in the stress propagation analysis graph structure; marking nodes whose betweenness centrality index exceeds the centrality threshold as key nodes of stress concentration; and counting the number of shortest paths passing through each edge, marking the edge with the fewest passes as the stress propagation bottleneck edge.

[0048] The graph-based shortest path stress propagation analysis algorithm maps the finite element discrete structure of stamped parts into a network topology, revealing the stress transmission mechanism and energy dissipation law within the material through graph theory tools. The Dijkstra algorithm searches for the optimal energy release path from the residual stress peak to the boundary; this path corresponds to the main deformation direction of stress unloading during actual springback, providing spatial location basis for identifying springback-sensitive areas. Floyd-Warshall global path analysis constructs a complete stress connectivity network, revealing the process by which local stress disturbances affect the overall deformation mode through mechanical coupling between elements. Betweenness centrality measures the pivotal role of nodes in the stress redistribution network; changes in material state at high-centrality nodes amplify their influence through multiple propagation paths, becoming key points for springback control. Identifying stress propagation bottlenecks locates weak points in stress transmission; these locations often correspond to geometrical abrupt changes or stiffness discontinuities in the material, representing the structural root cause of excessive local springback. The algorithm outputs topological feature parameters that establish an explicit correlation with the mechanical behavior of materials, providing a causal explanation framework from microstructure to macroscopic deformation for the formulation of springback compensation strategies, thereby improving the physical interpretability of springback prediction and the targeting of process optimization.

[0049] The betweenness centrality index represents the proportion of the number of shortest paths through the node to the total number of all shortest paths, and the betweenness centrality index reflects the importance of the node in the stress propagation network.

[0050] The centrality threshold is set to 1.5 times the average value of the betweenness centrality index of all nodes in the stress propagation analysis graph structure.

[0051] The stress propagation path characteristic data includes the path length of the dominant stress release channel, the average stress value of nodes on the path, the spatial coordinates of the key stress concentration nodes, and the betweenness centrality index value.

[0052] The rebound prediction fusion model adopts a feature fusion calculation framework based on multi-head cross-attention, and realizes deep correlation modeling and information integration optimization between features of different dimensions in the multimodal data processing steps through a dynamic weight allocation mechanism.

[0053] The specific structure of the springback prediction fusion model is as follows: The input layer receives the geometric shape data, the material property data, the contact pressure distribution data, and the stress propagation path feature data, and encodes them into geometric feature vectors, material feature vectors, contact feature vectors, and topological feature vectors, respectively; the multi-head cross-attention layer contains four attention heads: the first attention head calculates the attention weight matrix of the geometric feature vector to the material feature vector; the second attention head calculates the attention weight matrix of the material feature vector to the contact feature vector; the third attention head calculates the attention weight matrix of the contact feature vector to the topological feature vector; and the fourth attention head calculates the attention weight matrix of the topological feature vector to the geometric feature vector; the feature fusion layer concatenates the weighted feature vectors output by the four attention heads and maps them to a fused feature vector through a fully connected layer; the decoding layer maps the fused feature vector to the predicted springback deformation value of each node of the finite element mesh model of the stamping part through a three-layer fully connected network and an activation function.

[0054] The multi-head cross-attention feature fusion computing framework breaks through the limitations of traditional single-feature-channel independent processing. It captures implicit dependencies across modalities by constructing an interactive attention mechanism between heterogeneous data sources. Geometric features contain information on the curvature distribution and thickness variation of the stamped part; material property features reflect plastic deformation capacity and anisotropy; contact pressure distribution features characterize the mechanical boundary conditions of the forming process; and stress propagation path features reveal the topological laws of internal energy transfer. These four types of features belong to different physical dimensions but mutually constrain each other in the springback formation mechanism. The first attention head learns the law that geometric curvature modulates the direction of plastic flow in the material; the second attention head learns the law that material hardening behavior affects the frictional dissipation at the contact interface; the third attention head learns the law that the contact pressure gradient drives the non-uniform distribution of stress in space; and the fourth attention head learns the law that the stress topology feedback constrains the geometric deformation mode. The dynamic calculation of cross-attention weights enables the springback prediction fusion model to adaptively adjust the contribution of different information sources according to the feature combination of the stamped part, avoiding feature expression imbalance caused by fixed weights. The concatenation operation of the feature fusion layer preserves the differentiated semantic information extracted by each attention head, and the fully connected mapping realizes the nonlinear transformation from the high-dimensional feature space to the springback prediction space. The framework transforms discrete physical measurement data into a unified predictive knowledge representation, enabling the springback prediction fusion model to comprehensively consider the coupling effects of materials, geometry, process, and structural topology, thereby improving the prediction accuracy and generalization ability of the springback behavior of stamped parts.

[0055] The number of heads for each attention head in the multi-head cross-attention layer is determined jointly based on the spatial resolution of the contact pressure distribution data, the node density of the stress propagation path feature data, and the number of dimensions of the material property data. The calculation of the number of heads is expressed as follows: the number of heads is equal to the number of sampling points of the contact pressure distribution data divided by the standard value of the number of sampling points, plus the total number of nodes in the stress propagation analysis graph divided by the standard value of the total number of nodes, plus the number of dimensions of the material property data divided by the standard value of the number of dimensions, summed, divided by 3, and rounded up. The standard value of the number of sampling points is 1000, the standard value of the total number of nodes is 5000, and the standard value of the number of dimensions is 20.

[0056] The steps for establishing the training dataset for the springback prediction fusion model specifically include: selecting 2000 sets of stamped part samples with different material grades, different geometries, and different stamping process parameters; performing finite element simulation on each set of stamped part samples to obtain the geometric shape data, the material property data, the contact pressure distribution data, and the stress propagation path characteristic data as input samples; performing actual stamping forming on each set of stamped part samples and measuring the actual springback deformation using a coordinate measuring machine as output samples; and dividing the input samples and the output samples into a training set and a validation set in an 8:2 ratio.

[0057] The specific steps for training the rebound prediction fusion model include: initializing the network parameters of the rebound prediction fusion model; inputting the input samples of the training set into the rebound prediction fusion model to obtain the predicted rebound deformation; calculating the mean square error between the predicted rebound deformation and the output samples as the loss function value; using the Adam optimizer to update the network parameters according to the gradient of the loss function value; repeating the above process until the loss function value on the validation set no longer decreases for 20 consecutive rounds; and saving the network parameters at this time as the trained rebound prediction fusion model.

[0058] The contact pressure distribution data includes the normal pressure value and tangential friction force value at each contact point on the contact interface. The springback deformation threshold is determined according to the design tolerance requirements of the stamped part; for Class A surface parts, the springback deformation threshold is set to 0.3 mm, and for Class B structural parts, the springback deformation threshold is set to 0.8 mm. The adjustment range of the blank holder force is 80% to 120% of the initial blank holder force, and the adjustment range of the stamping speed is 70% to 130% of the initial stamping speed. The measurement accuracy of the coordinate measuring machine is 0.01 mm, and the measurement points are distributed on the feature lines and feature surfaces of the stamped part, with a spacing of no more than 50 mm between measurement points. The representative volume element structure is a microscopic material unit containing multiple grains, used to simulate the microstructure behavior of the material in the crystalline plastic micro-unit. The macroscopic strain tensor is a description of the strain state at the integration point of the finite element mesh model, containing six strain components. The microscopic stress tensor is a description of the stress state calculated by the crystalline plastic micro-unit, containing six stress components. The penalty function method constrains the contact penetration depth by adding a penalty term to the objective function; the coefficient of the penalty term is called the penalty parameter. The Lagrange multiplier method precisely satisfies the contact constraint conditions by introducing Lagrange multiplier variables. The Coulomb friction model describes the relationship between the frictional force and the normal pressure at the contact interface, with the friction coefficient being a proportionality coefficient. The tangent stiffness matrix is ​​the matrix describing the relationship between element deformation and nodal forces in the finite element solution. The critical time step is the maximum time increment for the explicit dynamic algorithm to maintain stability. The residual stress peak node is the node location with the highest residual stress in the finite element mesh model. The boundary free end node is the unconstrained node location on the boundary of the finite element mesh model. The path weight sum is the cumulative weight value of all edges on the path. The shortest path distance matrix is ​​a matrix recording the shortest path length between any two nodes in the stress propagation analysis diagram structure. The Class A surface part is an appearance part with high surface quality requirements among stamped parts. The Class B structural part is a structural part with high strength requirements but low surface quality requirements among stamped parts. The feature line is the key contour line of the surface geometry of the stamped part. The feature surface is the key curved surface of the surface geometry of the stamped part.

[0059] The specific implementation methods of the above steps are described in detail below.

[0060] The specific implementation of step S01 involves using a 3D laser scanner or optical scanner to perform a full-surface scan of the stamping part to be analyzed. The scanning head moves along the surface of the stamping part and emits a laser beam or structured light. By receiving the reflected light signal, the distance between the scanning point and the sensor is calculated to obtain the 3D point cloud coordinate data of the stamping part surface. The point cloud density is set to no less than 100 sampling points per square centimeter to ensure geometric accuracy. An ultrasonic thickness gauge is used to measure the sheet thickness at multiple feature locations on the stamping part. The spacing between measurement points is set to 30mm to 50mm. The measured thickness values ​​are correlated with the corresponding point cloud coordinates to form thickness distribution data. For the acquisition of material property data, standard tensile specimens are cut from the same batch of sheet metal as the stamping part. A universal testing machine is used to perform a uniaxial tensile test. During the test, load and displacement data are recorded in real time. Based on the initial dimensions of the specimen, the load and displacement data are converted into an engineering stress-strain curve. Furthermore, the true stress-strain curve is obtained through the conversion relationship between true strain and engineering strain, and the conversion relationship between true stress and engineering stress. Tensile specimens are cut along the rolling direction, transverse direction, and 45-degree direction of the sheet metal. During the tensile process, the strain values ​​in the width and thickness directions of the specimens are measured. The ratio of width strain to thickness strain is calculated to obtain the Lankford coefficients in the three directions. The Lankford coefficients are used to characterize the plastic anisotropy of the sheet metal.

[0061] The specific implementation of step S02 is to generate a surface triangular mesh for the stamped part using the Delaunay triangulation algorithm based on surface point cloud coordinate data. The mesh quality is optimized by controlling the maximum distance between adjacent nodes and the minimum triangle quality index, and the triangular mesh is converted into a quadrilateral shell element mesh to improve the accuracy of finite element calculations. Each shell element is assigned a corresponding thickness attribute based on the thickness distribution data, and a linear interpolation method is used to calculate the element thickness value for the region between thickness measurement points. A crystalline plastic micro-element is established at each integration point of the finite element mesh model. This crystalline plastic micro-element uses a representative volume element method to describe the microstructure of the material. Each representative volume element contains 200 to 500 randomly oriented grains, and the slip system of each grain is determined according to the material's crystal structure. The homogenization theory is used to realize the information transfer between the macroscopic and microscopic scales. The strain tensor calculated by the macroscopic finite element model is applied as a boundary condition to the representative volume element. The representative volume element calculates the microscopic stress response through the crystal plastic constitutive model. The microscopic stress tensor is averaged in the representative volume element and then fed back to the macroscopic integration point. The scale transfer process is iterated in each load increment step until the macroscopic and microscopic stress and strain states are consistent.

[0062] The specific implementation of step S03 involves defining contact surfaces between the mold geometry and the sheet metal geometry in the finite element mesh model. These contact surfaces include the contact between the punch and the upper surface of the sheet metal, the contact between the die and the lower surface of the sheet metal, and the contact between the blank holder and the edge of the sheet metal. A contact algorithm combining the penalty function method and the Lagrange multiplier method is used to handle contact constraints. The penalty function method adds a penalty term proportional to the square of the contact penetration depth to the system energy function to prevent node penetration. The penalty parameter ranges from 10 to 100 times the material's elastic modulus; too small a penalty parameter leads to excessive penetration, while too large a parameter causes numerical oscillations. The Lagrange multiplier method introduces additional constraint equations to precisely satisfy the contact conditions, simultaneously solving for the displacement field and contact force field during the iterative solution process. An adaptive friction coefficient function is established to describe the friction behavior of the contact interface. The friction coefficient is dynamically calculated based on the normal pressure, tangential sliding velocity, and temperature at the contact point. An increase in normal pressure reduces the friction coefficient, simulating the lubricating film rupture effect; an increase in sliding velocity reduces the friction coefficient, simulating dynamic friction characteristics. The hyperbolic tangent function smooth approximation of the Coulomb friction model is used to avoid the discontinuity of the tangent stiffness matrix caused by abrupt changes in the direction of frictional force. The initial blank holder force is set to 5kN to 50kN, and the initial stamping speed is set to 1mm / s to 10mm / s. The stamping process parameters are determined according to the material type and geometry of the stamped part.

[0063] The specific implementation of step S04 involves using an implicit time integration method to solve the dynamic equations of the finite element mesh model. This implicit method has unconditional stability, allowing for a larger time step. A mass scaling technique is introduced to artificially increase the material density and improve the critical time step. The mass scaling factor ranges from 100 to 1000. An excessively large mass scaling factor introduces excessive inertial forces, affecting the accuracy of the quasi-static solution. An adaptive time step control strategy is established to dynamically adjust the time step based on the energy error estimate during the solution process. The sum of the system's kinetic energy, strain energy, and contact energy is calculated as the total energy. The relative difference between the current total energy and the initial total energy is used as the energy error estimate. When the energy error estimate exceeds 5%, the time step is reduced to 0.5 times its original value; when the energy error estimate is below 1%, the time step is increased to 1.5 times its original value. This adaptive adjustment strategy balances computational efficiency and numerical accuracy. During the solution process, the position information of all contact points on the contact interface is extracted, and the normal pressure value and tangential friction force value of each contact point are recorded to form contact pressure distribution data. The contact pressure distribution data reflects the interaction intensity and distribution pattern between the sheet metal and the die during the stamping process.

[0064] The specific implementation of step S05 involves using the center points of the elements in the finite element mesh model after springback simulation calculations as nodes in the graph structure, and establishing edge connections between adjacent elements sharing edges or nodes to construct a stress propagation analysis graph structure. The stress gradient between adjacent elements is calculated as the driving force for stress transfer; the stress gradient is obtained by dividing the difference in equivalent stress between two elements by the distance between their center points. The equivalent stiffness of adjacent elements is calculated as the stress transfer impedance; the equivalent stiffness is characterized by the product of the element's elastic modulus and its volume. The stress transfer efficiency is defined as the ratio of the stress gradient to the equivalent stiffness, and the reciprocal of the stress transfer efficiency is used as the weight of the edges in the graph structure; a larger weight value indicates greater difficulty in stress transfer. The node with the largest equivalent stress in the finite element mesh model is identified as the residual stress peak node, and the unconstrained nodes located at the boundary of the stamped part are identified as boundary free end nodes. The Dijkstra shortest path algorithm is used to calculate the shortest paths from the residual stress peak node to all boundary free end nodes. The Dijkstra algorithm employs a greedy strategy to progressively expand the shortest path tree, adding the node with the smallest sum of path weights among currently unvisited nodes to the path tree at each step. The total weight values ​​of all shortest paths are compared, and the path with the smallest sum of weights is selected as the dominant stress release channel, representing the preferred direction of stress unloading during rebound. The Floyd-Warshall algorithm is used to calculate the shortest path distance between any two nodes in the stress propagation analysis graph structure. The Floyd-Warshall algorithm gradually relaxes the path lengths using dynamic programming, ultimately obtaining a global shortest path distance matrix. For each node in the stress propagation analysis graph structure, a betweenness centrality index is calculated. The betweenness centrality index is defined as the proportion of the number of shortest paths passing through that node to the total number of shortest paths between all node pairs in the graph. Nodes with high betweenness centrality play a pivotal role in the stress propagation network. Calculate the average betweenness centrality index of all nodes in the stress propagation analysis graph structure. Use 1.5 times the average as the centrality threshold, and mark nodes with betweenness centrality indices exceeding this threshold as key stress concentration nodes. Count the number of times each edge in the stress propagation analysis graph structure is traversed by the shortest path, and mark the edges with the lowest 10% traversal counts as stress propagation bottleneck edges. Extract the path length of the dominant stress release channel, the average equivalent stress of all nodes on the path, the three-dimensional spatial coordinates of the key stress concentration nodes, and the betweenness centrality index values ​​to form stress propagation path feature data.

[0065] The specific implementation of step S06 involves inputting the geometric shape data into an encoding network and converting it into a 128-dimensional geometric feature vector. The encoding network employs a three-layer fully connected neural network. The first layer flattens the point cloud coordinates and thickness data into a one-dimensional vector. The second layer extracts spatial features through a nonlinear activation function. The third layer outputs a geometric feature vector of fixed dimensions. The material property data is input into the encoding network and converted into a 64-dimensional material feature vector. The encoding process extracts the hardening index and anisotropy parameters of the stress-strain curve. The contact pressure distribution data is input into the encoding network and converted into a 96-dimensional contact feature vector. The encoding process extracts the spatial distribution pattern and amplitude characteristics of the contact pressure. The stress propagation path feature data is input into the encoding network and converted into an 80-dimensional topological feature vector. The encoding process extracts the statistical characteristics of path length, nodal stress, and centrality index. The rebound prediction fusion model's multi-head cross-attention layer comprises four attention heads. The first attention head calculates the attention level of each element in the geometric feature vector to each element in the material feature vector, obtains an attention score through the inner product of the geometric and material feature vectors, normalizes the attention scores to obtain an attention weight matrix, and uses the attention weight matrix to perform a weighted summation of the material feature vectors to obtain a first weighted feature vector. The second, third, and fourth attention heads calculate the attention weights of the material feature vector to the contact feature vector, the contact feature vector to the topological feature vector, and the topological feature vector to the geometric feature vector, respectively, and generate weighted feature vectors. The feature fusion layer concatenates the four weighted feature vectors in the dimensional direction to form a 368-dimensional fused feature vector, and maps the fused feature vector to a 256-dimensional intermediate representation through two fully connected network layers. The decoding layer maps the intermediate representation to the output space step by step through a three-layer fully connected network. The first layer outputs a 512-dimensional vector, the second layer outputs a vector with three times the number of nodes in the finite element mesh model, and the third layer reshapes the vector into the predicted values ​​of the springback deformation of each node in the finite element mesh model in three coordinate directions.

[0066] The specific implementation methods of S07, S08 and S09 need not be described in detail.

[0067] It should be noted that the first key technical idea of ​​this invention is a macro-micro multi-scale coupled modeling method based on homogenization theory. This method embeds crystalline plastic micro-units at each integration point of the macro-finite element model, transferring the influence of micro-grain orientation and slip system on plastic deformation to the macro-response through a scale transfer mechanism. Traditional single-scale models can only describe the macro-average behavior of materials and cannot capture the contribution of grain-scale anisotropy and microstructure evolution to springback. The multi-scale coupled method incorporates microstructure information into the macro-computation framework, enabling springback prediction to include the intrinsic physical mechanisms of the material. Macro-strain, as a micro-boundary condition, drives the plastic slip of grains in the volume element, while micro-stress is fed back to the macro-integration point through volume averaging. This bidirectional information transfer is iteratively executed in each load step to ensure consistency across scales. The multi-scale method reveals the influence of grain orientation distribution on residual stress distribution, providing a micro-level design basis for material microstructure optimization.

[0068] The second key technical idea of ​​this invention is a stress propagation analysis algorithm based on graph theory's shortest path. This algorithm abstracts the finite element discrete structure into a weighted network graph, using graph theory tools to analyze the stress propagation paths and redistribution patterns within the material. Traditional finite element post-processing can only provide the numerical distribution of the stress field, making it difficult to reveal the topological characteristics and key control nodes of stress propagation. Graph theory methods, however, transform the mechanical problem into a network analysis problem, making the stress propagation process quantifiable and traceable. The Dijkstra algorithm identifies the optimal energy unloading channel from the residual stress peak to the boundary. This channel corresponds to the dominant deformation direction of springback, providing spatial location for compensation strategies. The Floyd-Warshall algorithm constructs a global stress connectivity network, with betweenness centrality measuring the pivotal role of nodes in stress redistribution. Changes in the material state of highly central nodes amplify their impact through multiple paths. These topological characteristic parameters establish an explicit correlation with the material's mechanical behavior, improving the physical interpretability of springback prediction and the targeting of process optimization.

[0069] The third key technical idea of ​​this invention is a feature fusion computing framework based on multi-head cross-attention. This framework achieves cross-modal information integration by constructing an interactive attention mechanism between heterogeneous data sources. Traditional prediction models process different types of features independently or simply concatenate them, ignoring the inherent correlations and mutual modulation relationships between features. In contrast, multi-head cross-attention captures cross-modal dependencies by learning the dynamic weight allocation between features. Geometric features, material features, contact features, and topological features belong to different physical dimensions but are mutually constrained in the springback formation mechanism. The first attention head learns the law of geometric curvature modulating the plastic flow of materials; the second attention head learns the law of material hardening affecting contact friction; the third attention head learns the law of contact pressure driving stress distribution; and the fourth attention head learns the law of stress topology constraining geometric deformation. The cross-attention weights adaptively adjust the contribution of information sources according to the feature combination of the specific stamped part, avoiding the imbalance of feature expression with fixed weights, and enabling the prediction model to comprehensively consider the coupling effect of material geometry and structural topology.

[0070] The synergistic effect of the three key technological approaches mentioned above lies in constructing a complete prediction chain from microstructure to macroscopic deformation. The multi-scale coupling method provides the microscopic mechanical response based on the intrinsic physical mechanisms of the material; the graph theory analysis algorithm reveals the spatial patterns of stress propagation from a structural topological perspective; and the multi-headed cross-attention framework integrates multi-source heterogeneous information from a data-driven perspective. The results of microscopic crystal plasticity calculations are transmitted to the macroscopic finite element model through homogenization theory, influencing the residual stress distribution. The residual stress distribution is then used to extract topological feature parameters through graph theory algorithms. These topological feature parameters, along with the geometric material contact characteristics, are input into the attention fusion model to generate springback predictions. This synergistic mechanism combines physical modeling with data-driven approaches, possessing both mechanistic interpretability and predictive accuracy, providing a systematic solution for springback control of automotive stamping parts.

[0071] It should be noted that this invention also solves the following technical problem: Existing technologies often suffer from the difficulty in quantifying and analyzing the stress propagation mechanism of stamped parts. Traditional springback prediction methods treat stamped parts as continuous media, observing stress distribution only through stress cloud diagrams. This fails to quantitatively describe the stress propagation path and efficiency within the material, making it difficult to identify the dominant direction of stress release and the key locations of stress concentration. This invention maps the finite element discrete structure into a stress propagation analysis graph structure, defines the stress transfer efficiency between adjacent elements as the edge weight of the graph, uses the Dijkstra algorithm to search for the shortest path from the residual stress peak node to the boundary free end node to identify the dominant stress release channel, and uses the Floyd-Warshall algorithm to construct a complete stress connectivity network and calculate the node betweenness centrality index to identify key nodes of stress concentration. This transforms the abstract stress field into a quantifiable and analyzable network topology, revealing the stress propagation mechanism and energy dissipation law within the material. This provides a causal explanation for springback control from a microscopic to a macroscopic perspective, solving the technical problem of the difficulty in quantifying and analyzing the stress propagation mechanism of stamped parts.

[0072] Specifically, the principle of this invention is as follows: By constructing a multi-scale coupled analysis framework of microcrystalline plasticity and macroscopic finite element method, this invention incorporates the modulation effect of material microstructure behavior on plastic deformation into the springback calculation system, enabling the prediction model to reflect the true response characteristics of material anisotropy under different strain paths, thus improving the physical accuracy of the material constitutive description. The discrete structure of the stamped part is mapped as a stress propagation graph network. Graph theory algorithms are used to quantify the stress transmission efficiency between elements and the pivotal role of nodes in stress redistribution, identifying the optimal path for stress release and the key locations of stress concentration, providing spatial positioning basis for springback-sensitive areas, and revealing the propagation mechanism of local stress disturbance affecting the overall deformation mode through mechanical coupling. A multi-head cross-attention mechanism is employed to learn the cross-modal dependencies of geometric curvature modulating plastic flow, material hardening affecting frictional dissipation, contact pressure driving stress distribution, and stress topology constraining deformation modes. Deep fusion of heterogeneous features is achieved through dynamic weight allocation, enabling the prediction model to comprehensively consider the coupling effects of materials, geometry, process, and structural topology, establishing a causal explanation framework from microstructure to macroscopic deformation, and improving the physical interpretability of springback prediction.

[0073] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0074] The specific implementation of step S01 involves using a 3D scanner to scan and collect data on the surface of the stamping part to be analyzed, obtaining a set of point cloud coordinate data and thickness distribution data at each point. Simultaneously, a tensile testing machine is used to perform a uniaxial tensile test on the sheet metal, recording true stress and true strain data points under different strain rate conditions to construct a stress-strain curve. The Lankford coefficients in the rolling direction, transverse direction, and 45-degree direction are obtained by measuring the ratio of width strain to thickness strain during the sheet metal stretching process. The above data serve as the basic input for subsequent finite element model establishment and material constitutive parameter calibration.

[0075] The specific implementation of step S02 is to establish a finite element mesh discretization model of the stamped part based on the collected surface point cloud coordinates and thickness distribution. Crystalline plastic micro-units are embedded at each integration point of this model as representative volumetric elements. These elements contain several grains with random orientation and slip systems. A scale transfer relationship between the macroscopic finite element model and the microcrystalline plastic units is established using homogenization theory. The implementation steps for scale transfer are as follows: first, obtain the macroscopic strain tensor at the integration points of the finite element mesh model. ,in The macroscopic strain tensor components are dimensionless. This macroscopic strain tensor is then used as a boundary condition input into the crystal plastic micro-unit to solve for the microscopic stress tensor at the microscale. Next, the macroscopic stress tensor is obtained by volume averaging the microscopic stress tensor within the representative volume element structure. The formula for volume averaging is as follows:

[0076] ;

[0077] In the formula, These are macroscopic stress tensor components, in units of... ; The volume of a volume element is represented by a unit of 1. ; These are the components of the microscopic stress tensor, with units of . ; For volume infinitesimal elements, the unit is . ; The tensor index is denoted by 1 to 3. Finally, the calculated macroscopic stress tensor is fed back to the integration points of the finite element mesh model for the next step of the calculation.

[0078] The specific implementation of step S03 involves setting the contact interface between the mold and the sheet metal in the finite element mesh model. A hybrid contact solution strategy combining the penalty function method and the Lagrange multiplier method is used to handle changes in the contact state. The penalty function method constrains the contact penetration depth by adding a penalty term to the objective function, while the Lagrange multiplier method accurately satisfies the contact constraint conditions by introducing multiplier variables. Simultaneously, an adaptive friction coefficient function is established based on the normal contact pressure, tangential sliding velocity, and contact temperature of the contact interface. This function adopts a smooth approximation of the Coulomb friction model, and the formula is expressed as follows:

[0079] ;

[0080] In the formula, The coefficient of friction is adaptive and dimensionless. The reference friction coefficient is typically taken as 0.1 to 0.15; The pressure influence coefficient has an empirical value of 0.05. Normal contact pressure, unit: ; For reference pressure, the material yield strength is used, in units of... ; The speed influence coefficient has an empirical value of 0.03. Tangential slip velocity, in units of ; For reference speed, the default value is 100. ; The temperature influence coefficient has an empirical value of 0.02. This refers to the contact temperature, expressed in °C. This refers to the ambient temperature, typically 20°C. The reference temperature difference is 50℃ by default. This formula achieves dimensionlessness by introducing normalization of pressure, velocity, and temperature terms, allowing the friction coefficient to be dynamically adjusted according to the real-time state of the contact interface. At the same time, the initial blank holder force and initial stamping speed are set as process parameters for subsequent simulation calculations.

[0081] The specific implementation of step S04 involves performing springback simulation calculations on the established finite element mesh model. An implicit dynamic solver combined with a mass scaling factor technique is used. The critical time step is increased by artificially increasing the material density to accelerate computational efficiency. The mass scaling factor ranges from 100 to 1000, determined based on the principle of balancing computational efficiency and accuracy. An adaptive time step control strategy is used to dynamically adjust the calculation step size based on the energy error estimate. The energy error estimate is calculated by comparing the relative change between the total system energy and the initial total energy, as expressed in the following formula:

[0082] ;

[0083] In the formula, This is an estimate of the energy error, dimensionless. for Total energy of the system at any given time, of which For time variables, the unit is , The unit is ; The initial total energy, in units of ; To achieve absolute value calculations, the time step is reduced when the energy error estimate exceeds 5% to ensure calculation accuracy, and increased when the energy error estimate is below 1% to improve calculation efficiency. This strategy is used to obtain the normal pressure value and tangential friction force value of each contact point on the contact interface as contact pressure distribution data throughout the entire rebound simulation process.

[0084] The specific implementation of step S05 is to abstract the finite element mesh model after springback simulation calculation into a stress propagation analysis graph structure. The nodes of this graph structure represent the center points of the elements in the finite element mesh model, and the edges represent the connection relationships between adjacent elements. The weight of the edge is defined as the reciprocal of the stress transfer efficiency between adjacent elements. The stress transfer efficiency is calculated based on the stress gradient of adjacent elements and the element stiffness, and the formula is expressed as follows:

[0085] ;

[0086] In the formula, For unit With unit The stress transfer efficiency between them is dimensionless. For unit The stress value, in units of ; For unit The stress value, in units of ; The reference stress is the material's yield strength, in units of... ; The distance between the centers of the two units is expressed in units of 1. ; The feature length is the average of the overall model dimensions, expressed in units of 1200 mm. ; For equivalent stiffness, the product of the material's elastic modulus and the element's characteristic dimension is used, with units of 1. ; For reference stiffness, the default value is... A graph-based shortest path stress propagation analysis algorithm was used to identify the dominant stress release channels and key stress concentration nodes. The algorithm steps are as follows: First, the peak nodes of residual stress and the free-end nodes of the boundary in the finite element mesh model were identified. Then, the Dijkstra algorithm was used to calculate the shortest path from the peak node of residual stress to each free-end node of the boundary. The shortest path with the smallest sum of path weights was selected as the dominant stress release channel. Next, the Floyd-Warshall algorithm was used to calculate the shortest path distance matrix between any two nodes in the stress propagation analysis graph structure. For each node in the graph structure, the betweenness centrality index was calculated. The betweenness centrality index represents the proportion of the number of shortest paths passing through that node to the total number of shortest paths, expressed by the following formula:

[0087] ;

[0088] In the formula, For nodes The betweenness centrality index is dimensionless; For the node To the node The shortest path passes through the nodes The number of paths; For the node To the node The total number of shortest paths; All are node indices in the graph structure. Nodes with betweenness centrality indices exceeding the centrality threshold are marked as key stress concentration nodes. The centrality threshold is set to 1.5 times the average betweenness centrality index of all nodes in the stress propagation analysis graph structure. The number of shortest paths passing through each edge is counted, and the edge with the fewest passes is marked as the stress propagation bottleneck edge. Finally, the stress propagation path characteristic data are obtained, including the path length of the dominant stress release channel, the average stress of the nodes on the path, the spatial coordinates of the key stress concentration nodes, and the betweenness centrality index value.

[0089] The specific implementation of step S06 involves inputting geometric shape data, material property data, contact pressure distribution data, and stress propagation path feature data into the springback prediction fusion model. This model employs a feature fusion calculation framework based on multi-head cross-attention, achieving deep correlation modeling between features of different dimensions through a dynamic weight allocation mechanism. The number of heads for each attention head in the multi-head cross-attention layer is jointly determined based on the spatial resolution of the contact pressure distribution data, the node density of the stress propagation path feature data, and the number of dimensions of the material property data, as expressed in the following formula:

[0090] ;

[0091] In the formula, This is the number of heads parameter; This represents the number of sampling points for the contact pressure distribution data. The total number of structural nodes in the stress propagation analysis diagram; The number of dimensions for material property data; This is for rounding up. The springback prediction fusion model outputs predicted springback deformation values ​​for each node of the stamped part for subsequent evaluation and process parameter optimization.

[0092] The specific implementation of step S07 involves calculating the deviation rate between the predicted value of the springback deformation and the springback deformation threshold. The formula for calculating the deviation rate is as follows:

[0093] ;

[0094] In the formula, The deviation rate is dimensionless. This is the predicted value of springback deformation, in units of... ; This is the threshold for springback deformation, in units of... When the deviation rate is greater than 15%, adjust the blank holder force and stamping speed in the stamping process parameters. The blank holder force is adjusted from 80% to 120% of the initial blank holder force, and the stamping speed is adjusted from 70% to 130% of the initial stamping speed. After adjustment, return to step S04 to recalculate the springback simulation until the deviation rate meets the requirements.

[0095] The specific implementation method of step S08 is the same as described above, and will not be repeated in detail here.

[0096] The specific implementation of step S09 involves calculating the prediction error between the predicted value of the springback deformation and the actual springback deformation. The formula for calculating the prediction error is as follows:

[0097] ;

[0098] In the formula, The prediction error is dimensionless. This is the predicted value of springback deformation, in units of... ; This represents the actual springback deformation, in units of... When the prediction error exceeds 10%, geometric data, material property data, contact pressure distribution data, stress propagation path characteristic data, and actual rebound deformation are added to the training dataset, and the rebound prediction fusion model is retrained to improve the model's prediction accuracy and generalization ability.

[0099] It should be noted that the variables involved in this embodiment are explained in detail in Table 1.

[0100] Table 1. Variable Explanation Table

[0101]

[0102] To better understand and implement this invention, a specific application scenario is provided below as Example 2: A technical team undertook a task to optimize the springback control of a stamped door outer panel. This stamped part is a Class A surface part, made of 5182 aluminum alloy sheet, 1.2mm thick, with overall dimensions of 1350mm × 980mm. During initial trial production, it was found that the formed door outer panel exhibited significant springback deformation after unloading, particularly around the door handle mounting holes and at the corner of the lower door beam. The springback deformation exceeded the design tolerance threshold of 0.3mm, resulting in uneven assembly gaps. The technical team decided to use the method of this invention to conduct systematic springback analysis and process optimization for this stamped part.

[0103] First, the technical team used an ATOS 3D scanner to collect surface point cloud data of the prototype door outer panel. The scanning accuracy was set to 0.05mm, resulting in 2,847,536 surface point cloud coordinate data points. Simultaneously collected thickness distribution data showed that the thinning rate of the stamped part in the deep-drawing region reached 18.7%, with a local minimum thickness of 0.976mm. For material property testing, an MTS universal testing machine was used to conduct uniaxial tensile tests on the 5182 aluminum alloy sheet. The test temperature was 23℃, and the strain rate was set to 0.001. 0.01 and 0.1 Three levels. The measured stress-strain curves show that the material has a yield strength of 132 MPa, a tensile strength of 278 MPa, and an elongation of 24.3%. Lankford coefficients were obtained through tensile tests in different directions: 0.687 in the rolling direction, 0.724 in the transverse direction, and 0.598 in the 45-degree direction, reflecting a moderate degree of anisotropy in the aluminum alloy sheet.

[0104] Based on the collected point cloud coordinates and thickness distribution data, the technical team established a finite element mesh model containing 58,742 shell elements, with element sizes controlled between 2.5 mm and 5.0 mm. Figure 2 As shown, crystalline plastic micro-elements are embedded at each integration point of the finite element mesh model, representing 500 grains within the volume element structure, with grain orientations generated using a random distribution. Homogenization theory is employed to establish a bidirectional transmission relationship between the macroscopic and microscopic scales. At each integration point, the macroscopic strain tensor is input as a boundary condition into the crystalline plastic micro-elements. The stress tensor obtained after solving the micro-elements is fed back to the macroscopic finite element model through volume averaging.

[0105] Regarding the contact interface settings, a hybrid contact solution strategy is adopted between the mold and the sheet metal, and the penalty parameter of the penalty function method is set as follows: The Lagrange multiplier method (N / m) is used to accurately calculate the contact pressure. The adaptive friction coefficient function comprehensively considers three factors: normal contact pressure, tangential sliding velocity, and contact temperature. The base friction coefficient is set to 0.12. When the contact pressure exceeds 15 MPa, the friction coefficient decreases to 0.09, and when the sliding velocity exceeds 50 mm / s, the friction coefficient increases to 0.15. The initial stamping process parameters are set as follows: blank holder force 850 kN, stamping speed 80 mm / s.

[0106] like Figure 3 As shown, the rebound simulation calculation uses the ABAQUS / Explicit implicit dynamics solver, with the mass scaling factor set to 500 to improve computational efficiency. The critical time step is adjusted from the original... s upgraded to The adaptive time step control strategy dynamically adjusts based on the energy error estimate. When the relative change between the total system energy and the initial total energy exceeds 5%, the time step automatically decreases to 0.6 times its original value; when the energy error is less than 1%, the time step increases to 1.3 times its original value. The simulation of the entire stamping process took 4.7 hours, obtaining detailed pressure distribution data at the contact interface. The contact pressure distribution data shows that the maximum contact pressure in the pressure ring area is 42.6 MPa, and the contact pressure gradient is largest in the area around the door handle hole, with a pressure change rate reaching 3.8 MPa / mm.

[0107] The finite element mesh model after springback simulation was abstracted into a stress propagation analysis graph structure, containing 58,742 nodes and 174,528 edges. Edge weights were calculated based on the stress transfer efficiency between adjacent elements, which considered stress gradient and element stiffness. The standard value of equivalent stiffness was the product of the material's elastic modulus of 70 GPa and the element's characteristic size of 3.5 mm. The technical team identified the residual stress peak node located at the corner of the lower side beam of the door, with a residual stress value of 185 MPa. There were 328 boundary free-end nodes distributed along the outer contour edge of the stamped part. Dijkstra's algorithm was used to calculate the shortest paths from the residual stress peak node to each boundary free-end node. The path with the minimum sum of path weights was selected as the dominant stress release channel, with a length of 567 mm and an average stress of 142 MPa at the nodes along this path. Figure 4 As shown, the shortest path distance matrix calculated by the Floyd-Warshall algorithm reveals the connectivity characteristics of stress throughout the structure. The betweenness centrality index calculation results show that 23 nodes have centrality values ​​exceeding the threshold of 0.0087. These key stress concentration nodes are mainly distributed in regions with drastic changes in geometric curvature and locations of abrupt thickness changes. A total of 47 stress propagation bottleneck edges were identified, corresponding to structural weak points where material stiffness is discontinuous.

[0108] The statistical results of stress propagation path characteristic data are shown in Table 2.

[0109] Table 2 Statistical data on stress propagation path characteristics

[0110]

[0111] The technical team input geometric shape data, material property data, contact pressure distribution data, and stress propagation path feature data into the springback prediction fusion model. The geometric feature vector dimension is 256, the material feature vector dimension is 64, the contact feature vector dimension is 512, and the topological feature vector dimension is 128. The number of heads in the multi-head cross-attention layer is calculated to be 4. The first attention head learns that the curvature concentration around the door handle hole restricts material flow in this area. The second attention head learns that the work hardening characteristics of aluminum alloy increase the frictional dissipation at the contact interface by 14.2%. The third attention head learns that the non-uniform distribution of the blank holder force drives the stress to exhibit an asymmetric distribution in the drawing region. The fourth attention head learns that the stress propagation bottleneck restricts the release path of elastic energy. The springback prediction fusion model outputs the predicted values ​​of springback deformation at each node of the door outer panel. The maximum predicted springback in the area around the door handle hole is 0.47 mm, and the predicted springback at the corner of the lower edge beam of the door is 0.52 mm.

[0112] The deviation rate between the predicted springback deformation and the 0.3mm threshold was calculated. The deviation rate was 56.7% in the door handle hole area and 73.3% in the lower door beam area, both exceeding the 15% adjustment trigger condition. The technical team decided to adjust the stamping process parameters, increasing the blank holder force from 850kN to 935kN and decreasing the stamping speed from 80mm / s to 68mm / s. After adjusting the parameters, the springback simulation was recalculated. The new contact pressure distribution showed that the maximum contact pressure in the blank holder area increased to 48.3MPa, and the average stress along the dominant stress propagation path decreased to 126MPa. After re-inputting the springback prediction fusion model, the predicted springback around the door handle hole decreased to 0.28mm, and the predicted springback at the corner of the lower door beam decreased to 0.26mm, both meeting the tolerance requirements for Class A surface parts.

[0113] like Figure 5As shown, the technical team used a Hexagon coordinate measuring machine to perform geometric measurements on the actual stamped door outer panel after optimizing process parameters. The measurement accuracy was 0.01mm. 487 measurement points were arranged on the feature lines and feature surfaces of the stamped part, with the spacing between the measurement points controlled within 45mm. The calculation of the difference between the measured actual geometric coordinates and the designed geometric coordinates showed that the actual springback deformation around the door handle hole was 0.31mm, and the actual springback deformation at the corner of the lower edge beam of the door was 0.29mm. The prediction error between the predicted and actual springback deformation values ​​was calculated: 9.7% for the door handle hole area and 10.3% for the lower edge beam area of ​​the door, meeting the accuracy requirement of within 10%, thus eliminating the need to retrain the springback prediction fusion model.

[0114] This invention represents a significant technological advancement over traditional trial-and-error methods and single finite element simulations. Traditional methods rely on the experience of process engineers to adjust blank holder force and stamping speed, lacking a deep understanding of the springback formation mechanism and often requiring multiple rounds of trial molding to achieve acceptable accuracy. This invention, through multi-scale coupling of crystalline plastic micro-units and macroscopic finite element models, incorporates the plastic deformation behavior of the material's microstructure into the simulation calculation, accurately capturing the influence mechanism of anisotropy on springback. A graph-based stress propagation analysis algorithm maps discrete finite element structures into network topology relationships, revealing the stress transmission path and energy dissipation laws within the material, identifying key nodes and weak points sensitive to springback, and providing clear spatial positioning basis for process optimization. The multi-head cross-attention feature fusion framework overcomes the limitations of traditional methods that treat geometric, material, process, and stress information independently. Through a dynamic weight allocation mechanism, it establishes deep correlations between cross-modal features, enabling the springback prediction model to comprehensively consider multi-physics coupling effects, improving prediction accuracy and generalization ability. The introduction of adaptive friction coefficient function and adaptive time step control strategy enhances the robustness of simulation calculations, ensuring solution stability under complex contact state changes and large deformation conditions. The overall technical solution organically combines physical modeling, topology analysis, and data-driven methods, forming a complete causal explanation framework from microstructure to macro deformation, and realizing a technological leap from empirical adjustment to accurate prediction in springback control.

[0115] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring and predicting the springback deformation of automotive stamping parts, characterized in that, A 3D scanner was used to collect the surface point cloud coordinates and thickness distribution of the stamping part to be analyzed as geometric data. A tensile testing machine was used to test the sheet metal to obtain stress-strain curves and Lankford coefficients as material property data. A finite element mesh model of the stamping part was established based on the surface point cloud coordinates and thickness distribution. Crystalline plastic micro-units were embedded at each integration point of the finite element mesh model. Homogenization theory was used to establish the scale transfer relationship between the finite element mesh model and the crystalline plastic micro-units. The contact interface between the die and the sheet metal was set in the finite element mesh model, and a hybrid contact solution strategy was used to handle changes in the contact state. An adaptive friction coefficient function is established based on contact pressure and sliding velocity. Initial blank holder force and initial stamping speed are set as stamping process parameters. Springback simulation calculation is performed on the finite element mesh model. The finite element mesh model after springback simulation calculation is abstracted into a stress propagation analysis graph structure. The stress propagation analysis algorithm based on graph theory shortest path is used to identify the dominant stress release channel and key stress concentration nodes to obtain stress propagation path characteristic data. Geometric shape data, material property data, contact pressure distribution data and stress propagation path characteristic data are input into the springback prediction fusion model to output the predicted value of springback deformation of each node of the stamped part. Among them, the crystalline plastic micro-unit is the representative volume element structure, which contains several grains, each grain having random orientation and slip system; the hybrid contact solution strategy adopts a combination of the penalty function method and the Lagrange multiplier method. The penalty function method is used to handle contact penetration constraints, and the Lagrange multiplier method is used to handle the accurate solution of contact forces.

2. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 1, characterized in that, The stress-strain curves are obtained through uniaxial tensile tests, recording the true stress and true strain data points of the sheet metal at different strain rates. The stress-strain curves are used for parameter calibration of the material constitutive model in the finite element mesh model.

3. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 2, characterized in that, The Lankford coefficient includes the rolling direction Lankford coefficient, the transverse Lankford coefficient, and the 45-degree direction Lankford coefficient. It is obtained by measuring the ratio of width strain to thickness strain through sheet tensile testing. The Lankford coefficient is used to characterize the degree of anisotropy of the sheet.

4. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 3, characterized in that, The steps for establishing scale transfer relationships using homogenization theory are as follows: obtain the macroscopic strain tensor at each integration point of the finite element mesh model, use the macroscopic strain tensor as the boundary condition input for the crystal plastic micro-unit, solve the microscopic stress tensor for the crystal plastic micro-unit at the microscale, perform volume averaging on the microscopic stress tensor within the representative volume element structure to obtain the macroscopic stress tensor, and feed the macroscopic stress tensor back to the integration points of the finite element mesh model.

5. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 4, characterized in that, The adaptive friction coefficient function calculates the current friction coefficient value based on the normal contact pressure, tangential sliding velocity, and contact temperature at the contact interface. The adaptive friction coefficient function adopts a smooth approximation of the Coulomb friction model.

6. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 5, characterized in that, The rebound simulation calculation uses an implicit dynamic solver in conjunction with a mass scaling factor and an adaptive time step control strategy to dynamically adjust the calculation step size based on the energy error estimate to obtain the contact pressure distribution data at the contact interface.

7. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 6, characterized in that, The nodes of the stress propagation analysis graph structure represent the center points of elements in the finite element mesh model, and the edges of the stress propagation analysis graph structure represent the connection relationships between adjacent elements. The weight of the edge is defined as the reciprocal of the stress transfer efficiency between adjacent elements.

8. The method for measuring and predicting the springback deformation of automotive stamping parts according to claim 7, characterized in that, A graph-based shortest path stress propagation analysis algorithm identifies peak nodes and free-end nodes of residual stress in a finite element mesh model. The Dijkstra algorithm is used to calculate the shortest path from the peak node to each free-end node. The shortest path with the smallest sum of path weights is selected as the dominant stress release channel. The Floyd-Warshall algorithm is used to calculate the shortest path distance matrix between any two nodes in the stress propagation analysis graph structure. A betweenness centrality index is calculated for each node in the stress propagation analysis graph structure, and nodes with betweenness centrality indices exceeding the centrality threshold are marked as critical stress concentration nodes.

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