Method for predicting stamping springback of nickel-based alloy strip

Abstract

The invention provides a nickel-based alloy strip stamping springback prediction method, and relates to the technical field of nickel-based alloy stamping manufacturing, and the method comprises the steps: obtaining initial springback values corresponding to a plurality of groups of stamping process parameter combinations in the stamping process of a nickel-based alloy strip, and calculating the stamping springback value of the nickel-based alloy strip based on all the stamping process parameter combinations and the corresponding initial springback values; constructing a training data set and a test data set; the training data set serves as input data, the initial springback value corresponding to the training data set serves as output data, and a springback prediction model driven by physical information is constructed; using an adaptive cuckoo search algorithm to search a predicted springback value as an optimal springback value, wherein the difference value between the predicted springback value and the expected springback value is minimum in the springback prediction model driven by physical information, and using a stamping process parameter combination corresponding to the optimal springback value as an optimal process parameter combination; optimization can be carried out in a complex parameter space, the optimization efficiency and stability are effectively improved, and local optimization is avoided.

Description

Technical Field

[0001] This application generally relates to the field of nickel-based alloy stamping manufacturing technology, and specifically to a method for predicting the springback of nickel-based alloy strips during stamping. Background Technology

[0002] Nickel-based alloys, especially Inconel 718, are widely used in the manufacture of key components for high-end equipment in aerospace, energy, and chemical industries due to their excellent high-temperature strength, creep resistance, and corrosion resistance. For high-strength materials like Inconel 718, the stress gradient during deformation is significantly localized, and the yield trajectory exhibits nonlinear drift, causing the springback mechanism to deviate significantly from the linear law of traditional low-carbon steel. This complex nonlinear springback behavior makes it difficult to control the dimensional accuracy of stamped parts, severely affecting the assembly quality and service performance of the products.

[0003] Currently, methods for predicting and controlling stamping springback mainly rely on traditional optimization algorithms, such as standard genetic algorithms and particle swarm optimization. However, traditional optimization algorithms are prone to getting trapped in local optima and exhibit poor convergence stability in complex nonlinear optimization problems, making it difficult to quickly find the optimal process parameters. Therefore, we propose a method for predicting stamping springback of nickel-based alloy strips to address these issues. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a method for predicting the springback of nickel-based alloy strip stamping with improved prediction accuracy and stability.

[0005] This application provides a method for predicting the springback of nickel-based alloy strips during stamping, including the following steps: The initial springback amount corresponding to multiple combinations of stamping process parameters during the stamping process of nickel-based alloy strip is obtained, and a training dataset and a test dataset are constructed based on all the combinations of stamping process parameters and their corresponding initial springback amounts; the combinations of stamping process parameters include at least blank holder force, die-punch clearance, friction coefficient and stamping speed; Using the training dataset as input data and the initial rebound amount corresponding to the training dataset as output data, a physical information-driven rebound prediction model is constructed. Using the physical information-driven springback prediction model as the objective function and the desired springback amount as the optimization objective, the adaptive cuckoo search algorithm is used to search for the predicted springback amount with the smallest difference from the desired springback amount in the physical information-driven springback prediction model as the optimal springback amount, and the stamping process parameter combination corresponding to the optimal springback amount is taken as the optimal process parameter combination.

[0006] According to the technical solution provided in this application, the method further includes the following steps: The optimal combination of process parameters is input into the stamping equipment and executed, and the actual springback is measured. Based on the difference between the actual rebound amount and the optimal rebound amount, determine whether to update the physical information-driven rebound prediction model; If the difference between the actual rebound amount and the optimal rebound amount is greater than a preset difference, then the actual rebound amount and the optimal process parameters are combined as new sample data and added to the training dataset. The physical information-driven rebound prediction model is retrained using the training dataset with added data.

[0007] Based on the technical solution provided in this application, a physical information-driven rebound prediction model is constructed, specifically including the following steps: A data-driven model framework is constructed based on the support vector regression model. Based on the constitutive model of nickel-based alloys, a physical prior operator is constructed; the physical prior operator is used to characterize the elastic-plastic unloading and springback mechanism of the material. By embedding the physical prior operator into the loss function of the data-driven model framework, a physical information-driven rebound prediction model is obtained.

[0008] According to the technical solution provided in this application, the physical prior operator is a theoretical calculation framework for calculating elastic recovery strain; Based on the constitutive model of nickel-based alloys, a physical prior operator is constructed, which includes the following steps: Based on the constitutive model of nickel-based alloys, the stress-strain response of nickel-based alloys during stamping and unloading processes is simulated. The theoretical calculation framework is constructed based on the elastic recovery strain generated by the nickel-based alloy during unloading, and the geometric mapping relationship between the nickel-based alloy and its geometry and stamping conditions.

[0009] According to the technical solution provided in this application, the adaptive cuckoo search algorithm is used to search for the predicted rebound amount with the smallest difference from the expected rebound amount in the physical information-driven rebound prediction model as the optimal rebound amount, specifically including the following steps: Initialize the cuckoo population and randomly generate a set of stamping process parameters as the initial nest locations; Based on the rebound prediction model driven by the physical information, the rebound error between the predicted rebound amount and the expected rebound amount corresponding to each nest location is calculated. Based on the rebound error, calculate the fitness value of each nest in the current generation population and identify the current optimal nest; Based on the rebound error, the Levy flight step size is adjusted by gradient adjustment, and the position of all the nests is updated by an adaptive Levy flight mechanism. A preset adaptive discovery probability is obtained, and based on the preset adaptive discovery probability, some nests are randomly eliminated and the same number of new nests are generated; the adaptive discovery probability is negatively correlated with the dispersion of the fitness value of the current generation population. If the dispersion of fitness values ​​of all nests in the current generation population is greater than or equal to a preset dispersion, then the fitness value of each nest is recalculated and the iterative search continues until the dispersion of fitness values ​​of all nests in the current generation population is less than the preset dispersion. Then, the stamping process parameter combination corresponding to the current optimal nest is taken as the optimal process parameter combination.

[0010] According to the technical solution provided in this application, the expected rebound amount is obtained by following these steps: Obtain the theoretical profile height of the nickel-based alloy strip on the design drawings; Under ideal conditions with no springback, the contour height of the part after stamping of nickel-based alloy strip is measured to obtain the theoretical forming height. The difference between the theoretical profile height and the theoretical forming height is calculated to obtain the expected springback amount.

[0011] According to the technical solution provided in this application, the initial springback amount of nickel-based alloy strips corresponding to multiple combinations of stamping process parameters during the stamping process is obtained, specifically including the following steps: The Latin hypercube experimental design method is used to generate a combination of stamping process parameters with spatially uniform distribution characteristics within a preset process parameter range; Based on the stamping process parameter combination, the simulated springback amount corresponding to each process parameter combination is calculated by finite element simulation, and the simulated springback amount is used as the initial springback amount of the corresponding process parameter combination.

[0012] According to the technical solution provided in this application, a training dataset and a test dataset are constructed based on all the combinations of stamping process parameters and their corresponding initial springback amounts, specifically including the following steps: The combination of stamping process parameters and their corresponding initial springback are normalized to obtain a data sample set; The data sample set is divided into a training dataset and a test dataset according to a preset ratio.

[0013] Compared with the prior art, the beneficial effects of this application are: This application provides a method for predicting the springback of nickel-based alloy strips during stamping, comprising: obtaining the initial springback amount corresponding to multiple combinations of stamping process parameters during the stamping process of nickel-based alloy strips, and constructing a training dataset and a test dataset based on all combinations of stamping process parameters and their corresponding initial springback amounts; the combinations of stamping process parameters include at least blank holder force, die clearance, friction coefficient, and stamping speed; using the training dataset as input data and the initial springback amount corresponding to the training dataset as output data, constructing a physical information-driven springback prediction model; using the physical information-driven springback prediction model as the objective function and the expected springback amount as the optimization objective, using an adaptive cuckoo search algorithm to search for the predicted springback amount with the smallest difference from the expected springback amount in the physical information-driven springback prediction model as the optimal springback amount, and taking the stamping process parameter combination corresponding to the optimal springback amount as the optimal process parameter combination.

[0014] This application obtains multiple sets of stamping process parameter combinations and corresponding initial springback amounts, and constructs training and testing datasets based on all stamping process parameter combinations and corresponding initial springback amounts to ensure comprehensive data coverage and avoid prediction bias due to excessive data. Furthermore, the constructed physical information-driven springback prediction model uses the training dataset as input data and the corresponding initial springback amount as output data, integrating physical mechanisms into the model construction process. This overcomes the limitations of traditional pure data-driven models, which lack physical consistency and have poor extrapolation capabilities, effectively improving the accuracy and reliability of the model's prediction of complex stamping springback behavior in nickel-based alloys. Further, Furthermore, by employing an adaptive cuckoo search algorithm, with a physical information-driven springback prediction model as the objective function and the expected springback amount as the optimization objective, this application searches for the optimal springback amount and the corresponding optimal combination of process parameters. Compared to traditional optimization algorithms, this application uses an adaptive cuckoo search algorithm to balance global exploration and local search, thereby efficiently and stably finding the global optimal solution in a complex multi-process parameter space and avoiding getting trapped in local optima. Finally, by applying the optimal combination of process parameters to actual production and establishing a closed-loop feedback mechanism, the dimensional accuracy of nickel-based alloy strip stampings is continuously improved, reducing assembly quality problems and service performance risks caused by springback from the source. Attached Figure Description

[0015] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0016] Figure 1 This is a flowchart of a method for predicting the springback of nickel-based alloy strips during stamping.

[0017] Figure 2 A flowchart for updating the physical information-driven rebound prediction model.

[0018] Figure 3A flowchart for constructing a physical information-driven rebound prediction model.

[0019] Figure 4 This is a flowchart for searching for the optimal rebound amount.

[0020] Figure 5 This is an example diagram of a nickel-based alloy strip.

[0021] Figure 6 This is an example diagram showing the springback of a nickel-based alloy strip.

[0022] Figure 7 Example graph showing prediction results for the training dataset.

[0023] Figure 8 This is an example diagram of the fitness curve of A-CSO-PISVM.

[0024] Figure 9 This is an example graph showing the fitness curve of an SVM. Detailed Implementation

[0025] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0026] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0027] like Figure 1 As shown in the figure, this is a flowchart of the nickel-based alloy strip stamping springback prediction method provided in this application. The method includes the following steps: S100. Obtain the initial springback amount corresponding to multiple combinations of stamping process parameters during the stamping process of nickel-based alloy strips, and construct training datasets and test datasets based on all combinations of stamping process parameters and their corresponding initial springback amounts; the combinations of stamping process parameters include at least blank holder force, die-punch clearance, friction coefficient and stamping speed.

[0028] It should be noted that nickel-based alloy strips, such as Inconel 718 alloy strips, are examples. Figure 5As shown, w1 is an Inconel 718 alloy strip, which exhibits high strength and low ductility characteristics at room temperature with a work hardening index n≥0.65 and an elongation δ≤12%. Its stamping deformation zone shows stress gradient localization and nonlinear drift of the yield trajectory, leading to a springback mechanism that significantly deviates from that of traditional low-carbon steel. Blank holder force, die clearance, friction coefficient, and stamping speed are key variables for the stamping springback of nickel-based alloy strips. Blank holder force determines the degree of constraint during sheet forming; too small a force can easily lead to wrinkling, while too large a force can easily cause cracking and alter the springback distribution. The matching degree between the die clearance and the sheet thickness affects the forming pressure transmission; deviations in the die clearance can directly amplify the springback amount. The friction coefficient determines the force transmission efficiency of the contact surface between the sheet and the die, thus affecting the local stress and strain distribution. Stamping speed is related to the dynamic deformation response of nickel-based alloys; its high hardening characteristics make it sensitive to speed, and improper speed can easily lead to changes in the springback mechanism. Therefore, the combination of stamping process parameters should at least include blank holder force, die clearance, friction coefficient, and stamping speed.

[0029] The process of obtaining the initial springback amount of nickel-based alloy strips corresponding to multiple combinations of stamping process parameters during stamping includes the following steps: The Latin hypercube experimental design method is used to generate a combination of stamping process parameters with spatially uniform distribution characteristics within a preset process parameter range; Based on the combination of stamping process parameters, the simulated springback amount corresponding to each combination of process parameters is calculated by finite element simulation, and the simulated springback amount is used as the initial springback amount of the corresponding combination of process parameters.

[0030] Here, the Latin Hypercube Design (LHS) method, as a space-filling design approach, can uniformly divide each parameter dimension into several intervals within a preset process parameter range, and extract only one sample from each interval. The extracted values ​​are then randomly combined to generate a preset number of stamping process parameter combinations. These generated combinations are uniformly distributed throughout the parameter space, ensuring comprehensive sample coverage while effectively controlling the total sample size, thus adapting to the complex characteristics of nickel-based alloy strip stamping process parameters. The preset number can be set according to actual needs, for example, 50 or 100 sets. The preset process parameter range mainly includes extreme conditions in actual production, such as maximum / minimum finger pressure force, maximum / minimum die clearance, critical friction coefficient, and upper / lower limits of stamping speed. The preset process parameters can be set according to actual needs. For example, the blank holder force range is 50~300kN, the die clearance range is 1.02~1.1 times the sheet thickness, the friction coefficient range is 0.05~0.2, and the punching speed range is 5~50mm / s.

[0031] This method utilizes Dynaform finite element software for finite element simulation. This software has a rich set of built-in material constitutive models, such as the Voce-Chaboche nonlinear-isotropic hardening constitutive model, which can accurately characterize the stress-strain response of nickel-based alloy strips. It also includes contact algorithms and springback calculation modules, directly outputting the springback amount after unloading the stamped part, meeting the simulation requirements for springback in nickel-based alloy strip stamping. The contact algorithm, for example, is a penalty function contact algorithm, used to simulate the frictional contact behavior between the sheet metal and the die.

[0032] Specifically, firstly, geometric models of the nickel-based alloy strip, punch, die, and blank holder are established in the Dynaform finite element software. The geometric model of the nickel-based alloy strip needs to be set according to the actual product size, and the geometric models of the punch and die need to define the surface roughness, which is related to the friction coefficient. The actual product size is, for example, 100mm in length, 20mm in width, and 1mm in thickness.

[0033] Secondly, material parameters and Voce-Chaboche constitutive model parameters are assigned to the geometric model of the nickel-based alloy strip to ensure that the material model accurately reflects the elastoplastic hardening characteristics of Inconel 718. The material parameters include at least the elastic modulus, Poisson's ratio, and yield strength; for example, the elastic modulus is 205 GPa, the Poisson's ratio is 0.3, and the yield strength is 1100 MPa. The Voce-Chaboche constitutive model parameters include at least the saturation hardening amount and the hardening rate coefficient; the specific values ​​of the saturation hardening amount and the hardening rate coefficient can be obtained through material tensile testing. Then, each set of stamping process parameters is input into the model one by one; the blank holder force is applied through the blank holder ring load, the die clearance is achieved by adjusting the relative positions of the die and punch, the friction coefficient is defined on the contact surface between the sheet metal and the die, and the stamping speed is set by the punch movement speed.

[0034] Finally, the simulation parameters are set, including at least the time step and convergence criterion. After starting the simulation, the Dynaform finite element software will sequentially simulate three stages: blank holder pressing, punch downward forming, and punch upward unloading. After unloading, the springback calculation module of the Dynaform finite element software is used to calculate the difference between the actual profile height of the nickel-based alloy strip after stamping and the theoretical profile height on the design drawing, i.e., the springback amount. Figure 6 As shown, the simulation results are used as the initial springback amount for the corresponding stamping process parameter combination.

[0035] In addition, to ensure the reliability of the simulation results, calibration can be performed through experimental verification. Specifically, a combination of stamping process parameters is selected for actual stamping experiments, and the experimental springback is measured. This experimental springback is then compared with the simulated springback. If the relative error between the two is less than the preset error, the simulation results are considered reliable, and the current simulated springback can be used as the initial springback. If the relative error exceeds the preset error, the simulation model parameters, such as the friction coefficient and constitutive model coefficients, are adjusted, and the simulation is repeated until the error meets the requirements. Here, the preset error is, for example, 5%.

[0036] Furthermore, based on all combinations of stamping process parameters and their corresponding initial springback amounts, training and testing datasets are constructed, specifically including the following steps: The stamping process parameter combinations and their corresponding initial springback amounts are normalized to obtain a data sample set. The data sample set is divided into training dataset and test dataset according to a preset ratio.

[0037] Among the obtained combinations of stamping process parameters and their corresponding initial springback values, the dimensions and numerical ranges of different stamping process parameters differ significantly. For example, the blank holder force is in kN, the friction coefficient is dimensionless, and the initial springback value is in mm. If the original data is used directly to train the model, parameters with large numerical ranges will dominate the calculation of the model's loss function, causing the model to overemphasize these parameters and ignore parameters with small numerical ranges but crucial influence on springback, ultimately leading to reduced model prediction accuracy. Therefore, normalization is necessary to map all stamping process parameters to a unified numerical range, thereby eliminating the influence of differences in dimensions and ranges. Here, normalization can be achieved, for example, by deviation standardization, which linearly maps the original data to the [0, 1] interval. The normalized combinations of stamping process parameters and their corresponding initial springback values ​​are then used to generate a data sample set.

[0038] The training dataset is used for model training, and the test dataset is used to verify the model's generalization ability; the preset ratio is, for example, 8:2, that is, 80% of the samples in the data set are used for training and 20% of the samples are used for testing, to ensure the reliability of the model in practical applications.

[0039] S200. Using the training dataset as input data and the initial rebound amount corresponding to the training dataset as output data, construct a physical information-driven rebound prediction model.

[0040] Among them, such as Figure 3 As shown, the physical information-driven rebound prediction model is constructed, which includes the following steps: S201. Based on the support vector regression model, construct a data-driven model framework.

[0041] Here, nickel-based alloy stamping springback data exhibits characteristics of small sample size and strong nonlinearity. The small sample size refers to the limited number of samples in the initial data set due to simulation costs and experimental difficulty. The strong nonlinearity stems from the fact that, due to the material's high strength and low ductility (work hardening index n ≥ 0.65, elongation δ ≤ 12%), the mapping relationship between stamping process parameters and the corresponding springback amount is complex and nonlinear, making it difficult for traditional linear regression models to fit. In this method, the Support Vector Regression (SVR) model, through kernel function mapping technology, can transform low-dimensional nonlinear data into high-dimensional linearly separable data, accurately learning the nonlinear mapping relationship even in small sample scenarios. Furthermore, by introducing… - An insensitive loss function effectively suppresses the interference of noisy data on the model, adapting to potential simulation errors or measurement fluctuations in stamping springback data. The constructed data-driven model framework can learn the mapping relationship between stamping process parameter combinations and corresponding initial springback amounts.

[0042] S202. Based on the constitutive model of nickel-based alloys, a physical prior operator is constructed; the physical prior operator is used to characterize the elastic-plastic unloading and springback mechanism of the material.

[0043] Constitutive models for nickel-based alloys include, for example, the Voce-Chaboche nonlinear-isotropic hardening constitutive model. This model can simultaneously characterize the isotropic hardening (yield strength increases with increasing plastic strain) and the Bauschinger effect (yield strength decreases under reverse loading). The Voce-Chaboche nonlinear-isotropic hardening constitutive model is as follows: ; For stress, For elastic modulus, For total strain, For plastic strain, It is an integer sequence. The number of hardening terms. Let be the modulus parameter of the k-th hardening term. is the saturation parameter for the k-th hardening term.

[0044] The yield function is: ; in, It is a linear yield function under uniaxial stress. For stress, For the total return stress, The initial yield strength, It is isotropic hardening.

[0045] The formula for calculating isotropic hardening is: ; in, For isotropic hardening, This is the saturated hardening amount. The hardening rate coefficient, For equivalent plastic strain, This is the initial hardening value.

[0046] Plastic flow law: ; in, For plastic strain rate, As a plastic multiplier, For stress, This is the back stress.

[0047] Constitutive constraints are transformed into physical prior operators by constructing physical residual functions: ; in, For physical residuals, This represents the actual rebound amount. For physical a priori operators, This refers to the combination of input process parameters.

[0048] Based on the above constitutive model, a physical prior operator is constructed to characterize the elastic-plastic unloading and springback mechanism of materials, providing a mechanical basis for the subsequent fusion of data-driven frameworks.

[0049] S203. Embed the physical prior operator into the loss function of the data-driven model framework to obtain a physical information-driven rebound prediction model.

[0050] The loss function of the traditional SVR model only considers the data fitting error, and its expression is: ; For loss function, For SVR model parameters, For the first in the training dataset The actual rebound amount, To predict the rebound amount for the model, For the first in the training dataset Group stamping process parameter combination, The total number of samples in the training dataset. for - Insensitive loss function.

[0051] To address the shortcomings of traditional loss functions, a physical prior operator is introduced into the loss function to construct a total loss function, the mathematical expression of which is: ; For the total loss function, This is the loss function, and its value range is, for example, 0.1 to 1. For regularization parameters, For constitutive consistency constraints, For the first in the training dataset The actual springback amount corresponding to the combination of stamping process parameters. For the first in the training dataset The theoretical springback amount corresponding to a combination of stamping process parameters.

[0052] Based on the reconstructed total loss function, the model is trained using the training dataset. The total loss function is minimized through algorithms such as gradient descent and sequence minimization (SMO), and the parameters of the SVR model, regularization parameters, and physical prior operators are optimized. After training, the final physical information drives the rebound prediction model.

[0053] Furthermore, the physical prior operator serves as the theoretical computational framework for calculating elastically recoverable strain. Therefore, based on the constitutive model of nickel-based alloys, constructing the physical prior operator specifically includes the following steps: Based on the constitutive model of nickel-based alloys, the stress-strain response of nickel-based alloys during stamping and unloading processes is simulated. A theoretical calculation framework is constructed based on the elastic recovery strain generated by the nickel-based alloy during unloading, and the geometric mapping relationship between the nickel-based alloy and its geometry and stamping conditions.

[0054] It should be noted that by substituting the fitted parameters into the Voce-Chaboche nonlinear-isotropic hardening constitutive model and calculating the theoretical stress under different strains, and comparing it with the experimentally measured stress values, if the relative error is less than 3%, it indicates that the constitutive model parameters are calibrated and can be used for subsequent simulations; if the relative error exceeds 3%, the parameters need to be readjusted until the accuracy requirements are met.

[0055] Simulating the stamping of nickel-based alloys primarily involves determining the loading conditions based on the input stamping process parameters. The blank holder force determines the constraint pressure on the sheet metal, the die clearance determines the amount of sheet metal deformation, the friction coefficient affects the stress distribution at the contact surface between the sheet metal and the die, and the stamping speed affects the deformation rate. The stress-strain curve of the sheet metal during loading is calculated using a constitutive model until the maximum deformation state is reached, i.e., the punch reaches the bottom dead center. The peak stress (maximum stress on the sheet metal) and peak plastic strain (the amount of permanent plastic deformation generated in the sheet metal) at this point are recorded. These two parameters are the core basis for subsequent calculations of elastic recovery during unloading. The stress-strain response during the unloading process of the simulated nickel-based alloy mainly occurs when stamping is completed and the unloading stage begins (punch moves upward, blank holder force is released), as the stress on the sheet metal gradually decreases from the peak stress to 0. Based on the elastic unloading characteristics of the constitutive model, the material only undergoes elastic deformation recovery at this point (no new plastic deformation). It is necessary to calculate the change in elastic strain corresponding to the stress decreasing from the peak stress to any intermediate stress, laying the foundation for subsequent extraction of the elastic recovery strain during the full unloading process.

[0056] The elastic recovery strain during the unloading phase is the core input mechanical quantity of the physical prior operator. Essentially, it represents the amount of elastic deformation recovery of the sheet metal due to stress reduction during unloading. Specifically, according to the elastic unloading law of the constitutive model, the stress change and elastic recovery strain during unloading satisfy a linear relationship (because there is no plastic deformation during the unloading phase, the material is in a purely elastic state). However, the stiffness change caused by the plastic hardening of nickel-based alloys (i.e., a slight increase in the elastic modulus after hardening) needs to be considered. Therefore, the calculation formula is: ; in, For elastic recovery of strain, This represents the stress change during unloading. For elastic modulus, This represents the increase in stiffness caused by plastic hardening.

[0057] This formula can be used to calculate the total elastic recovery strain under full unloading conditions. This value can directly reflect the elastic recovery capability of the sheet at the micro level and is the key mechanical basis for subsequent calculation of macroscopic springback.

[0058] The geometric mapping relationship serves as a bridge connecting microscopic elastic recovery strain and macroscopic springback. Its core is establishing a quantitative conversion relationship between the two based on the geometry of the nickel-based alloy strip and the stamping boundary conditions. Specifically, the geometric mapping coefficient considers the sheet metal geometry, stamping die geometry, and stamping boundary conditions. Sheet metal geometry includes the length, width, and thickness of the nickel-based alloy strip; the smaller the thickness, the greater the macroscopic springback under the same elastic recovery strain. Stamping die geometry includes the punch radius and die depth; the smaller the radius, the more severe the sheet metal bending deformation, and the higher the sensitivity of the springback to elastic recovery strain. Stamping boundary conditions include the blank holder force constraint range and punch movement path; the stronger the constraint, the more uniform the sheet metal deformation, and the more stable the geometric mapping relationship. Therefore, the formula for calculating the geometric mapping coefficient is: ; in, For geometric mapping coefficients, This represents the macroscopic rebound amount. This represents the elastic strain recovery.

[0059] Multiplying the elastic recovery strain by the geometric mapping coefficient yields the final theoretical springback output of the physical prior operator, with the following formula: ; in, Theoretical rebound amount, For geometric mapping coefficients, This represents the elastic strain recovery.

[0060] During the unloading phase (i.e., when springback occurs), deformation enters the elastic dominant region. At this time, the formula for calculating the elastic strain recovery is: ; in, This is the elastic strain recovery amount. This represents the stress change during unloading. It is the elastic modulus.

[0061] After the physical information-driven rebound prediction model is trained, its training accuracy needs to be verified, such as... Figure 7 As shown, the deviation between the model's predicted rebound amount and the actual rebound amount in the training set is small, and the percentage error is controlled at a low level, proving that the current model fits the training data well.

[0062] S300: Using a physical information-driven springback prediction model as the objective function and the desired springback amount as the optimization objective, the adaptive cuckoo search algorithm searches for the predicted springback amount with the smallest difference from the desired springback amount in the physical information-driven springback prediction model as the optimal springback amount, and the stamping process parameter combination corresponding to the optimal springback amount is taken as the optimal process parameter combination.

[0063] The objective function is: ; in, Let be the objective function. Scalar rebound amount This is a secondary penalty item. This is a physical constraint penalty term. As a robust penalty term for uncertainty, , , , These are the weighting coefficients, where + + + =1.

[0064] Here, the expected springback amount refers to the allowable springback amount of the stamped parts required in actual production.

[0065] The expected rebound amount is obtained according to the following steps: Obtain the theoretical profile height of the nickel-based alloy strip on the design drawings; Under ideal conditions with no springback, the contour height of the part after stamping of nickel-based alloy strip is measured to obtain the theoretical forming height. The difference between the theoretical profile height and the theoretical forming height is calculated to obtain the expected springback amount.

[0066] Here, theoretical profile height refers to the final target height of a nickel-based alloy strip stamping part, explicitly marked in the design drawings. This is the ideal dimension that meets assembly accuracy and service performance requirements. Taking a typical U-shaped or V-shaped strip stamping part as an example, the theoretical profile height is usually defined as the vertical distance from a specific reference surface (such as the bottom surface of the die) to the top profile of the part after forming. For example, if the drawing indicates 10mm ± 0.02mm, then 10mm is the theoretical profile height. The theoretical profile height can be obtained through digital analysis or direct reading of the design drawings. If it is a paper drawing, high-precision measuring tools (such as vernier calipers or coordinate measuring machines) are needed to verify the dimensions marked on the drawing. If it is a digital drawing (such as a CAD file), the precise value of the theoretical profile height can be directly extracted from the dimensioning module of the drawing.

[0067] The ideal state of no springback refers to the scenario where, after stamping, the nickel-based alloy strip does not undergo any elastic recovery deformation during unloading (i.e., the plastic deformation is completely fixed, with no springback). In actual production, due to the elastic properties of the material, this state cannot be directly achieved, but the corresponding theoretical forming height can be indirectly obtained through finite element simulation or theoretical calculation.

[0068] In the simulation model under ideal conditions without springback, the measurement benchmark for the theoretical forming height is completely consistent with the theoretical profile height, such as using the bottom surface of the die as the benchmark to ensure comparability. For example, in the simulation of U-shaped strip stamping, the theoretical forming height is the vertical distance from the bottom surface of the die to the top of the U-shape under springback-free conditions. If the simulation calculates this distance to be 9.98mm, then 9.98mm is the theoretical forming height. Furthermore, when calculating the theoretical forming height, the corresponding combination of process parameters must be clearly defined, usually the center value of the initially set process parameter range, to ensure that the subsequent calculation of the expected springback amount matches the actual process scenario.

[0069] The difference between the theoretical profile height and the theoretical forming height is taken as the expected springback amount. Since springback cannot be completely eliminated in actual stamping, the expected springback amount is not zero springback, but rather the springback amount that makes the actual size after springback exactly equal to the theoretical profile height.

[0070] Furthermore, such as Figure 4 As shown, the adaptive cuckoo search algorithm is used to search for the predicted rebound amount with the smallest difference from the expected rebound amount in the physical information-driven rebound prediction model as the optimal rebound amount. The specific steps include: S301. Initialize the cuckoo population and randomly generate a set of stamping process parameters as the initial nest location.

[0071] In the adaptive cuckoo search algorithm, the cuckoo population corresponds to a set of stamping process parameter combinations to be optimized, and the nest location corresponds to a single stamping process parameter combination. For example, if the population size is set to 50, 50 nest locations are initially generated, and each nest location is an independent set of stamping process parameter combinations, representing a potential candidate solution for process optimization.

[0072] The process involves obtaining the preset process parameter range corresponding to each combination of stamping process parameters, and then randomly selecting values ​​within each preset process parameter range using a random number generation tool to form the initial nest positions. Here, the random number generation tool could be, for example, the `rand` function in MATLAB.

[0073] S302. Based on the rebound prediction model driven by physical information, calculate the rebound error between the predicted rebound amount and the expected rebound amount for each nest location.

[0074] Each initial nest location (stamping process parameter combination) is preprocessed using the aforementioned normalization method to ensure that the input format is consistent with the training input of the physical information driven springback prediction model (A-CSO-PISVM). Subsequently, the normalized stamping process parameter combination is input into the physical information driven springback prediction model, and the physical information driven springback prediction model outputs the corresponding predicted springback amount, which is then converted into the actual physical unit springback amount through inverse normalization.

[0075] Springback error refers to the absolute difference between the predicted springback amount and the expected springback amount corresponding to each nest position. It is used to reflect the degree of deviation of the candidate stamping process parameter combination from the expected springback amount.

[0076] S303. Based on the rebound error, calculate the fitness value of each nest in the current generation population and identify the current optimal nest.

[0077] The formula for calculating the fitness value of each nest is as follows: ; in, For the first The fitness value of each nest. For the first The rebound error of each nest, It is a minimum value, for example, 10⁻⁸.

[0078] The fitness values ​​of all nests in the current generation are sorted from largest to smallest. The nest with the largest fitness value is determined as the current optimal nest, and its corresponding predicted rebound is the predicted rebound with the smallest difference from the expected rebound in the current iteration. The corresponding combination of process parameters is the current optimal candidate solution. At the same time, the fitness value and rebound error of the current optimal nest are recorded as a benchmark for subsequent iterations.

[0079] S304. The Levy flight step size is adjusted based on the rebound error, and the position of all nests is updated using an adaptive Levy flight mechanism.

[0080] The formula for calculating the Lévy flight step size based on the gradient adjustment of rebound error is as follows: ; in, For the adjusted new step size, The step size before adjustment. This is the adjustment coefficient, with a value range of 0.5 to 1.0, representing the adjustment range of the balance step size. For the first The rebound error of each nest, This represents the maximum rebound error among all nests in the previous generation population.

[0081] When the bounce error is large, the step size is automatically increased to expand the search range and quickly move closer to the region with smaller errors; when the bounce error is small, the step size is automatically decreased to focus on a fine local search and avoid skipping the optimal solution.

[0082] Based on the adjusted Levy flight step size and the random walk characteristics of Levy flight, the position of each nest (combination of stamping process parameters) is updated using the following formula: ; in, For the first The updated location of the nest. For the first The location of the nest before the update. For the adjusted new step size, For random numbers that follow a Lévy distribution, We set it to 1.5 to ensure the randomness and traversal of the search.

[0083] After the update, the feasibility of the process for the new location needs to be verified. If a parameter exceeds the preset range (e.g., the blank holder force exceeds 300kN), it should be cut off to the boundary of the range (e.g., 300kN) to ensure that the new nest location is still a feasible solution.

[0084] like Figure 8 As shown, the A-CSO-PISVM algorithm reaches a stable value after approximately 30 iterations, and drops below 0.035 after 50 iterations, demonstrating that the adaptive step size mechanism effectively improves convergence speed and stability; Figure 9 As shown, the fitness value of SVM decreases slowly with the increase of the number of iterations, and is always higher than that of A-CSO-PISVM. Therefore, under the same number of iterations, the fitness value of A-CSO-PISVM is significantly lower than that of traditional SVM, and the convergence speed is faster, proving that the optimization efficiency and stability of this method are better than those of traditional SVM algorithm.

[0085] S305. Obtain the preset adaptive discovery probability, and based on the preset adaptive discovery probability, randomly eliminate some nests and generate the same number of new nests; the adaptive discovery probability is negatively correlated with the dispersion of the fitness value of the current generation population.

[0086] The adaptive discovery probability refers to the proportion of nests discovered and eliminated by other cuckoos in the adaptive cuckoo search algorithm. The default formula for calculating the adaptive discovery probability is: ; in, To preset the adaptive discovery probability, This represents the initial discovery probability, with a value ranging from 0.2 to 0.3. This is a coefficient, ranging from 0.6 to 0.8, used to adjust the degree of dispersion. Influence weight, To form energy density, This represents the maximum forming energy density.

[0087] Based on the calculated preset adaptive discovery probability, nests are randomly selected from the current generation population for elimination; then, according to the initial generation rule in step S301, the same number of new nests are randomly generated and added to the population to maintain the population size. This avoids the accumulation of invalid solutions and ensures population diversity, providing new search directions for subsequent iterations.

[0088] An improved adaptive cuckoo search algorithm is used to optimize the objective function, dynamically adjusting the step size and adaptive discovery probability: ; in, To dynamically adjust the step size, As the base step size, The optimal rebound amount for generation t. This represents the initial optimal rebound amount.

[0089] S306. If the dispersion of fitness values ​​of all nests in the current generation population is greater than or equal to the preset dispersion, then recalculate the fitness value of each nest and continue iteratively searching until the dispersion of fitness values ​​of all nests in the current generation population is less than the preset dispersion. Then, the stamping process parameter combination corresponding to the current optimal nest is taken as the optimal process parameter combination.

[0090] The preset dispersion level can be set to 5% to 10% of the initial population fitness standard deviation. For example, if the initial standard deviation of the current generation population fitness value is 500, then the preset dispersion level is 25 to 50.

[0091] If the dispersion of fitness values ​​of all nests in the current generation population is greater than or equal to the preset dispersion, it indicates that there are still significant differences in the current population. It is necessary to return to step S302, recalculate the springback error and fitness value of the new nest, and repeat the iteration process of S302 to S305. If the dispersion of fitness values ​​of all nests in the current generation population is less than the preset dispersion, it indicates that the quality of all candidate solutions in the population is highly similar, and it is difficult to improve the optimization effect by continuing iteration. This means that it has converged to the global optimum or near-optimal region. The search is stopped, and the stamping process parameter combination corresponding to the best nest in the current generation population is taken as the optimal process parameter combination, and its corresponding predicted springback amount is taken as the optimal springback amount.

[0092] The optimal rebound amount is: ; in, For optimal rebound, The objective function is denoted as .

[0093] The final optimal combination of process parameters can be directly converted into control commands for the stamping equipment, such as blank holder force setting value and die clearance adjustment amount, to guide the actual stamping production of nickel-based alloy strips, ensuring that the springback of the stamped parts is close to the expected value and meets the high-precision dimensional requirements.

[0094] like Figure 2 As shown, this method also includes the following steps: S400: Input the optimal combination of process parameters into the stamping equipment and execute it, then measure the actual springback amount.

[0095] The optimal combination of process parameters determined in step S300 is converted into control commands recognizable by the stamping equipment. For example, the blank holder force parameter is converted into a hydraulic system pressure command, the die clearance is converted into a displacement command for the die adjustment mechanism, and the stamping speed is converted into a speed command for the punch drive motor. These commands are then sent to the stamping equipment via a PLC (Programmable Logic Controller) to ensure that the equipment executes the stamping action precisely according to the optimal parameters. During the execution of the stamping action, "command smoothing" and safety checks must be performed simultaneously. Command smoothing is used to avoid equipment shocks caused by sudden parameter changes, such as a sudden increase in blank holder force causing die damage. Safety checks are used to verify the compliance of parameter ranges, such as preventing excessive extrusion and cracking of the sheet metal due to an excessively small die clearance, ensuring the stability and safety of the production process, and ensuring that the optimal process parameters can be effectively implemented under actual production conditions.

[0096] The measuring tools can use laser displacement sensors or online contour scanners as the core measuring devices. Laser displacement sensors can achieve non-contact, high-precision measurement (accuracy down to the micrometer level), avoiding damage to the surface of the stamped part caused by contact measurement; online contour scanners can acquire the overall contour data of the stamped part, and accurately calculate the actual springback by comparing it with the theoretical contour of the design drawings.

[0097] S500: Based on the difference between the actual rebound amount and the optimal rebound amount, determine whether to update the physical information-driven rebound prediction model.

[0098] The preset difference is usually set to a value slightly higher than the initial test error of the model, such as 0.0005~0.001. This avoids frequent model updates due to small random errors (such as measurement noise or small equipment fluctuations) and can also capture the accuracy decay of the model due to changes in production conditions (such as changes in friction coefficient caused by mold wear or fluctuations in constitutive parameters caused by batch differences in materials).

[0099] The formula for calculating the difference between the actual rebound amount and the optimal rebound amount is: ; in, This is the difference between the actual rebound amount and the optimal rebound amount. This represents the actual rebound amount. This represents the optimal rebound amount.

[0100] If the difference between the actual rebound amount and the optimal rebound amount is less than or equal to the preset difference, it means that the current optimal rebound amount is highly consistent with the actual production results, and the model can still accurately adapt to the current production scenario without needing to be updated. If the difference between the actual rebound amount and the optimal rebound amount is greater than the preset difference, it means that there is a significant deviation between the model prediction and the actual situation. This may be because the model does not cover new production variables (such as mold aging) or the initial training data does not include extreme working conditions. The model needs to be updated through subsequent steps to restore accuracy.

[0101] S600. If the difference between the actual springback amount and the optimal springback amount is greater than the preset difference, the actual springback amount and the optimal process parameter combination will be used as new sample data and added to the training dataset.

[0102] Referring to the data processing method in step S100, the new sample data is first normalized to eliminate the difference in units, and then added to the training dataset.

[0103] S700: Retrain the physical information-driven rebound prediction model using the training dataset after adding data.

[0104] By retraining the physical information-driven rebound prediction model using the training dataset with added data, the model's accuracy is restored and improved, ensuring that the model is adapted to production needs in the long term.

[0105] Table 1 shows a comparison of the prediction accuracy between A-CSO-PISVM and SVM. The R values ​​in Table 1... 2 The coefficient of determination (COP) quantifies the goodness of fit between the rebound prediction model output and the actual rebound amount; the mean absolute error (MAE) quantifies the average deviation between the model's predicted and actual rebound amounts. The A-CSO-PISVM model training set is R. 2 =0.9865, Test set R 2 =0.9623, significantly higher than that of traditional SVM (training set R). 2= 0.9012, Test Set R 2= The A-CSO-PISVM model has a higher MAE (0.8934) value, demonstrating its stronger explanatory power for the springback behavior of Inconel 718 alloy. The training set MAE of the A-CSO-PISVM model is 0.000246, and the test set MAE is 0.000432, which is much lower than that of the traditional SVM (training set MAE = 0.000614, test set MAE = 0.000853), proving that its prediction bias is smaller.

[0106] Table 1. Comparison of prediction accuracy between A-CSO-PISVM and SVM

[0107] This application obtains multiple combinations of stamping process parameters and their corresponding initial springback values. Based on all these combinations, training and testing datasets are constructed to ensure comprehensive data coverage and avoid prediction bias due to excessive data. Furthermore, the constructed physical information-driven springback prediction model uses the training dataset as input and the corresponding initial springback value as output, integrating physical mechanisms into the model construction process. This overcomes the limitations of traditional pure data-driven models, which lack physical consistency and have poor extrapolation capabilities, effectively improving the model's ability to predict complex stamping springback behavior in nickel-based alloys. To improve the accuracy and reliability of predictions, an adaptive cuckoo search algorithm is further employed. Using a physical information-driven springback prediction model as the objective function and the desired springback amount as the optimization objective, the algorithm searches for the optimal springback amount and the corresponding optimal combination of process parameters. Compared to traditional optimization algorithms, this application can more efficiently find the optimal solution in a complex parameter space, effectively improving optimization efficiency and stability, avoiding getting trapped in local optima. The final optimal combination of process parameters can guide actual stamping production, thereby improving the dimensional accuracy of nickel-based alloy strip stampings and reducing assembly quality problems and service performance risks caused by springback.

[0108] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for predicting the springback of nickel-based alloy strips during stamping, characterized in that, Includes the following steps: The initial springback amount corresponding to multiple combinations of stamping process parameters during the stamping process of nickel-based alloy strip is obtained, and a training dataset and a test dataset are constructed based on all the combinations of stamping process parameters and their corresponding initial springback amounts; the combinations of stamping process parameters include at least blank holder force, die-punch clearance, friction coefficient and stamping speed; Using the training dataset as input data and the initial rebound amount corresponding to the training dataset as output data, a physical information-driven rebound prediction model is constructed. Using the physical information-driven springback prediction model as the objective function and the desired springback amount as the optimization objective, the adaptive cuckoo search algorithm is used to search for the predicted springback amount with the smallest difference from the desired springback amount in the physical information-driven springback prediction model as the optimal springback amount, and the stamping process parameter combination corresponding to the optimal springback amount is taken as the optimal process parameter combination.

2. The method for predicting springback during stamping of nickel-based alloy strips according to claim 1, characterized in that, The method further includes the following steps: The optimal combination of process parameters is input into the stamping equipment and executed, and the actual springback is measured. Based on the difference between the actual rebound amount and the optimal rebound amount, determine whether to update the physical information-driven rebound prediction model; If the difference between the actual rebound amount and the optimal rebound amount is greater than a preset difference, then the actual rebound amount and the optimal process parameters are combined as new sample data and added to the training dataset. The physical information-driven rebound prediction model is retrained using the training dataset with added data.

3. The method for predicting springback during stamping of nickel-based alloy strips according to claim 1, characterized in that, Constructing a physical information-driven rebound prediction model includes the following steps: A data-driven model framework is constructed based on the support vector regression model. Based on the constitutive model of nickel-based alloys, physical prior operators are constructed; these physical prior operators are used to characterize the elastic-plastic unloading and springback mechanism of the material. By embedding the physical prior operator into the loss function of the data-driven model framework, a physical information-driven rebound prediction model is obtained.

4. The method for predicting springback during stamping of nickel-based alloy strips according to claim 3, characterized in that, The physical prior operators are the theoretical computational framework for calculating elastically recoverable strain; Based on the constitutive model of nickel-based alloys, a physical prior operator is constructed, which includes the following steps: Based on the constitutive model of nickel-based alloys, the stress-strain response of nickel-based alloys during stamping and unloading processes is simulated. The theoretical calculation framework is constructed based on the elastic recovery strain generated by the nickel-based alloy during unloading, and the geometric mapping relationship between the nickel-based alloy and its geometry and stamping conditions.

5. The method for predicting springback during stamping of nickel-based alloy strips according to claim 1, characterized in that, The optimal rebound amount is determined by searching the rebound prediction model driven by the physical information using an adaptive cuckoo search algorithm, which minimizes the difference between the predicted rebound amount and the expected rebound amount. This process includes the following steps: Initialize the cuckoo population and randomly generate a set of stamping process parameters as the initial nest locations; Based on the rebound prediction model driven by the physical information, the rebound error between the predicted rebound amount and the expected rebound amount corresponding to each nest location is calculated. Based on the rebound error, calculate the fitness value of each nest in the current generation population and identify the current optimal nest; Based on the rebound error, the Levy flight step size is adjusted by gradient adjustment, and the position of all the nests is updated by an adaptive Levy flight mechanism. A preset adaptive discovery probability is obtained, and based on the preset adaptive discovery probability, some nests are randomly eliminated and the same number of new nests are generated; the adaptive discovery probability is negatively correlated with the dispersion of the fitness value of the current generation population. If the dispersion of fitness values ​​of all nests in the current generation population is greater than or equal to a preset dispersion, then the fitness value of each nest is recalculated and the iterative search continues until the dispersion of fitness values ​​of all nests in the current generation population is less than the preset dispersion. Then, the stamping process parameter combination corresponding to the current optimal nest is taken as the optimal process parameter combination.

6. The method for predicting springback during stamping of nickel-based alloy strips according to claim 1, characterized in that, The desired rebound amount is obtained by following these steps: Obtain the theoretical profile height of the nickel-based alloy strip on the design drawings; Under ideal conditions with no springback, the contour height of the part after stamping of nickel-based alloy strip is measured to obtain the theoretical forming height. The difference between the theoretical profile height and the theoretical forming height is calculated to obtain the expected springback amount.

7. The method for predicting springback during stamping of nickel-based alloy strips according to claim 1, characterized in that, The initial springback of nickel-based alloy strips corresponding to multiple combinations of stamping process parameters during the stamping process includes the following steps: The Latin hypercube experimental design method is used to generate a combination of stamping process parameters with spatially uniform distribution characteristics within a preset process parameter range; Based on the stamping process parameter combination, the simulated springback amount corresponding to each process parameter combination is calculated by finite element simulation, and the simulated springback amount is used as the initial springback amount of the corresponding process parameter combination.

8. The method for predicting springback during stamping of nickel-based alloy strips according to claim 1, characterized in that, Based on all the aforementioned stamping process parameter combinations and their corresponding initial springback amounts, a training dataset and a test dataset are constructed, specifically including the following steps: The combination of stamping process parameters and their corresponding initial springback are normalized to obtain a data sample set; The data sample set is divided into a training dataset and a test dataset according to a preset ratio.

Images