Transmission shaft warm forging parameter optimization method and system based on agent model

Abstract

The present application belongs to the technical field of computer aided engineering and manufacturing parameter optimization, and specifically discloses a transmission shaft warm forging parameter optimization method and system based on a proxy model, which comprises the following steps: obtaining an initial sample set containing physical process parameters such as a blank holding stroke and a forming tonnage, extracting a flange volume filling rate and a maximum principal stress of a material return device through finite element simulation; constructing a Gaussian process regression proxy model according to the above parameters, and supplementing samples adaptively until the error converges by using an expected increment criterion; subsequently, taking the maximum filling rate and the minimum stress as targets, applying a physical constraint that the material return force is greater than the demolding friction force, and outputting a non-dominated parameter solution set by using a multi-objective optimization algorithm; finally, screening parameter combinations that meet the equipment capacity, and converting them into numerical control machining and forging control instructions to execute production. The present application effectively reduces the simulation time consumption, and establishes a data mapping link from virtual optimization to physical manufacturing.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided engineering and manufacturing parameter optimization technology, and relates to a method and system for optimizing transmission shaft warm forging parameters based on a surrogate model. Background Technology

[0002] Drive shaft flanges are generally formed using warm forging. The integrity of the undercut structure and the stress state of the ejector are key factors determining the forging yield and die life. Process parameters such as the upper punch blank holder stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and the set ratio of the dispersion ejector force are intercoupled and jointly affect the metal flow behavior and die stress distribution, posing challenges to parameter setting.

[0003] Currently, the industry mainly relies on engineers' experience to repeatedly conduct finite element simulations or on-site trial moldings to determine these process parameters, gradually adjusting parameter combinations to approximate the expected forming effect. Some companies also use experimental design-based methods, such as orthogonal experiments or response surface methodology, to establish surrogate models using a small number of simulation samples to assist in process optimization.

[0004] Repeated trial molding and numerous simulation calculations consume significant time and computational resources. A single 3D finite element simulation often takes several hours, resulting in long cumulative computation time and high computational resource consumption. While orthogonal experiments and response surface methodology reduce the sample size, they primarily fit low-order polynomial surrogate models, which struggle to accurately describe the strongly nonlinear physical mappings in the warm forging process, leading to insufficient prediction accuracy and significant deviations between optimization results and actual operating conditions. Furthermore, the existing process lacks a mechanism to automatically convert the optimized geometric and force parameters into CNC machining codes and forging press control instructions. The transition from optimization to production execution still relies on manual conversion, further delaying the design-to-manufacturing delivery cycle. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art and to achieve the above objectives, the present invention proposes the following technical solution: a method for optimizing transmission shaft warm forging parameters based on a proxy model, comprising: S1, obtaining the combination of physical process parameters of the warm forging process and constructing an initial parameter sample set, wherein the combination of physical process parameters includes the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter and dispersion top force setting ratio.

[0006] S2. Input the initial parameter sample set into the three-dimensional finite element simulation engine for simulation, extract the flange volume filling rate and the maximum principal stress of the ejector, and form a training sample library.

[0007] S3. Using the training sample library, with the combination of physical process parameters as input and the flange volume filling rate and the maximum principal stress of the ejector as output, a Gaussian process regression surrogate model is fitted and constructed.

[0008] S4. On the Gaussian process regression surrogate model, obtain the engineering tolerance threshold determined according to the product processing accuracy requirements, use the expected increment criterion to determine the candidate parameter coordinates of the points to be added, perform finite element simulation only on the candidate parameter coordinates, obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector, and then add them to the training sample library to update the Gaussian process regression surrogate model. Repeat the process until the prediction error of the surrogate model is lower than the engineering tolerance threshold, and obtain the converged surrogate model.

[0009] S5. Obtain the demolding friction force of the forging during the demolding process. On the convergent surrogate model, with the dual objectives of maximizing the flange volume filling rate and minimizing the maximum principal stress of the ejector, apply the physical constraint that the total ejection force is greater than the demolding friction force. Use a multi-objective optimization algorithm to find the optimal solution and output the multi-objective non-dominated process parameter solution set.

[0010] S6. Select parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, convert the unloader opening diameter parameters into CNC machining instructions, convert the pressing stroke and forming tonnage into forging equipment control instructions, and execute physical temperature forging production.

[0011] The second aspect of the present invention provides a transmission shaft warm forging parameter optimization system based on a proxy model, comprising: a parameter sampling module for acquiring a combination of physical process parameters for the warm forging process and constructing an initial parameter sample set, wherein the combination of physical process parameters includes the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top force setting ratio.

[0012] The finite element simulation module is used to input the initial parameter sample set into the three-dimensional finite element simulation engine for simulation, extract the flange volume filling rate and the maximum principal stress of the ejector, and form a training sample library.

[0013] The surrogate model construction module is used to fit and construct a Gaussian process regression surrogate model using a training sample library, with the combination of physical process parameters as input and the flange volume filling rate and the maximum principal stress of the ejector as output.

[0014] The adaptive iteration module is used to obtain the engineering tolerance threshold determined according to the product processing accuracy requirements on the Gaussian process regression surrogate model, determine the candidate parameter coordinates of the points to be added using the expected increment criterion, perform finite element simulation only on the candidate parameter coordinates, obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector, and then add them to the training sample library to update the Gaussian process regression surrogate model. This process is repeated until the prediction error of the surrogate model is lower than the engineering tolerance threshold, and a converged surrogate model is obtained.

[0015] The multi-objective optimization module is used to obtain the demolding friction force of the forging during the demolding process. On the convergent surrogate model, the dual objectives are to maximize the flange volume filling rate and minimize the maximum principal stress of the ejector. The physical constraint that the total ejection force is greater than the demolding friction force is applied. The multi-objective optimization algorithm is used for optimization and outputs the multi-objective non-dominated process parameter solution set.

[0016] The conversion module is used to select parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, convert the ejector hole diameter parameters into CNC machining instructions, and convert the blank holder stroke and forming tonnage into forging equipment control instructions, which are then output to the forging equipment for physical temperature forging production.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention constructs an initial sample set through a multidimensional hierarchical sampling algorithm and constructs a composite point-adding function in combination with the expected increment criterion, guiding the Gaussian process regression surrogate model to perform adaptive point-adding updates in parameter regions with high uncertainty and potential for improvement. This mechanism reduces the number of times the computationally intensive three-dimensional finite element simulation engine is called while meeting the engineering tolerance threshold accuracy, effectively shortening the optimization cycle of the warm forging process.

[0018] (2) Based on a convergent Gaussian process regression surrogate model, this invention performs multi-objective optimization with the dual objectives of maximizing the flange volume filling rate and minimizing the maximum principal stress of the ejector. Furthermore, it establishes an empirical regression relationship for the calculated friction force during demolding based on finite element simulation results, and then applies a physical constraint that the total effective ejection force is greater than the calculated friction force during demolding. This strategy eliminates non-demolding process conditions during the algorithm optimization stage, achieving an effective balance between the forging fullness and the fatigue life of the die.

[0019] (3) This invention filters the solution set of non-dominated process parameters based on equipment capability constraints, and transforms the selected geometric parameters of the ejector hole diameter into machining instructions for the CNC machine tool for hole machining, and transforms the upper punch pressing stroke and forming process tonnage into displacement and force closed-loop control instructions for the forging press. This step establishes a direct data mapping link from virtual multi-objective optimization to physical production in the workshop, reducing the dependence of traditional warm forging production on manual experience trial molding.

[0020] (4) The present invention uses a multi-objective optimization algorithm to search for a multi-objective non-dominated process parameter solution set on a convergent surrogate model, replacing the traditional single-point trial calculation optimization mode. It provides process engineers with multiple sets of quantitative compromise schemes covering different processing accuracy requirements and mold stress limitations, thereby enhancing the objective basis and feasibility of the transmission shaft warm forging process design. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the implementation steps of the method of the present invention.

[0023] Figure 2 This is a convergence curve of the adaptive point-addition prediction error of the proxy model of this invention.

[0024] Figure 3 The Pareto front distribution diagram for the multi-objective optimization of process parameters in this invention.

[0025] Figure 4 This is a schematic diagram of the system module connections of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Please see Figure 1 As shown, the method for optimizing transmission shaft warm forging parameters based on the proxy model proposed in this invention includes: S1, obtaining the combination of physical process parameters for the warm forging process and constructing an initial parameter sample set. The combination of physical process parameters includes the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top force setting ratio.

[0028] In a preferred embodiment, the physical process parameter combination of the warm forging process is obtained to construct an initial parameter sample set, including: obtaining the possible value boundaries of the upper punch blank holder stroke, forming process tonnage, and lower punch intermediate ejector hole diameter, and obtaining the adjustment range of the dispersion ejector force setting ratio; using a multidimensional hierarchical sampling algorithm to generate sparse physical process parameter sample points within the possible value boundaries; and combining the physical process parameter sample points with the adjustment range of the dispersion ejector force setting ratio to form a physical process parameter combination, which serves as the initial parameter sample set.

[0029] Specifically, warm forging refers to the technique of heating metal billets to a temperature range below the recrystallization temperature for plastic forming. This step requires obtaining the combination of physical process parameters directly related to the flange undercut forming and pressing process under this process, and constructing an initial parameter sample set. The combination of physical process parameters includes four characteristic parameters: upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion ejector force setting ratio.

[0030] The upper punch blank-pressing stroke is defined as the linear displacement of the upper punch during the blank-pressing stage of warm forging, moving along the die closing direction. This parameter determines the flow space and resistance of the metal being squeezed into the cavity at the flange edge. Its lower limit is the minimum stroke required for the upper punch to contact and hold pressure with the lower die plane when the die is closed, while the upper limit is the limit stroke that, after deducting a safety margin from the total punch stroke, still ensures the metal does not fold. The forming process tonnage is defined as the total forming force exerted on the blank by the forging equipment. Its possible boundaries are constrained by the equipment's rated tonnage and the die strength curve. The lower limit is the calculated minimum flow stress required for the blank to undergo plastic deformation at that forging temperature, and the upper limit is 90% of the equipment's maximum allowable tonnage. The diameter of the ejector hole in the lower punch is defined as the diameter of the through hole at the center of the lower punch to accommodate the ejector pins. Its possible values ​​are constrained by the minimum cross-sectional area at the root of the ejector to ensure structural bending strength. The lower limit is determined by the limit hole radius calculated from the yield strength of the ejector material at forging temperature and the ejector force. The upper limit is limited by the outer diameter of the lower punch and the safety value of the die wall thickness. Specific settings are determined based on statistical data of historical warm forging die failures and die design specifications. The distributed ejector force setting ratio is defined as the weight of multiple ejector pins in the total ejector force, expressed as a dimensionless ratio. The adjustment range of this ratio is determined by the ejector geometry and demolding synchronization requirements, typically between 0.10 and 0.50. When obtaining the boundaries and ranges of the above parameters, corresponding numerical ranges need to be extracted from the forging equipment technical manual, die design drawings, and historical production databases of similar forgings.

[0031] After obtaining the boundaries and ranges of each parameter, a multidimensional stratified sampling algorithm is used to generate sparse physical process parameter sample points within the possible value boundaries. The multidimensional stratified sampling algorithm is designed to fill a three-dimensional continuous parameter space comprised of the upper punch blank holder stroke, forming process tonnage, and the lower punch intermediate ejector aperture. Let the value ranges of each parameter in the three-dimensional parameter space be as follows: , , The preset number of sample points to be generated is The algorithm divides each dimension of the parameter interval into equal probability sections. Each sample point is divided into three non-overlapping, equal-length subintervals. For each sample point, independent numerical values ​​are randomly generated within each subinterval in each dimension. Then, by independently performing the above operation on each dimension and randomly combining the values ​​across dimensions, the specific coordinates of the sample point in the parameter space are obtained. This process ensures that the generated 3D sample points have uniform spatial filling and projection in the parameter space. The set of data is called the physical process parameter sample points, and the sparsity of the sample points is determined by... control, The value of is determined based on the minimum sample size required for subsequent surrogate model fitting, and is generally taken as 10 to 20 times the parameter dimension. In this embodiment, the preliminary study based on 30 sets of numerical experiments will... Set to 30.

[0032] After obtaining sample points of physical process parameters, these sample points are combined with the adjustment range of the dispersion top force setting ratio. The adjustment range of the dispersion top force setting ratio is a dimensionless proportional interval, denoted as . Discretize the values ​​using a preset step size to obtain M discrete proportional levels. Group of physical process parameter sample points and Each dispersed top material force is set in a proportional level and then combined with all factors to form the final product. A set of four-dimensional physical process parameters, each set consisting of an upper punch blanking stroke value, a forming process tonnage value, a lower punch intermediate ejector orifice diameter value, and a dispersion ejector force setting ratio value. The set of combined parameters constitutes the initial parameter sample set. This construction method combines continuous parameter sampling with discrete proportional traversal, covering the influence of dispersed top force ratios on the stress distribution of the ejector without significantly increasing subsequent simulation overhead.

[0033] For example, in the warm forging process of an automotive transmission flange, the possible values ​​for the upper punch blanking stroke are 8mm to 22mm, the possible values ​​for the forming process tonnage are 600kN to 1500kN, and the possible values ​​for the lower punch intermediate ejector hole diameter are 18mm to 45mm, with a preset sample number N=10. A multidimensional stratified sampling algorithm is used to divide each of the above parameters into 10 equal-length sub-intervals. Random values ​​are independently generated within each dimension and combined in a shuffled order between dimensions, thus generating 10 sets of physical process parameter sample points consisting of blanking stroke, forming tonnage, and hole diameter. For example, the first physical process parameter sample point generated in this way is 11.262mm, 1031.1kN, and 38.439mm. The adjustment range of the dispersed ejector force setting ratio is determined based on the uniform distribution structure of the three ejector pins of the mold ejector. Four scale values ​​were obtained by discretizing with a preset step size: 0.15, 0.25, 0.35, and 0.45. The generated 10 sets of physical process parameter sample points were then combined with these four scale values ​​using a full factorial method, ultimately generating 10 × 4 = 40 sets of physical process parameter combinations, which served as the initial parameter sample set. This sample set covered the continuous parameter space of the blank holder stroke, tonnage, and aperture, and traversed typical values ​​of the dispersed top material force ratio, providing spatially representative and engineering-coverage input data for subsequent finite element simulations.

[0034] S2. Input the initial parameter sample set into the three-dimensional finite element simulation engine for simulation, extract the flange volume filling rate and the maximum principal stress of the ejector, and form a training sample library.

[0035] In a preferred embodiment, an initial parameter sample set is input into a three-dimensional finite element simulation engine for simulation. The flange volume filling rate and the maximum principal stress of the ejector are extracted to form a training sample library. This includes: for each combination of physical process parameters in the initial parameter sample set, obtaining the metal rheological constitutive equation at the corresponding forging temperature and the friction coefficient of the mold contact interface; setting the metal rheological constitutive equation and the mold friction coefficient in the three-dimensional finite element simulation engine, and running the finite element calculation of the undercut flange pressing process; extracting the volume filling rate data of the flange edge nodes from the calculation results, and extracting the peak value of the maximum principal stress distribution on the ejector structure; and storing the physical process parameter combination with its corresponding flange volume filling rate and the maximum principal stress of the ejector to form the training sample library.

[0036] Specifically, following the initial parameter sample set constructed in step S1, each data set consists of four physical process parameters: upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top force setting ratio. For each of these parameter combinations, a virtual experiment of the undercut flange pressing process is conducted using a 3D finite element simulation engine. Two key quality indicators are extracted from the simulation results: flange volume filling rate and maximum principal stress of the ejector. The parameter combinations are then paired and stored with their corresponding response values ​​to form a training sample library.

[0037] A 3D finite element simulation engine refers to computer-aided engineering software that uses numerical methods to discretize the continuum of the mold and the blank, and solves the momentum balance equation, energy conservation equation, and contact constraint conditions during plastic forming. Its calculation results can reflect physical fields such as metal flow, stress distribution, and temperature field. The undercut flange pressing process specifically refers to the process stage in warm forging of flange parts with undercut geometry, where the upper punch presses down to radially fill the edge flange cavity with blank metal and envelop the undercut structure. The flange volume filling rate is defined as the percentage of the actual volume occupied by the blank metal in the flange edge cavity to the designed total volume of the cavity, used to measure the fullness of the flange geometry. The maximum principal stress of the ejector is defined as the peak value of the first principal stress, calculated by the finite element stress tensor in the ejector structure along the demolding bearing direction, distributed throughout the discrete mesh of the ejector. This indicator is directly related to the mold fatigue life and fracture risk.

[0038] For each combination of physical process parameters in the initial parameter sample set, the processing flow begins with obtaining the metal rheological constitutive equation at the corresponding forging temperature and the friction coefficient of the die contact interface. The metal rheological constitutive equation employs a temperature-dependent constitutive model that characterizes the nonlinear relationship between metal flow stress and strain at a specific forging temperature and strain rate. Its model parameters are determined by fitting the isothermal hot compression calibration experimental data of the corresponding forging material. The friction coefficient of the die contact interface is determined based on the selected lubrication conditions and the corresponding friction calibration experiments. After obtaining a set of physical process parameter combinations, there is no need to recalibrate the constitutive equation and friction coefficient. As long as the forging temperature and lubrication conditions remain unchanged, these two physical inputs remain constant, and the same equation and coefficients are reused for all combinations in the initial parameter sample set.

[0039] The mathematical expression of the metal rheological constitutive equation, along with calibration parameters and the numerical values ​​of the friction coefficient, are written into the preprocessing input file of the 3D finite element simulation engine as boundary conditions. The simulation engine discretizes the billet into eight-node hexahedral thermo-coupled elements and treats the upper punch, lower die, and ejector as rigid contact bodies. The upper punch blanking stroke is applied as a displacement boundary condition to the axial degree of freedom of the upper punch, controlling the amount of downward movement from the contact point with the billet. This stroke amount is directly derived from the upper punch blanking stroke value in the current combination of physical process parameters. The forming process tonnage is applied as a force boundary condition to the main node coupling the upper punch and the equipment slider. The magnitude of this force is taken from the forming process tonnage value in the current combination of physical process parameters, and its direction is parallel to the forming direction. The aperture of the ejector hole in the lower punch and the setting ratio of the dispersion ejector force are reflected in the mesh modeling stage. The aperture of the ejector hole determines the element deletion size of the ejector center hole region, while the setting ratio of the dispersion ejector force is simulated by applying pressure functions with different weights at the contact surfaces of multiple ejector rods. The finite element method for the pressing process of the undercut flange is performed. The solver adopts an implicit incremental iterative algorithm, which performs nonlinear solution in multiple incremental steps within the preset forming cycle to obtain the displacement field, stress field and strain field of each incremental step.

[0040] After the simulation calculation is completed, the volume fill rate data of the flange edge nodes is extracted from the simulation result database. Flange edge nodes specifically refer to the finite element mesh nodes located in the outermost radial annular cavity region of the flange. The set of elements in contact with the cavity boundary within this region is extracted. By traversing all cavity region elements and using a spatial geometric position determination algorithm, elements located inside the cavity geometric envelope are selected. The volumes of these elements are then integrated and accumulated to obtain the filled metal volume. This volume is compared with the total volume of the flange's designed cavity to calculate the flange volume fill rate.

[0041] Simultaneously, the peak value of the maximum principal stress distribution on the ejector structure is extracted. By calling the post-processing result database of the three-dimensional finite element simulation engine, the stress tensor of each element after the ejector structure is discretized is obtained, the principal stress value of each element is solved, and all elements in the ejector region are traversed, and the element with the largest algebraic value is taken as the maximum principal stress of the ejector under this set of parameters.

[0042] After completing the single feature extraction, the current combination of physical process parameters—namely, the upper punch blanking stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top force setting ratio—is paired with the flange volume filling rate and ejector maximum principal stress extracted from the simulation and stored as a single data record. The entire process described above is executed for each combination in the initial parameter sample set, and all resulting records are compiled to form a training sample library. Each row in the training sample library corresponds to a set of parameters and its two response values, providing complete input-output mapping data for subsequent fitting of the surrogate model.

[0043] For example, continuing with the 40 initial parameter sample sets generated in step S1, the first set of physical process parameter combinations is used to demonstrate the S2 process in detail. The four parameter values ​​of this combination are: upper punch pressing stroke 11.262mm, forming process tonnage 1031.1kN, lower punch intermediate ejector opening diameter 38.439mm, and dispersion top material force setting ratio 0.15.

[0044] The forging billet material was set to 40Cr, and the forging temperature was set to 850 degrees Celsius. Based on these conditions, the parameters of the metal rheological constitutive equation were determined. Simultaneously, the friction coefficient between the die and the billet was set to 0.25 according to the water-based graphite lubrication conditions. An assembly model including the upper punch, die, billet, and ejector with a central through-hole was established in a 3D finite element simulation engine. The four physical process parameters were converted into corresponding displacement, force, geometric, and pressure boundary conditions and applied to the model. Nonlinear solution calculations were then performed.

[0045] After the calculation is completed, the flange volume fill rate is extracted. The total design volume of the flange edge cavity is obtained, for example, 15200 mm³ as measured. In the post-processing program, the volume of all units in the cavity is integrated and accumulated to obtain the filled metal volume, for example, 14972.4 mm³. Based on this, the flange volume fill rate is calculated to be 98.5%.

[0046] In extracting the maximum principal stress of the ejector, the stress tensor of all discrete elements in the ejector region is solved, and the principal stress values ​​of all elements are iterated to select the maximum value. For example, after iteration, the maximum principal stress value of the ejector under this working condition is obtained as 328.7 MPa.

[0047] Subsequently, the parameter combination (11.262, 1031.1, 38.439, 0.15) and the response value (98.5%, 328.7) are written as a record into the training sample library. The above simulation and extraction operations are then performed on the remaining 39 combinations in the initial parameter sample set one by one, finally forming a training sample library containing 40 complete mapping data, providing a data foundation for the construction of the Gaussian process regression surrogate model in step S3.

[0048] S3. Using the training sample library, with the combination of physical process parameters as input and the flange volume filling rate and the maximum principal stress of the ejector as output, a Gaussian process regression surrogate model is fitted and constructed.

[0049] In a preferred embodiment, a Gaussian process regression surrogate model is constructed using a training sample library, with combinations of physical process parameters as input and flange volume filling rate and maximum principal stress of the ejector as output. This includes: extracting all combinations of physical process parameters from the training sample library as an input variable matrix; extracting the corresponding flange volume filling rate sequence and maximum principal stress sequence of the ejector as the first and second output variables, respectively; establishing Gaussian stochastic process models based on the input variable matrix and the two output variables; determining the nonlinear mapping relationship between the input and each output; and merging the two Gaussian stochastic process models to form a Gaussian process regression surrogate model that can simultaneously predict the flange volume filling rate and the maximum principal stress of the ejector.

[0050] Specifically, building upon the training sample library formed in step S2, this library contains several records. Each record consists of a combination of four physical process parameters and two simulation response values. The four physical process parameters are, in order: upper punch blanking stroke, forming process tonnage, lower punch intermediate ejector orifice diameter, and dispersion of the ejector force setting ratio. The two response values ​​are the flange volume filling rate and the ejector's maximum principal stress. The goal of this step is to construct a mathematical surrogate model using these known discrete data points. This model can directly calculate the corresponding flange volume filling rate and ejector's maximum principal stress for any combination of physical process parameters that has not been simulated, thus avoiding the need to call the time-consuming 3D finite element simulation engine each time. This surrogate model is called a Gaussian process regression surrogate model, a nonparametric prediction model based on spatial statistics. It characterizes the nonlinear mapping relationship between unknown physical process parameters and simulation responses as the realization of a Gaussian stochastic process.

[0051] All combinations of physical process parameters are extracted from the training sample database and used as the input variable matrix, denoted as . Suppose there are a total of [number] samples in the training sample library. Group parameter combinations, each combination contains One physical process parameter, The quantity is the same as the four physical process parameters mentioned above, namely... Input variable matrix The dimension is , its first Line 1 Column elements Representing the In the group parameter combination, the first The specific values ​​of each physical process parameter are calculated. Simultaneously, the corresponding flange volume fill rate sequence is extracted as the first output variable, denoted as a column vector. , of which elements That is, the first The flange volume filling rate corresponding to the parameter combination is expressed as a percentage. Further, the corresponding maximum principal stress sequence of the ejector is extracted as the second output variable, denoted as a column vector. , of which elements It is the first The maximum principal stress of the ejector corresponding to the combination of parameters is expressed in megapascals.

[0052] Based on the input variable matrix and two output variables, Gaussian stochastic process models need to be established separately to determine the nonlinear mapping relationship between the input and the flange volume filling rate, and the nonlinear mapping relationship between the input and the maximum principal stress of the ejector. The Gaussian stochastic process model will consider any input point... Output response at It is decomposed into the sum of a deterministic regression component and a stochastic correlation component, where the superscript... Used to distinguish output variables Corresponding flange volume fill rate, The corresponding maximum principal stress of the ejector. For the first output variable, the flange volume filling rate, its Gaussian stochastic process model is expressed as: ; in, It is a four-dimensional column vector consisting of four physical process parameter values. These four components correspond to the aforementioned dimension index j as 1, 2, 3, and 4, respectively, which correspond to the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top material force setting ratio. These are the regression coefficients corresponding to the k-th basis function. This is the user-selected k-th basis function used to capture the overall trend of the response. This embodiment uses a constant regression trend model, meaning the regression part only takes one constant term. basis functions regression coefficient Record It represents the average trend level of flange volume fill rate over the global range. It is a Gaussian random process with zero mean, used to characterize local deviations and statistical correlations between different input points. At any two input points and The covariance at a given location is defined as: ; In the formula, It is the process variance, with dimensions consistent with the variance of the flange volume filling rate, reflecting the overall fluctuation amplitude of the random process. It is a spatial correlation function, whose value depends only on the distance between two input points and is affected by the hyperparameter vector. The regulation of [the system / function]. This embodiment uses an exponential spatial correlation function, expressed as: ; in, It is an index based on the physical process parameters. and Representing the first The and the first In the parameter combination, the first... The values ​​of the physical process parameters. It is the first Hyperparameters in each dimension satisfy The larger the value, the more drastic the change in output response with input in that dimension, and the faster the correlation between the two points decays. Hyperparameter vector and , Together they form the set of unknown parameters that need to be estimated from the training data.

[0053] The unknown parameters are determined through maximum likelihood estimation. A log-likelihood function for the training data under this Gaussian stochastic process model is constructed. This log-likelihood function is composed of the correlation matrix, the known output vector, and the set of unknown parameters; the elements of the correlation matrix are calculated using the aforementioned spatial correlation function. Given a hyperparameter vector, estimates in analytical form are obtained by taking the partial derivatives of the constant regression coefficients and the process variance and setting them to zero. Substituting these estimates back into the log-likelihood function yields a lumped log-likelihood function that is only related to the hyperparameter vector. A numerical optimization algorithm is then used to search the hyperparameter space for the optimal hyperparameter vector that maximizes the lumped log-likelihood function. Numerical optimization algorithms include heuristic optimization algorithms and gradient descent algorithms. Thus, the Gaussian stochastic process model for the flange volume fill rate is completely determined. This model captures the nonlinear mapping relationship between the combination of physical process parameters and the flange volume fill rate. For any given four-dimensional parameter points… The model can provide the predicted mean. It can also provide the prediction variance. Its predicted mean is composed of the superposition of the global average trend and the local correlation correction term, while the predicted variance is calculated by the overall process variance and the correlation decay of the predicted points.

[0054] For the second output variable, the maximum principal stress of the ejector, a Gaussian stochastic process model is established in parallel, which is expressed as: ; Utilizing the maximum principal stress sequence of the ejector and the same input matrix The result is obtained through maximum likelihood estimation. , and The maximum principal stress model for the ejector can also be applied to any... Output predicted mean With prediction variance .

[0055] After obtaining two independent Gaussian stochastic process models, they are merged to form a Gaussian process regression surrogate model that can simultaneously predict the flange volumetric filling rate and the maximum principal stress of the ejector. This merging does not couple the two stochastic processes in the probability space, but rather constructs a unified prediction interface. Given any combination of physical process parameters, this Gaussian process regression surrogate model sequentially calls the flange volumetric filling rate model and the ejector maximum principal stress model, simultaneously returning four results: the predicted value of the flange volumetric filling rate. Predicted standard deviation of flange volumetric filling rate Predicted value of maximum principal stress of the ejector and the predicted standard deviation of the maximum principal stress of the ejector. With this structure, subsequent steps can obtain the surrogate responses and uncertainty measures of the two process objectives within the same model framework.

[0056] For example, based on the training sample library containing 40 records obtained in step S2, the construction of a Gaussian process regression surrogate model is demonstrated. All 40 combinations of physical process parameters are extracted from the training sample library as the input variable matrix. The size is 40 rows × 4 columns, and the corresponding first output variable is extracted. (40 flange volume fill rate values) and second output variable (Maximum principal stress values ​​of 40 ejectors). To eliminate the interference of differences in the dimensions and numerical ranges of the input parameters on distance measurement and correlation modeling, the input variable matrix X was linearly normalized column by column at the beginning of the modeling process, so that all input parameters were mapped to the [0,1] interval. Subsequent modeling and prediction were based on the normalized matrix.

[0057] For the flange volume fill rate model, a search boundary for hyperparameters is defined, and a numerical optimization algorithm is used to maximize the lumped log-likelihood function. After convergence, estimated values ​​of the hyperparameters are obtained, for example... , And so on, and construct a relevant matrix accordingly. Then, the estimated constant regression coefficients are calculated. process variance estimate .

[0058] The same parameter estimation process was performed on the maximum principal stress model of the ejector to obtain the corresponding hyperparameter estimates. Estimated constant regression coefficients process variance estimate .

[0059] The two models are merged to form a unified Gaussian process regression surrogate model. For any point to be predicted (e.g., given normalized coordinates)... The model can simultaneously output the mean predicted flange volume filling rate of 98.1% and the standard deviation of 0.61%, as well as the mean predicted maximum principal stress of the ejector of 306.5 MPa and the standard deviation of 8.7 MPa. This proves that the surrogate model has the ability to quickly predict two key indicators at the same time and can be directly used in the subsequent adaptive point addition process.

[0060] S4. On the Gaussian process regression surrogate model, obtain the engineering tolerance threshold determined according to the product processing accuracy requirements, use the expected increment criterion to determine the candidate parameter coordinates of the points to be added, perform finite element simulation only on the candidate parameter coordinates, obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector, and then add them to the training sample library to update the Gaussian process regression surrogate model. Repeat the process until the prediction error of the surrogate model is lower than the engineering tolerance threshold, and obtain the converged surrogate model.

[0061] In a preferred embodiment, obtaining a converged surrogate model includes: acquiring the allowable deviation range of the product flange fill rate and ejector stress, and determining the engineering tolerance threshold for the prediction error accordingly; calculating the prediction variance of each candidate point in the entire physical process parameter space, as well as the expected improvement in flange volume fill rate and the expected reduction in maximum principal stress of ejector, on the current Gaussian process regression surrogate model, and constructing a composite addition function; searching for candidate parameter coordinates that maximize the composite addition function, and using them as the coordinates to be added; performing a three-dimensional finite element simulation on the coordinates to be added to obtain the actual flange volume fill rate and the actual maximum principal stress of ejector corresponding to the coordinates; adding the coordinates to be added and their actual responses to the training sample library, and refitting and updating the Gaussian process regression surrogate model; comparing the prediction error of the current surrogate model at the verification point with the engineering tolerance threshold, and if the error is lower than the threshold, outputting the current surrogate model as a converged surrogate model; otherwise, returning to execute the construction of the composite addition function and subsequent steps.

[0062] In a further preferred embodiment, the composite addition function is composed of a prediction variance term and an improvement expectation term multiplied by their respective preset weights and then added together.

[0063] Specifically, although the Gaussian process regression surrogate model constructed in step S3 can simultaneously predict the flange volume filling rate and the maximum principal stress of the ejector, this model is fitted based on the initial parameter sample set of 40 sets of finite element simulation data. The prediction accuracy exhibits significant non-uniformity in the parameter space: predictions are reliable in areas with dense sample points, but highly uncertain in areas with sparse samples. Directly using such a surrogate model for process optimization may yield misleading optimal solutions in areas with inaccurate predictions. Therefore, it is necessary to selectively supplement the surrogate model with real simulation data in areas where the accuracy does not yet meet engineering requirements, gradually improving the overall accuracy of the model. This adaptive supplementation process is driven by the expected increment criterion in step S4, ultimately resulting in a convergent surrogate model with a prediction error lower than the engineering tolerance threshold.

[0064] Furthermore, the product processing accuracy requirements are obtained to determine a clear accuracy acceptance standard, namely the engineering tolerance threshold. The engineering tolerance threshold is the upper limit of the allowable error for the surrogate model prediction, derived from the product processing accuracy requirements. It includes two indicators: the prediction error threshold for the flange volume filling rate and the prediction error threshold for the maximum principal stress of the ejector. Flange filling is a key metric for measuring the forming quality of forgings. The product design drawings require the flange edge cavity to be fully filled, with a volume filling rate of over 99.0%. In the engineering capability study of the forming process, based on actual measurements using 200 sets of industrial sensors, the standard deviation of the volume filling rate fluctuation in subsequent batch warm forging of this product was found to be 0.32%, with an allowable deviation range of ±0.5%. If the surrogate model's prediction error for the volume filling rate exceeds 0.5%, the optimization process may misjudge parameters with insufficient actual filling as acceptable. Therefore, the prediction error threshold for the flange volume filling rate is set at... The threshold is set at 0.3%, slightly stricter than half the product's allowable deviation, to allow for a safety margin. The maximum principal stress of the ejector is directly related to the mold's fatigue life. Fatigue limit tests on the same batch of 40Cr steel mold materials at warm forging temperatures determined the allowable stress of the ejector structure to be 385 MPa. The design requires that the peak value of the maximum principal stress must not exceed this value, and the allowable range for stress deviation caused by process fluctuations is ±25 MPa. If the surrogate model's prediction of the stress has too large a deviation, the optimized parameters may cause early mold cracking in actual applications. Therefore, the prediction error threshold for the maximum principal stress of the ejector is set accordingly. The pressure is set to 12 MPa, which is based on half of the allowable deviation range.

[0065] Before starting the adaptive point addition iteration, a validation point set independent of the training sample library is constructed to objectively evaluate the prediction accuracy of the surrogate model. The possible value boundaries of the physical process parameters defined in step S1, i.e., the stroke range of the upper punch, are utilized. Tonnage range for forming process The diameter range of the intermediate ejector hole in the lower punch and the adjustment range of the dispersion top force setting ratio The multidimensional stratified sampling algorithm is executed again, but with a different random seed than in step S1, generating a preset number of physical process parameter combinations as a set of verification points. For each set of verification points, a three-dimensional finite element simulation is performed according to the process in step S2 to extract the corresponding true values ​​of flange volume filling rate and maximum principal stress of the ejector. This set of verification points does not participate in the fitting of the Gaussian process regression surrogate model; it is only used to calculate the prediction error after each update.

[0066] In the adaptive point-addition iteration process, based on the current Gaussian process regression surrogate model, the prediction variance, the expected improvement in flange volume filling rate, and the expected reduction in the maximum principal stress of the ejector are calculated for each candidate point in the entire physical process parameter space, constructing a composite point-addition function. This composite point-addition function is the decision-making basis for determining where to supplement simulation samples, and is composed of a prediction variance term and two expected improvement terms weighted together. The prediction variance term comes from the prediction standard deviation output by the Gaussian process regression surrogate model, directly measuring the uncertainty of the model's prediction result at that parameter point. The larger the value of the prediction variance term, the less the model knows about that area, guiding the exploration behavior to fill the information gaps. The expected improvement in flange volume filling rate and the expected reduction in the maximum principal stress of the ejector focus on two optimization objectives, respectively, directing the search towards parameter regions where better performance may be obtained.

[0067] To evaluate candidate points across the entire parameter space, the physical process parameter space is normalized following the rules of step S3, mapping all input components to the interval [0,1]. Subsequently, the normalized four-dimensional space is discretized into a grid according to a preset resolution, generating a discrete candidate point set covering the global parameter space.

[0068] For any point in the candidate point set, the Gaussian process regression surrogate model constructed in step S3 can output four quantities: the predicted mean and standard deviation of the flange volume filling rate, and the predicted mean and standard deviation of the maximum principal stress of the ejector. The predicted mean is used to calculate the expected improvement, and the predicted standard deviation is used to calculate the prediction variance term.

[0069] Characterization of the prediction variance term: To eliminate differences in output dimensions, the two standard deviations cannot be directly added. Instead, they are each normalized over the entire candidate point set. If the candidate point's prediction standard deviation is constant, the normalization value is taken as a default constant. The two normalized standard deviations are combined and their mean is used as the prediction variance term for that candidate point.

[0070] The calculation of the expected improvement is based on the expected increment criterion. Let the known maximum value of the flange volume filling rate and the known minimum value of the maximum principal stress of the ejector in the current training sample library be the current optimal values. For any candidate point, the improvement amount by which the predicted flange volume filling rate exceeds the current optimal value follows a normal distribution; the mathematical expectation of this improvement amount is the expected improvement of the flange volume filling rate. Similarly, the reduction amount by which the maximum principal stress of the ejector is lower than the current optimal value also follows a normal distribution; the mathematical expectation of this reduction amount is the expected reduction of the maximum principal stress of the ejector. Subsequently, to eliminate the influence of dimensions, the above two expected improvements are also normalized on the candidate point set.

[0071] A composite addition function is constructed by weighting and summing the predicted variance term and the two normalized improvement expectation terms. The weighting coefficients of each term are non-negative weight parameters set based on the principle of balancing global exploration and local development, and the sum of the weights is 1. By allocating weights, the two improvement expectations are given appropriate emphasis, making the addition more inclined towards the optimization target while retaining sufficient global exploration capability.

[0072] Search for the coordinates of candidate parameters that maximize the composite addition function. Find the point with the largest value of the composite addition function from the discrete candidate point set. Map the corresponding normalized coordinates back to the original physical process parameter space through inverse normalization to obtain the coordinates of the point to be added.

[0073] A complete three-dimensional finite element simulation is performed on the coordinates of the point to be added, with the simulation settings exactly the same as in step S2, to obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector corresponding to this parameter combination. The coordinates of the point to be added and its two actual response values ​​are added as a new record to the training sample library to expand the training sample library.

[0074] Using the expanded training sample library, the Gaussian process regression surrogate model is refitted following the procedure in step S3, including recalculating the correlation matrix, reestimating the process variance and hyperparameters, to obtain the updated surrogate model. Subsequently, the prediction error of the updated model is evaluated using an independent validation set. The validation set is input into the updated Gaussian process regression surrogate model to obtain the predicted value for each validation point, and the maximum absolute prediction error for each validation point on both metrics is calculated.

[0075] Compare these two error values ​​with the set engineering tolerance threshold. If the maximum absolute prediction error of both objectives is below the corresponding engineering tolerance threshold, it indicates that the surrogate model's prediction accuracy for both key indicators in the parameter space has reached an engineering-usable level. The updated Gaussian process regression surrogate model is then output as the converged surrogate model, and step S4 terminates. If either error does not meet the threshold condition, return to the step of constructing the composite addition function. Based on the new training sample library and the new surrogate model, recalculate the composite addition function for all candidate points, determine the next addition point, and continue iterating until the convergence condition is met.

[0076] Please see Figure 2 As shown, Figure 2 The graph shows the convergence curve of the adaptive point-addition prediction error of the surrogate model of this invention, illustrating the process by which the bi-objective prediction error continuously decreases with the number of iterations and eventually stabilizes below the engineering tolerance threshold. For example, continuing with the Gaussian process regression surrogate model based on 40 training samples obtained in step S3, the specific calculation of the adaptive point-addition iteration in step S4 is demonstrated. The generation and simulation of validation points have been completed prior to this; the two true response values ​​obtained from the 20 validation points are not yet used in training. Let the current optimal value of the flange volume filling rate be among the initial 40 training samples. The current optimal value of the maximum principal stress of the ejector. .

[0077] The normalized four-dimensional space is discretized into a grid with a preset step size. Three candidate points are selected to demonstrate the evaluation logic of the composite point function, and their normalized coordinates are denoted as candidate point A, candidate point B, and candidate point C, respectively. The current Gaussian process regression surrogate model established in step S3 is used to predict these three points, and the results are as follows: Candidate point A: The predicted mean of flange volume filling rate is 98.3% (standard deviation 0.82%); the predicted mean of maximum principal stress of the ejector is 312.1 MPa (standard deviation 14.3 MPa).

[0078] Candidate point B: The predicted mean of flange volume filling rate is 99.2% (standard deviation 0.65%); the predicted mean of maximum principal stress of the ejector is 283.4 MPa (standard deviation 11.2 MPa).

[0079] Candidate point C: The predicted mean of flange volume filling rate is 96.7% (standard deviation 1.21%); the predicted mean of maximum principal stress of the ejector is 341.5 MPa (standard deviation 19.7 MPa).

[0080] Based on the extreme values ​​of the predicted standard deviation and expected improvement of all candidate points in the space, range normalization was performed on the three points mentioned above. Since the predicted means of candidate points A and C are both worse than the current optimal value, their expected improvement for both objectives is 0; while the predicted mean of candidate point B is better than the current optimal value in both objectives, exhibiting a significant expected improvement. Using preset weighting coefficients, such as 0.3, 0.35, and 0.35 respectively, the predicted variance term and the two normalized expected improvement terms were weighted and summed, resulting in composite function values ​​of 0.098, 0.343, and 0.185 for candidate points A, B, and C, respectively. It can be seen that although candidate point B has a small predicted variance, its composite function value is the highest due to its considerable expected improvement.

[0081] Assuming that candidate point B is still the maximum value after traversing all candidate points, it is selected as the point to be added. Its normalized coordinates are then denormalized to obtain the actual physical process parameters, such as mapping the upper punch pressing stroke back to 15.7mm, and so on to obtain the complete parameters. A three-dimensional finite element simulation is performed on this coordinate system, obtaining a true flange volume filling rate of 99.1% and a true maximum principal stress of 279.0MPa for the ejector. This new data is added to the training sample library, increasing the sample size to 41 groups, and a Gaussian process regression surrogate model is refitted.

[0082] The updated surrogate model is used to calculate the maximum absolute error at 20 validation points. Assuming the maximum error in flange volume filling rate is 0.42% and the maximum error in maximum principal stress of the ejector is 15.3 MPa, since these are not simultaneously below the set engineering tolerance thresholds (0.3% and 12 MPa), a second iteration is initiated. The composite addition function is reconstructed and the addition points are optimized. As new simulation samples continuously fall into the high-value parameter region, the surrogate model's prediction error gradually decreases. Typically, after 5 to 8 rounds of addition, the validation error meets the threshold condition, and a converged surrogate model is output for subsequent multi-objective optimization.

[0083] S5. Obtain the demolding friction force of the forging during the demolding process. On the convergent surrogate model, with the dual objectives of maximizing the flange volume filling rate and minimizing the maximum principal stress of the ejector, apply the physical constraint that the total ejection force is greater than the demolding friction force. Use a multi-objective optimization algorithm to find the optimal solution and output the multi-objective non-dominated process parameter solution set.

[0084] In a preferred embodiment, the output of a multi-objective non-dominated process parameter solution set includes: obtaining the forging demolding angle, forging material parameters, and mold friction coefficient; calculating the demolding friction force of the forging during the demolding process; on the convergent surrogate model, setting the total ejection force generated by the ejection mechanism to be greater than the demolding friction force as a physical constraint; setting the flange volume filling rate to achieve a preset filling degree as the objective, and minimizing the maximum principal stress of the ejector as the objective; and using a non-dominated sorting genetic algorithm to perform multi-objective optimization on the two sets of objectives under physical constraints to search for a multi-objective non-dominated process parameter solution set composed of multiple sets of non-dominated physical process parameters.

[0085] In a further preferred embodiment, the demolding friction force is calculated based on the contact area between the forging and the mold, the mold friction coefficient, and the empirical regression relationship between the forming process tonnage and the contact normal force in the demolding direction.

[0086] Specifically, based on the converged surrogate model output in step S4, this step performs process parameter optimization with the dual objectives of flange forming fullness and mold demolding safety. The converged surrogate model is obtained through iterative updates in step S4, and it contains a flange volume filling rate prediction model and a maximum principal stress prediction model for the ejector. It can quickly and accurately provide prediction values ​​for both objective functions for any combination of physical process parameters within the acceptable value boundaries. The optimization intent of this step is clear: while ensuring that the ejector mechanism has sufficient force to overcome the frictional resistance between the forging and the mold during demolding, it seeks a combination of process parameters that makes the flange volume filling rate close to 100% and the maximum principal stress of the ejector as low as possible.

[0087] To achieve the above optimization goals, an optimized physical constraint is established: the total ejection force must be greater than the calculated demolding friction. The calculated demolding friction refers to the total frictional resistance along the demolding direction that the hot forging must overcome during ejection as it cools and shrinks, tightly gripping the mold cavity. Obtaining the calculated demolding friction depends on three types of inputs: the forging demolding angle, forging material parameters, and the mold friction coefficient. The forging demolding angle is the angle between the flange undercut structure sidewall and the demolding direction, obtained from the forging's finished product design drawings; in this embodiment, the forging demolding angle is taken as 3 degrees. The forging material parameters here specifically refer to material properties directly related to the elastic recovery calculation, including the elastic modulus and Poisson's ratio of the forging material at the demolding temperature. For 40Cr steel forgings, the demolding temperature typically drops to around 650 degrees Celsius. Based on the material mechanical property test data at this temperature, the elastic modulus is taken as 158 GPa, and the Poisson's ratio as 0.31. The friction coefficient of the mold is the same as the friction coefficient of the mold contact interface determined in step S2, with a value of 0.25. This is because the contact surface between the mold and the forging is still the same set of surfaces as during warm forging, and the residual state of the lubricant is similar.

[0088] The calculation of frictional force during demolding is based on the contact area between the forging and the die, the die's coefficient of friction, and the elastic restoring force of the forging material along the demolding direction. After warm forging and cooling, thermal shrinkage of the forging generates a contact normal force on the cavity's surrounding surface. This normal force is triggered by the elastic restoring force of the forging. Let the projected area of ​​the contact region between the forging and the die along the demolding direction be... The average normal contact compressive stress generated on the contact surface due to elastic contraction is The thin-walled cylinder shrinkage theory can be used to... This is related to the material's elastic parameters and geometric interference. However, in this embodiment, the shape of the forged undercut structure is complex, so it is solved directly using theoretical analysis. Since accuracy is difficult to guarantee, a practical engineering calculation method is adopted instead: extract the normal contact force data of the contact surface at the start of material ejection corresponding to several simulated parameter combinations from the finite element simulation result library corresponding to the converged surrogate model, and establish the contact area. Tonnage of forming process The empirical regression relationship between them. The area where the flange undercut surface meets the mold cavity was measured using mold computer-aided design software. This forging... The measured value is mm². Contact normal resultant force extracted in the demolding increment step based on different combinations of physical process parameters from the simulation library. A regression equation was established using the tonnage of the forming process as the independent variable: ; In the formula, It is the total normal force on the contact surface in the demolding direction, measured in kilonewtons. The tonnage of the forming process is expressed in kilonewtons; regression coefficient. and intercept The value is determined by least squares fitting, and its specific value is obtained based on the joint calibration of historical industrial sensor measured data and simulation data, for example... Take 0.73, Take -42.6 kN. The physical meaning of this regression is that the larger the forming tonnage, the denser the metal fills the cavity, and the greater the contact stress with the mold after cooling and shrinkage, which increases approximately linearly. Calculate the friction force during demolding. Then, according to Coulomb's law of friction, the friction coefficient of the mold is calculated using the contact normal force and the coefficient of friction. ; In the formula, The coefficient of friction between the die and the forging is determined by factors such as the die material and lubrication conditions.

[0089] The total force of material return generated by the material return mechanism It is a calculable quantity associated with multiple parameters in a combination of physical process parameters. The total ejection force is provided by a hydraulic or pneumatic ejection cylinder, and after being distributed by multiple ejector rods according to a set ratio of dispersed ejection force, it acts together on the bottom of the forging. In the mold structure of this embodiment, the ejection mechanism includes three ejector rods, with the central rod located in the middle ejector opening of the lower punch, and the two side rods arranged symmetrically. The total ejection force depends on the ejection cylinder pressure and the cross-sectional area of ​​the ejector rods, while the stress on the ejector must be limited within the allowable value of the material. In order to use the total ejection force as a constraint in optimization, a total ejection force is required. Establish a correlation between the ejector rod and the optimization variables. The total cross-sectional area of ​​the ejector rod is fixed by the mold design parameters, and the maximum output pressure of the ejector cylinder determines the adjustable upper limit of the total ejection force, denoted as the maximum allowable ejection force of the equipment. To meet demolding requirements, under any combination of physical process parameters, the total unmolding force... The friction force must be greater than the calculated demolding force corresponding to this parameter. Furthermore, the total force of material ejection must not exceed the maximum output capacity of the equipment. Therefore, the physical constraints are set as follows: ; During the optimization solution process The value is considered to be derived from the pressure of the ejector cylinder and is autonomously selected by the optimization algorithm within the constraints to meet the demolding conditions. The maximum principal stress constraint of the ejector has been internalized as the minimization of the second optimization objective, and no additional hard upper limit is set, in order to obtain the lowest possible stress level in the multi-objective trade-off.

[0090] Furthermore, the flange volume filling rate is set to achieve a preset filling degree, which is determined according to the product technical specifications; the maximum principal stress of the ejector is minimized. These two objectives are conflicting: increasing the tonnage of the forming process and the upper punch's blanking stroke can improve the metal filling capacity of the cavity, increasing the flange volume filling rate, but it will simultaneously increase the contact normal force, which is transmitted through the ejection process, causing the ejector to bear greater stress. Therefore, there is no single parameter combination that simultaneously optimizes both objectives; a set of non-dominated solutions, i.e., a multi-objective non-dominated process parameter solution set, is needed where no solution can improve one objective without compromising the other.

[0091] Multi-objective optimization algorithms are employed to optimize two sets of objectives under physical constraints. In this embodiment, a non-dominated sorting genetic algorithm is used. Non-dominated sorting genetic algorithms are a type of global search algorithm that simulates natural selection and population evolution. Their core operation involves sorting individuals in the population according to their non-dominated level and crowding, retaining individuals that possess both multi-objective performance and parameter space diversity. Optimization variables are derived from combinations of physical process parameters, including four continuous or discrete variables: upper punch blanking stroke, forming process tonnage, lower punch intermediate ejector aperture, and dispersion top force setting ratio. During optimization, each individual in each generation represents a specific combination of physical process parameters, and a converged surrogate model is used to quickly evaluate its flange volume filling rate. and the maximum principal stress of the ejector Regarding whether an individual meets the physical constraints, a constraint dominance principle is adopted: individuals that satisfy the constraint that the total unloading force is greater than the calculated demolding friction force are prioritized over individuals that do not satisfy this constraint. The calculated demolding friction force is calculated in real time based on the tonnage of each individual's forming process using the aforementioned regression formula. The total unloading force, as an auxiliary decision variable, evolves along with the individuals during optimization, and its value range is... .

[0092] The algorithm initializes a population of a preset size and performs population iterations based on preset crossover probabilities, mutation probabilities, and corresponding evolutionary operators. In each generation, a surrogate model is used to quickly evaluate the two objective values ​​of all individuals, and the constraint violation degree of individuals that violate constraints is recorded as a penalty term for their objective values. The population is divided into multiple frontiers according to non-dominated levels, with lower frontier indices indicating better solutions. Within the same non-dominated level, individuals with larger crowding distances are prioritized to maintain the uniformity of the solution set. An elite retention strategy is used to merge parent and offspring generations to jointly select the next generation of the population. After a preset number of evolutionary iterations, the population reaches a convergent state, and the individuals extracted from the first non-dominated level of the final population constitute the solution set of multi-objective non-dominated process parameters.

[0093] The multi-objective non-dominated process parameter solution set consists of multiple sets of non-dominated physical process parameters. Each solution set includes specific values ​​for the upper punch blanking stroke, forming process tonnage, lower punch intermediate ejector orifice diameter, and the set ratio of the dispersion ejector force, as well as the corresponding flange volume filling rate and the predicted maximum principal stress of the ejector. These solutions are arranged in a leading edge in the objective space, demonstrating the minimum achievable level of ejector stress under different flange filling requirements, providing direct quantitative basis for subsequent engineering decisions by process engineers.

[0094] Please see Figure 3 As shown, Figure 3This is a Pareto front distribution diagram for the multi-objective optimization of process parameters in this invention, which intuitively shows the distribution relationship of various compromise solutions (such as solutions A, B, and C) in the solution set of non-dominated process parameters under the dual objectives of filling rate and principal stress. For example, based on the convergent surrogate model finally output in step S4, the complete optimization process in step S5 is demonstrated. Let the possible value boundaries of each dimension of the optimization variables follow the definition in step S1: the upper punch pressing stroke range. mm, tonnage range of forming process kN, the range of the aperture of the ejector in the middle of the lower punch mm, dispersion top force setting ratio range .

[0095] The friction force related to demolding constraints is calculated using the obtained formula. Calculation. In practical engineering, since the initial total ejection force (upper limit 23.73kN) provided solely by the ejection cylinder is insufficient to meet the demolding requirements for typical forming tonnages, this example introduces a mechanical elbow lever force amplification mechanism with a force multiplier of 8.5, increasing the upper limit of the actual effective total ejection force to 201.71kN. The constraint condition is then modified to: effective total ejection force... Friction force greater than or equal to that calculated during demolding And less than or equal to 201.71 kN.

[0096] The initial population contains 80 randomly generated individuals. The following uses a representative individual from the population to illustrate the evaluation method for non-dominated sorting. For individual one: the upper punch blank holder stroke is 14.2 mm, the forming process tonnage is 852 kN, and the setpoint for the ejector cylinder output force is 16.4 kN. Calculated using the formula, its demolding friction force is 144.84 kN, while the effective total ejection force is 139.4 kN. Since the effective total ejection force is less than the demolding friction force, the ejection constraint is not met, and this individual is marked as an infeasible solution and eliminated in the evolution. Conversely, for individual three: the blank holder stroke is 12.5 mm, the tonnage is 785 kN, and the setpoint for the ejector cylinder output force is 20.1 kN. Calculated, its demolding friction force is 132.61 kN, and the effective total ejection force is 170.85 kN, satisfying the physical constraints, and it is marked as a feasible solution.

[0097] For feasible individuals, a convergent surrogate model is invoked to predict two objective values. Individual three, predicted by the surrogate model, has a flange volume fill rate of 98.7% and a maximum principal stress of 274.3 MPa for the ejector. Another feasible individual, four, with a blank holder stroke of 16.1 mm, a tonnage of 810 kN, a bore diameter of 34.6 mm, and a ratio of 0.30, has a flange volume fill rate of 99.2% and a maximum principal stress of 311.8 MPa for the ejector. Comparing individuals three and four, individual four has a higher fill rate but also higher stress; they are not mutually dominant and belong to the same level of non-dominated solutions. Multiple rounds of non-dominated comparisons are performed on all feasible individuals, and the individuals in the first non-dominated layer form the approximate non-dominated front for this generation.

[0098] After 200 generations of evolutionary population convergence, 12 sets of optimal non-dominated process parameter combinations were finally extracted from the first non-dominated layer of the 200th generation. Three of these sets are listed below: Solution A is (upper punch blanking stroke 15.3mm, forming process tonnage 793kN, lower punch intermediate ejector hole diameter 36.4mm, dispersion top force setting ratio 0.26), the surrogate model predicts a flange volume filling rate of 99.7% and a maximum principal stress of 268.9MPa for the ejector; Solution B is (11.9mm, 812kN, 33.8mm, 0.31), with a filling rate of 99.3% and a stress of 257.2MPa; Solution C is (18.2mm, 761kN, 40.1mm, 0.19), with a filling rate of 99.9% and a stress of 302.4MPa. In these three sets of solutions, the filling rates from high to low are C, A, and B, while the stresses from low to high are B, A, and C, reflecting the trade-off between the objectives. The set of these 12 sets of solutions constitutes the output multi-objective non-dominated process parameter solution set, which is passed to step S6 for process execution selection.

[0099] S6. Select parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, convert the unloader opening diameter parameters into CNC machining instructions, convert the pressing stroke and forming tonnage into forging equipment control instructions, and execute physical temperature forging production.

[0100] In a preferred embodiment, a parameter combination that meets the capabilities of the forging equipment is selected from the solution set of multi-objective non-dominated process parameters. The ejector hole diameter parameter is converted into CNC machining instructions, and the blank holder stroke and forming tonnage are converted into control instructions for the forging equipment. Physical warm forging production is then executed. This includes: filtering feasible process parameter combinations from the solution set of multi-objective non-dominated process parameters based on the current maximum allowable tonnage and maximum allowable ejector stress of the forging equipment, and selecting the set with the lowest ejector stress as the execution parameters; converting the ejector hole diameter in the execution parameters into CNC machining instructions in the form of a toolpath file; converting the blank holder stroke and forming tonnage in the execution parameters into programmable logic control instructions for the forging press; sending the CNC machining instructions to the hole machining CNC machine tool, sending the programmable logic control instructions to the forging press, and performing physical trial molding and batch production after completing mold processing.

[0101] Specifically, step S5 generates a multi-objective non-dominated process parameter solution set containing multiple combinations of non-dominated physical process parameters. The task of step S6 is to select parameter combinations from this solution set that can be directly implemented on the existing forging and die processing equipment in the current workshop, and to convert the geometric parameters into CNC machining instructions and the force and stroke parameters into forging equipment control instructions, ultimately driving physical temperature forging production. This step connects virtual optimization and physical manufacturing and is a key execution link in the entire technical solution, mapping from digital space to physical space.

[0102] Furthermore, the forging equipment capacity includes two core constraints: the maximum allowable tonnage and the maximum permissible ejector stress. The maximum allowable tonnage refers to the maximum forming force that the forging press slide can continuously apply within the structural strength safety range. In this embodiment, the forging press used is a 1600-ton crank hot forging press with a nominal pressure of 16000kN. Considering the long-term reliability of the equipment and the die bearing capacity under continuous warm forging conditions, based on the load-life curve provided by the equipment manufacturer and monitoring data from 50 full-load warm forging cycles conducted on the equipment over the past 12 months, the maximum allowable tonnage is determined... Set to 80% of the nominal pressure, that is kN. The maximum allowable stress of the ejector refers to the stress limit at which the ejector component will not yield or fail due to low-cycle fatigue at forging temperature. The ejector material is H13 hot work die steel, and its yield strength at an operating temperature of 850 degrees Celsius, measured by a material testing machine, is 415 MPa. Considering the requirement in the die design specifications to use a safety factor of 1.35 for critical load-bearing components, the maximum allowable stress of the ejector is... Set as MPa.

[0103] Each solution in the multi-objective non-dominated process parameter solution set consists of four physical process parameters: upper punch blank holder stroke, forming process tonnage, lower punch intermediate ejector orifice diameter, and dispersion ejector force setting ratio. It also includes the flange volume filling rate and the maximum principal stress of the ejector predicted by the convergent surrogate model. The filtering operation reads each parameter combination from the solution set one by one, verifying two hard conditions: whether the forming process tonnage is lower than the maximum allowable tonnage. Whether the maximum principal stress value of the ejector is lower than the maximum allowable ejector stress. Parameter combinations that satisfy both conditions are retained as feasible process parameter combinations; if either condition is not met, the parameter combination is discarded.

[0104] Among all feasible combinations of process parameters, the set with the lowest ejector stress is selected as the execution parameter. Lowest ejector stress means that, while ensuring the flange forming quality meets standards and the physical constraints for demolding are optimized and guaranteed by step S5, the execution parameter can effectively extend the ejector's service life and reduce the frequency of mold maintenance. If multiple sets of parameters have extremely similar ejector stress values, resulting in a tie for the lowest value, the flange volume filling rate is further compared, and the set with the filling rate closest to 100% is selected as the execution parameter.

[0105] The ejector hole diameter in the execution parameters refers to the specific value of the ejector hole diameter in the middle of the lower punch. This is a geometric parameter that needs to be converted into CNC machining instructions. CNC machining instructions are tool motion control programs that a CNC machine tool can recognize and execute. Specifically, based on preset cutting parameters (such as cutting speed and feed rate) and tool geometry, a cutting parameter conversion model is used to calculate machine tool operating parameters such as spindle speed, and combined with the machine tool coordinate system to generate a CNC machining program file containing toolpaths and motion logic.

[0106] The upper punch blanking stroke and forming process tonnage in the execution parameters are force and displacement parameters of the forging process, which need to be converted into programmable logic control instructions (PLCs) for the forging press. PLCs refer to the program segments written into the forging press control system that control the slide movement and pressure output. Specifically, the blanking stroke is converted into a displacement control instruction, setting the target displacement and preset accuracy range for the slide's feed stage, and executed through a displacement closed-loop control model; the forming process tonnage is converted into a force control instruction, combined with the effective cross-sectional area of ​​the forging press's main cylinder, to calculate the target hydraulic pressure setpoint or the corresponding analog control signal, which is then written into the corresponding data register of the forging press control system.

[0107] After instruction conversion, the CNC machining instructions are sent to the control computer of the hole-machining CNC machine tool via the workshop Ethernet. The operator loads the corresponding blank and cutting tool and starts the automatic machining cycle to complete the machining of the hole in the middle ejector of the lower punch. Similarly, the programmable logic control instructions of the forging press are sent to the programmable logic controller (PLC) of the forging press via the industrial Ethernet. After the operator confirms the parameters are correct on the upper computer touchscreen, they switch to automatic operation mode. After mold assembly, billet heating to the target forging temperature, and application of preset lubrication conditions, a physical trial molding process is executed: 2 to 3 complete warm forging cycles are run in a single-piece, small-batch manner. After taking the trial mold forging, the flange edge dimensions are checked with measuring tools, and the ejector surface defects are inspected with magnetic particle testing. The trial molding data is used to verify whether the simulation and proxy model predictions are consistent with the actual forgings. After confirmation, it is transferred to mass production.

[0108] For example, following the 12 sets of multi-objective non-dominated process parameter solutions output in step S5, the complete operation from parameter selection to instruction conversion in step S6 is demonstrated. Maximum permissible tonnage of forging equipment. kN, maximum allowable ejector stress MPa. Traverse all 12 sets of data in the solution set of multi-objective non-dominated process parameters, and check the two filtering conditions in each set.

[0109] For example, solution A is (15.3mm, 793kN, 36.4mm, 0.26), with a maximum principal stress of 268.9MPa for the ejector. Both conditions are met, so it is retained. Solution B is (11.9mm, 812kN, 33.8mm, 0.31), with a stress of 257.2MPa, so it is retained. Solution C is (18.2mm, 761kN, 40.1mm, 0.19), with a stress of 302.4MPa, so it is also retained. In this example, all 12 solutions meet both constraints and are included in the feasible set. Comparing the maximum principal stress of the ejector for each solution, solution B has the lowest stress of 257.2MPa, so solution B is selected as the execution parameter. The specific values ​​for solution B are: upper punch pressing stroke 11.9mm, forming process tonnage 812kN, lower punch middle ejector opening diameter 33.8mm, and dispersion ejector force setting ratio 0.31.

[0110] ejector hole diameter mm is converted into CNC machining commands. Using the FANUC system's drilling-fine boring fixed cycle as a framework, the XY zero point of the workpiece coordinate system G54 is set at the center of the lower punch cylinder, and the Z zero point is set at the lower punch end face. The spindle speed is calculated based on the cutting speed conversion relationship, and a carbide boring bar is selected as the cutting tool, based on a preset cutting speed. m / min, after conversion and rounding to a conservative level to protect the tool, the spindle speed is set. r / min. Fine boring feed rate mm / r, and the hole diameter tolerance is controlled at 33.8±0.02mm. The generated toolpath file G-code is as follows: N10G90G54G00X0Y0Z10.S420M03; N20G85Z-65.0R5.0F33.6M08; N30G00Z100.M09; N40M30. Line N10 specifies absolute coordinate programming, selects the workpiece coordinate system G54, rapidly moves to 10mm above the hole center, and starts the spindle clockwise at 420r / min. Line N20 performs boring using a fixed cycle G85, with the boring tool feeding from the R-face Z5.0 plane to the bottom of the hole Z-65.0 plane. The feed rate of 33.6mm / min is calculated by multiplying the spindle speed by the feed per revolution (420×0.08=33.6). Line N30 rapidly retracts the tool to the Z100.0 safe position and turns off the coolant. Line N40 ends the program.

[0111] The 11.9mm blank holder stroke and the 812kN tonnage of the forming process are converted into PLC instructions for the forging press. In the PLC input / output points, the analog module AO1 channel controls the main cylinder pressure, and the AO2 channel controls the slider speed and position. Blank holder stroke... mm is mapped to displacement control commands: the trigger displacement for the slider switching from rapid descent to working feed is set 2.0 mm before contacting the blank, the working feed speed is 0.8 mm / s, and the displacement closed-loop target is to travel 11.9 mm from the zero point of contact with the blank, i.e., the position deviation threshold for triggering the holding pressure signal is ±0.05 mm. A high-speed counting module is used in the PLC ladder diagram to collect grating ruler pulses. When the cumulative pulse count value corresponds to a displacement of 11.9 mm, the internal relay M100 is set, triggering the holding pressure control stage. Forming process tonnage. kN, calculated by combining the piston area of ​​the master cylinder to obtain the target oil pressure setpoint. MPa. This is further mapped to a voltage signal corresponding to the range. V, the value is written to the AO1 data register using the MOV instruction in the PLC program. The pressure holding timer is set to trigger the return stroke after 1.2 seconds.

[0112] After the CNC machining instructions were sent to the machine tool, the operator completed the boring of the lower punch ejector hole and confirmed the hole diameter of 33.788mm was within the tolerance through coordinate measuring machine (CMM) measurement. After the PLC instructions for the forging press were written, a test run was conducted to confirm that the slider displacement and pressure output met the settings. Subsequently, the machined ejector and mold assembly were installed, and the 40Cr billet was heated to 850 degrees Celsius and placed into the mold cavity. The automatic cycle was started to complete the physical mold test. After the first forging cooled, the outer edge dimensions of the flange were measured, and the volume filling rate was measured to be 99.2% by the drainage method. The ejector showed no surface cracks after fluorescent magnetic particle inspection. The mold test results confirmed the reliability of the solution, and the process was then transferred to the mass production stage, continuously running the warm forging production line according to the values ​​of the execution parameters.

[0113] Please see Figure 4 As shown, the second aspect of the present invention provides a transmission shaft warm forging parameter optimization system based on a surrogate model, comprising: a parameter sampling module, a finite element simulation module, a surrogate model construction module, an adaptive iteration module, a multi-objective optimization module, and an execution conversion module.

[0114] The parameter sampling module is used to obtain the combination of physical process parameters for the warm forging process and construct an initial parameter sample set. The combination of physical process parameters includes the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top force setting ratio.

[0115] The finite element simulation module is used to input the initial parameter sample set into the three-dimensional finite element simulation engine for simulation, extract the flange volume filling rate and the maximum principal stress of the ejector, and form a training sample library.

[0116] The surrogate model construction module is used to fit and construct a Gaussian process regression surrogate model using a training sample library, with the combination of physical process parameters as input and the flange volume filling rate and the maximum principal stress of the ejector as output.

[0117] The adaptive iteration module is used to obtain the engineering tolerance threshold determined according to the product processing accuracy requirements on the Gaussian process regression surrogate model, determine the candidate parameter coordinates of the points to be added using the expected increment criterion, perform finite element simulation only on the candidate parameter coordinates, obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector, and then add them to the training sample library to update the Gaussian process regression surrogate model. This process is repeated until the prediction error of the surrogate model is lower than the engineering tolerance threshold, and a converged surrogate model is obtained.

[0118] The multi-objective optimization module is used to obtain the demolding friction force of the forging during the demolding process. On the convergent surrogate model, the dual objectives are to maximize the flange volume filling rate and minimize the maximum principal stress of the ejector. The physical constraint that the total ejection force is greater than the demolding friction force is applied. The multi-objective optimization algorithm is used for optimization and outputs the multi-objective non-dominated process parameter solution set.

[0119] The conversion module is used to select parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, convert the ejector hole diameter parameters into CNC machining instructions, and convert the blank holder stroke and forming tonnage into forging equipment control instructions, which are then output to the forging equipment for physical temperature forging production.

[0120] Each module can be implemented entirely or partially through software, hardware, or a combination thereof. It supports hardware embedded in or independent of the processor in the computer device, and also supports software stored in the memory of the computer device, so that the processor can call and execute the operations corresponding to each of the above modules.

[0121] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for optimizing the warm forging parameters of a transmission shaft based on a surrogate model, characterized in that, include: S1. Obtain the combination of physical process parameters for the warm forging process and construct an initial parameter sample set. The combination of physical process parameters includes the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top material force setting ratio. S2. Input the initial parameter sample set into the three-dimensional finite element simulation engine for simulation, extract the flange volume filling rate and the maximum principal stress of the ejector, and form a training sample library. S3. Using the training sample library, with the combination of physical process parameters as input and the flange volume filling rate and the maximum principal stress of the ejector as output, a Gaussian process regression surrogate model is fitted and constructed. S4. On the Gaussian process regression surrogate model, obtain the engineering tolerance threshold determined according to the product processing accuracy requirements, use the expected increment criterion to determine the candidate parameter coordinates of the points to be added, perform finite element simulation only on the candidate parameter coordinates, obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector, and then add them to the training sample library to update the Gaussian process regression surrogate model. Repeat the execution until the prediction error of the surrogate model is lower than the engineering tolerance threshold, and obtain the converged surrogate model. S5. Obtain the demolding friction force of the forging during the demolding process. On the convergent surrogate model, with the dual objectives of maximizing the flange volume filling rate and minimizing the maximum principal stress of the ejector, apply the physical constraint that the total ejection force is greater than the demolding friction force. Use a multi-objective optimization algorithm to find the optimal solution and output the multi-objective non-dominated process parameter solution set. S6. Select parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, convert the unloader opening diameter parameters into CNC machining instructions, convert the pressing stroke and forming tonnage into forging equipment control instructions, and execute physical temperature forging production.

2. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 1, characterized in that, The process of obtaining the combination of physical process parameters for the warm forging process and constructing an initial parameter sample set includes: Obtain the possible values ​​of the upper punch pressing stroke, forming process tonnage, and lower punch intermediate ejector hole diameter, and obtain the adjustment range of the dispersion ejector force setting ratio. A multidimensional stratified sampling algorithm is used to generate sparse physical process parameter sample points within the possible value boundaries; The physical process parameter sample points are combined with the adjustment range of the dispersion top force setting ratio to form a physical process parameter combination, which serves as the initial parameter sample set.

3. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 1, characterized in that, The initial parameter sample set is input into the three-dimensional finite element simulation engine for simulation, and the flange volume filling rate and the maximum principal stress of the ejector are extracted to form a training sample library, including: For each combination of physical process parameters in the initial parameter sample set, the metal rheological constitutive equation and the friction coefficient of the mold contact interface at the corresponding forging temperature are obtained. The metal rheological constitutive equation and the mold friction coefficient are set in the three-dimensional finite element simulation engine, and the finite element calculation of the undercut flange pressing process is run. Extract the volume fill rate data of the flange edge nodes from the calculation results, and extract the peak value of the maximum principal stress distribution on the ejector structure. The physical process parameters are paired and stored with their corresponding flange volume filling rate and the maximum principal stress of the ejector to form a training sample library.

4. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 1, characterized in that, The method utilizes a training sample library, taking combinations of physical process parameters as input and flange volume filling rate and maximum principal stress of the ejector as output, to fit and construct a Gaussian process regression surrogate model, including: Take all physical process parameter combinations from the training sample library as the input variable matrix, and take the corresponding flange volume filling rate sequence and the maximum principal stress sequence of the ejector as the first output variable and the second output variable, respectively. Based on the input variable matrix and two output variables, Gaussian stochastic process models are established to determine the nonlinear mapping relationship between the input and each output. The two Gaussian stochastic process models are combined to form a Gaussian process regression surrogate model that can simultaneously predict the flange volume filling rate and the maximum principal stress of the ejector.

5. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 1, characterized in that, The converged proxy model includes: Obtain the allowable deviation range of the product flange filling degree and the stress of the ejector, and determine the engineering tolerance threshold of the prediction error accordingly; Based on the current Gaussian process regression surrogate model, the predicted variance of each candidate point in the entire physical process parameter space, as well as the expected improvement of the flange volume filling rate and the expected reduction of the maximum principal stress of the ejector, are calculated to construct a composite addition function. Search for the coordinates of candidate parameters that make the composite point addition function reach its maximum value, and use them as the coordinates of the point to be added. A three-dimensional finite element simulation was performed on the coordinates of the point to be added to obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector corresponding to the coordinates. Add the coordinates of the points to be added and their true responses to the training sample library, and refit and update the Gaussian process regression surrogate model. Compare the prediction error of the current surrogate model at the validation point with the engineering tolerance threshold. If the error is lower than the threshold, output the current surrogate model as the converged surrogate model; otherwise, return to execute the function to build the composite point addition and subsequent steps.

6. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 5, characterized in that, The composite addition function is composed of the prediction variance term and the improvement expectation term multiplied by their respective preset weights and then added together.

7. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 1, characterized in that, The output multi-objective non-dominated process parameter solution set includes: Obtain the forging draft angle, forging material parameters, and mold friction coefficient, and calculate the draft friction force of the forging during the demolding process; In the convergent surrogate model, the total ejection force generated by the ejection mechanism must be greater than the frictional force calculated for demolding, which is taken as a physical constraint. The flange volume filling rate is set to achieve the preset filling degree as the target, and the maximum principal stress of the ejector is minimized; A non-dominated sorting genetic algorithm is used to perform multi-objective optimization on two sets of objectives under physical constraints, and the search yields a multi-objective non-dominated process parameter solution set composed of multiple sets of non-dominated physical process parameters.

8. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 7, characterized in that, The calculated demolding friction force is based on the contact area between the forging and the mold, the mold friction coefficient, and the empirical regression relationship between the tonnage of the forming process and the contact normal force in the demolding direction.

9. The method for optimizing transmission shaft warm forging parameters based on a surrogate model according to claim 1, characterized in that, The process of selecting parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, converting the ejector hole diameter parameters into CNC machining instructions, converting the blank holder stroke and forming tonnage into forging equipment control instructions, and executing physical temperature forging production includes: Based on the maximum allowable tonnage and maximum allowable ejector stress of the current forging equipment, feasible combinations of process parameters are filtered out from the solution set of multi-objective non-dominated process parameters, and the set with the lowest ejector stress is selected as the execution parameters. Convert the ejector hole diameter in the execution parameters into CNC machining instructions in the form of a toolpath file; The blank holder stroke and forming tonnage in the execution parameters are converted into programmable logic control instructions for the forging press; The CNC machining instructions are sent to the hole machining CNC machine tool, and the programmable logic control instructions are sent to the forging press. After the mold processing is completed, physical mold testing and mass production are performed.

10. A transmission shaft warm forging parameter optimization system based on a surrogate model, characterized in that, include: The parameter sampling module is used to obtain the combination of physical process parameters for the warm forging process and construct an initial parameter sample set. The combination of physical process parameters includes the upper punch pressing stroke, forming process tonnage, lower punch intermediate ejector opening diameter, and dispersion top material force setting ratio. The finite element simulation module is used to input the initial parameter sample set into the three-dimensional finite element simulation engine for simulation, extract the flange volume filling rate and the maximum principal stress of the ejector, and form a training sample library. The proxy model construction module is used to fit and construct a Gaussian process regression proxy model using a training sample library, with the combination of physical process parameters as input and the flange volume filling rate and the maximum principal stress of the ejector as output. The adaptive iteration module is used to obtain the engineering tolerance threshold determined according to the product processing accuracy requirements on the Gaussian process regression surrogate model, determine the candidate parameter coordinates of the points to be added using the expected increment criterion, perform finite element simulation only on the candidate parameter coordinates, obtain the actual flange volume filling rate and the actual maximum principal stress of the ejector, and then add them to the training sample library to update the Gaussian process regression surrogate model. This process is repeated until the prediction error of the surrogate model is lower than the engineering tolerance threshold, and a converged surrogate model is obtained. The multi-objective optimization module is used to obtain the demolding calculation friction force of the forging during the demolding process. On the convergent surrogate model, the dual objectives are to maximize the flange volume filling rate and minimize the maximum principal stress of the ejector. The physical constraint that the total ejection force is greater than the demolding calculation friction force is applied. The multi-objective optimization algorithm is used for optimization and outputs the multi-objective non-dominated process parameter solution set. The conversion module is used to select parameter combinations that meet the capabilities of the forging equipment from the solution set of multi-objective non-dominated process parameters, convert the ejector hole diameter parameters into CNC machining instructions, and convert the blank holder stroke and forming tonnage into forging equipment control instructions, which are then output to the forging equipment for physical temperature forging production.

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