Finite element simulation of super large wall thickness difference multi-cavity profile extrusion die control system

Abstract

The application relates to the technical field of auxiliary design, and discloses a finite element simulation super-large wall thickness difference multi-cavity profile extrusion die control system, which comprises the following modules: a discretization extraction module generates a finite element grid to divide a thick and thin wall area, obtains a flow velocity deviation and a weak node principal stress vector; a hierarchical judgment flow adjustment module adjusts a shunt hole proportion or triggers local calculation according to a flow velocity difference threshold value; an agent model construction module trains an agent model based on geometric parameters to solve a Jacobian matrix; a penalty weight calculation module generates a penalty weight matrix in combination with principal stress derivation; and a grid reconstruction optimization module substitutes a target equation to solve an update step to drive grid deformation, and executes closed loop iteration until a condition is met to output a final numerical model. The application realizes accurate finite element simulation super-large wall thickness difference multi-cavity profile extrusion die control by relying on bottom stress constraints and closed loop deformation optimization, and effectively eliminates eccentricity and cracking defects.

Description

Technical Field

[0001] This invention relates to the field of auxiliary design technology, specifically to a finite element simulation control system for multi-cavity profile extrusion dies with large wall thickness differences. Background Technology

[0002] With the development of the new energy vehicle industry, components such as battery end plates often require the connection parts and the end plate body to be formed in one step by aluminum alloy extrusion. These multi-cavity profiles have thin-walled cavities and thick-walled solid areas coexisting on the same cross-section, exhibiting a significant difference in wall thickness ratio. Extrusion dies are the core equipment guiding the plastic deformation of metal billets under high temperature and pressure. To accurately control the metal distribution during the forming process, finite element simulation technology is often introduced in industry to numerically solve and predict the flow patterns and stress fields inside the die's flow channels.

[0003] Existing mold parameter control typically relies on manual experience to adjust the size of the flow divider orifice or to passively intervene in the flow resistance by using a full shielding structure after obtaining the basic flow field distribution through finite element simulation. The discharge speed of different wall thickness areas is balanced through repeated trial and error mold repair operations.

[0004] However, when faced with extremely large wall thickness differences, the resistance changes of the metal flow through the cross-sectional channel are very complex, and conventional structural adjustments are difficult to establish an effective balance between microscopic flow resistance characteristics and macroscopic pressure differences. Simply limiting the flow velocity in the thick-walled area by physical blocking can easily lead to insufficient local flow supply, causing incomplete filling in the thick-walled area and uneven defects on the forming surface. If the flow is supplied to the thin-walled area by significantly changing the flow channel size, the unbalanced fluid-structure interaction pressure will cause the small tongue structure inside the die to bear overload stress, resulting in swaying or even cracking. Due to the lack of quantitative parameter closed-loop optimization control based on internal stress constraints, the current intervention methods are prone to problems such as excessive coplanarity and excessive bottom surface clearance of the extruded products.

[0005] Therefore, this invention proposes a finite element simulation-based control system for multi-cavity profile extrusion dies with large wall thickness differences to address the shortcomings of existing technologies. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a finite element simulation-based control system for multi-cavity profile extrusion dies with large wall thickness differences. This system solves the problems that existing control methods, when dealing with multi-cavity profiles with large wall thickness differences, lack quantitative closed-loop optimization based on internal stress constraints, which leads to problems such as insufficient thick-walled material, cracking of the small tongue core under load, and excessive coplanarity of the final product.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a finite element simulation-based control system for multi-cavity profile extrusion dies with large wall thickness differences, comprising: The discretization extraction module is used to read the three-dimensional parametric digital model of the extrusion die and generate a finite element mesh to divide the thick-walled solid region and the thin-walled cavity region. Through simulation calculation, the average outlet flow velocity of the thick-walled solid region and the thin-walled cavity region are extracted to construct the flow velocity deviation vector, the maximum flow velocity difference, and the first principal stress vector of the weak node. The spatial mapping relationship between the coordinates of the discrete mesh nodes in the free deformation mesh control box constructed in the thick-walled solid region and the preset independent geometric parameter vector is established. The hierarchical determination and flow adjustment module is used to compare the maximum flow velocity difference with the macro control threshold and the micro control threshold. When the maximum flow velocity difference is greater than the macro control threshold, the flow diversion orifice area ratio constant is adjusted. When the maximum flow velocity difference is greater than or equal to the micro control threshold and less than or equal to the macro control threshold, a local solution operation is triggered. The surrogate model construction module is used to generate geometric feature perturbation samples based on the preset independent geometric parameter vector and perform the local solution operation to train the local kriging surrogate model, and to obtain the Jacobian matrix by performing partial derivative operations on the local kriging surrogate model; the penalty weight calculation module is used to derive and construct a virtual deformation trend vector based on the first principal stress vector and the Jacobian matrix and calculate the gradient projection dot product, and to generate a penalty weight matrix based on the gradient projection dot product. The mesh reconstruction and optimization module is used to substitute the Jacobian matrix, the penalty weight matrix, and the flow velocity deviation vector into the parameter correction objective equation to solve for the parameter update step size to drive the finite element mesh to undergo topological smoothing deformation. Based on the deformed finite element mesh, closed-loop iteration is performed until the yield safety threshold verification condition is met, and then the final state of the three-dimensional parameterized digital model of the extrusion die is output.

[0008] Preferably, the discretization extraction module is specifically used to calculate the statistical median of the overall normal thickness, multiply the statistical median by a benchmark reference multiple to set the wall thickness boundary threshold, divide the set of grid cells with a normal thickness greater than the wall thickness boundary threshold into the thick-walled solid region, and divide the set of grid cells with a normal thickness less than or equal to the wall thickness boundary threshold and with a cantilever structure into the thin-walled cavity region.

[0009] Preferably, the discretization extraction module is further configured to perform eigenvalue decomposition on the three-dimensional stress tensor matrix of the mesh nodes contained in the thin-walled cavity region to calculate the scalar equivalent stress value, define the mesh node with the largest scalar equivalent stress value as the weak node, extract the largest positive eigenvalue contained in the three-dimensional stress tensor matrix of the weak node and the feature direction vector corresponding to the largest positive eigenvalue to form the first principal stress vector; extract the mesh vertex coordinate data wrapped by the free deformation mesh control box, and call the polynomial interpolation function to bind and map the discrete mesh node coordinates with the preset independent geometric parameter vector, wherein the preset independent geometric parameter vector includes the occlusion area ratio parameter, the inverted cone angle parameter, and the boundary offset parameter.

[0010] Preferably, the hierarchical determination and flow adjustment module is specifically used to extract the standard deviation of the global average outlet flow velocity and the outlet flow velocity of each cavity region, extract the ratio of the standard deviation to the global average outlet flow velocity as the coefficient of variation, multiply the global average outlet flow velocity by the coefficient of variation to obtain the basic flow deviation value, and set the macro control threshold and the micro control threshold based on the basic flow deviation value.

[0011] Preferably, the hierarchical determination and flow adjustment module is further used to change the cross-sectional area distribution ratio of the upper mold flow divider channel structure feature by using volume scaling operation to update the flow divider area ratio constant. The updated flow divider area ratio constant is equal to the current flow divider area ratio constant multiplied by the volume correction coefficient. The volume correction coefficient is equal to a product of the macroscopic adjustment step size coefficient and the local relative deviation. The local relative deviation is equal to the difference between the local average outlet velocity and the global average outlet velocity, divided by the global average outlet velocity. The macroscopic adjustment step size coefficient is the ratio of the maximum velocity difference to the global average outlet velocity.

[0012] Preferably, the proxy model construction module is specifically used to extract the absolute values ​​of each parameter dimension contained in the preset independent geometric parameter vector, multiply the absolute values ​​of each parameter dimension by a dynamic scaling factor to obtain the trust region radius boundary of the corresponding dimension, apply a sampling algorithm within the trust region radius boundary to generate discretely distributed geometric feature perturbation samples, and call the finite element solver to calculate the average outlet velocity corresponding to the geometric feature perturbation samples as flow field physical response data.

[0013] Preferably, the surrogate model construction module is further configured to train the local kriging surrogate model by using the geometric feature perturbation samples as training sample data and the flow field physical response data as label data, perform differential operations on the explicit regression function of the local kriging surrogate model, parse the discrete partial derivative set data of the average outlet velocity with respect to each parameter dimension of the preset independent geometric parameter vector, and combine and arrange the discrete partial derivative set data to form the Jacobian matrix.

[0014] Preferably, the penalty weight calculation module is specifically used to extract the partial derivative row vectors corresponding to the average outlet velocity of the thick-walled solid region and the thin-walled cavity region respectively from the Jacobian matrix, perform a difference subtraction operation on the partial derivative row vectors to obtain the relative velocity difference vector, call the fluid-structure interaction flexibility transformation matrix to perform coordinate space multiplication operation on the relative velocity difference vector to construct the virtual deformation trend vector, and perform a three-dimensional vector dot product operation on the virtual deformation trend vector and the first principal stress vector to obtain the gradient projection dot product.

[0015] Preferably, the penalty weight calculation module is further configured to generate a unit feature matrix with all diagonal elements being one when the gradient projection dot product is determined to be less than or equal to zero, as the penalty weight matrix; calculate the ratio of the magnitude of the first principal stress vector to the yield stress limit value when the gradient projection dot product is determined to be greater than zero, as the conflict amplification penalty factor; and use a nonlinear exponential transformation function to mathematically map the product of the conflict amplification penalty factor and the gradient projection dot product to generate a diagonal matrix with a diagonal eigenvalue greater than one as the penalty weight matrix.

[0016] Preferably, the mesh reconstruction optimization module is specifically used to solve the parameter correction objective equation through matrix cross operation to output the parameter update step size, extract the absolute modulus value corresponding to the parameter update step size and compare it with the trust region radius boundary. When it is determined that the absolute modulus value is greater than the trust region radius boundary, the update step size exceeding the boundary dimension is forcibly set to be equal to the trust region radius boundary value. The truncated parameter update step size is converted into the control point displacement of the free deformable mesh control box. Finally, the coordinates of the outer surface boundary nodes of the finite element mesh that finally meet the conditions are extracted and the surface reconstruction algorithm is applied to output the final state of the three-dimensional parameterized digital model of the extrusion die.

[0017] This invention provides a finite element method (FEM)-based control system for multi-cavity profile extrusion dies with large wall thickness differences. It offers the following advantages: 1. This invention constructs a hierarchical judgment and flow adjustment module, compares the maximum flow velocity difference with the control threshold to dynamically adjust the area of ​​the flow diversion hole, thereby adapting to the drastic changes in metal resistance within the channel and avoiding the abnormal flow caused by conventional full-coverage structures. It effectively eliminates material shortage and uneven lower surface defects caused by uneven flow. While solving the resistance problem in working conditions with ultra-large wall thickness differences, it also achieves precise flow velocity distribution and extrusion die control for multi-cavity profiles.

[0018] 2. This invention extracts the principal stress vector of weak nodes and derives the deformation trend vector and generates the penalty weight matrix by combining the Jacobian matrix. Based on the physical response state analyzed by finite element simulation, it accurately and quantitatively identifies the risk tendency of thin-walled small tongue core to wobble or crack. In this way, a precise balance mechanism is established between the geometric optimization of the micro-flow obstruction structure and the distribution of the macro-fluid-structure coupling pressure field, so as to prevent local flow correction operations from damaging the internal fragile structure.

[0019] 3. This invention applies a proxy model and substitutes the penalty weight into the objective equation to solve the parameter update step size, driving the mesh to undergo smooth deformation and perform closed-loop iterative optimization. This replaces manual trial and error to continuously correct the flow extrema caused by resistance imbalance, ensuring that the output three-dimensional parameterized model strictly meets the yield safety condition. It fundamentally solves the frequent coplanarity and large surface gap deviation problems of complex cross-section products, and improves the forming control level of extrusion dies. Attached Figure Description

[0020] Figure 1 This is a finite element simulation diagram of the control system architecture for a multi-cavity profile extrusion die with a large wall thickness difference, based on the present invention. Figure 2 This is a flowchart of the finite element simulation method for controlling the extrusion die of multi-cavity profiles with large wall thickness differences according to the present invention. Figure 3 This is a flowchart of the branch control logic judgment of the hierarchical determination and flow adjustment module of the present invention. Figure 4 This is a flowchart of the closed-loop iterative verification process of the mesh reconstruction optimization module of the present invention; Figure 5 The bar charts show the experimental verification and effect comparison of the present invention; where (a) is a comparison chart of the maximum flow rate difference; and (b) is a comparison chart of the mold throughput.

[0021] Among them, 100 is the discretization extraction module; 200 is the hierarchical judgment and flow adjustment module; 300 is the proxy model construction module; 400 is the penalty weight calculation module; and 500 is the mesh reconstruction and optimization module. Detailed Implementation

[0022] The technical solutions in 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.

[0023] Reference Figure 1 The present invention provides a finite element simulation control system for a multi-cavity profile extrusion die with a large wall thickness difference. The finite element simulation control system for a multi-cavity profile extrusion die with a large wall thickness difference includes a discretization extraction module 100, a hierarchical determination and flow adjustment module 200, a proxy model construction module 300, a penalty weight calculation module 400, and a mesh reconstruction and optimization module 500.

[0024] The discretization extraction module 100 is used to read the three-dimensional parametric digital model of the extrusion die and generate a finite element mesh. Based on the finite element mesh, it divides the thick-walled solid region and the thin-walled cavity region. Through simulation calculation, it extracts the average outlet velocity of the thick-walled solid region and the thin-walled cavity region to construct a velocity deviation vector. Based on the velocity deviation vector, it extracts the maximum velocity difference between the thick-walled solid region and the thin-walled cavity region. It extracts the first principal stress vector of the weak nodes in the thin-walled cavity region. It constructs a free-deformable mesh control box in the thick-walled solid region and establishes a spatial mapping relationship between the coordinates of the discrete mesh nodes in the free-deformable mesh control box and the preset independent geometric parameter vector.

[0025] The hierarchical determination and flow adjustment module 200 is used to receive the maximum flow rate difference transmitted by the discretization extraction module 100, compare the maximum flow rate difference with a preset macro control threshold and a preset micro control threshold, and adjust the flow orifice area ratio constant of the three-dimensional parameterized digital model of the extrusion die until the maximum flow rate difference is less than or equal to the macro control threshold. When the maximum flow rate difference is greater than or equal to the micro control threshold and less than or equal to the macro control threshold, the proxy model construction module 300 is triggered to perform local solution operation.

[0026] The surrogate model construction module 300 is used to generate geometric feature perturbation samples based on the independent geometric parameter vector established by the discretization extraction module 100, and to perform local solution on the geometric feature perturbation samples to train a local kriging surrogate model, and to perform partial derivative operations on the local kriging surrogate model to obtain the Jacobian matrix.

[0027] The penalty weight calculation module 400 is used to derive and construct a virtual deformation trend vector based on the first principal stress vector output by the discretization extraction module 100 and the Jacobian matrix output by the surrogate model construction module 300, calculate the gradient projection dot product of the virtual deformation trend vector and the first principal stress vector, and generate a penalty weight matrix based on the gradient projection dot product determination result.

[0028] The mesh reconstruction and optimization module 500 is used to substitute the Jacobian matrix obtained by the proxy model construction module 300, the penalty weight matrix obtained by the penalty weight calculation module 400, and the flow velocity deviation vector issued by the discretization extraction module 100 into the parameter correction objective equation to solve for the parameter update step size. The parameter update step size is converted into the control point displacement of the free deformation mesh control box to drive the finite element mesh to undergo topological smooth deformation. Based on the finite element mesh after topological smooth deformation, closed-loop iteration is performed until the maximum flow velocity difference at the current time is less than the micro-control threshold and the modulus of the first principal stress vector at the current time is lower than the preset yield safety threshold. The finite element mesh that finally meets the conditions is backfitted and output as the final state three-dimensional parameterized digital model of the extrusion die.

[0029] Reference Figure 2 This invention provides a control method for a multi-cavity profile extrusion die with a large wall thickness difference based on finite element simulation. The method is executed by the aforementioned finite element simulation control system for the multi-cavity profile extrusion die with a large wall thickness difference, and includes the following steps: S1. Read the three-dimensional parametric model of the extrusion die and generate a finite element mesh to divide the thick-walled solid area and the thin-walled cavity area. Obtain the flow velocity deviation vector, the maximum flow velocity difference, and the first principal stress vector of the weak node through simulation calculation. Construct a free-deformable mesh control box and establish a spatial mapping relationship between the coordinates of the internal discrete mesh nodes and the independent geometric parameter vectors. S2, compare the maximum flow velocity difference with the preset macro control threshold and the preset micro control threshold. When the maximum flow velocity difference is greater than the macro control threshold, adjust the flow diversion orifice area ratio constant. When the maximum flow velocity difference is greater than or equal to the micro control threshold and less than or equal to the macro control threshold, trigger the local solution operation. S3, generate geometric feature perturbation samples based on independent geometric parameter vectors and perform local calculations to train a local kriging surrogate model, and perform partial derivative operations on the local kriging surrogate model to obtain the Jacobian matrix; S4. Based on the first principal stress vector and the Jacobian matrix, a virtual deformation trend vector is constructed and its gradient projection dot product with the first principal stress vector is calculated. Based on the gradient projection dot product determination result, a penalty weight matrix is ​​generated. S5 substitutes the Jacobian matrix, penalty weight matrix, and flow velocity deviation vector into the parameter correction objective equation to solve for the parameter update step size to drive the finite element mesh to undergo topological smoothing deformation. Based on the deformed finite element mesh, a closed-loop iteration is performed until the yield safety threshold verification condition is met, and then the final state of the extrusion die three-dimensional parameterized digital model is output.

[0030] To further clarify the implementation of each technical aspect of the present invention, the following will provide a detailed description of the implementation of each functional module involved above and its internal processing flow.

[0031] Reference Figure 1 and Figure 2 In this embodiment, the discretization extraction module 100 includes the following sub-steps.

[0032] S101, read the three-dimensional parametric digital model of the extrusion die to generate a finite element mesh, and divide the thick-walled solid region and the thin-walled cavity region based on the finite element mesh.

[0033] In this embodiment, the discretization extraction module 100 reads the three-dimensional parametric model of the extrusion die output by the computer-aided design software through a general data interface, and generates a three-dimensional finite element mesh after performing geometric topology cleaning on the three-dimensional parametric model of the extrusion die. Considering that the cross-section of the internal structural profile of the power battery often contains load-bearing skeletons and heat dissipation fins of varying thicknesses, the discretization extraction module 100 extracts the local normal thickness dimension data of the finite element mesh and compares it with a preset wall thickness boundary threshold.

[0034] As a preferred approach, the wall thickness boundary threshold is not set arbitrarily. Instead, the discretization extraction module 100 scans the entire profile cross-section and calculates the statistical median of the overall normal thickness. This statistical median is then multiplied by 1.5 as the benchmark reference for extracting the wall thickness boundary threshold.

[0035] For example, if the median thickness of the profile section is 3 mm, then the wall thickness boundary threshold is 4.5 mm. Based on the determination result, the discretization extraction module 100 divides the finite element mesh into thick-walled solid regions and thin-walled cavity regions. Mesh element sets with normal thickness dimensions greater than the wall thickness boundary threshold are classified as thick-walled solid regions, while mesh element sets with normal thickness dimensions less than or equal to the wall thickness boundary threshold and possessing cantilever structures are classified as thin-walled cavity regions. For the mesh generation and application of conventional boundary conditions in the three-dimensional parametric model of the extrusion die, those skilled in the art can utilize mature commercial pre-processing software algorithms; the operational details are well-known in the field and will not be elaborated upon here.

[0036] S102, the average outlet velocity of the thick-walled solid region and the thin-walled cavity region are extracted by simulation calculation to construct the velocity deviation vector.

[0037] To address the uneven metal flow velocity across different regions during the extrusion molding process, the discretization extraction module 100 invokes the underlying solver to perform non-isothermal hydrodynamic simulation calculations on the three-dimensional flow field domain that generates the finite element mesh, obtaining the instantaneous velocity response data of all fluid mesh nodes on the outlet section of the working zone. The global average outlet velocity of the entire extrusion die profile is extracted through simulation calculations, and the average outlet velocity of the thick-walled solid region and the thin-walled cavity region are extracted separately to construct a velocity deviation vector. This extraction process uses an area-weighted average algorithm to calculate the representative velocity value within each divided region; the calculation formula is as follows: ; In the formula, Indicates the first Average outlet flow rate of each extraction zone; This indicates the total number of fluid mesh nodes contained in the outlet section of the corresponding extraction region; Indicates the first The instantaneous velocity scalar value output by each fluid mesh node; Indicates the first The cross-sectional area of ​​the micro-element corresponding to each fluid grid node. The discretization extraction module 100 subtracts the extracted global average outlet velocity from the average outlet velocity values ​​calculated for all thick-walled solid regions and thin-walled cavity regions, and then arranges and extracts them according to the spatial topology numbering order on the wide cross-section of the solid profile, combining them to form a one-dimensional array-form velocity deviation vector. This velocity deviation vector represents the uneven distribution of metal supply on the wide cross-section of the profile at the data level.

[0038] S103, based on the velocity deviation vector, extract the maximum velocity difference between the thick-walled solid region and the thin-walled cavity region.

[0039] The discretization extraction module 100 iterates through all velocity element data contained in the velocity deviation vector, searching for and extracting the maximum and minimum average velocity element values. This maximum velocity difference characterizes the relative velocity deviation between the fastest extrusion position in the thick-walled solid region and the slowest extrusion position in the thin-walled cavity region, reflecting the degree of supply-flow imbalance between the two regions. The calculation formula is: ; In the formula, This indicates the maximum flow rate difference obtained; This represents the velocity deviation vector constructed in the preceding steps; and These represent mathematical functions that take the maximum and minimum values ​​of the elements inside a vector, respectively.

[0040] S104, locate the weak node where stress concentration occurs, and extract the first principal stress vector of the weak node in the thin-walled cavity region.

[0041] During the profile extrusion process, the imbalance in metal flow at the interface between thick and thin walls can trigger fluid-structure interaction. Metal flowing at higher velocities exerts lateral drag and asymmetric extrusion forces on the die metal separators in slower-flowing areas. When this asymmetric extrusion force is transmitted into the die, it induces tensile tearing stress at the root of the die's small tongue core, which has a long cantilever in the thin-walled cavity region, leading to die structural swaying or even cracking. The discretization extraction module 100 iterates through the three-dimensional stress tensor matrix of each mesh node after deformation under load in the solid domain of the die in the thin-walled cavity region. It performs eigenvalue decomposition on the three-dimensional stress tensor matrix, calculates the scalar equivalent stress value for each mesh node, and selects the mesh node with the largest equivalent stress value in descending order as the weakest node.

[0042] Subsequently, the discretization extraction module 100 extracts the first principal stress vector of the weak node in the thin-walled cavity region. The first principal stress vector extracts the maximum positive eigenvalue representing the maximum tensile failure tendency and its corresponding eigendirection vector. The calculation formula is as follows: ; In the formula, This indicates the extraction of the first principal stress vector; This indicates the magnitude of the calculated first principal stress scalar; The first principal stress vector represents the specific spatial direction in which the maximum tensile stress points in the three-dimensional physical coordinate system. This first principal stress vector characterizes the magnitude of the maximum tensile stress and its corresponding spatial extension direction.

[0043] S105, construct a free-deformable mesh control box in the thick-walled solid region, and establish a spatial mapping relationship between the coordinates of the discrete mesh nodes in the free-deformable mesh control box and the preset independent geometric parameter vector.

[0044] To effectively control the excessively high metal flow velocity at the thick-walled solid body location, a direct-impact semi-obstruction flow-blocking structure is typically arranged at the location of the thickest solid body wall in the upper mold. The discretization extraction module 100 constructs a free-deformable mesh control box in this thick-walled solid area, specifically by wrapping the direct-impact semi-obstruction flow-blocking structure in this thick-walled solid area with a three-dimensional free-deformable mesh control box.

[0045] The discretization extraction module 100 extracts the shielding area ratio parameter, inverted cone angle parameter, and boundary offset parameter within the defined range of the direct-flow semi-shielded flow-blocking structure and combines them to form a preset independent geometric parameter vector. The expression for the independent geometric parameter vector is: ; In the formula, Represents the completed independent geometric parameter vector; This parameter represents the percentage of the obstructed area. Indicates the inverted cone angle parameter; This represents the boundary offset parameter. Based on this, the discretization extraction module 100 generates the initial preset values ​​of this independent geometric parameter vector according to the original geometric dimensions of the initial extrusion die three-dimensional parameterized digital model.

[0046] After obtaining the parameters, the discretization extraction module 100 establishes a spatial mapping relationship between the coordinates of the discrete mesh nodes within the free-deformable mesh control box and the preset independent geometric parameter vector. The discretization extraction module 100 extracts the coordinate data of all mesh vertices enclosed within the three-dimensional space of the free-deformable mesh control box, and calls the Bernstein polynomial interpolation function to bind and map the coordinates of the discrete mesh nodes contained within the free-deformable mesh control box to the independent geometric parameter vector, thereby establishing a low-level linkage control mechanism for geometric variables to drive mesh displacement.

[0047] This mapping mechanism transforms complex finite element mesh node coordinates into a mathematical expression dominated by a few geometric control points. When the values ​​within this independent geometric parameter vector change, the underlying algorithm directly drives all relevant discrete mesh nodes to shift their coordinates according to interpolation weights through the local coordinate transformation of the control box. This mapping mechanism directly drives local coordinate shifts in discrete mesh nodes to perform subsequent parameter iterative optimization.

[0048] Reference Figure 1 , Figure 2 , Figure 3 In this embodiment, the hierarchical determination and flow adjustment module 200 includes the following sub-steps.

[0049] S201, Receive the maximum flow velocity difference and calculate and obtain the preset macroscopic control threshold and microscopic control threshold.

[0050] In this embodiment, the hierarchical judgment and flow adjustment module 200 receives the maximum flow velocity difference calculated and output by the discretization extraction module 100. The introduction of a macroscopic control threshold and a microscopic control threshold avoids the algorithm from blindly performing local microscopic geometric optimization under conditions of severe macroscopic flow imbalance, which could lead to wasted computing power and iterative divergence. To ensure the objectivity of the judgment, the macroscopic control threshold and the microscopic control threshold are not arbitrarily specified based on human experience, but are dynamically calculated and obtained based on the inherent statistical characteristics of the flow field itself.

[0051] Specifically, the hierarchical determination and flow adjustment module 200 extracts the global average outlet velocity obtained in the previous steps, and simultaneously calculates the standard deviation of the outlet velocity in each cavity region. The ratio of this standard deviation to the global average outlet velocity is extracted as the coefficient of variation. The hierarchical determination and flow adjustment module 200 multiplies the global average outlet velocity by this coefficient of variation to obtain the basic flow deviation value. Twice this basic flow deviation value is set as the macroscopic control threshold, thus characterizing the macroscopic boundary where there is a significant imbalance in the flow supply volume between the cavities inside the extrusion die. Simultaneously, one-quarter of this basic flow deviation value is extracted and set as the microscopic control threshold, thus characterizing the lower limit of the microscopic tolerance for slight flow differences at local characteristic locations.

[0052] S202, compare the maximum flow rate difference with the preset macro control threshold and the preset micro control threshold to form a branch flow logic.

[0053] After obtaining the comparison benchmark, the hierarchical judgment and flow adjustment module 200 compares the maximum flow velocity difference with the macro control threshold and the micro control threshold, including the following branch execution logic: when it is determined that the maximum flow velocity difference is greater than the macro control threshold, the program flows to the macro supply volume adjustment stage; when it is determined that the maximum flow velocity difference is greater than or equal to the micro control threshold and less than or equal to the macro control threshold, the program flows to the local micro calculation stage; when it is determined that the maximum flow velocity difference is less than the micro control threshold, the program flows to the closed-loop verification stage to end the flow velocity optimization cycle.

[0054] S203, when the maximum flow rate difference is greater than the macroscopic control threshold, adjust the flow rate ratio constant of the flow branch area of ​​the three-dimensional parameterized digital model of the extrusion die until the maximum flow rate difference is less than or equal to the macroscopic control threshold.

[0055] Entering the macro-adjustment branch typically signifies a large deviation in the flow distribution of the molten metal into each initial cavity of the die. In this case, the hierarchical determination and flow adjustment module 200 extracts the structural features of the upper die flow channel from the three-dimensional parametric model of the extrusion die. The cross-sectional area of ​​the upper die flow channel directly controls the initial volume distribution of the molten metal into each independent cavity of the die. The hierarchical determination and flow adjustment module 200 uses volume scaling operations to change the cross-sectional area distribution ratio of the upper die flow channel structural features to update the flow channel area ratio constant. The volume scaling update formula is: ; In the formula, Indicates the updated first generation used to drive mesh deformation. The area ratio constant of each diversion orifice; Indicates the current number The first iteration phase The area ratio constant of each diversion orifice; Indicates the relationship with the first The local average outlet velocity of the cavity region corresponding to each diversion hole; This represents the extracted global average outlet flow rate; This represents the step size coefficient for macroeconomic adjustments.

[0056] As a preferred approach, the macroscopic adjustment step size coefficient is not constant. The hierarchical determination flow adjustment module 200 calculates the ratio of the maximum flow velocity difference obtained in the current iteration to the global average outlet flow velocity, and uses this ratio as the macroscopic adjustment step size coefficient to ensure that the adjustment range is larger when the deviation is larger and the adjustment range is smoother when the deviation is smaller, thereby preventing numerical oscillation.

[0057] After the calculation is completed, the hierarchical judgment and flow adjustment module 200 passes the updated flow distribution orifice area ratio constant to the underlying solution kernel, driving the update of the finite element mesh and recalculating the velocity distribution results inside the forming region. The hierarchical judgment and flow adjustment module 200 performs iterative extraction on the reconstructed flow field until the latest obtained maximum velocity difference is less than or equal to the macroscopic control threshold, thereby establishing a macroscopic supply volume balance at the mold inlet end, and returning the latest obtained maximum velocity difference to the execution threshold comparison judgment to proceed to the corresponding subsequent stage.

[0058] S204, when the maximum flow velocity difference is greater than or equal to the micro-control threshold and less than or equal to the macro-control threshold, the proxy model construction module 300 is triggered to perform local solution operation.

[0059] When the flow field state falls within this intermediate judgment range, it indicates that the macroscopic metal flow rate between the chambers of the extrusion die has basically established a volume balance. At this time, the remaining flow velocity deviation is mainly induced by unreasonable local micro-geometric dimensions such as the direct-flow semi-obstruction flow-blocking structure. Based on the clear state flow-diversion conditions, the hierarchical judgment flow adjustment module 200 sends a command signal to the proxy model construction module 300, triggering the proxy model construction module 300 to perform local solution operations. The trigger operation will stop adjusting the area ratio constant of the flow-diversion orifice and switch to performing solutions for local micro-geometric features.

[0060] S205, when the maximum flow velocity difference is less than the micro-control threshold, mark the fluid dynamics balance as achieved and perform state verification closed loop.

[0061] During the comparison and judgment phase, if the hierarchical judgment and flow adjustment module 200 determines that the maximum flow velocity difference is directly less than the microscopic control threshold, it indicates that the metal flow field corresponding to the current finite element mesh has met the high-precision supply and flow balance requirements. The hierarchical judgment and flow adjustment module 200 terminates the flow velocity optimization iteration, marks the current mold state as qualified by the fluid dynamics test, and guides the overall algorithm program into the closed-loop verification phase to perform verification condition judgment and finally output the three-dimensional parameterized digital model of the extrusion mold.

[0062] Reference Figure 1 and Figure 2 In this embodiment, the agent model construction module 300 includes the following sub-steps.

[0063] S301, establish a preset trust region radius boundary, and generate the geometric feature perturbation sample based on the independent geometric parameter vector.

[0064] In this embodiment, when the execution state transitions to local microscopic solution, the proxy model construction module 300 generates geometric feature perturbation samples based on the independent geometric parameter vector. Considering the massive computational overhead associated with full-scale finite element simulation, to ensure the efficiency of sampling and the local approximation accuracy of the subsequent proxy model, the proxy model construction module 300 establishes a preset trust region radius boundary centered on the spatial coordinate system where the acquired independent geometric parameter vector is located.

[0065] As a preferred approach, the value of the trust region radius boundary is dynamically calculated by the surrogate model construction module 300. Specifically, the surrogate model construction module 300 extracts the absolute values ​​of each parameter dimension within the current independent geometric parameter vector, and multiplies them by a dynamic scaling factor to obtain the trust region radius boundary for the corresponding dimension. To objectively reflect the velocity error magnitude and prevent abrupt changes in the flow field geometry and topology during local optimization, the dynamic scaling factor is set to the ratio of the currently extracted maximum velocity difference to the global average outlet velocity.

[0066] After defining the boundary, since the independent geometric parameter vector contains three variable dimensions with different physical dimensions—the occlusion area ratio parameter, the inverted cone angle parameter, and the boundary offset parameter—the surrogate model construction module 300 performs a maximum-minimum value normalization preprocessing operation on these parameter dimensions, mapping them to a dimensionless reference interval. After preprocessing, the surrogate model construction module 300 applies the Latin hypercube sampling algorithm within the boundary of the trust region radius to generate discretely distributed geometric feature perturbation samples. The Latin hypercube sampling algorithm generates multiple geometric parameter combination data that are uniformly distributed within the safe optimization interval and have no projection overlap by dividing the probability interval of each parameter dimension with equal probability and independently sampling randomly within each sub-interval.

[0067] S302, perform local solution on the geometric feature disturbance sample to obtain the flow field physical response data, and train and construct the local kriging surrogate model.

[0068] After obtaining the sample data, the surrogate model construction module 300 performs local solution calculations on the geometric feature perturbation sample to train a local kriging surrogate model. Specifically, the surrogate model construction module 300 calls the finite element solver to perform a small-scale simulation solution on the geometric feature perturbation sample. For each generated geometric feature perturbation sample, the program performs an inverse normalization operation on its contained geometric parameter combination data to restore it to its true physical dimensions, then substitutes it into the underlying spatial mapping relationship to directly drive the corresponding mesh node to undergo local deformation. Subsequently, it calls the underlying fluid solution kernel to calculate the local flow field distribution after deformation, extracting the average outlet velocity for each corresponding region as the physical response data of the flow field.

[0069] In the model training phase, the input feature data of this local kriging surrogate model consists of three-dimensional normalized geometric parameter variables, while the output is a multi-dimensional average outlet flow velocity for each chamber region. In specific business contexts, this output corresponds to the local metal flow state during the extrusion molding process. Internally, this local kriging surrogate model includes a global polynomial trend module and a local Gaussian stochastic process residual module. The global polynomial trend module is used to fit the macroscopic trend of the relationship between geometric parameters and flow velocity, while the local Gaussian stochastic process residual module is used to capture the complex local fluctuation characteristics caused by nonlinear fluid-structure interaction.

[0070] To ensure accurate model construction, the surrogate model construction module 300 uses the geometric feature perturbation sample as training sample data and the obtained flow field physical response data as label data. In the training step, the surrogate model construction module 300 calculates the spatial correlation matrix of the Gaussian correlation function based on the Euclidean spatial distance between the input sample points. Subsequently, aiming to maximize the probability of observing the flow field physical response data, the surrogate model construction module 300 constructs a log-maximum likelihood function as the training loss function. By solving for the extremum of this maximum likelihood function using a built-in optimization algorithm, the surrogate model construction module 300 determines the optimal hyperparameter configuration in the spatial correlation matrix. After parameter convergence and update, the initial mathematical model completes weight solidification, formally generating the local kriging surrogate model, which mathematically establishes an explicit smooth mapping expression from independent geometric parameters to the average outlet velocity of each region.

[0071] S303, perform partial derivative operations on the local Kriging proxy model to obtain the Jacobian matrix.

[0072] After the model training is complete, the surrogate model construction module 300 performs partial derivative calculations on the local Kriging surrogate model to obtain the Jacobian matrix. Conventional finite difference methods rely on multiple mesh reconstruction simulations to calculate gradients, which easily introduces numerical truncation errors. Given the smooth and continuously differentiable mathematical properties of this local Kriging surrogate model, the surrogate model construction module 300 directly performs pure mathematical differential calculations term by term on the explicit regression function of the trained local Kriging surrogate model. This calculation program parses the set of discrete partial derivatives of the average outlet velocity with respect to each parameter dimension corresponding to the independent geometric parameter vector.

[0073] After acquiring the gradient data, the surrogate model construction module 300 arranges the discrete partial derivative set data according to the corresponding positional relationship between the rows containing the fluid characteristic regions and the columns containing the geometric parameter variables, forming the Jacobian matrix in a two-dimensional matrix format. This Jacobian matrix is ​​used in mechanical optimization analysis to transform geometric spatial parameter perturbations into physical field response gradients, and its construction formula is as follows: ; In the formula, This indicates the generated Jacobian matrix; to This indicates that the model corresponds to the calculated first to the second... The average outlet flow rate of each extraction zone; to This indicates the three geometric parameter variables contained within the independent geometric parameter vector: the occlusion area ratio parameter, the inverted cone angle parameter, and the boundary offset parameter. Indicates the first The average outlet flow rate of the extraction region is related to the first extraction region. The partial derivatives of each geometric parameter variable are calculated, forming the fundamental matrix elements of this discrete partial derivative set. This Jacobian matrix explicitly quantifies the mathematical sensitivity of each flow control variable to different chamber velocities, providing a complete gradient data matrix for the parameter update step size in subsequent optimization iterations.

[0074] Reference Figure 1 and Figure 2 In this embodiment, the penalty weight calculation module 400 includes the following sub-steps.

[0075] S401, the virtual deformation trend vector is constructed based on the first principal stress vector and the Jacobian matrix.

[0076] In this embodiment, the penalty weight calculation module 400 receives the first principal stress vector output by the discretization extraction module 100 and the Jacobian matrix output by the surrogate model construction module 300. The destructive tensile stress experienced by the cantilever node in the thin-walled cavity region, located by the first principal stress vector, typically originates from the lateral shear drag force generated by the difference in metal flow velocity between adjacent regions on either side.

[0077] Therefore, the penalty weight calculation module 400, based on the weak stress region indicated by the first principal stress vector, extracts the partial derivative row vectors in the Jacobian matrix corresponding to the average outlet velocity of the thick-walled solid region and the thin-walled cavity region adjacent to the two sides of the weak node, and performs a difference subtraction operation on the two sets of partial derivative row vectors to obtain the relative velocity difference vector reflecting the trend of fluid dynamics.

[0078] To convert the velocity difference gradient in the parameter space into structural deformation in the physical space, the penalty weight calculation module 400 calls the preset fluid-structure interaction flexibility transformation matrix to perform coordinate space multiplication on the relative velocity difference vector, thereby deriving and constructing the virtual deformation trend vector used to predict the future displacement direction and displacement amplitude of weak nodes.

[0079] As a preferred approach, the fluid-structure interaction compliance transformation matrix is ​​not a directly set fixed parameter. Instead, it is obtained by the penalty weight calculation module 400 during the mold mesh initialization phase. This is achieved by extracting the material elastic modulus and Poisson's ratio of the current mold mesh nodes, substituting them into the finite element elasticity equations to construct a global stiffness matrix, and then inverting this global stiffness matrix. The formula for calculating the virtual deformation trend vector is as follows: ; In the formula, This represents the virtual deformation trend vector derived and constructed; This represents the fluid-structure interaction compliance transformation matrix obtained from the aforementioned calculations; and These represent the row vectors of partial derivatives extracted from the Jacobian matrix, corresponding to the average outlet velocity of the thick-walled solid region and the thin-walled cavity region, respectively. This represents the matrix transpose operator.

[0080] S402, calculate the gradient projection dot product of the virtual deformation trend vector and the first principal stress vector.

[0081] After obtaining the derived three-dimensional spatial displacement vector, the penalty weight calculation module 400 calculates the gradient projection dot product of the virtual deformation trend vector and the first principal stress vector. This spatial mathematical operation not only considers the absolute amplitude increment of the stress deformation but also checks the coincidence of the three-dimensional vector directions. The first principal stress vector indicates the mechanical orientation of the weak node of the mold under significant tensile stress, while the virtual deformation trend vector indicates the orientation of the physical displacement that will occur under the current geometric parameter adjustment strategy. The penalty weight calculation module 400 performs a three-dimensional vector dot product operation on the two to obtain the projection component of the deformation trend in the direction of the maximum tensile stress. The calculation formula is as follows: ; In the formula, This represents the calculated gradient projection dot product; This represents the virtual deformation trend vector constructed by the preceding derivation; This indicates that the first principal stress vector has been extracted and obtained.

[0082] Through the projection mechanism of dot product operation, the multi-dimensional fluid-structure interaction is transformed into a single projected scalar, which physically characterizes the degree of influence of fluid dynamics changes on the stress of solid structures. This is used to predict in advance whether adjustment actions aimed solely at optimizing the flow field will cause abnormal displacement of the mold tongue core structure.

[0083] S403, generate the penalty weight matrix based on the determination result of the gradient projection dot product.

[0084] Based on the calculated projection scalar, the penalty weight calculation module 400 establishes branch control logic for determining the safety of the optimization path according to the positive or negative polarity of the gradient projection dot product. When the gradient projection dot product is determined to be less than or equal to zero, it indicates that the angle between the virtual deformation trend vector and the first principal stress vector is greater than or equal to 90 degrees. This indicates that the subsequent geometric parameter adjustment actions to be performed have not exacerbated the stretching trend, and may even generate a reverse unloading thrust to alleviate the tensile stress concentration in the mold. Based on this determination, the system confirms that the current optimization path is in a safe state, and the penalty weight calculation module 400 directly generates a unit feature matrix with all elements on the main diagonal being one as the penalty weight matrix, that is, no additional penalty intervention is applied to the current fluid dynamics optimization step size.

[0085] When the gradient projection dot product is determined to be greater than zero, it indicates that the virtual deformation trend vector has a positive superposition component in the direction of the first principal stress vector. At this point, the local optimization performed to achieve macroscopic metal flow velocity balance may trigger mechanical conflicts. To adjust this optimization tendency, the penalty weight calculation module 400 uses a nonlinear exponential transformation function to mathematically amplify the degree of danger corresponding to the gradient projection dot product, generating a penalty weight matrix with a diagonal eigenvalue greater than one. Its calculation formula is as follows: ; In the formula, This represents the generated penalty weight matrix; This represents a mathematical function that generates a diagonal matrix based on the diagonal elements given in parentheses. This represents the calculated dot product of the gradient projection; This represents a nonlinear exponential transformation function with the natural constant as its base; This indicates a conflict amplification and punishment factor.

[0086] To ensure that the applied penalty intensity matches the material's mechanical properties, the penalty weight calculation module 400 extracts the current yield stress limit value of the mold matrix material, calculates the ratio of the modulus of the first principal stress vector to the yield stress limit value, and uses this ratio as the conflict amplification penalty factor. The generated penalty weight matrix serves as the penalty term coefficient in the subsequent optimization algorithm, increasing the iterative resistance of the objective function to reduce the parameter update step size towards the dangerous direction, thus establishing a structural protection mechanism that balances fluid equilibrium and solid safety.

[0087] Reference Figure 1 , Figure 2 , Figure 4 In this embodiment, the mesh reconstruction optimization module 500 includes the following sub-steps.

[0088] S501, substitute the Jacobian matrix, the penalty weight matrix, and the velocity deviation vector into the objective equation for parameter correction and solve to obtain the parameter update step size.

[0089] In this embodiment, the mesh reconstruction optimization module 500 is used to substitute the Jacobian matrix obtained by the proxy model construction module 300, the penalty weight matrix obtained by the penalty weight calculation module 400, and the flow velocity deviation vector issued by the discretization extraction module 100 into the parameter correction objective equation to solve for the parameter update step size. The multi-objective equation solution integrates the fluid dynamics equilibrium error and solid mechanical safety penalty of the mold into the same mathematical solution system through matrix cross-operation.

[0090] At the implementation level, the velocity deviation vector is a discrete sequence of differences formed by subtracting the actual average outlet velocity of each locally extracted region from the global average outlet velocity of the entire extrusion die. The mesh reconstruction and optimization module 500 uses a weighted Gauss-Newton iterative algorithm to construct the objective equation for this parameter correction. By performing a combination of transpose, multiplication, and inversion operations on the substituted matrices, the mesh reconstruction and optimization module 500 calculates and outputs the parameter update step size affected by local stress intervention. The specific solution formula for the objective equation for this parameter correction is as follows: ; In the formula, This represents the update step size of the parameter obtained from the solution, and is expressed as a vector containing the correction increments of each independent geometric parameter; The learning rate constant is represented by a value between 0.1 and 0.5, which is preferred to balance the absolute convergence speed of a single optimization iteration with the numerical stability of the solution process. This indicates the Jacobian matrix obtained by the proxy model building module 300; Let represent the transpose of the Jacobian matrix; This indicates the penalty weight matrix obtained by the penalty weight calculation module 400; This represents the flow velocity deviation vector emitted by the discretization extraction module 100; superscript This symbol represents the matrix inversion operation. Through the operation mechanism of this mathematical equation, when there is a trend of motion that may induce polarization cracking, the penalty elements with eigenvalues ​​greater than 1 inside the penalty weight matrix will increase the condition number of the corresponding cross-product matrix. During the inversion process, the parameter update amplitude in the tensile stress direction is limited, thereby guiding the output parameter update step size to evolve within the safe region.

[0091] S502, extract the absolute modulus value corresponding to the parameter update step size and compare it with the value of the trust region radius boundary to perform forced mathematical step size truncation processing.

[0092] To prevent extrapolation deviations during optimization iterations, the mesh reconstruction optimization module 500 performs strict boundary-based failure prevention checks on the calculated update step size of this parameter. Since the local kriging surrogate model only achieves high fitting accuracy within the selected sample interval, an excessively large update step size for this parameter could lead to subsequent mesh parameters exceeding their limits, easily causing prediction distortion in the surrogate model and mesh penetration distortion.

[0093] Based on this, the mesh reconstruction optimization module 500 extracts the absolute modulus value for each geometric variable dimension in the parameter update step size and compares it with the trust region radius boundary value set by the surrogate model construction module 300. When it is determined that one or more extracted absolute modulus values ​​are greater than the trust region radius boundary value, the mesh reconstruction optimization module 500 performs a numerical truncation operation on the step size of the dimension exceeding the boundary. Specifically, the mesh reconstruction optimization module 500 forcibly sets the update step size value of the dimension exceeding the boundary to be equal to the trust region radius boundary value, while keeping the positive and negative signs of the original solution calculation output unchanged. If it is determined that the absolute modulus value is less than or equal to the trust region radius boundary value, the parameter update step size of the original solution calculation output is retained. This forced truncation operation guides each optimization adjustment action to be constrained within the reliable interpolation range of the surrogate model.

[0094] S503, the parameter update step size is converted into the control point displacement of the free deformable mesh control box to drive the finite element mesh to undergo topological smooth deformation. Based on the deformed finite element mesh, closed-loop iterative verification is performed until the convergence condition is met and the result is output.

[0095] After completing the security verification, the mesh reconstruction and optimization module 500 adds the truncated parameter update step size to the current independent geometric parameter vector to obtain the updated independent geometric parameter vector. By calling the spatial mapping relationship established by the discretization extraction module 100 in the previous step, the mesh reconstruction and optimization module 500 converts the parameter update step size into the control point displacement of the free-deformable mesh control box. The spatial movement of the control points on the surface of the free-deformable mesh control box changes the Bernstein polynomial interpolation weight distribution in the three-dimensional space inside the control box. This change in the weight field drives the nodes inside the finite element mesh contained therein to undergo topological smoothing deformation. This control box-based driving mechanism can better maintain the Jacobian mesh quality after the mesh undergoes local deformation, thereby reducing the computational cost of re-meshing.

[0096] To verify the accuracy of the surrogate model's predictions and the final mechanical safety, the mesh reconstruction and optimization module 500 calls the underlying full-scale physical solver to perform closed-loop iterative verification based on the finite element mesh after topological smoothing deformation. For this full-scale physical solver, those skilled in the art can use existing commercial finite element simulation software kernels or open-source numerical solving engines, which utilize the fundamental principles of finite element analysis to re-perform dual-field calculations of fluid mechanics and solid mechanics on the deformed mesh. This verification solution execution process is well-known in the field and will not be elaborated upon here. The mesh reconstruction and optimization module 500 extracts the maximum velocity difference and the magnitude of the first principal stress vector at the current moment obtained from the verification solution in real time and performs dual threshold condition judgment.

[0097] If the maximum flow velocity difference at the current moment is greater than or equal to the micro-control threshold, or the magnitude of the first principal stress vector at the current moment is greater than or equal to the preset yield safety threshold, then the finite element mesh after the current deformation is taken as the initial state, and the process returns to step S1 to perform a new round of extraction, surrogate model reconstruction and parameter solving loop.

[0098] As a preferred method, for setting the yield safety threshold, those skilled in the art can extract the yield stress limit value of the mold matrix material at the working environment temperature, multiply it by a safety factor between 0.7 and 0.85, and obtain the specific calculation and selection rules, which are well known in the art and will not be elaborated here.

[0099] When the judgment result shows that the maximum flow velocity difference at the current moment is less than the micro-control threshold and the magnitude of the first principal stress vector at the current moment is lower than the yield safety threshold, the mesh reconstruction optimization module 500 confirms that the control process has reached the dual standards of fluid dynamics equilibrium and solid structure mechanical safety, and terminates the optimization closed-loop iteration.

[0100] Subsequently, the mesh reconstruction and optimization module 500 extracts the coordinates of the outer surface boundary nodes of the finite element mesh that finally meets the conditions. It then applies a non-uniform rational B-spline surface reconstruction algorithm to reconstruct the discrete mesh node network into a smooth, continuous geometric surface. Finally, it inversely fits the finite element mesh that meets the conditions to output the final three-dimensional parametric digital model of the extrusion die. This operation realizes the parameter conversion from the underlying simulation mesh space to the standard drawing space of computer-aided design. The output model file can be directly used to guide the CNC machine tools under its jurisdiction in the solid machining of the die.

[0101] To further illustrate the implementation process and technical effects of this invention, the following description is provided in conjunction with specific application scenarios and experimental data. The specific numerical values, scenario parameters, and comparative experiments described below are only used to explain the implementation principle of this invention and do not limit the scope of protection of this invention.

[0102] For the processing of wide battery end plate components for new energy vehicles, the profile cross-section width is 317.5mm. This component comprises a hollow body and a solid body, with the thinnest wall thickness in the thin-walled cavity region being 2.0mm and the thickest wall thickness in the thick-walled solid region reaching 37mm × 24mm, a difference of nearly 20 times. To ensure molding quality, a finite element method (FEM)-based control method for extrusion dies of multi-cavity profiles with ultra-large wall thickness differences is adopted. Analysis and calculations are performed based on the data output from the FEM simulation to achieve die control during the production process of multi-cavity profiles.

[0103] The discretization extraction module 100 reads the three-dimensional parametric digital model of the extrusion die and generates a finite element mesh. Based on this finite element mesh, it divides the region into a thick-walled solid area and a thin-walled cavity area. After simulation calculation, the statistical median of the overall normal thickness is 3 mm, and the preset wall thickness boundary threshold is set to 4.5 mm. The average outlet velocity of the thick-walled solid area and the thin-walled cavity area are extracted through simulation calculation to construct a velocity deviation vector. Based on the velocity deviation vector, the maximum velocity difference between the thick-walled solid area and the thin-walled cavity area is extracted. The value of the maximum velocity difference is equal to the maximum value minus the minimum value in the velocity deviation vector. The initially extracted maximum velocity difference value is 45 mm / s. The discretization extraction module 100 extracts the first principal stress vector of the weak node at a wall thickness of 2.0 mm in the thin-walled cavity area. The first principal stress vector extracts the maximum positive eigenvalue representing the maximum tensile failure tendency and its corresponding characteristic direction vector. A free-deformable mesh control box is constructed in the thick-walled solid area, and a spatial mapping relationship is established between the coordinates of the discrete mesh nodes in the free-deformable mesh control box and the preset independent geometric parameter vector.

[0104] The hierarchical determination and flow adjustment module 200 receives the maximum velocity difference transmitted by the discretization extraction module 100. Based on the global average outlet velocity and coefficient of variation, it calculates and obtains a preset macroscopic control threshold of 30 mm / s and a preset microscopic control threshold of 22 mm / s. The maximum velocity difference is compared with the preset macroscopic and microscopic control thresholds. Since the initial maximum velocity difference of 45 mm / s is greater than the preset macroscopic control threshold of 30 mm / s, the hierarchical determination and flow adjustment module 200 adjusts the area ratio constants of the 13 flow branch holes in the three-dimensional parameterized digital model of the extrusion die. The updated flow branch hole area ratio constant is then calculated, and its value is equal to the current flow branch hole area ratio constant multiplied by one minus the product of the macroscopic adjustment step size coefficient and the local relative deviation, where the local relative deviation is equal to the difference between the local average outlet velocity and the global average outlet velocity, divided by the global average outlet velocity. After macroscopic adjustment iterations, the maximum velocity difference decreases to 25 mm / s. At this point, the maximum flow velocity difference is greater than or equal to the preset micro-control threshold and less than or equal to the preset macro-control threshold, triggering the proxy model construction module 300 to perform a local solution operation.

[0105] The surrogate model construction module 300 generates geometric feature perturbation samples based on the independent geometric parameter vectors established by the discretization extraction module 100. These independent geometric parameter vectors include the occlusion area ratio parameter, the inverted cone angle parameter, and the boundary offset parameter. The initially extracted occlusion area ratio parameter is set to 0.5, the inverted cone angle parameter to 30°, and the boundary offset parameter to 3.0 mm. Local solutions are performed on the geometric feature perturbation samples to train a local kriging surrogate model. Partial derivative calculations are then performed on the local kriging surrogate model to obtain the Jacobian matrix. This Jacobian matrix is ​​formed by combining and arranging the calculated values ​​of the partial derivatives of the average outlet velocity of each divided region with respect to the three geometric parameter variables: the occlusion area ratio parameter, the inverted cone angle parameter, and the boundary offset parameter.

[0106] The penalty weight calculation module 400 derives and constructs a virtual deformation trend vector based on the first principal stress vector output by the discretization extraction module 100 and the Jacobian matrix output by the surrogate model construction module 300. The process involves: calling a preset fluid-structure interaction compliance transformation matrix and multiplying it by the transpose of the difference between the row vectors of partial derivatives of the average outlet velocities of the thick-walled solid region and the thin-walled cavity region. The gradient projection dot product of the virtual deformation trend vector and the first principal stress vector is calculated, i.e., a three-dimensional vector dot product operation is performed. If the calculated gradient projection dot product is greater than zero, a penalty weight matrix is ​​generated based on the gradient projection dot product determination result. This is achieved by using a nonlinear exponential transformation function to mathematically map the product of the conflict amplification penalty factor and the gradient projection dot product, generating a diagonal matrix with eigenvalues ​​greater than one on the main diagonal.

[0107] The mesh reconstruction and optimization module 500 substitutes the Jacobian matrix obtained by the proxy model construction module 300, the penalty weight matrix obtained by the penalty weight calculation module 400, and the velocity deviation vector issued by the discretization extraction module 100 into the parameter correction objective equation to solve for the parameter update step size. It extracts the absolute modulus value corresponding to the parameter update step size and compares it with the preset trust region radius boundary value to perform forced mathematical step size truncation. The truncated parameter update step size is converted into the control point displacement of the free-deformation mesh control box to drive the finite element mesh to undergo topological smooth deformation. Based on the finite element mesh after topological smooth deformation, closed-loop iteration is performed until the maximum velocity difference at the current moment is less than the preset micro-control threshold and the modulus of the first principal stress vector at the current moment is less than the preset yield safety threshold. After closed-loop iteration, the maximum velocity difference at the current moment decreases to 21.035 mm / s, which is less than the preset micro-control threshold of 22 mm / s. The final finite element mesh that meets the conditions is then backfitted and output as the final state three-dimensional parameterized digital model of the extrusion die.

[0108] Experimental verification and effect comparison: To verify the actual operating data of the control system of the ultra-large wall thickness difference multi-cavity profile extrusion die in the finite element simulation under the environment of a 3600-ton extruder, a control group and a test group were set up to carry out physical processing and on-machine testing.

[0109] The control group used a traditional fully shielded flow-blocking cone mold structure that was not optimized by calculation. This control group only relied on manual experience to set up fully shielded flow-blocking blocks in the thick-walled solid area, lacking macroscopic control of the area ratio constant of each diversion hole and microscopic gradient optimization calculation for shielding area and inverted cone angle.

[0110] The test group used the finite element method to simulate the final state of the extrusion die, which output a three-dimensional parameterized digital model of the extrusion die. The test group extracted the first principal stress vector obtained by the discretization extraction module, obtained the Jacobian matrix through the surrogate model construction module, and combined the penalty weight matrix to multiply the mathematical gradient with the first principal stress vector to obtain the parameter update step size for crack prevention intervention in order to reconstruct the direct-impact semi-blocking flow-blocking frustum structure.

[0111] Test conclusion: Combining Figure 5 It can be seen that, as Figure 5 As shown in Figure (a), the maximum flow velocity difference at the outlet section of the working zone in the control group reached as high as 48.5 mm / s, while in the extrusion test of the test group, this value converged to 21.035 mm / s. The data results verified that the method, through hierarchical judgment and the Jacobian matrix output by the surrogate model, can improve the macroscopic and microscopic flow imbalance between the thick-walled solid area and the thin-walled cavity area. Due to the more uniform flow velocity distribution, the lateral shear drag force on the small tongue core structure decreased, and the test group completely avoided the swaying and cracking phenomena caused by the excessive metal flow velocity at the thick-walled solid body position in the control group. In terms of forming quality, compared with the control group profile where the coplanarity of the four small faces of the upper half of the profile was greater than 0.4 mm, the gap of the bottom large face was greater than 0.6 mm, and there were uneven defects on the lower surface, the metal filling of the thick-walled solid body position of the profile produced by the test group was complete, and all the above-mentioned geometric tolerances were strictly controlled within the qualified range.

[0112] At the same time, such as Figure 5 As shown in Figure (b), due to the significant reduction in mechanical losses, the actual throughput of the mold in the test group jumped from 8.5t in the control group to 66.942t. This indicates that the system introduces the first principal stress vector as an anti-cracking intervention condition through the penalty weight calculation module to update parameters, thus avoiding the wobble and tensile cracking of the mold's small tongue core structure caused by excessively high local flow velocity.

[0113] In summary, this solution achieves geometric optimization of the direct-punch semi-obstructed flow-blocking truncated cone structure, improving the mechanical safety and service life of the extrusion die while ensuring the coplanarity and gap dimension accuracy of the extruded profile.

[0114] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A finite element method simulation-based control system for multi-cavity profile extrusion dies with large wall thickness differences, characterized in that, include: The discretization extraction module is used to read the three-dimensional parametric digital model of the extrusion die and generate a finite element mesh to divide the thick-walled solid region and the thin-walled cavity region. Through simulation calculation, the average outlet flow velocity of the thick-walled solid region and the thin-walled cavity region are extracted to construct the flow velocity deviation vector, the maximum flow velocity difference, and the first principal stress vector of the weak node. The spatial mapping relationship between the coordinates of the discrete mesh nodes in the free deformation mesh control box constructed in the thick-walled solid region and the preset independent geometric parameter vector is established. The hierarchical determination and flow adjustment module is used to compare the maximum flow velocity difference with the macro control threshold and the micro control threshold. When the maximum flow velocity difference is greater than the macro control threshold, the flow diversion orifice area ratio constant is adjusted. When the maximum flow velocity difference is greater than or equal to the micro control threshold and less than or equal to the macro control threshold, a local solution operation is triggered. The surrogate model construction module is used to generate geometric feature perturbation samples based on the preset independent geometric parameter vector and perform the local solution operation to train the local kriging surrogate model, and to perform partial derivative operations on the local kriging surrogate model to obtain the Jacobian matrix. The penalty weight calculation module is used to derive and construct a virtual deformation trend vector based on the first principal stress vector and the Jacobian matrix, calculate the gradient projection dot product, and generate a penalty weight matrix based on the gradient projection dot product. The mesh reconstruction and optimization module is used to substitute the Jacobian matrix, the penalty weight matrix, and the flow velocity deviation vector into the parameter correction objective equation to solve for the parameter update step size to drive the finite element mesh to undergo topological smoothing deformation. Based on the deformed finite element mesh, closed-loop iteration is performed until the yield safety threshold verification condition is met, and then the final state of the three-dimensional parameterized digital model of the extrusion die is output.

2. The finite element simulation control system for multi-cavity profile extrusion dies with large wall thickness differences according to claim 1, characterized in that, The discretization extraction module is specifically used to calculate the statistical median of the overall normal thickness, multiply the statistical median by the benchmark reference multiple and set it as the wall thickness boundary threshold, divide the set of grid cells with a normal thickness size greater than the wall thickness boundary threshold into the thick-walled solid region, and divide the set of grid cells with a normal thickness size less than or equal to the wall thickness boundary threshold and with a cantilever structure into the thin-walled cavity region.

3. The finite element simulation control system for multi-cavity profile extrusion dies with large wall thickness differences according to claim 1, characterized in that, The discretization extraction module is further used to perform eigenvalue decomposition on the three-dimensional stress tensor matrix of the mesh nodes contained in the thin-walled cavity region to calculate the scalar equivalent stress value, define the mesh node with the largest scalar equivalent stress value as the weak node, extract the largest positive eigenvalue contained in the three-dimensional stress tensor matrix of the weak node and the feature direction vector corresponding to the largest positive eigenvalue to form the first principal stress vector; extract the mesh vertex coordinate data wrapped by the free deformation mesh control box, and call the polynomial interpolation function to bind and map the coordinates of the discrete mesh nodes to the preset independent geometric parameter vector, the preset independent geometric parameter vector including the occlusion area ratio parameter, the inverted cone angle parameter and the boundary offset parameter.

4. The finite element simulation control system for multi-cavity profile extrusion die with large wall thickness difference according to claim 1, characterized in that, The hierarchical determination and flow adjustment module is specifically used to extract the standard deviation of the global average outlet flow velocity and the outlet flow velocity of each cavity region, extract the ratio of the standard deviation to the global average outlet flow velocity as the coefficient of variation, multiply the global average outlet flow velocity by the coefficient of variation to obtain the basic flow deviation value, and set the macro control threshold and the micro control threshold based on the basic flow deviation value.

5. The finite element simulation control system for multi-cavity profile extrusion die with large wall thickness difference according to claim 4, characterized in that, The hierarchical determination and flow adjustment module is also used to change the cross-sectional area distribution ratio of the upper mold flow channel structure feature by using volume scaling operation to update the flow channel area ratio constant. The updated flow channel area ratio constant is equal to the current flow channel area ratio constant multiplied by the volume correction coefficient. The volume correction coefficient is equal to the product of the macroscopic adjustment step size coefficient and the local relative deviation. The local relative deviation is equal to the difference between the local average outlet velocity and the global average outlet velocity, divided by the global average outlet velocity. The macroscopic adjustment step size coefficient is the ratio of the maximum velocity difference to the global average outlet velocity.

6. The finite element simulation control system for multi-cavity profile extrusion die with large wall thickness difference according to claim 1, characterized in that, The proxy model construction module is specifically used to extract the absolute values ​​of each parameter dimension contained in the preset independent geometric parameter vector, multiply the absolute values ​​of each parameter dimension by a dynamic scaling factor to obtain the trust region radius boundary of the corresponding dimension, apply a sampling algorithm within the trust region radius boundary to generate discretely distributed geometric feature perturbation samples, and call the finite element solver to calculate the average outlet velocity corresponding to the geometric feature perturbation samples as flow field physical response data.

7. The finite element simulation control system for multi-cavity profile extrusion dies with large wall thickness differences according to claim 6, characterized in that, The surrogate model construction module is further used to train the local kriging surrogate model by using the geometric feature perturbation samples as training sample data and the flow field physical response data as label data, perform differential operations on the explicit regression function of the local kriging surrogate model, parse out the set of discrete partial derivatives of the average outlet velocity with respect to each parameter dimension of the preset independent geometric parameter vector, and combine and arrange the set of discrete partial derivatives to form the Jacobian matrix.

8. The finite element simulation control system for multi-cavity profile extrusion die with large wall thickness difference according to claim 1, characterized in that, The penalty weight calculation module is specifically used to extract the partial derivative row vectors corresponding to the average outlet velocity of the thick-walled solid region and the thin-walled cavity region from the Jacobian matrix, perform a difference subtraction operation on the partial derivative row vectors to obtain the relative velocity difference vector, call the fluid-structure interaction flexibility transformation matrix to perform coordinate space multiplication on the relative velocity difference vector to construct the virtual deformation trend vector, and perform a three-dimensional vector dot product operation on the virtual deformation trend vector and the first principal stress vector to obtain the gradient projection dot product.

9. The finite element simulation control system for multi-cavity profile extrusion dies with large wall thickness differences according to claim 8, characterized in that, The penalty weight calculation module is further configured to generate a unit feature matrix with all diagonal elements equal to one as the penalty weight matrix when the gradient projection dot product is determined to be less than or equal to zero, and to calculate the ratio of the magnitude of the first principal stress vector to the yield stress limit value as the conflict amplification penalty factor when the gradient projection dot product is determined to be greater than zero. The module also uses a nonlinear exponential transformation function to mathematically map the product of the conflict amplification penalty factor and the gradient projection dot product to generate a diagonal matrix with a diagonal eigenvalue greater than one as the penalty weight matrix.

10. The finite element simulation control system for multi-cavity profile extrusion dies with large wall thickness differences according to claim 6, characterized in that, The mesh reconstruction optimization module is specifically used to solve the parameter correction objective equation through matrix cross operation and output the parameter update step size. It extracts the absolute modulus value corresponding to the parameter update step size and compares it with the trust region radius boundary. When it is determined that the absolute modulus value is greater than the trust region radius boundary, the update step size exceeding the boundary dimension is forcibly set to be equal to the trust region radius boundary value. The truncated parameter update step size is converted into the control point displacement of the free deformable mesh control box. Finally, the coordinates of the outer surface boundary nodes of the finite element mesh that finally meet the conditions are extracted and the surface reconstruction algorithm is applied to output the final state of the three-dimensional parameterized digital model of the extrusion die.

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