Automobile parts die casting mold temperature field and stress field coupling simulation method

Abstract

The application is suitable for the technical field of die casting mold simulation, in particular to a die casting mold temperature field and stress field coupling simulation method for automobile parts, which comprises: a closed-loop iteration process of determining the interface gap distribution according to the current temperature field, updating the interface heat transfer coefficient according to the gap distribution, and then re-solving the temperature field, which introduces the dynamic feedback relationship between the interface gap and the heat transfer coefficient, the temperature field into the simulation framework, and solves the problem of ignoring the dynamic change of the gap in the traditional one-way decoupling mode. Through iteration convergence judgment, it is ensured that the temperature field and the stress field reach a consistent state of coupling, effectively improving the simulation accuracy of the temperature field and the stress field in the gap sensitive scene such as thin-walled complex cavity, and providing a more reliable numerical basis for mold life assessment and process parameter optimization.

Description

Technical Field

[0001] This application belongs to the field of die casting mold simulation technology, and in particular relates to a coupled simulation method of temperature field and stress field of automotive part die casting mold. Background Technology

[0002] Under cyclic loading of repeated filling and cooling of high-temperature molten metal, die-casting molds exhibit a strong coupling relationship between their temperature and stress fields: the temperature field drives the stress field through thermal expansion, while the stress field causes mold deformation, altering the interfacial gap between the mold and the casting. This interfacial gap, in turn, affects heat transfer efficiency, forming a closed-loop feedback loop. Currently, mainstream simulation methods typically treat the temperature and stress fields as two independent steps for unidirectional calculation. Specifically, the temperature field is solved under a given fixed interfacial heat transfer coefficient, and the temperature field result is then used as a load input to the stress field solver for mechanical analysis. This unidirectional decoupling method ignores the dynamic impact of real-time changes in the interfacial gap on the heat transfer coefficient. This leads to a significant decrease in the simulation accuracy of the temperature and stress fields in gap-sensitive scenarios such as thin-walled complex cavities, failing to provide reliable numerical data for mold life assessment and process parameter optimization. Summary of the Invention

[0003] This application provides a method for simulating the coupled temperature and stress fields of die-casting molds for automotive parts. This method can solve the problem of insufficient simulation accuracy caused by the unidirectional decoupling calculation of temperature and stress fields in the prior art, which ignores the dynamic feedback of interface gaps.

[0004] In a first aspect, embodiments of this application provide a method for coupled simulation of temperature and stress fields in die-casting molds for automotive parts, including: Obtain the current temperature field of the die-casting mold for automotive parts; The gap distribution at the interface between the die-casting mold and the casting is determined based on the current temperature field; wherein, the gap distribution is the distribution of the separation distance between the die-casting mold and the casting along the normal direction of the interface; The interface heat transfer coefficient is updated based on the gap distribution and the pre-calibrated gap heat transfer mapping relationship; wherein, the gap heat transfer mapping relationship characterizes the correspondence between the interface gap value and the interface heat transfer coefficient value. The updated temperature field of the die-casting mold is determined based on the updated interface heat transfer coefficient. If the maximum node temperature difference between the updated temperature field and the current temperature field is less than a preset temperature threshold, the updated temperature field is determined as the coupled temperature field of the die-casting mold.

[0005] The technical solutions described in this application embodiment have at least the following technical effects: The temperature and stress field coupling simulation method for automotive component die-casting molds provided in this application incorporates the dynamic feedback relationship between interface gaps, heat transfer coefficients, and temperature fields into the simulation framework through a closed-loop iterative process: determining the interface gap distribution based on the current temperature field, updating the interface heat transfer coefficient based on the gap distribution, and then resolving the temperature field. This solves the problem of traditional unidirectional decoupling methods ignoring dynamic changes in gaps. Through iterative convergence determination, the method ensures that the temperature and stress fields achieve a consistent coupling state, effectively improving the simulation accuracy of temperature and stress fields in gap-sensitive scenarios such as thin-walled complex cavities. This provides a more reliable numerical basis for mold life assessment and process parameter optimization.

[0006] Secondly, embodiments of this application provide a coupled simulation system for the temperature field and stress field of die-casting molds for automotive parts, comprising: The acquisition unit is used to acquire the current temperature field of the die-casting mold for automotive parts; A distribution unit is used to determine the gap distribution at the interface between the die-casting mold and the casting based on the current temperature field; wherein the gap distribution is the distribution of the separation distance between the die-casting mold and the casting along the normal direction of the interface; A coefficient unit is used to update the interface heat transfer coefficient of the interface according to the gap distribution and the pre-calibrated gap heat transfer mapping relationship; wherein, the gap heat transfer mapping relationship characterizes the correspondence between the interface gap value and the interface heat transfer coefficient value. An update unit is used to redetermine the updated temperature field of the die-casting mold based on the updated interface heat transfer coefficient. The determining unit is configured to determine the updated temperature field as the coupled temperature field of the die-casting mold when the maximum node temperature difference between the updated temperature field and the current temperature field is less than a preset temperature threshold.

[0007] Thirdly, embodiments of this application provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method as described in any of the foregoing aspects.

[0008] Fourthly, embodiments of this application provide a computer program product that, when run on an electronic device, causes the electronic device to perform the method described in any of the above aspects.

[0009] It is understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant descriptions in the above aspects, and will not be repeated here. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic flowchart of a simulation method for coupled temperature and stress fields of die-casting molds for automotive parts provided in an embodiment of this application. Figure 2 This is a schematic diagram illustrating the operating principle of a coupled simulation method for temperature and stress fields of automotive parts die-casting molds provided in an embodiment of this application. Figure 3 This is a schematic diagram of the interface section of a simulation method for the coupling of temperature field and stress field in a die-casting mold for automotive parts provided in an embodiment of this application; Figure 4 This is an iterative schematic diagram of a simulation method for the coupling of temperature field and stress field in a die-casting mold for automotive parts provided in an embodiment of this application; Figure 5 This is a schematic diagram of the structure of a coupled simulation system for temperature and stress fields of automotive parts die-casting molds provided in an embodiment of this application; Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0012] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0013] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0014] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0015] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determination" or "if the described condition or event is detected" may be interpreted, depending on the context, as "once determination," "in response to determination," "once the described condition or event is detected," or "in response to the detection of the described condition or event."

[0016] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0017] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0018] Automotive parts (such as engine blocks, transmission housings, new energy battery trays, motor housings, etc.) are largely made by high-pressure die casting of aluminum or magnesium alloys. During service, die casting molds are subjected to extreme thermal cyclic loads, with molten metal temperatures reaching 620 to 680 degrees Celsius (aluminum alloys) or 600 to 640 degrees Celsius (magnesium alloys), filling the cavity at a high speed of 30 to 80 meters per second, and then rapidly solidifying and cooling under a holding pressure of 50 to 150 MPa. A single cycle typically lasts 20 to 60 seconds, and the mold is designed to last for 10,000 to 100,000 cycles.

[0019] The root cause of mold failure (thermal cracking, thermal fatigue, plastic deformation, erosion) lies in the temperature gradient and thermal stress experienced by the mold cavity surface during cycling. Accurate simulation and prediction of the temperature and stress field distribution of the mold are the core basis for mold material selection, structural optimization, cooling system design, and process parameter formulation.

[0020] Typical thermal simulation methods for die-casting molds in the industry include sequential coupling simulation and fully coupled simulation. Sequential coupling simulation first solves the mold temperature field using the finite volume method or finite element method, then imports the temperature field results as thermal loads into the structural mechanics model to calculate thermal stress. In this method, the mold geometry is assumed to remain unchanged during temperature field solving, and the interface heat transfer coefficient is kept at its initial static value during stress field calculation. This physically severs the real closed-loop feedback path from temperature gradient to thermal expansion deformation to changes in the mold-casting interface gap to changes in the interface heat transfer coefficient to temperature field redistribution. Fully coupled simulation uses thermo-mechanical coupling elements to simultaneously solve the temperature and displacement fields, theoretically preserving bidirectional feedback. However, for mold-level models (typically hundreds of thousands to millions of degrees of freedom), the stiffness ratio between the hyperbolic elastic equation and the parabolic heat conduction equation in the fully coupled matrix results in extremely slow convergence at each time step, making the computation time unacceptable in industrial applications.

[0021] In addition, there are digital twin-based correction methods that use measured data from embedded sensors to drive the digital twin updates and correct simulation deviations afterward. This method relies on additional sensor hardware deployment and is a post-correction rather than restoring coupled feedback within the simulation framework. Multiphysics unified simulation methods cover flow, temperature, pressure, and stress fields within the same model framework, but the interfacial heat transfer coefficients are preset by empirical formulas and do not dynamically update with changes in interfacial gaps caused by mold thermal deformation.

[0022] The essential flaw of the aforementioned prior art lies in the fact that after the die-casting mold expands due to heat, the contact gap at the interface of the mold casting changes (usually on the order of micrometers to sub-millimeters). The change in the gap directly affects the interface heat transfer coefficient (the increase in gap leads to an increase in air gap thermal resistance and a decrease in interface heat transfer coefficient). The change in interface heat transfer coefficient, in turn, affects the temperature boundary conditions on the mold surface. Under the sequential coupling framework, the structural fragmentation makes it impossible to predict the subsequent deformation when solving the temperature field, and the temperature results under the old boundary conditions are used when calculating the stress field.

[0023] To address the aforementioned issues, this application provides a coupled simulation method for temperature and stress fields in automotive component die-casting molds. This method employs a closed-loop iterative process: determining the interface gap distribution based on the current temperature field, updating the interface heat transfer coefficient according to the gap distribution, and then resolving the temperature field. This incorporates the dynamic feedback relationship between interface gaps, heat transfer coefficients, and temperature fields into the simulation framework, solving the problem of traditional unidirectional decoupling methods neglecting dynamic changes in gaps. Through iterative convergence determination, the coupling consistency between the temperature and stress fields is ensured, effectively improving the simulation accuracy of temperature and stress fields in gap-sensitive scenarios such as thin-walled complex cavities. This provides a more reliable numerical basis for mold life assessment and process parameter optimization.

[0024] The temperature field and stress field coupling simulation method for automotive parts die casting molds provided in this application embodiment can be applied to electronic devices. In this case, the electronic device is the execution subject of the temperature field and stress field coupling simulation method for automotive parts die casting molds provided in this application embodiment. This application embodiment does not impose any restrictions on the specific type of electronic device.

[0025] It is understandable that electronic devices can be various smart devices. For example, electronic devices can be mobile phones, tablets, wearable devices, in-vehicle devices, augmented reality (AR) / virtual reality (VR) devices, laptops, ultra-mobile personal computers (UMPCs), netbooks, personal digital assistants (PDAs), desktop computers, smart screens, smart TVs, and other terminal devices.

[0026] To better understand the simulation method for coupled temperature and stress fields of automotive component die-casting molds provided in this application, the specific implementation process of the simulation method for coupled temperature and stress fields of automotive component die-casting molds provided in this application will be described below by way of example.

[0027] Figure 1 This paper presents a schematic flowchart illustrating the coupled simulation method for temperature and stress fields of automotive part die-casting molds provided in an embodiment of this application. The coupled simulation method for temperature and stress fields of automotive part die-casting molds includes: S100, obtain the current temperature field of the die-casting mold.

[0028] It can be understood that the current temperature field refers to the temperature distribution formed by the temperature values ​​of each node in the finite element model of the die-casting mold at the current time step or the current iteration step. The temperature field is the basic input quantity of thermo-mechanical coupling simulation, and subsequent steps such as determining the gap distribution, updating the interface heat transfer coefficient, and correcting the temperature field all depend on the current temperature field.

[0029] In this embodiment, the temperature field of the die-casting mold originates from the output of the preceding simulation steps. At the initial moment of the simulation, the current temperature field can be the initial preheating temperature distribution of the mold; during the weakly coupled iteration process, the current temperature field is the updated temperature field output from the previous iteration step; during the time step progression, the current temperature field is the temperature field at the end of the previous time step. This application does not impose any restrictions on the specific source and acquisition method of the current temperature field.

[0030] Obtaining an accurate current temperature field is a prerequisite for initiating a weakly coupled iterative closed loop. In sequential coupling methods, the temperature field is directly used for stress calculation after solution, and there is no step of obtaining the current temperature field to drive gap updates, because the interface heat transfer coefficient does not update with iteration in sequential coupling methods. This application uses obtaining the current temperature field as the first step of the method, making it an input condition for weakly coupled iteration. This provides a clear iterative starting point for subsequent gap updates, heat transfer coefficient corrections, and temperature field convergence determination, giving the entire coupled simulation process clear input-output boundaries and a reproducible iterative structure.

[0031] For example, the current temperature field can be stored in memory as an array of node temperatures. The processor reads this array from memory to obtain the current temperature field. For instance, at the initial moment of the simulation, if the mold preheating temperature is 180 degrees Celsius, then the current temperature field is a uniform temperature field where all mold node temperatures are 180 degrees Celsius. In the second iteration of the weakly coupled iteration, the current temperature field is the updated temperature field obtained after the first iteration. At this time, the temperature values ​​of each node may change due to the correction of the interface heat transfer coefficient. For example, the temperature of the cavity surface node may rise from 285 degrees Celsius to 292 degrees Celsius.

[0032] S200, determine the gap distribution of the interface between the die-casting mold and the casting based on the current temperature field; wherein, the gap distribution is the distribution of the separation distance between the die-casting mold and the casting along the normal direction of the interface.

[0033] The interface can be understood as the contact or separation surface formed between the cavity surface of the die-casting mold and the outer surface of the casting. The gap distribution refers to the spatial distribution of the separation distance between the die-casting mold and the casting at various nodes along the normal direction of this interface. A positive value in the gap distribution indicates that the mold and casting are separated at that interface node, while zero or negative values ​​indicate that they remain in contact or interpenetrate (physically zero). The gap distribution is the core mediating variable connecting the temperature field and the interface heat transfer coefficient. The temperature gradient drives the mold to produce a normal displacement through thermal strain, forming the interface gap; the interface gap, in turn, determines the value of the interface heat transfer coefficient through the gap heat transfer mapping relationship.

[0034] In this embodiment, the process of determining the gap distribution based on the current temperature field essentially maps the thermal expansion deformation of the mold to the normal separation of the interface between the mold and the casting. When the mold expands due to heat, its cavity surface generates a normal displacement. If the direction of this normal displacement is away from the casting (i.e., the cavity expands outward), the interface gap increases; if the direction of the normal displacement is towards the casting (i.e., the cavity contracts inward), the interface gap decreases. The specific value of the gap distribution depends on the temperature increment distribution of the current temperature field, the linear expansion coefficient of the mold material, and the geometric constraints of the mold. Determining the gap distribution requires solving a thermoelastic problem, converting the temperature load into a displacement field, and then extracting the normal components of the interface nodes from the displacement field.

[0035] In existing sequential coupling methods, the interface heat transfer coefficient is a static preset value, and there is no definite gap distribution, so the impact of gap changes on heat transfer cannot be perceived. This application introduces the gap distribution as an intermediary variable with clear physical meaning, so that changes in the temperature field can be fed back to the interface heat transfer coefficient through this controllable path of gap distribution, thereby naturally restoring the physical essence of bidirectional temperature stress coupling within the simulation framework.

[0036] For example, the interface gap can be quickly calculated using the physical basis function reduction method of the interface layer. This involves first pre-calculating the physical basis function matrix of the interface extraction layer offline, and then quickly obtaining the interface gap distribution by superimposing the basis function coefficients in the online simulation. This reduces the thermoelastic solution of each iteration from full-order finite element method to algebraic operations of basis function coefficients. Alternatively, the full-order finite element method can be used directly. In this method, the current temperature field is directly applied to the finite element model of the mold as a thermal strain load in each iteration step, the static equilibrium equation is solved, and the normal displacement of the interface nodes is extracted as the gap distribution. Although the computational load is large, the accuracy is the highest. This method is suitable for backtracking calculations when the accuracy verification of the basis function reduction method fails or for direct solutions of small-scale mold models.

[0037] Optionally, the implementation process of the full-order finite element direct solution method is as follows: The current temperature field of the die-casting mold is applied as a thermal strain load to the finite element model of the die-casting mold, where the thermal strain load ε_therm = α·ΔT, α is the linear expansion coefficient of the mold material, and ΔT is the temperature increment of the nodal temperature relative to the reference temperature. The static equilibrium equation K·u = F_therm is solved, where K is the stiffness matrix of the mold, u is the nodal displacement vector, and F_therm is the thermal strain equivalent nodal force vector. From the displacement field u obtained by the solution, the displacement components of each node on the cavity surface along the normal direction of the cavity surface are extracted. These displacement components are the gap values ​​at each node. If the displacement component is positive (pointing to the outside of the casting), it indicates that the interface is separating and opening; if it is negative, it indicates that the interface is compressing.

[0038] In one possible implementation, S200, determining the gap distribution at the interface between the die-casting mold and the casting based on the current temperature field includes: S210, Determine the physical basis function matrix of the interface layer; wherein, the physical basis function matrix of the interface layer is a matrix constructed based on the normal displacement response vector of the interface extraction layer under the action of multiple sets of preset temperature distributions and orthogonally normalized.

[0039] It can be understood that the physical basis function matrix of the interface layer is a set of standard displacement response modes that have undergone orthogonal normalization. Each column vector represents the normal displacement response of each node in the interface extraction layer under a standard temperature load mode. The interface extraction layer is a thin region near the cavity surface in the finite element model of a die-casting mold. The normal displacement of the nodes in this region is most sensitive to temperature changes and is the core data source for gap distribution calculation. Orthogonal normalization ensures that the basis function vectors are linearly independent and have a modulus of 1, which is beneficial to the numerical stability of subsequent projection and superposition calculations.

[0040] In this embodiment, the construction of the interface layer physical basis function matrix utilizes the superposition principle of linear thermoelasticity problems. Since the relationship between thermal strain and displacement is linear under the small deformation assumption, the normal displacement of the interface extraction layer under any temperature field can be expressed as a linear combination of the normal displacement response vectors under several standard temperature load modes. The interface layer physical basis function matrix is ​​generated through offline pre-calculation. That is, before the actual simulation begins, several representative standard temperature load modes are applied to the finite element model of the mold, the normal displacement response vectors under each mode are solved, and then these response vectors are orthogonally normalized to form a set of standard orthogonal bases. This basis function matrix can be permanently reused after generation, without needing to repeat the full-order finite element solution in each iteration step.

[0041] Offline pre-calculation of the physical basis function matrix of the interface layer is a prerequisite for achieving rapid gap calculation in online simulation. In existing technologies, each coupled iteration step requires a full-order finite element solution to obtain thermal deformation. For mold models with hundreds of thousands of nodes, the single solution time can reach several seconds to tens of seconds, and the accumulated computational cost of multiple iterations is unacceptable. This application moves the most computationally intensive full-order finite element solution to the offline stage, reducing gap calculation in online simulation to algebraic operations on basis function coefficients. The computational complexity is reduced from a polynomial relationship with the mesh size to a constant complexity proportional to the number of basis functions, significantly reducing the overall computational cost of the simulation.

[0042] Optionally, S210, determine the physical basis function matrix of the interface layer, including: S211, offset the cavity surface of the finite element model of the die-casting mold inward to a preset depth along the opposite direction of the normal, and extract the area between the offset surface and the cavity surface as the interface extraction layer.

[0043] The interface extraction layer can be understood as a thin region adjacent to the cavity surface in the finite element model of a die-casting mold. Geometrically, it is surrounded by two surfaces: one is the cavity surface itself, and the other is the offset surface obtained by offsetting the cavity surface inwards by a preset depth along the opposite direction of the normal (i.e., towards the interior of the mold matrix). The area between the offset surface and the cavity surface is the interface extraction layer. The preset depth of the interface extraction layer can be reasonably selected according to the geometric complexity of the mold cavity and the depth of heat penetration.

[0044] In this embodiment, the thickness of the interface extraction layer directly affects the accuracy and efficiency of the gap calculation. If the interface extraction layer is too thin, it may miss some of the contribution of normal displacement caused by thermal strain, resulting in an underestimation of the gap; if the interface extraction layer is too thick, it contains too many nodes far from the cavity surface. The contribution weight of the normal displacement of these nodes to the interface gap is small, but the computational load is increased. Based on the main penetration depth of thermal strain on the die-casting mold cavity surface (usually 2 to 5 mm), the preset depth is generally 2 to 3 mm. The node mesh size in the interface extraction layer should be smaller than the mesh size inside the mold matrix. For example, the side length of the unit in the interface extraction layer should not exceed 0.5 mm to ensure the accuracy of the gap calculation.

[0045] By extracting a thin layer near the cavity surface as the interface extraction layer, the scope of gap calculation is limited to nodes that directly contribute to the interface gap, avoiding wasting computational resources on a large number of irrelevant nodes inside the mold matrix. This design is based on the physical characteristics of the thermodynamic response of die-casting molds, because the surface thermal strain of the mold cavity mainly occurs in the heat-permeable layer near the surface, and the temperature changes in the deep interior of the mold matrix have a negligible impact on the interface gap. Therefore, by establishing the basis function matrix only for the interface extraction layer and performing online projection calculations, the accuracy of gap calculation can be guaranteed while significantly reducing the dimensionality and computational cost of the reduced-order model.

[0046] For example, a preset depth of 3 mm is used. For each node on the cavity surface in the finite element model of the mold, offset by 3 mm along the normal direction of the cavity surface at that node (pointing in the opposite direction to the interior of the mold base), and record the set of node coordinates obtained by the offset. The area enclosed by these offset surface nodes and the original cavity surface nodes is the interface extraction layer. This interface extraction layer contains, for example, 2847 nodes, each node retaining temperature and displacement degrees of freedom.

[0047] S212, apply multiple sets of standard temperature load modes to the interface extraction layer and solve the combination to obtain the physical basis function matrix of the interface layer.

[0048] It can be understood that a standard temperature load pattern refers to a set of temperature increment functions with a specific spatial distribution applied to the interface extraction layer. Each pattern captures the influence of a typical temperature distribution pattern on the interface gap. The number and spatial distribution of the standard temperature load patterns need to be able to cover various temperature distribution patterns that may occur in online simulation to ensure that the basis function space has sufficient representational power.

[0049] The selection of standard temperature load patterns follows two principles: completeness and orthogonality. Completeness requires that the selected pattern set cover the main temperature increment patterns on the interface extraction layer in online simulation, including uniform heating, linear gradients, and local hotspots at different scales. Orthogonality requires low spatial correlation between patterns to facilitate subsequent orthogonal normalization. Standard temperature load patterns can include: a uniform substrate heating pattern, a linear gradient pattern along the cavity normal, and multiple local hotspot patterns at different spatial scales (e.g., Gaussian local hotspots with half-widths of 2 mm, 5 mm, 10 mm, and 20 mm). After applying temperature loads to each pattern, the static equilibrium equations are solved, and the normal displacement response vectors of all nodes within the interface extraction layer are extracted. The displacement response vectors of each pattern are then column-wise combined into a matrix, which is then orthogonally normalized to obtain the physical basis function matrix of the interface layer.

[0050] Constructing a basis function matrix using multiple standard temperature load modes is a mathematical method that discretizes a continuous temperature distribution space into a set of orthonormal bases. In online simulations, the temperature increment distribution at any given time can be projected onto this basis function space and described by a set of basis function coefficients, thus achieving a reduced-order representation. Compared to simplification methods using only a few empirical modes, a comprehensive multi-mode basis function library can cover various temperature distribution patterns with high accuracy; and compared to performing full-order finite element solutions in each iteration step, the computational cost of algebraic operations for basis function projection and superposition is reduced by several orders of magnitude.

[0051] For example, in S212, multiple sets of standard temperature load modes are applied to the interface extraction layer and their combinations are solved to obtain the physical basis function matrix of the interface layer, including: S2121, apply multiple sets of standard temperature load modes to the interface extraction layer, and solve the normal displacement response vector under each set of standard temperature load modes; wherein, each set of standard temperature load modes is a temperature increment function with a preset spatial distribution applied to the interface extraction layer; the normal displacement response vector is a vector composed of the displacement of each node in the interface extraction layer along the normal direction of the cavity surface.

[0052] It can be understood that the temperature increment function refers to a scalar field defined on the nodes of the interface extraction layer, and its function value is the temperature increment value applied to that node under the standard temperature load mode. The normal displacement response vector refers to a column vector composed of the displacement components along the normal direction of the cavity surface of each node in the interface extraction layer under the action of the standard temperature load mode alone, arranged according to the node number. Each standard temperature load mode corresponds to a normal displacement response vector, which describes the normal deformation mode of the interface extraction layer under this type of temperature distribution.

[0053] For each set of standard temperature load modes, the temperature increment function is applied as a nodal temperature load to the nodes of the interface extraction layer of the mold finite element model. All displacement degrees of freedom of the mold base plate are fixed, and the linear static equilibrium equation Ku = f_th is solved, where K is the mold stiffness matrix, u is the nodal displacement vector, and f_th is the equivalent thermal nodal force vector caused by the temperature load. After solving, the displacement components of each node in the interface extraction layer in the normal direction of the cavity surface are extracted from the nodal displacement vector and arranged by node number as the normal displacement response vector. The number of sets of standard temperature load modes determines the number of columns in the basis function matrix; the more sets, the stronger the representational power of the reduced-order model, but the greater the computational load of offline pre-calculation.

[0054] Solving for the normal displacement response vector under each standard temperature load mode using a static equilibrium approach is the core data generation step in constructing the physical basis function matrix of the interface layer. This application fully utilizes the superposition principle of linear thermoelastic problems. Since thermal strain and displacement are linear under the small deformation assumption, the interface gap under any complex temperature field can be expressed as a linear combination of the basic modes. Therefore, it is sufficient to pre-calculate the displacement response of only a finite number of standard modes (e.g., 6 modes) offline to represent the temperature distribution patterns that may occur in most actual simulations online, significantly reducing the dimensionality and computational cost of online gap calculation.

[0055] For example, six standard temperature load modes are defined: (1) Uniform substrate heating mode, where the temperature increment is 100 degrees Celsius across the entire interface extraction layer; (2) Linear gradient mode along the cavity normal, where the temperature increment is the gradient coefficient of 50 degrees Celsius / mm multiplied by the normal distance from the node to the cavity surface; (3) Small-scale local hot spot mode, where the temperature increment is 100 multiplied by a Gaussian function with a half-width of 2 mm centered on the bearing housing mounting surface; (4) Medium-scale local hot spot mode, where the temperature increment is 80 multiplied by a Gaussian function with a half-width of 5 mm centered on the reinforcing rib intersection area; (5) Large-scale local hot zone mode, where the temperature increment is 60 multiplied by a Gaussian function with a half-width of 10 mm centered on the oil passage column area; (6) Ultra-large-scale hot zone mode, where the temperature increment is 50 multiplied by a Gaussian function with a half-width of 20 mm centered on the flange surface geometry. The normal displacement response vectors φ_1 to φ_6 under each mode are solved respectively.

[0056] S2122, combine the normal displacement response vectors corresponding to each group of standard temperature load modes column by column, and perform orthogonal normalization on the combined matrix to obtain the physical basis function matrix of the interface layer.

[0057] It can be understood that column-wise combination refers to using the normal displacement response vectors corresponding to each standard temperature load mode as column vectors, and concatenating them sequentially according to the mode number to form a matrix with the number of rows equal to the number of nodes in the interface extraction layer and the number of columns equal to the number of standard temperature load mode groups. Orthogonal normalization is a mathematical transformation that transforms each column vector of the matrix into a set of pairwise orthogonal standard orthogonal basis vectors with a magnitude of 1. The purpose of orthogonal normalization is to eliminate the linear correlation between the response vectors of each mode, making the subsequent projection and superposition calculations of basis function coefficients more numerically stable.

[0058] Orthogonal normalization can be achieved using Singular Value Decomposition (SVD) or Gram-Schmidt orthogonalization. When using SVD, the normal displacement response vector is column-wise combined into a matrix Φ. Singular value decomposition is then performed on Φ = UΣVᵀ. The first M columns of the left singular matrix U are taken as the column vectors of the interface layer physical basis function matrix, where M is determined by a preset modal energy retention threshold, i.e., Σᵢ₌1ᴹσᵢ / Σⱼσⱼ≥η, where η is a preset modal energy retention ratio. For example, η is taken as not less than 95%, preferably not less than 99%. When using Gram-Schmidt, the normal displacement response vector column is directly orthogonalized using Gram-Schmidt, and truncated according to the norm of the orthogonalized vector, retaining components with a norm not less than 1% of the maximum norm. The typical range for the number of basis functions M is 4 to 16.

[0059] For example, the Gram-Schmidt orthogonalization algorithm is used. The normal displacement response vectors of the six modes are used as initial vectors. Each vector is then subtracted from its projection component onto the orthogonalized preceding vector, and normalized to unit length. This results in six orthonormal basis vectors. The space spanned by these vectors is the same as that spanned by the original six normal displacement response vectors, but with better numerical properties. The interface layer physical basis function matrix is ​​a column-wise concatenation of these six orthonormal basis vectors. Its number of rows is equal to the number of nodes in the interface extraction layer, for example, 2847 rows, and its number of columns is equal to the number of standard temperature load mode groups, for example, 6 columns. This matrix is ​​used as a projection operator in subsequent online simulations and does not need to be generated repeatedly.

[0060] Orthogonal normalization of the normal displacement response vector is a crucial step in ensuring the numerical stability of online projection calculations. The original normal displacement response vectors may exhibit high linear correlation; for example, the responses of uniform heating models and ultra-large-scale thermal zone models may have similar distributions at certain nodes. This linear correlation leads to ill-conditioned coefficient matrices in the projection calculations, making the basis function coefficients sensitive to small noises in the temperature increment distribution. Orthogonal normalization eliminates the linear correlation between basis function vectors, transforming the projection calculation into a stable least-squares projection, thus improving the robustness and accuracy of gap calculations.

[0061] For example, the normal displacement response vectors φ_1 to φ_6 of the six modes are concatenated column-wise into a matrix Φ of 2847 rows by 6 columns. Gram-Schmidt orthogonal normalization is performed on Φ: let u_1 = φ_1 / modulus of φ_1; for j = 2 to 6, calculate w_j = φ_j minus Σ_{k=1}^{j-1}(φ_j·u_k)u_k; let u_j = w_j / modulus of w_j. The final interface layer physical basis function matrix Φ_orth = [u_1, u_2, ..., u_6] is an orthonormal matrix of 2847 rows by 6 columns.

[0062] This setup shifts the computationally intensive full-order finite element method solution to the offline stage, where the physical basis function matrix of the interface layer is pre-calculated. In online simulation, only algebraic operations for the projection and superposition of basis function coefficients need to be performed. This facilitates rapid calculation of gaps in large-scale mold models to achieve engineering-feasible cost calculations. Simultaneously, orthogonal normalization ensures the numerical stability of the projection calculations, improving the robustness of the gap calculation results.

[0063] S220 projects the temperature increment distribution of the current temperature field on the interface extraction layer to the basis function space of the physical basis function matrix of the interface layer, and obtains the basis function coefficient vector.

[0064] It can be understood that the temperature increment distribution refers to the vector formed by the temperature change of the current temperature field relative to the reference temperature field (such as the initial preheating temperature or the temperature field of the previous iteration step) at each node of the interface extraction layer. The basis function coefficient vector is a set of scalar coefficients, each coefficient representing the projection intensity of the temperature increment distribution onto the corresponding basis function direction. That is, the current temperature increment distribution can be described by coordinates in the basis function space.

[0065] In this embodiment, the projection operation employs the least squares projection method. Let the number of nodes in the interface extraction layer be N (e.g., 2847), the basis function matrix Φ_orth be an N-row, M-column (e.g., M=6) orthonormal matrix, and the temperature increment distribution ΔT_surf be an N-dimensional column vector. The basis function coefficient vector a = the transpose of Φ_orth multiplied by ΔT_surf, i.e., a_j = u_j · ΔT_surf (inner product operation). Since Φ_orth is an orthonormal matrix, this projection is equivalent to the best approximation in the least squares sense. The computational cost is approximately N×M floating-point operations (e.g., approximately 1.7×10^4), far lower than the computational cost of full-order finite element analysis.

[0066] Projecting the temperature increment distribution onto the basis function space to obtain the coefficient vector is the core computational step for achieving fast gap calculation. This step compresses the high-dimensional nodal temperature increment vector (N-dimensional) into a low-dimensional basis function coefficient vector (M-dimensional, where M is much smaller than N), achieving spatial dimensionality reduction. The dimensionality-reduced coefficient vector contains all the effective information of the temperature increment distribution (within the capabilities of the basis function space representation). Subsequent gap distribution reconstruction only requires a simple linear superposition of the basis function coefficients and the pre-stored normal displacement response vector. This dimensionality reduction strategy is one of the key technical means for achieving engineering-feasible computational cost in this application. Compared to the traditional method of performing full-order finite element solutions in each iteration step, the computational load is reduced by several orders of magnitude.

[0067] For example, the number of nodes in the interface extraction layer is N=2847, and the number of columns in the basis function matrix Φ_orth is M=6. The temperature increment distribution ΔT_surf on the interface extraction layer is a 2847-dimensional column vector. Multiplying the transpose of the basis function coefficient vector a=Φ_orth by ΔT_surf yields a 6-dimensional column vector. In a certain simulation iteration, the transpose of a=[0.183,0.072,0.041,0.028,0.015,0.008] indicates that the current temperature field is dominated by a uniform heating mode (a_1=0.183) and a linear gradient mode (a_2=0.072), while the components of other local hotspot modes are relatively small.

[0068] S230, based on the linear superposition of the basis function coefficient vector and the normal displacement response vector, yields the gap distribution.

[0069] Linear superposition can be understood as using the components in the basis function coefficient vector as weights to perform a weighted summation of the normal displacement response vectors corresponding to each standard temperature load mode. Since the normal displacement response vectors have already been recorded when constructing the basis function matrix, there is no need to resolve the finite element equations; only the algebraic operation of the weighted summation is required to reconstruct the interface gap distribution.

[0070] In this embodiment, the gap distribution reconstruction operation is based on the principle of linear superposition. Within the basis function space framework, the gap value g(x_i) of any node i in the interface extraction layer is g(x_i) = Σ_{j=1}^{M}a_j×φ_j(x_i), where a_j is the j-th component of the basis function coefficient vector, and φ_j(x_i) is the value of the j-th basis function vector at node i. The computational complexity of this operation is approximately N×M floating-point operations (e.g., approximately 1.7×10^4). After reconstructing the gap value, physical constraints are applied to the gap value: positive values ​​indicate gap opening and are retained as the original value; negative values ​​(physically representing the interpenetration between the mold and the casting) are set to zero. Simultaneously, a full-order finite element solution is performed every few iterations (e.g., every 10 macro time steps) as an accuracy check. If the relative error of the basis function reduction result exceeds a preset threshold (e.g., 5%), a supplementary full-order finite element solution is triggered, and the result is added to the basis function library as a new load mode. Orthogonal normalization is then performed again to update the basis function matrix.

[0071] By rapidly reconstructing the gap distribution through the linear superposition of basis function coefficients, the computational complexity of gap calculation in online simulation is reduced from the order of full-order finite element solution (which can be set to O(N^α), 1<α≤3) to the order of algebraic operations O(N×M). This order reduction strategy makes performing multiple weakly coupled iterations on large-scale mold models an engineeringly feasible solution. Furthermore, the introduction of accuracy verification and over-limit rollback mechanisms ensures the reliability of the order reduction method—under most conventional temperature distributions, the relative error of the basis function order reduction method can be controlled within 5%; in the rare cases where the error exceeds the limit, it automatically rolls back to full-order finite element solution, ensuring the stability of simulation accuracy.

[0072] For example, taking the transpose of the basis function coefficient vector a = [0.183, 0.072, 0.041, 0.028, 0.015, 0.008], a weighted sum is calculated for each node in the interface extraction layer. For a node in the bearing housing mounting surface region, the values ​​of the six basis function components are 1.2, -0.8, 0.5, 0.3, 0.1, and 0.05 mm, respectively. The weighted sum gives the node gap value = 0.183 × 1.2 + 0.072 × (-0.8) + 0.041 × 0.5 + 0.028 × 0.3 + 0.015 × 0.1 + 0.008 × 0.05 ≈ 0.192 mm. This value is constrained: 192 micrometers is a positive value, and the original value is retained. Thus, the determination of the interface gap distribution is complete.

[0073] This setup, employing a basis function order reduction method to determine the interface gap distribution, lowers the interface gap calculation cost in each iteration from full-order finite element solution to algebraic operations on basis function coefficients. This helps maintain an engineering-acceptable overall simulation calculation time on large-scale mold models. Simultaneously, accuracy verification and over-limit rollback mechanisms ensure the reliability of the order reduction calculation results.

[0074] S300, based on the gap distribution and the pre-calibrated gap heat transfer mapping relationship, updates the interface heat transfer coefficient of the interface; wherein, the gap heat transfer mapping relationship characterizes the correspondence between the interface gap value and the interface heat transfer coefficient value.

[0075] The gap heat transfer mapping relationship can be understood as a functional correspondence between the interfacial gap value (the separation distance of the interface along the normal direction) and the interfacial heat transfer coefficient value. The physical basis of this mapping relationship is that when a gap appears between the mold and the casting, the air gap within it creates additional thermal resistance, leading to a decrease in the overall heat transfer capacity of the interface. The larger the gap, the greater the air gap thermal resistance, and the lower the interfacial heat transfer coefficient. The gap heat transfer mapping relationship can be pre-calibrated through steady-state heat flux experiments for a specific combination of mold and casting materials, or determined through theoretical models (such as the air gap thermal resistance series model).

[0076] In this embodiment, the process of updating the interface heat transfer coefficient is driven by the gap distribution and executed based on a pre-calibrated gap heat transfer mapping relationship. Once the gap values ​​of each node on the interface are determined, for nodes with zero gap (where the mold and casting remain in contact), the interface heat transfer coefficient is taken as the baseline heat transfer coefficient value (corresponding to a metal-to-metal contact state); for nodes with non-zero gap, the interface heat transfer coefficient is reduced according to the attenuation mapping relationship. This interface heat transfer coefficient update method, directly driven by physical gaps, replaces the existing practice of statically presetting or using empirical formulas to preset the interface heat transfer coefficient. This allows the change in the interface heat transfer coefficient to be automatically determined by physical mechanisms within the simulation framework, rather than being externally set.

[0077] The gap distribution (from the positive transfer of temperature to deformation) is transformed into the interface heat transfer coefficient through the gap heat transfer mapping relationship. The interface heat transfer coefficient then serves as the thermal boundary condition to influence the solution of the temperature field, thereby closing the bidirectional coupling loop of temperature stress. In existing sequential coupling methods, the interface heat transfer coefficient is always a static preset value, and there is no dynamic update step, so it is impossible to perceive the decrease in heat transfer coefficient caused by gap changes. This application introduces the physically real gap heat transfer feedback into the simulation framework through this step.

[0078] In one possible implementation, S300 updates the interface heat transfer coefficient based on the gap distribution and a pre-calibrated gap heat transfer mapping relationship, including: S310, based on the gap value of each interface node in the gap distribution and the pre-calibrated attenuation constant, determine the interface heat transfer coefficient value corresponding to the interface node; wherein, the attenuation constant is a parameter characterizing the rate at which the interface heat transfer coefficient decreases as the gap value increases.

[0079] The attenuation constant is a physical parameter related to material pairing, characterizing the rate at which the interfacial heat transfer coefficient decreases as the gap size increases. A larger attenuation constant indicates a faster decrease in the interfacial heat transfer coefficient with increasing gap size, meaning that the air gap thermal resistance has a more significant hindering effect on heat transfer under that material pairing. The attenuation constant is pre-calibrated through steady-state heat flux experiments for specific mold and casting material combinations.

[0080] In this embodiment, for each interface node in the gap distribution, the corresponding interface heat transfer coefficient is calculated according to the gap value and a pre-calibrated attenuation constant, based on the gap heat transfer mapping relationship. Specifically, an exponential attenuation model is adopted: h(g) = h_0 × e^{-α × g} + h_gap × (1 - e^{-α × g}), where h(g) is the interface heat transfer coefficient when the gap value is g, h_0 is the first coefficient (the baseline heat transfer coefficient in metal-metal contact), h_gap is the second coefficient (the gap heat transfer coefficient when the gap value is greater than the preset upper limit), α is the attenuation constant, and g is the interface gap value. This model has a clear physical meaning: the first term represents the attenuation contribution of the baseline heat transfer, and the second term represents the growth contribution of the air gap heat transfer; the two are weighted by the e^{-α × g} factor.

[0081] The attenuation constant λ described in this application was calibrated through a steady-state heat flux experiment. The experimental setup employed a counter-pressure steady-state heat flux test bench, comprising: an upper pressure head (made of mold steel H13), a lower pressure head (made of die-cast aluminum alloy ADC12), a ring-shaped heating furnace (temperature control accuracy ±2℃), a precision displacement sensor (resolution 0.1μm), and a heat flux density sensor (response time <0.1s). During the specific calibration, the upper and lower pressure heads were concentrically mounted on the test bench, and the initial contact pressure was set to 50 MPa. The upper pressure head was heated to 620°C using a ring furnace, while the lower pressure head was kept at 250°C via a water-cooled base. A controllable gap value g was introduced between the upper and lower pressure heads using a precision displacement sensor, ranging from 0 to 50 μm with a step size of 2 μm. At each gap value, after the temperature field stabilized (temperature change rate < 0.5°C / min), the steady-state heat flux Q and the contact surface temperature difference ΔT were recorded. The interfacial heat transfer coefficient h(g) corresponding to each gap value g was calculated according to h = Q / ΔT. The data points (g, h) were fitted to the exponential decay model h(g) = h0·e^{-λ·g} + h∞·(1-e^{-λ·g}), and λ was obtained through least squares regression. For example, for the combination of H13 mold steel and ADC12 aluminum alloy, the calibration results are: h0=8500 W / (m²·K), h∞=350 W / (m²·K), λ=0.42 μm⁻¹ (goodness of fit R²>0.98).

[0082] Determining the interfacial heat transfer coefficient using a node-by-node attenuation calculation method can accurately reflect the heat transfer differences caused by varying gaps at different locations on the interface. In the actual working conditions of die-casting molds, the distribution of interfacial gaps is non-uniform. Areas with strong geometric constraints (such as the intersection of reinforcing ribs) have limited thermal expansion and smaller gaps; areas with weaker geometric constraints (such as the edge of the flange face) have free thermal expansion and larger gaps. This spatial non-uniformity of gaps directly leads to a spatial non-uniform distribution of the interfacial heat transfer coefficient on the interface. The node-by-node independent calculation method can accurately characterize this spatial non-uniformity, avoiding the accuracy loss caused by using a single average value or preset value for the entire interface in existing technologies.

[0083] Optionally, S310, based on the gap value of each interface node in the gap distribution and the pre-calibrated attenuation constant, the interface heat transfer coefficient value corresponding to the interface node is determined, including: S311, for each interface node, the first coefficient is multiplied by a power of the product of the natural constant e and the gap value, with the negative attenuation constant as the base and the product as the exponent, and the difference between the second coefficient multiplied by 1 and the exponent is added to obtain the interface heat transfer coefficient value corresponding to the interface node; where the first coefficient is the reference heat transfer coefficient of the die casting mold and the casting in the metal-to-metal contact state, the second coefficient is the gap heat transfer coefficient when the gap value is greater than the preset gap upper limit, and the attenuation constant is pre-calibrated by a steady-state heat flux experiment for the combination of the die casting mold material and the casting material of the casting.

[0084] It can be understood that the first coefficient (baseline heat transfer coefficient h_0) is the interfacial heat transfer coefficient under ideal conditions of complete tight contact between the mold and the casting (zero gap). Its value is determined by the combination of mold material and casting material. For example, the baseline heat transfer coefficient of the material combination of hot work die steel H13 and ADC12 aluminum alloy can be calibrated as approximately 8000 W / (m²·K). The second coefficient (lower limit of gap heat transfer coefficient h_gap) is the stable lower limit value to which the interfacial heat transfer coefficient tends when the gap is sufficiently large (greater than the preset upper limit of the gap). It is mainly determined by the air gap thermal resistance, and can be taken as 200 W / (m²·K). The preset upper limit of the gap is the threshold gap value that distinguishes between contact-dominated and gap-dominated heat transfer mechanisms, and can be taken as 50 micrometers.

[0085] In this embodiment, the exponential decay calculation formula for the interface heat transfer coefficient, h(g)=h_0×e^{-α×g}+h_gap×(1-e^{-α×g}), has the following physical characteristics: when the gap g=0, e^{-α×0}=1, therefore h(0)=h_0×1+h_gap×0=h_0, that is, the interface heat transfer coefficient under the complete contact state is equal to the reference heat transfer coefficient; when the gap g→∞, e^{-α×∞}→0, therefore h(∞)→h_0×0+h_gap×1=h_gap, that is, the interface heat transfer coefficient under the large gap tends to the lower limit of the gap heat transfer coefficient; within the intermediate gap range, the interface heat transfer coefficient smoothly transitions from h_0 to h_gap at an exponential rate controlled by the decay constant α. The attenuation constant α is determined by steady-state heat flux experiment: under experimental conditions with known gap value g, the steady-state heat flux density q through the interface and the temperature difference ΔT on both sides of the interface are measured, the interface heat transfer coefficient h_exp=q / ΔT is calculated, and then the attenuation constant α is determined by least squares fitting.

[0086] Employing an exponential decay function as the mathematical model for the gap heat transfer mapping relationship offers both good physical rationality and mathematical properties. Physically, the decrease in the interfacial heat transfer coefficient with increasing gap size is a process driven by both contact heat conduction and air gap heat conduction mechanisms. The exponential form naturally describes the physical process of the changing weights of these two mechanisms. Mathematically, the exponential function is smooth and continuous, with a first derivative that exists and is not zero, making it suitable for gradient-based numerical optimization and convergence analysis. Compared to piecewise linear or piecewise constant models, the exponential model can more accurately characterize the continuous change of the interfacial heat transfer coefficient when the gap varies at the micrometer level, which is beneficial for improving the convergence stability of weakly coupled iterations.

[0087] For example, for the combination of H13 mold steel and ADC12 aluminum alloy, the baseline heat transfer coefficient h_0 is taken as 8000 W / (m²·K), the lower limit of the gap heat transfer coefficient h_gap is taken as 200 W / (m²·K), and the attenuation constant α is taken as 0.35 μm⁻¹. For the contact node with gap g=0, h(0)=8000×1+200×0=8000W / (m²·K). For the node with gap g=5μm, h(5)=8000×exp(-1.75)+200×(1-exp(-1.75))=8000×0.174+200×0.826=1392+165=1557W / (m²·K). For a node with a gap of g=15μm, h(15)=8000×exp(-5.25)+200×(1-exp(-5.25))≈8000×0.0053+200×0.9947≈42+199=241W / (m²·K).

[0088] This setup, using an exponential decay formula to calculate the interface heat transfer coefficient node by node, automatically captures the sharp drop in interface heat transfer coefficient caused by increased gap size within the simulation framework. Taking the bearing housing mounting surface area as an example, when the interface gap increases from 0 to 6.8 micrometers, the interface heat transfer coefficient automatically decreases from 8000 to approximately 1059 W / (m²·K), a decrease of 87%. Such a significant change cannot be accurately predicted through empirical presets or sensor corrections. This solution automatically achieves this mapping through a gap-based physical drive, restoring the physical integrity of the temperature-stress coupling feedback.

[0089] S320 combines the interface heat transfer coefficient values ​​corresponding to each interface node on the interface into an updated interface heat transfer coefficient.

[0090] It can be understood that the updated interface heat transfer coefficient refers to the set of interface heat transfer coefficient values ​​of all nodes on the interface after the gap heat transfer mapping relationship is updated in the current iteration step. The updated interface heat transfer coefficient is a node-level field quantity. When used as a thermal boundary condition, it is usually passed to the thermal solver in the form of a node array. Therefore, after the node-by-node calculation is completed, the interface heat transfer coefficient values ​​of each node need to be combined into a whole data structure.

[0091] In this embodiment, the interface heat transfer coefficient values ​​of each interface node are combined according to the spatial location of the node and the mesh topology to form an updated interface heat transfer coefficient field. This combination process is a simple data aggregation operation and does not involve additional physical calculations. After the combination is completed, the updated interface heat transfer coefficient can replace the interface heat transfer coefficient used in the previous iteration step as the interface thermal boundary condition for solving the temperature field in the next iteration step or the next time step.

[0092] The node-by-node calculated interface heat transfer coefficient values ​​are explicitly combined into the updated interface heat transfer coefficient, completing the final step of updating the interface heat transfer coefficient in the current iteration and providing a clear data input interface for subsequent iterations. This explicit input-output boundary design makes the data transfer relationships between steps in the weakly coupled iterative process clear and traceable, which is beneficial for the modular implementation, debugging, and maintenance of simulation code, and also facilitates tracking the iterative change history of the interface heat transfer coefficient during convergence analysis.

[0093] For example, the interface heat transfer coefficient values ​​of the 2847 nodes on the interface are stored in a one-dimensional array of length 2847 in order of node number. This array represents the updated interface heat transfer coefficient. In subsequent steps, the thermal solver reads this array and uses the interface heat transfer coefficient value of each node as the thermal boundary condition parameter of the interface at that node. For instance, the interface heat transfer coefficient of a node in the bearing housing mounting surface region is updated from 8000 W / (m²·K) in the previous iteration to 1557 W / (m²·K).

[0094] This setup, which updates and combines the results node by node to form the updated interface heat transfer coefficient, accurately reflects the heat transfer differences at different locations on the interface due to varying gaps, avoiding the coarse approximation of using a uniform preset value across the entire interface in existing technologies. This refined processing helps improve the overall prediction accuracy of thermo-mechanical coupling simulations.

[0095] S400 redetermines the updated temperature field of the die-casting mold based on the updated interface heat transfer coefficient.

[0096] It can be understood that updating the temperature field refers to the temperature distribution obtained by resolving the temperature field of the finite element model of the die-casting mold in the current iteration step using the updated interfacial heat transfer coefficient as the interfacial thermal boundary condition. The updated temperature field is the output of the current iteration step and will be used for the convergence determination in the next step.

[0097] In this embodiment, re-determining the updated temperature field is a crucial step in feeding back the updated interfacial heat transfer coefficient to solve the temperature field, completing the reverse propagation link in the weakly coupled iterative closed loop. In steps S200 and S300, the change in the temperature field is transformed into a correction of the interfacial heat transfer coefficient through the gap distribution and gap heat transfer mapping relationship; in step S400, the corrected interfacial heat transfer coefficient again affects the distribution of the temperature field as a thermal boundary condition, thus forming a complete closed-loop iteration.

[0098] The recalculation of the updated temperature field is the last forward computation step in each iteration of a weakly coupled iteration. Its output (updated temperature field) is directly compared with the current temperature field to determine convergence. This step ensures that the temperature field is no longer a static solution, but rather an iterative product that gradually approximates the physical reality as the interface heat transfer coefficient is dynamically updated. In sequentially coupled methods, the temperature field is solved only once under the initial interface heat transfer coefficient and remains fixed, lacking an iterative correction mechanism. Therefore, it cannot capture the redistribution of the temperature field caused by changes in the gap.

[0099] In one possible implementation, S400 redetermines the updated temperature field of the die-casting mold based on the updated interfacial heat transfer coefficient, including: S410 uses the updated interface heat transfer coefficient as the thermal boundary condition of the interface to solve the transient heat conduction problem of the finite element model of the die-casting mold, and obtains the updated temperature field.

[0100] It can be understood that thermal boundary conditions refer to the thermal constraints applied to the boundary of the computational domain when solving for the temperature field. In this application, the thermal boundary conditions of the interface refer to the relationship between the heat flux density through the interface of the mold casting and the temperature difference across the interface. The transient heat conduction solution refers to the heat conduction solution process that considers the temperature change over time. Its governing equation is a parabolic partial differential equation (transient heat conduction equation), and the solution results give the evolution of the temperature at each node over time.

[0101] In this embodiment, when the updated interface heat transfer coefficient is used as the thermal boundary condition of the interface, the value of the interface heat transfer coefficient determines the magnitude of the heat flux density through the interface—the larger the interface heat transfer coefficient, the greater the heat flux density through the interface under the same temperature difference, the faster the mold dissipates heat, and the lower the temperature; conversely, the smaller the interface heat transfer coefficient, the lower the temperature. The initial condition for solving the transient heat conduction problem is the temperature field at the beginning of the current iteration step (or the temperature field at the end of the previous micro-time step), and the solution process advances one or more micro-time steps in time. The solution method can employ standard transient algorithms such as Newmark-β time integration or backward Euler difference in the finite element method.

[0102] Using the updated interfacial heat transfer coefficient as the thermal boundary condition for transient heat conduction solution is a concrete way to realize the inverse coupling link of interfacial heat transfer coefficient correction → temperature field redistribution. Through transient solution (rather than steady-state solution), the dynamic evolution of the temperature field of the die-casting mold under cyclic thermo-mechanical loads can be accurately reflected, especially the non-steady-state characteristic of the temperature gradually decreasing over time during the holding and cooling stage. Transient solution can capture the cumulative effect of the temperature field over time, making the updated temperature field closer to the actual thermal state of the mold.

[0103] Optionally, in S410, the updated interfacial heat transfer coefficient is used as the thermal boundary condition of the interface to solve the transient heat conduction problem of the finite element model of the die-casting mold, resulting in an updated temperature field, including: S411, substitute the updated interfacial heat transfer coefficient into the third type of thermal boundary condition, which characterizes the proportional relationship between the heat flux density through the interface and the temperature difference across the interface.

[0104] As can be understood, the third type of thermal boundary condition (also known as the Robin boundary condition or convective heat transfer boundary condition) refers to a thermal constraint where the normal heat flux density through the boundary is proportional to the temperature difference across the boundary. Its mathematical expression is: q·n = h × (T_surface - T_bulk), where q·n is the normal heat flux density through the boundary, h is the interfacial heat transfer coefficient, T_surface is the temperature of the mold cavity surface, and T_bulk is the average temperature of the casting solidification front or the molten metal. The third type of thermal boundary condition is the standard thermal description of heat transfer at the mold-casting interface.

[0105] In this embodiment, the updated interface heat transfer coefficient value is substituted node by node into the expression for the third type of thermal boundary condition. That is, for each node i on the interface, the thermal boundary condition is: q_i = h_i × (T_i - T_casting). Here, h_i is the updated interface heat transfer coefficient value for that node, T_i is the temperature of that node, and T_casting is the casting-side temperature. The above-described node-by-node form of the third type of thermal boundary condition is assembled into the right-hand side of the finite element system in the form of a node thermal load vector, so that the updated interface heat transfer coefficient affects the control of the heat conduction equation.

[0106] Using the third type of thermal boundary condition as the interface between the interfacial heat transfer coefficient and the temperature field solution conforms to the standard treatment method in heat transfer and is beneficial for using mature finite element thermal solvers. The third type of thermal boundary condition allows the interfacial heat transfer coefficient to be directly substituted as a boundary condition parameter without additional intermediate conversion, ensuring that the updated interfacial heat transfer coefficient can accurately affect the value of the thermal boundary condition and thus accurately reflect it in the solution results.

[0107] For example, for a node with an interface gap of g = 5 μm, its updated interfacial heat transfer coefficient h_i = 1557 W / (m²·K), and the casting-side temperature T_casting is taken as the current solidification front temperature of the casting, which is approximately 600 degrees Celsius. Then, the third type of thermal boundary condition for this node is: the normal heat flux density through the interface at this node q_i = 1557 × (T_i - 600) W / m². This heat flux density value will affect the temperature update of this node and its neighboring nodes.

[0108] S412, with the third type of thermal boundary condition as constraint, solves the transient heat conduction equation to obtain the updated temperature field; the transient heat conduction equation includes a heat diffusion term and a latent heat source term, and the latent heat source term is treated using the equivalent specific heat capacity method. The transient heat conduction equation is understood to be a partial differential equation describing the evolution of the temperature field over time. Its standard form is ρ×c_p×∂T / ∂t=∇·(κ∇T)+Q, where ρ is density, c_p is specific heat capacity, κ is thermal conductivity, and Q is the internal heat source term. The heat diffusion term ∇·(κ∇T) describes the heat conduction process within the material; the latent heat source term Q_latent describes the effect of the latent heat released during metal solidification on the temperature field. The equivalent specific heat capacity method is a numerical method for handling latent heat. Its core idea is to equate the latent heat of solidification to an additional increase in specific heat capacity within the solidification temperature range, thereby avoiding the complexity of explicitly tracking the solid-liquid interface.

[0109] In this embodiment, the process of solving the transient heat conduction equation with the third type of thermal boundary condition as a constraint is as follows: The node-by-node third type of thermal boundary condition established in step S411 is assembled into the finite element discrete equation to form a semi-discrete equation system containing convection boundary terms. The equivalent specific heat capacity method is used to handle latent heat: Between the liquidus temperature and solidus temperature of the casting material, the latent heat of solidification L is divided by the solidification temperature range ΔT_sol to obtain the equivalent specific heat capacity increment Δc_p = L / ΔT_sol. This increment is superimposed on the material's specific heat capacity, allowing the energy equation to automatically absorb latent heat within the solidification temperature range. The transient discrete equation system can be integrated over time using the implicit Newmark-β method (β = 0.5) to solve for the node temperature distribution after each micro-time step, ultimately obtaining the updated temperature field.

[0110] Including latent heat source terms in the transient heat conduction equation and employing the equivalent specific heat capacity method is of great significance for the simulation of die-casting molds. The release of latent heat during the solidification process of castings is one of the most significant heat sources on the mold surface, and its spatial distribution and release rate directly affect the temperature gradient and thermal stress on the mold cavity surface. Ignoring the latent heat effect (or using only a constant specific heat capacity approximation) will lead to underestimation of the temperature field and thermal stress, resulting in missed detections of hot cracking risks. The equivalent specific heat capacity method, while ensuring solution accuracy, avoids the complexity of explicitly tracking the solid-liquid interface, facilitating efficient implementation within the finite element framework.

[0111] For example, for ADC12 aluminum alloy, the liquidus temperature is 580 degrees Celsius, the solidus temperature is 510 degrees Celsius, and the latent heat of solidification L = 3.89 × 10⁻⁶. 5 J / kg. Solidification temperature range ΔT_sol = 580 - 510 = 70 degrees Celsius, equivalent specific heat capacity increment Δc_p = 3.89 × 10⁻⁶. 5 / 70≈5557J / (kg·K). At each node within this temperature range, the effective specific heat capacity is c_p_eff(T) = c_p(T) + 5557J / (kg·K). The time integration uses an implicit algorithm with a micro-time step of 1 millisecond. After advancing through 100 micro-time steps, the updated temperature field at the end of the current macro-time step is obtained.

[0112] This setup allows the updated interfacial heat transfer coefficient to be incorporated into the transient heat conduction equation using third-type thermal boundary conditions to update the temperature field. This ensures that the correction of the interfacial heat transfer coefficient accurately affects the thermal boundary conditions of the mold surface nodes and drives the redistribution of the temperature field through the transient heat transfer process. Incorporating a latent heat source term into the transient heat conduction equation and using the equivalent specific heat capacity method helps to accurately simulate the impact of the release of latent heat during casting solidification on the mold temperature field, thus improving the physical realism of the simulation.

[0113] S500: If the maximum node temperature difference between the updated temperature field and the current temperature field is less than the preset temperature threshold, the updated temperature field is determined as the coupled temperature field of the die-casting mold.

[0114] The maximum node temperature difference can be understood as the maximum absolute value of the temperature difference between the updated and current temperature fields across all nodes. The preset temperature threshold is a user-defined convergence criterion parameter used to determine whether the weakly coupled iteration has reached convergence. When the maximum node temperature difference is less than the preset temperature threshold, it indicates that the updated and current temperature fields are numerically close enough that continuing the iteration will not significantly improve accuracy, and the iteration can be terminated. The coupled temperature field is the final temperature field after the weakly coupled iteration has converged, taking into account the bidirectional coupling effect of temperature and stress.

[0115] In this embodiment, convergence determination is the termination control step of the weakly coupled iteration. After completing step S400 and obtaining the updated temperature field in each iteration step, the absolute value of the temperature difference between each node and the current temperature field is calculated, and the maximum value among all nodes is taken as the maximum node temperature difference. The maximum node temperature difference is compared with a preset temperature threshold (e.g., 1.0 degrees Celsius): if it is less than the preset temperature threshold, convergence is determined, the updated temperature field is determined as the coupled temperature field, and the weakly coupled iteration of this macro time step ends; if it is greater than or equal to the preset temperature threshold, convergence is determined, and iterative processing or rollback processing is required according to subsequent steps.

[0116] The preset temperature threshold is a convergence criterion parameter, which can be pre-calibrated using the following method: On the finite element model of the die-casting mold, select three sets of meshes with sequentially increasing mesh densities (coarse mesh, medium mesh, and fine mesh), and perform a complete weakly coupled iteration (without threshold truncation) under the same initial and boundary conditions. Record the sequence of maximum node temperature differences between two adjacent iterations under each mesh. Based on the results of the fine and medium meshes, use the Richardson extrapolation method to estimate the spatial discretization error ε_disc. The preset temperature threshold is calibrated to 10% to 50% of ε_disc.

[0117] Using the maximum node temperature difference as a convergence criterion has clear physical meaning and numerical reliability. The maximum node temperature difference reflects the upper limit of the temperature field change between two iterations; when this value is less than a threshold, it indicates that the temperature field of the entire mold has stabilized. Compared with overall indicators such as average temperature difference or root mean square temperature difference, the maximum node temperature difference can capture potential non-convergence phenomena in local hotspot areas, avoiding situations where overall indicators are acceptable but large errors exist locally. Choosing an appropriate preset temperature threshold (e.g., 1.0 degrees Celsius) is a balance between convergence accuracy and computational cost; a threshold that is too small leads to too many unnecessary iterations, while a threshold that is too large leads to premature termination and insufficient accuracy.

[0118] For example, the preset temperature threshold is set to 1.0 degrees Celsius. After the k=3th iteration, the absolute value of the temperature difference between all nodes in the updated temperature field T³_final and the current temperature field T²_final is calculated. The maximum node temperature difference is found to be 0.7 degrees Celsius (located in the bearing housing mounting surface area), which is less than the preset temperature threshold of 1.0 degrees Celsius, and the iteration is determined to have converged. T³_final is then defined as the coupled temperature field of the die-casting mold.

[0119] In one possible implementation, the method also includes: S600: If the maximum node temperature difference is not less than a preset temperature threshold, the updated temperature field is used as the new current temperature field. The process returns to the step of determining the gap distribution based on the current temperature field and subsequent iterations until the maximum node temperature difference between the updated temperature field and the current temperature field is less than the preset temperature threshold. Iterative processing can be understood as follows: when the current iteration step has not converged, the updated temperature field of the current iteration step is used as the current temperature field of the next iteration step (i.e., the new value replaces the old value), and the complete weakly coupled iterative process from S200 to S500 is re-executed. This method of replacing the old value with the new value is the standard practice for numerical iterative solutions, and each iteration brings the solution result one step closer to the actual physical state.

[0120] In this embodiment, when the convergence criterion is not met, the updated temperature field is assigned to the current temperature field. This means that the next iteration will recalculate the gap distribution, update the interface heat transfer coefficient, and solve for the updated temperature field based on the temperature field results of this iteration. Since the updated interface heat transfer coefficient is usually lower than that of the previous iteration (the increased gap leads to deteriorated heat dissipation), the heat dissipation capacity of the mold surface is weakened, and the updated temperature field will be higher than that of the previous iteration. As the iteration progresses, the change in the interface heat transfer coefficient gradually decreases, and the temperature field gradually approaches the convergence state.

[0121] The core advantage of weakly coupled methods lies in replacing the static unidirectional transmission in sequential coupling with an iterative advancement mechanism of feedback to correction and then feedback. Each iteration essentially completes a full information flow cycle, gradually adjusting the interface heat transfer coefficient from its initial static preset value to a physical value consistent with the current thermo-mechanical state. This gradual correction approach ensures that the final converged coupled temperature field comprehensively reflects the bidirectional coupling effect between temperature and stress, resulting in prediction accuracy superior to that of sequential coupling methods that only consider unidirectional influences.

[0122] For example, after the k=1th iteration, the maximum node temperature difference is 4.3 degrees Celsius, which is greater than the preset temperature threshold of 1.0 degrees Celsius, and convergence has not occurred. Using T¹_final as the new current temperature field, the process returns to S200 to redetermine the gap distribution (at which point the gap increases from 3.2 μm to 4.1 μm), executes S300 to update the interface heat transfer coefficient (decreasing from 2743 W / (m²·K) to 2056 W / (m²·K)), and executes S400 to solve for and update the temperature field T²_final. After the k=2nd iteration, the maximum temperature difference is still 1.8 degrees Celsius, and iteration continues. After the k=3rd iteration, the maximum temperature difference decreases to 0.7 degrees Celsius, satisfying the convergence condition, and the iteration terminates.

[0123] This setup, through a basic iterative progression mechanism that returns to iteration if convergence fails, allows the weakly coupled simulation to automatically approach the convergence state as the interface heat transfer coefficient is gradually adjusted, without requiring manual intervention in the iteration process. This mechanism enables the automatic operation of the physical feedback closed loop of bidirectional temperature-stress coupling within the simulation framework.

[0124] In one possible implementation, the method also includes: S700, when the number of iterations reaches the preset maximum number of iterations and the maximum node temperature difference is still not less than the preset temperature threshold, the current time step is subdivided into multiple sub-time steps, and each sub-time step is taken as the new current time step. The step of determining the gap distribution based on the current temperature field and subsequent iterations are executed sequentially until the maximum node temperature difference between the updated temperature field and the current temperature field is less than the preset temperature threshold.

[0125] It's understandable that the preset maximum number of iterations is an upper limit parameter for the number of iterations in weakly coupled iterations. This limits the maximum number of coupled iterations within each time step, preventing infinite iterations under extreme conditions. The time step subdivision backoff strategy means that when the maximum number of iterations is reached but the temperature field has not yet converged, instead of directly abandoning convergence or outputting a non-converged result, the current time step is subdivided (e.g., a 100-millisecond time step is split into two 50-millisecond sub-time steps or five 20-millisecond sub-time steps). For each sub-time step, the complete weakly coupled iteration process from S200 to S500 is re-executed sequentially. Because the time span of the sub-time steps is reduced, the magnitude of temperature field changes within each sub-time step decreases, the nonlinearity is reduced, and convergence is more easily achieved within a limited number of iterations.

[0126] In this embodiment, the activation condition for the time step subdivision backoff strategy is that the number of iterations reaches a preset maximum number of iterations and the maximum node temperature difference is still not less than a preset temperature threshold. Once activated, the original time span Δt of the current time step is subdivided into n sub-time steps, each with a time span of Δt / n. For each sub-time step, the initial temperature field of that sub-time step is taken as the current temperature field, and the weakly coupled iteration process from S200 to S500 is executed sequentially within the time span of that sub-time step. Since the change in temperature field within the sub-time step is significantly reduced compared to the original time step, the change in interface gap and the change in interface heat transfer coefficient are also correspondingly reduced, reducing the nonlinearity of the weakly coupled iteration and making it easier to achieve convergence. After all sub-time steps have converged, the coupled temperature field at the end of the last sub-time step is output as the coupled temperature field of the original current time step.

[0127] In certain special operating conditions of die-casting molds (such as the rapid thermal shock stage near the gate area), the temperature field may change drastically within a single time step, leading to excessively large nonlinear changes in the interfacial gap and interfacial heat transfer coefficient, making it difficult for the weakly coupled iteration to converge within the preset maximum number of iterations. If no measures are taken and the non-converged result is directly output, significant simulation errors may be introduced; if the preset maximum number of iterations is simply increased, the simulation computation time may become uncontrollable. The time-step subdivision backoff strategy reduces the degree of nonlinearity by decreasing the step size, thus controlling the computational cost while ensuring convergence accuracy, and is an important guarantee for the robustness of the weakly coupled method.

[0128] For example, the preset maximum number of iterations is 5, and the current time step length Δt = 100 milliseconds. After the k=5th iteration, the maximum node temperature difference is 2.3 degrees Celsius, which is greater than the preset temperature threshold of 1.0 degree Celsius, and the number of iterations has reached the preset maximum number of iterations of 5, so the S700 time step subdivision backoff strategy is activated. The 100-millisecond time step is subdivided into n=2 sub-time steps, each with a length of 50 milliseconds.

[0129] For the first sub-time step (50 milliseconds), the starting temperature field of the original time step is taken as the current temperature field, and the weakly coupled iterative process S200-S500 is executed. Since the temperature change amplitude within this 50 milliseconds is reduced by about half compared to the original 100 milliseconds, the change in the interface gap is also reduced accordingly. After 3 iterations, the maximum node temperature difference drops to 0.5 degrees Celsius, satisfying the convergence condition, and the coupled temperature field after the convergence of the first sub-time step is output.

[0130] For the second sub-time step (50 milliseconds), the coupled temperature field of the first sub-time step is taken as the current temperature field, and the weakly coupled iterative process S200-S500 continues. After two iterations, the maximum node temperature difference drops to 0.6 degrees Celsius, satisfying the convergence condition. At this point, both sub-time steps have successfully converged, and the coupled temperature field at the end of the second sub-time step is output as the coupled temperature field of the original 100-millisecond time step. The total number of iterations is 3+2=5 (3 iterations for the two sub-time steps and 2 iterations for the original time step), plus the 5 iterations of the original time step, for a total of 10 iterations. Compared to simply increasing the preset maximum number of iterations to more than 10, the time step subdivision strategy improves convergence efficiency by reducing the degree of single-step nonlinearity.

[0131] With this setup, the time step subdivision backoff strategy provides an effective guarantee for the convergence of weakly coupled iteration under large gradient and strong nonlinear conditions. This enables the method to maintain numerical stability and simulation accuracy under extreme conditions such as mold thermal shock, avoiding simulation interruption or accuracy loss due to iteration non-convergence. It is beneficial to improve the robustness of thermo-mechanical coupling simulation of die-casting molds under complex conditions.

[0132] Corresponding to the above embodiment of the simulation method for coupled temperature and stress fields of automotive part die-casting molds, this application embodiment also provides a simulation system for coupled temperature and stress fields of automotive part die-casting molds. Each unit of this device can realize each step of the simulation method for coupled temperature and stress fields of automotive part die-casting molds. Figure 5 The diagram shows a structural block diagram of the coupled simulation system for temperature and stress fields of automotive part die-casting molds provided in this application embodiment. For ease of explanation, only the parts related to this application embodiment are shown.

[0133] Reference Figure 5 The coupled simulation system for temperature and stress fields of automotive component die-casting molds includes: The acquisition unit is used to acquire the current temperature field of the die-casting mold for automotive parts; A distribution unit is used to determine the gap distribution at the interface between the die-casting mold and the casting based on the current temperature field; wherein the gap distribution is the distribution of the separation distance between the die-casting mold and the casting along the normal direction of the interface; A coefficient unit is used to update the interface heat transfer coefficient of the interface according to the gap distribution and the pre-calibrated gap heat transfer mapping relationship; wherein, the gap heat transfer mapping relationship characterizes the correspondence between the interface gap value and the interface heat transfer coefficient value. An update unit is used to redetermine the updated temperature field of the die-casting mold based on the updated interface heat transfer coefficient. The determining unit is configured to determine the updated temperature field as the coupled temperature field of the die-casting mold when the maximum node temperature difference between the updated temperature field and the current temperature field is less than a preset temperature threshold.

[0134] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0135] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit module can exist physically separately, or two or more unit modules can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above device can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0136] This application also provides an electronic device. Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 6 As shown, the electronic device 6 of this embodiment includes: at least one processor 60 ( Figure 6 Only one is shown in the image), at least one memory 61 ( Figure 6 (Only one is shown in the image) and a computer program 62 stored in the at least one memory 61 and executable on the at least one processor 60. When the processor 60 executes the computer program 62, it causes the electronic device 6 to perform the steps in any of the above embodiments of the coupling simulation method for temperature field and stress field of die-casting molds for automotive parts, or causes the electronic device 6 to perform the functions of each unit in the above embodiments of the devices.

[0137] For example, the computer program 62 may be divided into one or more units, which are stored in the memory 61 and executed by the processor 60 to complete this application. The one or more units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program 62 in the coupled simulation of temperature field and stress field of automotive part die-casting mold 6.

[0138] The electronic device may include, but is not limited to, a processor 60 and a memory 61. Those skilled in the art will understand that... Figure 6 This is merely an example of electronic device 6 and does not constitute a limitation on electronic device 6. It may include more or fewer components than shown, or combine certain components, or different components, such as input / output devices, network access devices, buses, etc.

[0139] The processor 60 can be a Central Processing Unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0140] In some embodiments, the memory 61 may be an internal storage unit of the electronic device 6, such as a hard disk or memory of the electronic device 6. In other embodiments, the memory 61 may be an external storage device of the electronic device 6, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the electronic device 6. Furthermore, the memory 61 may include both internal and external storage units of the electronic device 6. The memory 61 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory 61 can also be used to temporarily store data that has been output or will be output.

[0141] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0142] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0143] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for coupled simulation of temperature and stress fields in die-casting molds for automotive parts, characterized in that, include: Obtain the current temperature field of the die-casting mold for automotive parts; The gap distribution at the interface between the die-casting mold and the casting is determined based on the current temperature field; wherein, the gap distribution is the distribution of the separation distance between the die-casting mold and the casting along the normal direction of the interface; The interface heat transfer coefficient is updated based on the gap distribution and the pre-calibrated gap heat transfer mapping relationship; wherein, the gap heat transfer mapping relationship characterizes the correspondence between the interface gap value and the interface heat transfer coefficient value. The updated temperature field of the die-casting mold is determined based on the updated interface heat transfer coefficient. If the maximum node temperature difference between the updated temperature field and the current temperature field is less than a preset temperature threshold, the updated temperature field is determined as the coupled temperature field of the die-casting mold.

2. The method of claim 1, wherein, The method further includes: If the maximum node temperature difference is not less than the preset temperature threshold, the updated temperature field is taken as the new current temperature field, and the step of determining the gap distribution based on the current temperature field and subsequent iterations are returned until the maximum node temperature difference between the updated temperature field and the current temperature field is less than the preset temperature threshold.

3. The method of claim 2, wherein, The method further includes: If the number of iterations reaches the preset maximum number of iterations and the maximum node temperature difference is still not less than the preset temperature threshold, the current time step is subdivided into multiple sub-time steps, and each sub-time step is taken as the new current time step. The step of determining the gap distribution based on the current temperature field and subsequent iterations are executed sequentially until the maximum node temperature difference between the updated temperature field and the current temperature field is less than the preset temperature threshold.

4. The method of claim 1, wherein, Determining the gap distribution at the interface between the die-casting mold and the casting based on the current temperature field includes: Determine the physical basis function matrix of the interface layer; wherein, the physical basis function matrix of the interface layer is a matrix constructed based on the normal displacement response vector of the interface extraction layer under the action of multiple sets of preset temperature distributions and subjected to orthogonal normalization. The temperature increment distribution of the current temperature field on the interface extraction layer is projected onto the basis function space of the physical basis function matrix of the interface layer to obtain the basis function coefficient vector; The gap distribution is obtained by linearly superimposing the basis function coefficient vector and the normal displacement response vector.

5. The method of claim 4, wherein, The determination of the physical basis function matrix of the interface layer includes: The cavity surface of the finite element model of the die-casting mold is offset inward by a preset depth along the opposite direction of the normal, and the area between the offset surface and the cavity surface is extracted as the interface extraction layer. Multiple sets of standard temperature load modes are applied to the interface extraction layer and their combinations are solved to obtain the physical basis function matrix of the interface layer.

6. The method of claim 5, wherein, The process of applying multiple sets of standard temperature load modes to the interface extraction layer and solving their combination yields the physical basis function matrix of the interface layer, including: Multiple standard temperature load modes are applied to the interface extraction layer, and the normal displacement response vector under each standard temperature load mode is solved. Each standard temperature load mode is a temperature increment function with a preset spatial distribution applied to the interface extraction layer. The normal displacement response vector is a vector composed of the displacement of each node in the interface extraction layer along the normal direction of the cavity surface. The normal displacement response vectors corresponding to each group of standard temperature load modes are combined column by column, and the combined matrix is ​​orthogonally normalized to obtain the physical basis function matrix of the interface layer.

7. The method of claim 1, wherein, The step of updating the interface heat transfer coefficient based on the gap distribution and the pre-calibrated gap heat transfer mapping relationship includes: Based on the gap value of each interface node in the gap distribution and the pre-calibrated attenuation constant, the interface heat transfer coefficient value corresponding to the interface node is determined; wherein, the attenuation constant is a parameter characterizing the rate at which the interface heat transfer coefficient decreases as the gap value increases. The interface heat transfer coefficient values ​​corresponding to each interface node on the interface are combined to form the updated interface heat transfer coefficient.

8. The method of claim 7, wherein, The step of determining the interface heat transfer coefficient value corresponding to each interface node based on the gap value of each interface node in the gap distribution and the pre-calibrated attenuation constant includes: For each interface node, the interface heat transfer coefficient value corresponding to the interface node is obtained by multiplying the first coefficient by a power of the product of the natural constant e and the gap value, with the product as the base and the product as the exponent, and adding the second coefficient multiplied by 1 minus the difference of the exponent. The first coefficient is the reference heat transfer coefficient of the die-casting mold and the casting in the metal-to-metal contact state, the second coefficient is the gap heat transfer coefficient when the gap value is greater than the preset gap upper limit, and the attenuation constant is pre-calibrated by a steady-state heat flux experiment on the combination of the die-casting mold material and the casting material of the casting.

9. The method of claim 1, wherein, The step of re-determining the updated temperature field of the die-casting mold based on the updated interfacial heat transfer coefficient includes: Using the updated interface heat transfer coefficient as the thermal boundary condition of the interface, the transient heat conduction solution is performed on the finite element model of the die-casting mold to obtain the updated temperature field.

10. The method according to claim 9, characterized in that, The step of using the updated interface heat transfer coefficient as the thermal boundary condition of the interface to perform transient heat conduction solution on the finite element model of the die-casting mold to obtain the updated temperature field includes: Substitute the updated interface heat transfer coefficient into the third type of thermal boundary condition, which characterizes the proportional relationship between the heat flux density through the interface and the temperature difference across the interface. The transient heat conduction equation is solved using the third type of thermal boundary condition as a constraint to obtain the updated temperature field; wherein the transient heat conduction equation includes a heat diffusion term and a latent heat source term, and the latent heat source term is treated using the equivalent specific heat capacity method.

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