Metal additive manufacturing topology optimization method considering mechanical performance and weight reduction

Abstract

The application relates to a metal additive manufacturing topology optimization method considering mechanical properties and weight reduction. The method comprises the following steps: obtaining a design space of a final state target configuration, service boundary conditions and material attribute data of a to-be-processed metal material, and constructing a heat treatment digital twin engine based on the material attribute data; obtaining a topology configuration of an initial iteration based on the design space, and performing performance evaluation on the topology configuration based on the service boundary conditions and the heat treatment digital twin engine to obtain a performance evaluation result; updating the topology configuration through sensitivity analysis based on the performance evaluation result to obtain a topology configuration of the current iteration; and obtaining an optimal design meeting the final state service performance requirements and the printing state manufacturability requirements through iteration convergence. The method can effectively solve the industry pain points that the geometric precision of an additive manufacturing topology optimization part is out of tolerance due to heat treatment deformation and the service reliability is reduced due to performance evolution.

Description

Technical Field

[0001] This invention belongs to the field of topology optimization technology in metal additive manufacturing, and in particular relates to a topology optimization method for metal additive manufacturing that takes into account both mechanical properties and weight reduction. Background Technology

[0002] With the rapid development of additive manufacturing technology, metal additive manufacturing processes such as laser powder bed melting have made near-net-shape forming of complex topology-optimized structures possible due to their extremely high degree of design freedom. This, in turn, has driven the urgent demand for lightweight and high-performance co-design in fields such as aerospace and medical devices. Topology optimization, as a core design method for achieving ultimate weight reduction and mechanical performance matching, can automatically generate the optimal material distribution configuration based on given loads and boundary conditions. Its complex curved surfaces and hollow features are increasingly becoming the preferred structural forms for key load-bearing components in high-end equipment.

[0003] In the traditional topology optimization design process, engineers first optimize the design based on an ideal geometric model and homogeneous material properties. After obtaining the optimal topology configuration, it is directly used as the printing model for additive manufacturing. Subsequently, heat treatment processes such as stress-relief annealing and solution aging are used to eliminate residual stress and microstructure inhomogeneity present in the printed state, thereby improving the overall mechanical properties of the final part. This sequential process of "design first, then print, then heat treat" separates design, manufacturing, and post-processing into independent stages, and the optimization process is entirely based on the ideal model without heat treatment.

[0004] However, the aforementioned traditional methods have significant technical drawbacks: stress release, phase transformation volume effects, and recrystallization creep during heat treatment can cause complex geometric deformations in parts. Furthermore, heat treatment itself fundamentally restructures the microstructure and mechanical property distribution of the material, leading to severe deviations in the final part's geometric accuracy and significant discrepancies between actual service performance and design objectives. Current engineering practice relies solely on experience to allow for machining allowances or on secondary corrections through CNC machining after heat treatment, failing to accurately predict and proactively compensate for the geometric distortions and performance evolution caused by heat treatment during the design phase. Summary of the Invention

[0005] Therefore, it is necessary to provide a topology optimization method that can embed the heat treatment process into the optimization process and reverse-engineer the printed configuration from the final service performance to address the above-mentioned technical problems.

[0006] In a first aspect, this application provides a topology optimization method for metal additive manufacturing that balances mechanical properties and weight reduction, including:

[0007] Step S1: Obtain the design space, service boundary conditions, and material property data of the metal material to be processed for the final target configuration, and construct a heat treatment digital twin engine based on the material property data; wherein, the heat treatment digital twin engine is used to process the topology configuration and output the deformation field and material property field of the topology configuration after undergoing the preset heat treatment process.

[0008] Step S2: Based on the design space, obtain the topology configuration of the first iteration, and perform performance evaluation on the topology configuration based on the service boundary conditions and the heat treatment digital twin engine to obtain the performance evaluation results; wherein, the performance evaluation results include final state performance indicators and manufacturability evaluation indicators.

[0009] Step S3: Based on the final state performance index and manufacturability evaluation index in the performance evaluation results, update the topology configuration through sensitivity analysis to obtain the topology configuration for this iteration.

[0010] Step S4: Repeat steps S2 and S3 until the iteration termination condition is met, and set the topology configuration of the iteration round that meets the iteration termination condition as the final topology configuration; wherein, the iteration termination condition is that the final state performance index meets the service performance requirements and the manufacturability evaluation index meets the manufacturability requirements.

[0011] Furthermore, the material property data includes thermophysical parameters, phase transformation kinetic parameters, and thermodynamic parameters. Based on this material property data, a digital twin engine for heat treatment is constructed, including:

[0012] Based on the thermophysical parameters, phase transformation kinetic parameters, and thermo-mechanical parameters of the metal material to be treated, a thermo-metallurgical-mechanical multi-field coupled constitutive model is constructed. The thermo-metallurgical-mechanical multi-field coupled constitutive model is used to describe the mechanical behavior of the metal material to be treated under the coupled action of temperature field, phase transformation field, and stress field.

[0013] By discretizing and coupling the equations of the thermo-metallurgical-mechanical multi-field coupled constitutive model, a multi-field coupled finite element simulation model of the heat treatment process is generated.

[0014] Multiple topological configuration samples are input into a multi-field coupled finite element simulation model of the heat treatment process, and the heat treatment deformation field and heat treatment material property field corresponding to each topological configuration sample are output; among them, the topological configurations have different geometric characteristics;

[0015] A training sample set is constructed based on topological configuration samples, heat treatment deformation field, and heat treatment material property field;

[0016] Based on the training sample set, a pre-built deep learning agent model is trained to obtain a heat-processing digital twin engine.

[0017] Furthermore, based on the design space, the topology configuration of the initial iteration is obtained, and based on the service boundary conditions and the heat treatment digital twin engine, the performance of the topology configuration is evaluated to obtain the performance evaluation results, including:

[0018] Based on the design space, the topological configuration of the initial iteration is obtained, and the topological configuration is input into the heat treatment digital twin engine to output the final deformation field and the final material property field.

[0019] Based on the final-state deformation field, the geometry of the topological configuration is corrected to obtain the corrected topological configuration. Then, based on the final-state material property field, material properties are assigned to the corrected topological configuration to obtain the analysis model.

[0020] Based on the service boundary conditions, finite element analysis is performed on the analysis model to obtain the final state performance index;

[0021] Input the topology configuration into the inverse compensation operator and output the printed state pre-compensation configuration corresponding to the topology configuration;

[0022] Feasibility of additive manufacturing process was checked on the pre-compensated printed configuration to obtain manufacturability evaluation indicators;

[0023] By summarizing the final performance indicators and manufacturability evaluation indicators, the performance evaluation results are obtained.

[0024] Furthermore, the topology configuration is input into the inverse compensation operator, and the output is the pre-compensated printed state configuration corresponding to the topology configuration, including:

[0025] Step S241: Set the topological configuration as the initial guess value of the printing state configuration to obtain the current printing state configuration of this iteration, and initialize the iterative printing state configuration based on the current printing state configuration;

[0026] Step S242: Input the iterative printing state configuration of the previous second-layer iteration into the heat treatment digital twin engine to obtain the predicted deformation field corresponding to the current printing state configuration; wherein, the iterative printing state configuration of the previous second-layer iteration of the first second-layer iteration is the current printing state configuration;

[0027] Step S243: Based on the predicted deformation field and the final deformation field, calculate the geometric error between the predicted final configuration and the target final configuration obtained after heat treatment of the current printed configuration;

[0028] Step S244: When the geometric error is greater than the geometric error threshold, the current printed state configuration is updated by reverse node movement based on the predicted deformation field to obtain the iterative printed state configuration of the second layer of this round.

[0029] Step S245: Repeat steps S242, S243 and S244 until the geometric error is less than the geometric error threshold. Set the iterative printing state configuration with the geometric error less than the geometric error threshold as the printing state pre-compensation configuration corresponding to the topology configuration.

[0030] Furthermore, the feasibility of additive manufacturing process was checked on the pre-compensated printed configuration to obtain manufacturability evaluation indicators, including:

[0031] The overhang angle of the pre-compensated printed configuration is detected to obtain the number of overhang violation units and the degree of violation of the overhang violation units. Based on the number and degree of violation, the overhang angle penalty value is calculated.

[0032] The original density field of the pre-compensated printed configuration is morphologically processed to obtain the morphologically processed density field. Based on the difference between the original density field and the morphologically processed density field, the feature size penalty value is calculated.

[0033] The manufacturability evaluation index is obtained by weighted summation of the overhang angle penalty value and the feature size penalty value.

[0034] Secondly, this application also provides a metal additive manufacturing topology optimization device that balances mechanical properties and weight reduction, comprising:

[0035] The data acquisition module is used in step S1 to acquire the design space, service boundary conditions and material property data of the final target configuration and the metal material to be processed, and to construct a heat treatment digital twin engine based on the material property data; wherein, the heat treatment digital twin engine is used to process the topology configuration and output the deformation field and material property field of the topology configuration after undergoing the preset heat treatment process.

[0036] The performance evaluation module, used in step S2, obtains the topology configuration of the initial iteration based on the design space, and performs performance evaluation on the topology configuration based on service boundary conditions and a heat treatment digital twin engine to obtain performance evaluation results; wherein, the performance evaluation results include final state performance indicators and manufacturability evaluation indicators.

[0037] The configuration update module, used in step S3, updates the topology configuration based on the final performance index and manufacturability evaluation index in the performance evaluation results through sensitivity analysis to obtain the topology configuration for this iteration.

[0038] The configuration determination module is used in step S4 to repeat steps S2 and S3 until the iteration termination condition is met, and sets the topology configuration of the iteration round that meets the iteration termination condition as the final topology configuration; wherein, the iteration termination condition is that the final state performance index meets the service performance requirements and the manufacturability evaluation index meets the manufacturability requirements.

[0039] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement a metal additive manufacturing topology optimization method that balances mechanical performance and weight reduction as described in any of the embodiments of this application.

[0040] Fourthly, this application also provides a computer-readable storage medium storing at least one piece of program code, which is loaded and executed by a processor to implement a metal additive manufacturing topology optimization method that balances mechanical performance and weight reduction as described in any of the embodiments of this application.

[0041] The aforementioned topology optimization method for metal additive manufacturing, which balances mechanical performance and weight reduction, constructs a digital twin engine for heat treatment based on experimental data. In each optimization iteration cycle, the current topology configuration is input into the engine to predict its true geometry and material properties after heat treatment. Service performance is evaluated on this true final-state model. A pre-compensated printing configuration that satisfies additive manufacturing process constraints is derived using an inverse compensation operator, and its manufacturability is assessed. Based on the performance evaluation results, the topology configuration is updated through sensitivity analysis. Iterative convergence yields the optimal design that simultaneously satisfies both final-state service performance requirements and printing-state manufacturability requirements. This method effectively addresses the industry pain points of geometric accuracy deviations caused by heat treatment deformation and service reliability degradation due to performance evolution in additively manufactured topology-optimized parts. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying 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.

[0043] Figure 1 This is a flowchart illustrating a topology optimization method for metal additive manufacturing that balances mechanical properties and weight reduction in one embodiment.

[0044] Figure 2 In one embodiment, the material property data includes thermal property parameters, phase transformation kinetic parameters, and thermo-dynamic parameters. Based on the material property data, a flowchart illustrating the steps for constructing a heat treatment digital twin engine is provided.

[0045] Figure 3 This is a schematic diagram of a metal additive manufacturing topology optimization device that balances mechanical performance and weight reduction in one embodiment. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0047] In one embodiment, a topology optimization method for metal additive manufacturing that balances mechanical performance and weight reduction is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and further to a system including both a terminal and a server, and can be implemented through the interaction between the terminal and the server. Figure 1 As shown, in this embodiment, the method includes the following steps:

[0048] Step S1: Obtain the design space, service boundary conditions, and material property data of the metal material to be processed for the final target configuration, and construct a heat treatment digital twin engine based on the material property data; wherein, the heat treatment digital twin engine is used to process the topology configuration and output the deformation field and material property field of the topology configuration after undergoing the preset heat treatment process.

[0049] The final target configuration refers to the geometric shape that the designer expects to obtain after the part undergoes a complete heat treatment process, satisfying all service performance requirements. The design space is a three-dimensional continuous geometric domain used to define the spatial range of the entire optimization process, within which all topological configurations must reside. Service boundary conditions refer to all external action conditions that the final target configuration will experience in the actual service environment, including mechanical boundary conditions and thermal boundary conditions. Mechanical boundary conditions include the fixed constraint positions and directions at the connection between the part and other components, and the magnitude and point of application of the structural loads applied during service. Thermal boundary conditions include the temperature field distribution, heat flux density, convective heat transfer coefficient, and radiative heat transfer parameters in the service environment of the part. The preset heat treatment process refers to the pre-determined post-processing system for the metal material to be treated, used to eliminate residual stress from additive manufacturing, homogenize the microstructure, and adjust the phase composition to obtain the target mechanical properties.

[0050] For example, a design space for the final target configuration is obtained, and precise service boundary conditions, including mechanical and thermal boundary conditions, are acquired within this design space. Material property data of the metallic material to be treated, including thermophysical parameters, phase transformation kinetic parameters, and thermodynamic parameters, can be obtained through standard experiments. Thermophysical parameters include the functional relationships of thermal conductivity, specific heat capacity, and density as a function of temperature; these parameters can be determined using laser scintillation and differential scanning calorimetry. Phase transformation kinetic parameters include the phase transformation initiation temperature, phase transformation end temperature, and latent heat of phase transformation determined by differential scanning calorimetry, as well as curves showing the volume fraction of each phase as a function of temperature at different cooling rates, measured using a quenching expander, used to calibrate the coefficients in the phase transformation kinetic equation. Thermodynamic parameters include the elastic modulus, yield strength, and tangential modulus at different temperatures and with different phase compositions determined by high-temperature tensile tests, and creep parameters determined by creep tests. For example, a heat treatment digital twin engine is constructed based on material property data. This engine is used to receive density field inputs of arbitrary topological configurations and output the corresponding heat treatment deformation field and heat treatment material property field within milliseconds. Among them, standard experiments refer to a set of material physical and mechanical property tests performed on the metal materials to be treated, with clear operating procedures and repeatability; laser flare method is the mainstream transient method for measuring the thermal diffusivity of materials. It involves heating one side of the sample with a short laser pulse and measuring the temperature rise time on the back side to infer the thermal conductivity; differential scanning calorimetry is a thermal analysis technique that measures the difference in heat flow / power between a sample and a reference under programmed temperature control, and can quantitatively detect the heat absorption, heat release, and heat capacity changes of materials; quenching dilatometer is a high-precision instrument used to measure the length or volume changes of materials during heat treatment. It obtains the linear expansion coefficient and volumetric strain caused by phase transformation of materials by recording the dimensional changes of samples during controlled heating, holding, and cooling; high-temperature tensile test refers to a standard test that applies axial tensile load to a material sample at a controllable high temperature to determine its high-temperature mechanical properties. Its core is to simulate the real stress behavior of materials in high-temperature service scenarios; creep test refers to measuring the process of continuous increase in material strain over time under constant temperature and constant tensile / compressive stress, which is used to determine the stability of materials in long-term high-temperature service.

[0051] Step S2: Based on the design space, obtain the topology configuration of the initial iteration, and perform performance evaluation on the topology configuration based on the service boundary conditions and the heat treatment digital twin engine to obtain the performance evaluation results; wherein, the performance evaluation results include final state performance indicators and manufacturability evaluation indicators.

[0052] Among them, performance evaluation refers to performing comprehensive performance simulation calculations on the topological configuration, including mechanical and thermal properties.

[0053] For example, an initial iteration of the topology configuration is initialized within the design space, and this topology configuration is represented in the form of a density field. Based on the service boundary conditions and the heat treatment digital twin engine, the final-state performance indicators and manufacturability assessment of the topology configuration are performed, resulting in performance evaluation results including final-state performance indicators and manufacturability evaluation indicators.

[0054] Step S3: Based on the final state performance index and manufacturability evaluation index in the performance evaluation results, update the topology configuration through sensitivity analysis to obtain the topology configuration for this iteration.

[0055] Sensitivity analysis refers to the process of calculating the rate of change or gradient of the objective function or constraint function with respect to the design variables; the design variables are the density values ​​of each element in the topology.

[0056] For example, an optimization problem is constructed based on final-state performance indices and manufacturability evaluation indices. The final-state performance indices define the objective function, such as minimizing structural compliance, while the manufacturability evaluation indices define constraint functions, such as limiting the penalty values ​​for overhang angles and characteristic dimensions to no more than a set threshold, and setting volume fraction constraints to ensure weight reduction. When calculating the final-state performance sensitivity, the adjoint method can be used to handle the complex chain dependency between the objective function and design variables: the objective function first depends on the nodal displacements and element material properties in the analysis model; the nodal displacements then depend on the heat treatment deformation field; and both the heat treatment deformation field and the heat treatment material property field directly depend on the density field distribution of the topological configuration. By obtaining the partial derivatives of the objective function with respect to nodal displacements through a single adjoint solution, and combining these with the partial derivatives of the deformation field and material property field with respect to the density field extracted from the heat treatment digital twin engine, the above partial derivatives are multiplied and summed step-by-step along the dependency path according to the chain rule to obtain the sensitivity value of the objective function with respect to the density value of each element, thus forming the final-state performance sensitivity field. When calculating manufacturability sensitivity, the manufacturability evaluation index directly affects the pre-compensated configuration in the printed state rather than the topological configuration. The pre-compensated configuration is obtained iteratively from the topological configuration using an inverse compensation operator, resulting in a nonlinear mapping relationship between the two, making direct analytical differentiation difficult. A numerical approximation can be performed using the finite difference method: a small perturbation is applied to the density value of each element in the topological configuration. The perturbed density field is then input into the inverse compensation operator to re-solve for the corresponding pre-compensated configuration in the printed state. The manufacturability evaluation index for this configuration is calculated, and the change in the evaluation index is divided by the density perturbation to obtain an approximate value for the manufacturability sensitivity of that element. This process is repeated for all elements in the design space to form a complete manufacturability sensitivity field. The final-state performance sensitivity field and the manufacturability sensitivity field are then weighted and superimposed according to preset weighting coefficients to obtain the comprehensive sensitivity field. The current topology density field, integrated sensitivity field, and volume fraction constraints are input into the moving asymptote optimization algorithm. Based on the current design point and sensitivity information, the algorithm constructs a convex approximation subproblem for each design variable, transforming the original nonlinear optimization problem into a series of strictly convex quadratic programming subproblems. Solving these subproblems yields the update direction and step size for the density value of each element, resulting in the updated density field distribution, which serves as the topology for this iteration. Within the boundary constraints of the design space, the density distribution of this topology reflects the combined effects of final-state performance optimization and manufacturability optimization, providing new design inputs for the next iteration.

[0057] The adjoint method is a highly efficient mathematical approach for calculating the sensitivity (gradient) of an objective function to a large number of input parameters. By introducing an adjoint variable, i.e., the solution to the adjoint equation, the computational workload, which was originally proportional to the number of design variables, is reduced to be proportional to the number of objective functions. Only one additional finite element solution is needed to obtain the complete sensitivity information of the objective function with respect to all design variables. A single adjoint solution refers to the process of solving the adjoint equation. After completing the finite element solution of the analysis model, the nodal displacements are obtained. Based on these displacement results, an adjoint equation is constructed and solved. The structure of this equation is similar to the original finite element equation, but the right-hand side consists of the partial derivatives of the objective function with respect to the nodal displacements. Solving this adjoint equation yields the adjoint displacement field. By combining the partial derivatives of the adjoint displacement field with the heat treatment deformation field and the material property field, the density values ​​of the objective function with respect to all elements in the design space can be calculated simultaneously. Sensitivity; the chain rule of differentiation refers to finding the derivative of a composite function by taking the derivative layer by layer and then multiplying them together; iterative solution refers to the process of gradually approximating the exact solution through repeated calculations; the finite difference method is a numerical calculation method whose core idea is to use the difference quotient at discrete points to approximate the derivative in the differential equation, transforming the continuous differential equation into a set of linear algebraic equations for solution; numerical approximation refers to not pursuing absolutely accurate results, but using numbers or expressions that are close to the true value and sufficiently usable to replace the exact solution; preset weight coefficients refer to pre-set values ​​used to represent the importance of each factor, which can be preset according to the specific application scenario and manufacturing difficulty of the part; the moving asymptote optimization algorithm is an iterative convex approximation optimization algorithm, the core of which is to transform complex nonlinear programming into a series of easily solvable convex subproblems, and rely on dynamically adjusted asymptotes to control the approximation accuracy and step size, achieving stable convergence.

[0058] Step S4: Repeat steps S2 and S3 until the iteration termination condition is met, and set the topology configuration of the iteration round that meets the iteration termination condition as the final topology configuration; wherein, the iteration termination condition is that the final state performance index meets the service performance requirements and the manufacturability evaluation index meets the manufacturability requirements.

[0059] For example, the current iteration's topology configuration is used as the input for the next iteration, and the performance evaluation in step S2 and the sensitivity analysis and topology update in step S3 are repeated. Each time step S2 is executed, the current iteration's topology configuration is input into the heat treatment digital twin engine to obtain the heat treatment deformation field and the material property field after heat treatment corresponding to that configuration. Based on this, an analysis model is constructed and the final-state performance index is calculated. Simultaneously, the pre-compensated printing state configuration corresponding to that configuration is calculated using the inverse compensation operator, and the manufacturability evaluation index is evaluated. Each time step S3 is executed, the comprehensive sensitivity is calculated based on the latest obtained index, and the topology configuration is updated. After each iteration, it is determined whether the iteration termination condition is met: first, it is determined whether the final-state performance index meets the pre-set service performance requirements, including compliance being less than the preset maximum value, maximum stress being less than the material yield strength divided by the safety factor, and nodal displacement being less than the preset allowable displacement value; second, it is determined whether the manufacturability evaluation index is less than the pre-set manufacturability threshold, i.e., the weighted sum of the overhang angle penalty value and the feature size penalty value is lower than the acceptable level. When the change in the topology density field of the current two iterations is less than the preset minimum value and the final performance index and manufacturability evaluation index simultaneously meet the above requirements, the iteration termination condition is determined to be met, the iteration loop is terminated, the topology of the current round is set as the final topology, and the corresponding printing state pre-compensation configuration can be generated as an STL format printing model file, while outputting the heat treatment process parameters that match the printing state pre-compensation configuration. Among them, the preset maximum value is the upper limit of compliance set in advance; the safety factor is a safety margin reserved by humans to offset uncertainties such as load fluctuations and calculation errors; the material yield strength refers to the critical stress at which the material begins to undergo permanent deformation; the preset minimum value is a very small value set in advance, which indicates that the material / density distribution obtained from the two calculations is almost no longer changing, and the change is so small as to be negligible; STL (Standard Tessellation Language) is the most common pure geometric triangular mesh format in the fields of 3D (Three-Dimensional) printing and CAD (Computer-Aided Design), which only describes the surface shape of the model and does not contain information such as color, material, and texture.

[0060] In this embodiment, a digital twin engine for heat treatment is constructed using experimental data. In each optimization iteration cycle, the current topology configuration is input into the engine to predict its true geometry and material properties after heat treatment. Service performance is evaluated on this true final-state model. A pre-compensated printing configuration that satisfies additive manufacturing process constraints is derived using a reverse compensation operator, and its manufacturability is evaluated. The comprehensive sensitivity is calculated based on the performance evaluation results to update the topology configuration. The optimal design that simultaneously satisfies both final-state service performance requirements and printing-state manufacturability requirements is obtained through iterative convergence. This transforms heat treatment deformation and performance evolution, traditionally considered uncontrollable post-processing aspects, into predictable, compensable, and optimizable design variables during the design phase. This achieves a technological leap from "forward design - passive deformation" to "reverse design - active pre-compensation," fundamentally solving the industry pain points of geometric accuracy deviations caused by heat treatment deformation and service reliability degradation due to performance evolution in additive manufacturing topology-optimized parts. This significantly shortens the R&D cycle and reduces manufacturing costs.

[0061] In one embodiment, such as Figure 2 As shown, the material property data includes thermophysical parameters, phase transformation kinetic parameters, and thermodynamic parameters. Based on the material property data, a heat treatment digital twin engine is constructed, including:

[0062] Step S11: Based on the thermophysical parameters, phase transformation kinetic parameters, and thermo-mechanical parameters of the metal material to be treated, a thermo-metallurgical-mechanical multi-field coupled constitutive model is constructed; wherein, the thermo-metallurgical-mechanical multi-field coupled constitutive model is used to describe the mechanical behavior of the metal material to be treated under the coupled action of temperature field, phase transformation field, and stress field.

[0063] For example, based on the thermophysical parameters, phase transformation kinetic parameters, and thermo-mechanical parameters of the metallic material to be processed, a thermo-metallurgical-mechanical multi-field coupled constitutive model is constructed. This model can use the Leblond model to describe diffusion-type phase transformation and the Koistinen-Marburger model to describe martensitic phase transformation, incorporating the phase transformation plasticity effect into the constitutive equations. In this model, the total strain tensor is decomposed into five components: elastic strain, thermal strain, plastic strain, creep strain, and phase transformation plastic strain. Among them, the phase transformation plastic strain is linearly related to the phase transformation rate and the current stress bias. The core of this constitutive model lies in establishing a two-way coupling relationship between the temperature field, the phase transformation field, and the stress field: temperature changes drive phase transformation, the phase transformation process releases or absorbs latent heat and reacts on the temperature field, while the volume change and phase transformation plasticity caused by the phase transformation generate a stress field, which in turn affects the phase transformation driving force and reacts on the phase transformation process. This constitutive model is solidified in the form of a set of mathematical equations, serving as the core of the material response in subsequent finite element simulations. The Leblond model is a mathematical model used to describe the dynamics of diffusion-type phase transitions. Its core idea is that, under isothermal or continuous cooling conditions, the rate of change of the volume fraction of the newly formed phase is proportional to the degree to which the current phase fraction deviates from the equilibrium phase fraction. Its mathematical expression is: , Indicates the volume fraction of the target phase. Indicates time, Indicates temperature The equilibrium phase fraction can be determined through thermodynamic equilibrium calculations or phase diagrams. Indicates temperature The phase transformation relaxation time under certain conditions can be calibrated using continuous cooling transformation curves or isothermal transformation curves to reflect the speed of the phase transformation kinetics. When the temperature changes, this model can accurately describe diffusion-controlled phase transformation processes such as pearlite transformation and ferrite transformation, and can naturally extend to continuous cooling conditions. It can be used to describe slow phase transformation behavior driven by temperature changes during heat treatment. The Koistinen-Marburger model is a kinetic model for describing diffusionless martensitic phase transformations. This model is suitable for describing diffusionless phase transformations occurring during rapid cooling. Its basic assumption is that the martensite volume fraction increases exponentially with decreasing temperature. The mathematical expression is: , This indicates the volume fraction of martensite. For material constants, This is the temperature at which the martensitic phase transformation begins. The model is simple and matches the experimental data well, representing the temperature reached during quenching. It can be used to describe the instantaneous completion characteristics of the martensitic phase transformation during quenching. Solidifying in the form of a set of mathematical equations refers to the process of transforming physical concepts and laws into a set of mathematical expressions consisting of partial differential equations, ordinary differential equations, and algebraic equations, and clarifying the coupling relationship and solution order between these equations.

[0064] Step S12: By discretizing and coupling the equations of the thermo-metallurgical-mechanical multi-field coupled constitutive model, a multi-field coupled finite element simulation model of the heat treatment process is generated.

[0065] Discretization coupling solution refers to cutting the continuous domain into a grid, replacing the differential equations with algebraic equations, solving these discrete equations together, and iteratively calculating all fields to ensure self-consistency of interactions.

[0066] For example, a thermo-metallurgical-mechanical multi-field coupled constitutive model is embedded in a nonlinear finite element solution framework, serving as the core material response law of the entire simulation model, thus establishing a multi-field coupled finite element simulation model of the heat treatment process. In the spatial domain, this simulation model employs a finite element discretization method, dividing the geometry to be simulated into a three-dimensional finite element mesh composed of nodes and elements. Each element is assigned initial material properties based on material density interpolation. In the time domain, the model discretizes the complete curve of the preset heat treatment process into several time increment steps, each increment step corresponding to a heating, holding, or cooling stage. Within each time increment step, a fully coupled solution strategy can be employed to simultaneously solve the temperature field control equation, the phase transformation field control equation, and the stress field control equation. The temperature field governing equation is a heat conduction equation including a latent heat term for phase change, where the heat source term is composed of the phase change rate multiplied by the latent heat of phase change. The phase change field governing equation can be derived from the phase change kinetic equation, whose driving force is jointly determined by the degree of temperature deviation from the equilibrium phase change temperature and the contribution of applied stress. The stress field governing equation is established based on the principle of virtual work, and its constitutive relation adopts a thermo-metallurgical-mechanical multi-field coupled constitutive model. The stress increment is obtained by multiplying the total strain increment by the inelastic strain increment and the elastic stiffness tensor. The equations of the three physical fields can be solved by coupling them using the Newton-Raphson iterative method. In each iteration step, the temperature field solution provides the current temperature to the phase change field, updates the phase fraction and provides the latent heat source term to the temperature field, and simultaneously provides the phase change strain and phase change plasticity to the stress field. The stress field solution obtains the stress distribution and feeds it back to the phase change field to correct the phase change driving force. The aforementioned solution process is encapsulated into a simulation model that can be called in batches. This simulation model is used to receive inputs with arbitrary geometry and material distribution, output the evolution data of temperature field, phase transformation field and stress field over time during the entire heat treatment process, and finally extract the displacement field at the end of heat treatment as the heat treatment deformation field, and extract the elastic modulus and yield strength obtained by mapping the phase fraction field and stress field at the end of heat treatment as the heat treatment material property field.Finite element discretization refers to breaking down a continuous solution domain into a finite number of simple small elements, using element assembly to approximate the original continuum, and transforming complex partial differential equations into easily solvable algebraic equations. The geometry to be simulated refers to the three-dimensional solid geometry corresponding to the topological configuration sample of the multi-field coupled finite element simulation model of the heat treatment process. The fully coupled solution strategy refers to solving all governing equations and unknown field variables as a whole, without splitting, iterating, or solving them sequentially. The phase transition dynamics equations are the mathematical framework describing the evolution of phase states over time / space. The principle of virtual work refers to the principle of applying virtual work in a mechanical system in equilibrium. Applying a set of arbitrary, tiny, and constrained virtual displacements to the system results in zero virtual work done by all active forces on these virtual displacements. The Newton-Raphson iterative method approximates the nonlinear equations using tangents and iteratively corrects the solution to quickly approximate the true root. Encapsulation involves packaging the previously step-by-step solution logic into independent, closed modules, hiding complex internal code / steps, and leaving only a simple interface from input parameters to output results. Embedding involves writing the constitutive relationship between the temperature field, metallurgical phase transformation field, and stress-strain field into the nonlinear solution process of the finite element software, allowing the three to iterate synchronously and be coupled during calculation.

[0067] Step S13: Input multiple topological configuration samples into the multi-field coupled finite element simulation model of the heat treatment process, and output the heat treatment deformation field and heat treatment material property field corresponding to each topological configuration sample; wherein, the topological configurations have different geometric features.

[0068] For example, multiple topological configuration samples with different geometric features can be generated within the design space using the Latin hypercube sampling method. Each sample is represented by a three-dimensional density field, which defines the continuous value of the presence or absence of material in each element within the design space. The density field of each sample is input into a multi-field coupled finite element simulation model of the heat treatment process. The model records the temperature field distribution, the volume fraction field distribution of each phase, and the stress field distribution at each time increment step, and continues to update until the preset heat treatment process ends. After the solution is completed, the displacement field data at the end of the heat treatment is extracted from the simulation results. This displacement field includes the displacement increment of each node in three spatial directions, forming the heat treatment deformation field. Based on the phase fraction field and residual stress field at the end of the heat treatment, the equivalent elastic modulus and equivalent yield strength of each element can be calculated using the mixing law. The equivalent elastic modulus can be obtained by weighted averaging of the volume fractions of each phase, and the equivalent yield strength is corrected considering the contribution of residual stress, forming the heat treatment material property field. Each topological configuration sample and its corresponding heat treatment deformation field and heat treatment material property field are saved as a set of output data. Among them, Latin hypercube sampling is a stratified random sampling method. For each input variable, its value range is first evenly divided into N equal-width intervals. A point is randomly sampled in each interval, and the sample points of all variables are randomly paired to ensure that each interval is used only once. The mixture law is a basic law applicable to many fields. Its core is to calculate the overall properties of the mixture by weighting the components according to their proportions. The weighted average is not simply adding up all the numbers and dividing by the number of numbers. Instead, it calculates the average value according to the importance (weight) of each number.

[0069] Step S14: Construct a training sample set based on the topological configuration sample, the heat treatment deformation field, and the heat treatment material property field.

[0070] For example, the three-dimensional density field of each topological configuration sample is discretized to a uniform grid resolution, and the density value of each element is flattened into a one-dimensional vector with a dimension equal to the total number of elements in the design space, serving as the input feature of the training sample. Similarly, the heat treatment deformation field corresponding to each topological configuration sample is discretized to a uniform grid resolution, and the displacement increment of each node in three directions is flattened into a one-dimensional vector with a dimension equal to three times the total number of nodes, serving as one of the output labels of the training sample; the heat-treated elastic modulus and yield strength of each element are flattened into one-dimensional vectors, serving as the other two components of the output label of the training sample. The input features and output labels of all samples are paired according to a one-to-one correspondence to form the original sample set. Data augmentation processing can be performed on the original sample set to generate more samples. The augmented sample set is then divided according to a preset ratio into a training subset for learning model parameters, a validation subset for hyperparameter tuning and overfitting monitoring, and a test subset for independent evaluation of the final model performance. The input features and output labels in the training subset are normalized to scale each feature dimension to the same numerical range, accelerating model convergence and avoiding training instability caused by feature scale differences, thus obtaining the training sample set. Flattening refers to decomposing multi-dimensional, nested structured data into a single-level, continuously arranged linear sequence, eliminating all dimensional nesting and retaining only one dimension. Data augmentation involves reasonably transforming, expanding, and generating existing training data without collecting new data, making the dataset more diverse and richer, thereby improving model generalization ability and reducing overfitting. Preset proportions refer to pre-defined, fixed allocation / composition ratios. Normalization involves compressing data of different magnitudes and units into a unified range through mathematical transformations.

[0071] Step S15: Based on the training sample set, train the pre-built deep learning agent model to obtain the heat-processing digital twin engine.

[0072] For example, a deep learning proxy model is pre-constructed, which can employ a 3D convolutional neural network structure to handle the spatial correlation of 3D density field data. The input features from the training sample set are used as the model's input layer, and the corresponding output labels are used as the model's output targets. The model structure consists of an encoder and a decoder: the encoder progressively extracts high-order features of the input density field through multiple 3D convolutional layers and downsampling layers, compressing the high-dimensional density field data into low-dimensional feature vectors; the decoder progressively restores the feature vectors to deformation and material property fields of the same dimension as the output labels through multiple 3D transposed convolutional layers and upsampling layers. Skip connections between the encoder and decoder preserve spatial detail information at different scales. During model training, a mean squared error loss function can be used to measure the difference between predicted and true values. The specific form of the function is as follows: ,in, This represents the total loss value; and These are the weighting coefficients for the prediction errors of the heat treatment deformation field and the heat treatment material property field, respectively, used to balance the importance of the two prediction tasks. This represents the total number of nodes in the deformation field output multiplied by the spatial dimension, which is the total number of displacement increments of all nodes in the three directions. The model represents the first Predicted values ​​of each displacement component Indicates the first The mean square error of the deformation field prediction is obtained by taking the squared difference between the true values ​​of each displacement component and the true values ​​of the two components, summing the squared differences over all displacement components, and averaging the summation. This represents the total number of output units of the material property field multiplied by the number of material property types, i.e., the total number of elastic moduli and yield strengths of all units; The model represents the first Predicted values ​​of each material property component. Indicates the first The mean squared error of the predicted material property field is obtained by summing the squared differences between the true values ​​of each material property component and the predicted values ​​of the two components, and then averaging the sums of all the predicted material property components. An adaptive moment estimator optimizer can be used to iteratively update the model parameters. In each iteration, a batch of samples is randomly selected from the training subset and input into the model. The loss function value is calculated and backpropagated to update the network weights. After each training epoch, the model performance is evaluated using a validation subset. Training is terminated when the validation set loss function value no longer decreases for several consecutive epochs to prevent overfitting. After training is complete, the model is finally evaluated using a test subset. Once the prediction error meets the preset accuracy requirements, the trained deep learning proxy model is deployed as a thermal processing digital twin engine. Among them, a 3D convolutional neural network is a deep learning model specifically designed to process 3D data with temporal or depth dimensions; an encoder is a module that transforms continuous / analog / complex information into discrete / digital / concise encoding; a 3D convolutional layer is a neural network layer that extracts local features from the input by sliding 3D convolutional kernels along the width, height, and time or depth dimensions; a downsampling layer is a network layer used to reduce the spatial dimensions of the input feature map, i.e., height and width, while typically increasing the number of channels; a decoder is a module that restores the encoded data to the original, directly usable information; a 3D transposed convolution is a learnable upsampling layer for 3D data, essentially a transpose of convolution, used to restore a small-volume feature map to a large-volume one; upsampling... A sample layer is a layer that enlarges the feature map to restore it from low resolution to high resolution; a skip connection refers to directly passing the output of a layer to a deeper layer in a neural network, rather than just through layer-by-layer forward propagation, and is usually added to or concatenated with the output of the subsequent layer; an adaptive moment estimation optimizer is a gradient descent optimization method widely used in deep learning and machine learning training. It combines first-order moment estimation (the exponential moving average of the gradient) to estimate the mean, and second-order moment estimation (the exponential moving average of the squared gradient) to estimate the uncentered variance, adaptively adjusting the learning rate for each parameter; backpropagation refers to calculating the gradient backward from the output layer to the input layer, using the chain rule to propagate the error back layer by layer, fine-tuning the weights to make the prediction more accurate.

[0073] In this embodiment, a high-fidelity finite element simulation model of the heat treatment process is established by constructing a thermo-metallurgical-mechanical multi-field coupled constitutive model and then discretizing and solving this constitutive model. This simulation model is then used to perform batch simulations on a large number of topological configuration samples with different geometric features, generating a training dataset. Based on this dataset, a deep learning proxy model is trained to obtain a digital twin engine for heat treatment. This approach can improve the calculation speed of the heat treatment deformation field and material property field by several orders of magnitude while maintaining prediction accuracy, laying a technical foundation for embedding heat treatment effects into the topology optimization iterative loop.

[0074] In one embodiment, based on the design space, the topology configuration of the initial iteration is obtained, and based on the service boundary conditions and a heat treatment digital twin engine, the performance of the topology configuration is evaluated to obtain the performance evaluation results, including:

[0075] Step S21: Based on the design space, obtain the topological configuration of the initial iteration, input the topological configuration into the heat treatment digital twin engine, and output the final deformation field and the final material property field.

[0076] For example, an initial iteration of the topology is initialized within the coordinate system of the mesh nodes defined in the design space. This topology is represented as a three-dimensional density field, where the value of each element continuously varies between 0 and 1, where 1 represents solid material, 0 represents voids, and intermediate values ​​represent the interpolated state of the composite material. The density field data of this initial iteration of the topology is vectorized and flattened into a one-dimensional feature vector. The input feature vector is fed into the heat treatment digital twin engine, which performs a complete forward propagation calculation and outputs two results: the first result is the final deformation field, represented as a vector field, containing the displacement increments of each mesh node in the design space relative to the initial coordinates in three directions at the end of heat treatment; the second result is the final material property field, represented as a scalar field, containing the equivalent elastic modulus and equivalent yield strength of each element at the end of heat treatment. Vectorization refers to replacing the scattered data that originally needed to be calculated one by one in a loop with a whole batch of vectors / arrays for simultaneous computation; initialization refers to the process of assigning initial states or initial values ​​to variables / objects / programs; the mesh node coordinate system is a local Cartesian coordinate system attached to each node of the finite element mesh, used to define the node degrees of freedom, load / constraint directions, and output directions of node results.

[0077] Step S22: Based on the final-state deformation field, correct the geometry of the topological configuration to obtain the corrected topological configuration, and assign material properties to the corrected topological configuration based on the final-state material property field to obtain the analysis model.

[0078] For example, the initial finite element mesh corresponding to the current iterative topology is obtained. This mesh is generated by discretizing the design space and includes the initial coordinates of all nodes and the element connection relationships. The original coordinates of each node in the initial finite element mesh and the displacement increments of the corresponding nodes in the final deformation field are vector-superimposed to obtain the deformation coordinates of each node after heat treatment. Based on the deformation coordinates of all nodes, the finite element mesh is reconstructed to generate a deformed mesh with the same element connection relationships as the original mesh but with updated node coordinates. This deformed mesh is the geometric representation of the corrected topology. Each element in the deformed mesh is spatially matched with the final material property field. Since the final material property field is based on the output of the original design space mesh, and the element center coordinates of the deformed mesh have changed, a reverse mapping method can be used. For each element in the deformed mesh, the elastic modulus and yield strength values ​​at the corresponding positions in the final material property field in the original mesh are found, and these values ​​are assigned to the current element. After assigning material property values ​​to all elements, the analysis model is obtained. Among them, vector superposition refers to connecting multiple vectors end to end or adding their coordinates directly to synthesize a single vector; spatial position matching refers to comparing the positions, orientations, and relative relationships of two or more objects in space to determine whether they overlap, correspond, or are consistent; reverse mapping is a mapping logic that deduces the source from the result, starting from the target and tracing back to the source.

[0079] Step S23: Based on the service boundary conditions, perform finite element analysis on the analysis model to obtain the final performance index.

[0080] Finite element analysis refers to breaking down a complex, continuous object into many elements, calculating the force, deformation, temperature, etc. of each element, and then piecing them back together to obtain the mechanical response of the entire structure.

[0081] For example, since the constraint locations and load application points in the service boundary conditions are initially defined on the geometric features of the original design space, and the geometry of the analysis model has been deformed, the service boundary conditions such as constraints and loads can be mapped from their original locations to the corresponding nodes or element surfaces of the deformed mesh using spatial interpolation methods. A finite element solution equation set is constructed: based on the analysis model, for each element, the element stiffness matrix is ​​calculated according to its elastic modulus and assembled into a global stiffness matrix. A load vector is established based on the applied load, and displacement constraints are introduced to correct the global stiffness matrix, resulting in a solution equation set. A nonlinear solver can be selected to solve the equation set, considering the spatial inhomogeneity of material properties during the solution process. After the solution is completed, various final-state performance indicators are extracted from the calculation results: the displacement field of all nodes is extracted, and the overall compliance of the structure is calculated. This compliance is equal to the dot product of the load vector and the displacement vector, i.e., ... The von Mises equivalent stress of each element is extracted and compared with the yield strength of the corresponding element. The stress-to-yield strength ratio is calculated to assess whether the structure meets the strength requirements. The displacement values ​​of key nodes are extracted and compared with preset allowable displacement values ​​to assess whether the structural deformation is within the allowable range. Compliance, maximum stress ratio, and maximum displacement are used as final-state performance indicators. Let T be the load vector, and let T denote the transpose. For displacement vectors, a smaller compliance indicates a larger structural stiffness; spatial interpolation is a method of extrapolating values ​​for unknown regions using values ​​at known discrete points; mapping refers to mapping a set / concept / data in A to a specific location, object, or result in B according to certain rules; a nonlinear solver is a numerical calculation tool specifically used to solve nonlinear equations / systems of equations; von Mises equivalent stress is the scalar equivalent stress corresponding to the fourth strength theory (distortion energy theory) in mechanics of materials, which determines whether a ductile material yields by equating a complex three-dimensional stress state to uniaxial tensile stress; the preset allowable displacement value refers to a pre-set allowable displacement value used to determine whether structural deformation exceeds the limit and whether it meets safety requirements.

[0082] Step S24: Input the topology configuration into the inverse compensation operator and output the pre-compensated printed state configuration corresponding to the topology configuration.

[0083] Among them, the reverse compensation operator is a mathematical / logical operation unit used to undo / cancel the forward operation and restore the system state. Its core is reverse order, reverse, and compensability. Since the heat treatment process will deform the parts, a given final topological configuration must have a specific pre-deformation shape before heat treatment so that it can be deformed into the final configuration after heat treatment. The reverse compensation operator achieves this by iteratively solving this geometric inversion problem: taking the topological configuration as the optimization target, it predicts the heat treatment result of the current printed configuration by repeatedly calling the heat treatment digital twin engine, and compares it with the target final configuration. Based on the comparison result, it continuously adjusts the geometry of the printed configuration until the two are consistent.

[0084] For example, the topology configuration is input into the inverse compensation operator, and the output is the pre-compensated printed state configuration corresponding to the topology configuration.

[0085] Step S25: Perform an additive manufacturing process feasibility check on the pre-compensated printed configuration to obtain manufacturability evaluation indicators.

[0086] Among them, the feasibility check of additive manufacturing process refers to a comprehensive evaluation of part design, materials, equipment, cost, quality, etc. before formal additive manufacturing to determine whether it can be done by additive manufacturing and how easy it is to do.

[0087] For example, overhang angle detection is performed on the pre-compensated configuration in the printed state to obtain the number and degree of violation of overhang units, and the overhang angle penalty value is calculated. Morphological processing is applied to the original density field of the pre-compensated configuration in the printed state to obtain a morphologically processed density field, and the feature size penalty value is calculated based on the difference between the original density field and the morphologically processed density field. The overhang angle penalty value and the feature size penalty value are weighted and summed to obtain a manufacturability evaluation index.

[0088] Step S26: Summarize the final performance indicators and manufacturability evaluation indicators to obtain the performance evaluation results.

[0089] For example, compliance, maximum stress ratio, maximum displacement, and manufacturability evaluation indicators are summarized to obtain performance evaluation results. Among them, the final-state performance indicators are used to determine whether the current design meets the service performance requirements, and the manufacturability evaluation indicators are used to determine whether the current design meets the additive manufacturing process constraints.

[0090] In this embodiment, a heat treatment digital twin engine maps the current topology configuration to the final deformation field and material property field after heat treatment. Based on this mapping result, the geometry is corrected and material properties are assigned, an analysis model is constructed, and finite element analysis is performed on the analysis model to obtain the final performance indicators. The printing state pre-compensated configuration corresponding to the final design is inverted using a reverse compensation operator, and the indicators of this printing state configuration are evaluated. The final performance indicators and manufacturability evaluation indicators are then summarized and output. This approach unifies the previously separate design, printing, and post-heat treatment stages into a single evaluation framework, ensuring that the performance evaluation results of each iteration simultaneously reflect the final service performance and manufacturing process feasibility. This provides complete optimization guidance information for subsequent multi-objective sensitivity analysis and topology updates.

[0091] In one embodiment, the topology configuration is input into the inverse compensation operator, and the output is a pre-compensated printed state configuration corresponding to the topology configuration, including:

[0092] Step S241: Set the topological configuration as the initial guess value of the printing state configuration to obtain the current printing state configuration of this iteration, and initialize the iterative printing state configuration based on the current printing state configuration.

[0093] For example, the topological configuration of the current iteration is used as the initial guess for the reverse compensation iteration. This topological configuration is represented by a three-dimensional density field and the corresponding finite element mesh node coordinates. The geometric data of this final topological configuration is copied as the initial guess for the printing configuration, resulting in the current printing configuration for the first iteration of this round. The current printing configuration is geometrically identical to the topological configuration in its initial state, meaning that the printed part retains its original shape after heat treatment. The iterative printing configuration is initialized based on this current printing configuration, and the node coordinate matrix of the current printing configuration is assigned to the iteration variable as the starting point for the reverse compensation iteration. At the same time, the original mesh connection relationship of the current printing configuration is recorded to ensure that the topological structure of the mesh remains unchanged during subsequent reverse node movement, with only the node coordinates being updated.

[0094] Step S242: Input the iterative printing state configuration of the previous second-layer iteration into the thermal processing digital twin engine to obtain the predicted deformation field corresponding to the current printing state configuration; wherein, the iterative printing state configuration of the previous second-layer iteration of the first second-layer iteration is the current printing state configuration.

[0095] For example, the iterative printed configuration generated in the previous second-layer iteration is used as input and fed into the heat treatment digital twin engine for forward prediction. For the first second-layer iteration, since there is no result from the previous iteration, the initialized current printed configuration is used as the printed configuration of the previous iteration. After receiving the density field and grid coordinate data of the printed configuration, the heat treatment digital twin engine performs forward propagation: the encoder extracts the spatial features of the input configuration, and the decoder recovers the corresponding heat treatment deformation field based on these features. This predicted deformation field is represented in the form of a vector field, containing the expected displacement increments in three directions for each grid node in the input printed configuration after undergoing a preset heat treatment process. The predicted deformation field output by the engine perfectly matches the grid topology of the input printed configuration, that is, each node corresponds to a displacement vector. Here, forward propagation refers to the process of the neural network calculating layer by layer sequentially from input to output.

[0096] Step S243: Based on the predicted deformation field and the final deformation field, calculate the geometric error between the predicted final configuration and the target final configuration obtained after heat treatment of the current printed configuration.

[0097] For example, the original coordinates of each mesh node in the current printed configuration and the displacement increment of the corresponding node in the predicted deformation field are vector-superimposed to obtain the predicted coordinates of that node after heat treatment. The predicted coordinates of all nodes together constitute the geometric representation of the predicted final configuration. The target final configuration is obtained by applying the final deformation field to the current topology configuration; that is, the target final configuration is the final geometric shape expected to be achieved in the optimization iteration. Subsequently, the geometric error between the predicted final configuration and the target final configuration is calculated. The sum of the L2 norms of the displacement deviation vectors of each node can be used as the error metric, and the calculation formula is as follows: ,in, To predict the coordinate vector of the i-th node in the final configuration, Let N be the coordinate vector of the corresponding node in the target final configuration, and N be the total number of nodes.

[0098] Step S244: When the geometric error is greater than the geometric error threshold, the current printing state configuration is updated by reverse node movement based on the predicted deformation field to obtain the iterative printing state configuration of the second layer of this round.

[0099] Among them, reverse node movement update means not printing directly according to the initial configuration, but moving each node in the opposite direction of the predicted deformation, performing deformation compensation in advance, and then updating the configuration for printing.

[0100] For example, the geometric error is compared with a preset geometric error threshold. When the geometric error exceeds the threshold, it indicates that the current printed configuration cannot be deformed to the target final configuration after heat treatment, and the printed configuration needs to be corrected. The current printed configuration can be updated using a reverse node movement method, taking the reverse of the predicted deformation field as the correction direction. The update formula is: Perform the reverse node movement operation on all mesh nodes to obtain the updated node coordinate matrix, while maintaining the mesh connectivity, thus generating the iterative printing configuration for the second iteration of this round. Here, the preset geometric error threshold refers to the acceptable upper limit pre-set for geometric deviations; Let be the coordinate vector of the node in the current printed configuration. To predict the displacement vector of the corresponding node in the deformation field. This is a relaxation factor, with a value ranging from 0 to 1 in the open interval. It is used to control the step size of each update and prevent the iteration process from diverging.

[0101] Step S245: Repeat steps S242, S243 and S244 until the geometric error is less than the geometric error threshold. Set the iterative printing state configuration with the geometric error less than the geometric error threshold as the printing state pre-compensation configuration corresponding to the topology configuration.

[0102] For example, an inner iterative loop for reverse compensation is established, repeatedly executing steps S242, S243, and S244. In each loop, based on the latest iterative printed configuration, the thermal processing digital twin engine is invoked again to obtain a new predicted deformation field, the geometric error is recalculated, and the next reverse node movement update is determined based on the error magnitude. As the number of iterations increases, the printed configuration gradually approaches the ideal pre-compensated shape, causing the geometric error between the predicted final configuration and the target final configuration to gradually decrease. After each calculation of the geometric error, it is compared with a preset geometric error threshold. When the geometric error is less than the threshold, it is determined that the reverse compensation iteration has converged, and the loop is terminated. At this time, the iterative printed configuration in the current iteration is the desired printed pre-compensated configuration.

[0103] In this embodiment, the final state topological configuration is used as an initial guess. The heat treatment digital twin engine is repeatedly invoked to obtain the predicted deformation field of the current printing configuration. The geometric error between the predicted final state and the target final state is calculated. The node coordinates are updated based on the reverse of the predicted deformation field until the geometric error converges to within a preset threshold. Finally, the pre-compensated printing configuration corresponding to the topological configuration is output. This enables accurate inverse calculation from the desired final state geometry to the actual printing geometry, solving the technical problem of uncontrollable and uncompensable heat treatment deformation.

[0104] In one embodiment, the pre-compensated printed configuration is subjected to an additive manufacturing process feasibility check to obtain manufacturability evaluation indicators, including:

[0105] Step S251: Perform overhang angle detection on the pre-compensated configuration in the printed state to obtain the number of overhang violation units and the degree of violation of the overhang violation units, and calculate the overhang angle penalty value based on the number and degree of violation.

[0106] Among them, overhang angle detection refers to identifying the overhang area and quantifying the overhang angle of the target configuration that has been deformed / sized compensated, and determining whether it meets the unsupported printing constraint.

[0107] For example, a pre-compensated configuration for printing is obtained, represented in the form of a three-dimensional finite element mesh, containing the normal vector information of each surface element. The printing direction is determined, typically vertically upward, i.e., the positive Z-axis direction. For all lower surface elements in the pre-compensated configuration for printing, the angle between the normal vector of each element and the printing direction is calculated, i.e., the overhang angle, which reflects whether there is supporting material below the element during additive manufacturing. The smaller the angle, the closer the element is to a horizontal lower surface, and the more likely it is to collapse or deform due to lack of support during forming. The overhang angle of each element is compared with a preset critical overhang angle. When the overhang angle is less than the critical overhang angle, the element is marked as an overhang violation element, and its number is recorded. For each overhang violation element, its violation degree is calculated. The violation degree is defined as the difference between the critical overhang angle and the actual overhang angle of the element. The larger the difference, the more dangerous the overhang state of the element, and the more support or design correction is needed. Based on the number of all overhang violation elements and the violation degree of each element, the overhang angle penalty value is calculated using the following formula: ,in, This is the overhang angle penalty value. The higher the value, the less manufacturable the current pre-compensated configuration in terms of overhang features is, and it needs to be suppressed in the optimization. For the set of suspended violation units, The actual overhang angle of the i-th unit. The preset critical overhang angle is a pre-set threshold angle for determining whether a suspended structure can form independently without support. is the weighting coefficient for the i-th cell, which is related to the cell area or volume.

[0108] Step S252: Morphological processing is performed on the original density field of the pre-compensated printed configuration to obtain the morphologically processed density field, and the feature size penalty value is calculated based on the difference between the original density field and the morphologically processed density field.

[0109] Morphological processing is a fundamental operation in digital image processing based on the shape and structure of an image. Its core is to use structuring elements to perform local operations on image pixels, and it is mainly used for binary images.

[0110] For example, a three-dimensional density field representation of the pre-compensated printed configuration is obtained, where each voxel has a value between 0 and 1, representing the degree of material filling at that location. Morphological opening operations can be used to remove isolated solid features smaller than a preset minimum wall thickness threshold from the density field, and morphological closing operations can be used to fill isolated void features smaller than a preset minimum aperture threshold. After this opening-then-closing morphological processing, a morphologically processed density field is obtained. The difference between the original density field and the morphologically processed density field is calculated; the difference region corresponds to those tiny features that cannot be reliably formed by additive manufacturing processes. The L2 norm of the difference is used as the feature size penalty value. The larger the feature size penalty value, the more unmanufacturable tiny features exist in the current pre-compensated printed configuration, requiring adjustment. Feature size penalty value The calculation formula is: .in, For the original density field, This refers to the density field after morphological processing. Morphological opening is a fundamental morphological operation in image processing, defined as first eroding the image, then dilating the erosion result. Both operations use the same structuring element to eliminate bright areas smaller than the structuring element, smooth object boundaries, and break narrow connections, while essentially maintaining the overall area and shape of the object. The preset minimum wall thickness threshold refers to the minimum allowable thickness specified in advance. Morphological closing is a mathematical morphology operation that involves dilation followed by erosion. It is used to fill small holes inside the target object, connect adjacent objects, and smooth the concave parts of the object's contour, while essentially maintaining the overall size and shape of the object. The preset minimum aperture threshold refers to the lower limit value of the aperture size set in advance.

[0111] Step S253: The overhang angle penalty value and the feature size penalty value are weighted and summed to obtain the manufacturability evaluation index.

[0112] Weighted summation refers to assigning weights to different values ​​according to their importance, multiplying them separately, and then summing them up.

[0113] For example, a manufacturability evaluation index is obtained by weighted summation of the overhang angle penalty value and the feature size penalty value. The calculation formula is as follows: ,in, As a manufacturability evaluation indicator, This is the overhang angle penalty value. This is the feature size penalty value. The overhang angle penalty weighting coefficient is... The feature size penalty weight coefficient, and All are positive numbers and can be adjusted according to the different sensitivities to overhang features and minimum feature size in specific application scenarios. For example, for parts with finely hollowed-out features, the feature size penalty weight coefficient can be increased.

[0114] In this embodiment, overhang angle detection is performed on the pre-compensated printed configuration, and all non-compliant units with overhang angles less than the critical value are counted. Overhang angle penalty values ​​are calculated based on the degree of non-compliance. Morphological processing (open-then-close) is performed on the density field of the pre-compensated printed configuration, and the difference between the original and processed density fields is compared to calculate the feature size penalty value. The two penalty values ​​are then weighted and summed to obtain a unified manufacturability evaluation index. This transforms the overhang angle constraint and minimum feature size constraint in additive manufacturing processes into quantifiable penalty functions, enabling the topology optimization algorithm to receive manufacturing feasibility feedback during the iteration process. This proactively avoids unmanufacturable features from the design stage, significantly reducing the risk of subsequent printing failures and dependence on support structures.

[0115] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0116] Based on the same inventive concept, this application also provides a topology optimization device for metal additive manufacturing that balances mechanical performance and weight reduction, for implementing the aforementioned method for topology optimization in metal additive manufacturing that balances mechanical performance and weight reduction. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the topology optimization device for metal additive manufacturing that balances mechanical performance and weight reduction provided below can be found in the limitations of the topology optimization method for metal additive manufacturing that balances mechanical performance and weight reduction described above, and will not be repeated here.

[0117] In one exemplary embodiment, such as Figure 3 As shown, a metal additive manufacturing topology optimization device 300 that balances mechanical properties and weight reduction is provided, comprising:

[0118] The data acquisition module 301 is used in step S1 to acquire the design space, service boundary conditions and material property data of the final target configuration and the metal material to be processed, and to construct a heat treatment digital twin engine based on the material property data; wherein, the heat treatment digital twin engine is used to process the topology configuration and output the deformation field and material property field of the topology configuration after undergoing the preset heat treatment process.

[0119] The performance evaluation module 302 is used in step S2 to obtain the topology configuration of the first iteration based on the design space, and to evaluate the performance of the topology configuration based on the service boundary conditions and the heat treatment digital twin engine to obtain the performance evaluation results; wherein, the performance evaluation results include final state performance indicators and manufacturability evaluation indicators.

[0120] The configuration update module 303 is used in step S3 to update the topology configuration based on the final performance index and manufacturability evaluation index in the performance evaluation results through sensitivity analysis, and obtain the topology configuration of this iteration.

[0121] The configuration determination module 304 is used in step S4 to repeatedly execute steps S2 and S3 until the iteration termination condition is met, and to set the topology configuration of the iteration round that meets the iteration termination condition as the final topology configuration; wherein, the iteration termination condition is that the final state performance index meets the service performance requirements and the manufacturability evaluation index meets the manufacturability requirements.

[0122] In one embodiment, the data acquisition module 301 is further configured to:

[0123] Based on the thermophysical parameters, phase transformation kinetic parameters, and thermo-mechanical parameters of the metal material to be treated, a thermo-metallurgical-mechanical multi-field coupled constitutive model is constructed. The thermo-metallurgical-mechanical multi-field coupled constitutive model is used to describe the mechanical behavior of the metal material to be treated under the coupled action of temperature field, phase transformation field, and stress field.

[0124] By discretizing and coupling the equations of the thermo-metallurgical-mechanical multi-field coupled constitutive model, a multi-field coupled finite element simulation model of the heat treatment process is generated.

[0125] Multiple topological configuration samples are input into a multi-field coupled finite element simulation model of the heat treatment process, and the heat treatment deformation field and heat treatment material property field corresponding to each topological configuration sample are output; among them, the topological configurations have different geometric characteristics;

[0126] A training sample set is constructed based on topological configuration samples, heat treatment deformation field, and heat treatment material property field;

[0127] Based on the training sample set, a pre-built deep learning agent model is trained to obtain a heat-processing digital twin engine.

[0128] In one embodiment, the performance evaluation module 302 is further configured to:

[0129] Based on the design space, the topological configuration of the initial iteration is obtained, and the topological configuration is input into the heat treatment digital twin engine to output the final deformation field and the final material property field.

[0130] Based on the final-state deformation field, the geometry of the topological configuration is corrected to obtain the corrected topological configuration. Then, based on the final-state material property field, material properties are assigned to the corrected topological configuration to obtain the analysis model.

[0131] Based on the service boundary conditions, finite element analysis is performed on the analysis model to obtain the final state performance index;

[0132] Input the topology configuration into the inverse compensation operator and output the printed state pre-compensation configuration corresponding to the topology configuration;

[0133] Feasibility of additive manufacturing process was checked on the pre-compensated printed configuration to obtain manufacturability evaluation indicators;

[0134] By summarizing the final performance indicators and manufacturability evaluation indicators, the performance evaluation results are obtained.

[0135] In one embodiment, the performance evaluation module 302 is further configured to:

[0136] Step S341: Set the topological configuration as the initial guess value of the printing state configuration to obtain the current printing state configuration of this iteration, and initialize the iterative printing state configuration based on the current printing state configuration;

[0137] Step S342: Input the iterative printing state configuration of the previous second-layer iteration into the heat treatment digital twin engine to obtain the predicted deformation field corresponding to the current printing state configuration; wherein, the iterative printing state configuration of the previous second-layer iteration of the first second-layer iteration is the current printing state configuration;

[0138] Step S343: Based on the predicted deformation field and the final deformation field, calculate the geometric error between the predicted final configuration and the target final configuration obtained after heat treatment of the current printed configuration;

[0139] Step S344: When the geometric error is greater than the geometric error threshold, the current printed state configuration is updated by reverse node movement based on the predicted deformation field to obtain the iterative printed state configuration of the second layer of this round.

[0140] Step S345: Repeat steps S342, S343 and S344 until the geometric error is less than the geometric error threshold. Set the iterative printing state configuration with the geometric error less than the geometric error threshold as the printing state pre-compensation configuration corresponding to the topology configuration.

[0141] In one embodiment, the performance evaluation module 302 is further configured to:

[0142] The overhang angle of the pre-compensated printed configuration is detected to obtain the number of overhang violation units and the degree of violation of the overhang violation units. Based on the number and degree of violation, the overhang angle penalty value is calculated.

[0143] The original density field of the pre-compensated printed configuration is morphologically processed to obtain the morphologically processed density field. Based on the difference between the original density field and the morphologically processed density field, the feature size penalty value is calculated.

[0144] The manufacturability evaluation index is obtained by weighted summation of the overhang angle penalty value and the feature size penalty value.

[0145] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the metal additive manufacturing topology optimization method that balances mechanical performance and weight reduction as described above.

[0146] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0147] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0148] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A topology optimization method for metal additive manufacturing that balances mechanical properties and weight reduction, characterized in that, The method includes: Step S1: Obtain the design space, service boundary conditions, and material property data of the metal material to be processed for the final target configuration, and construct a heat treatment digital twin engine based on the material property data; wherein, the heat treatment digital twin engine is used to process the topological configuration and output the deformation field and material property field of the topological configuration after undergoing a preset heat treatment process. Step S2: Based on the design space, obtain the topology configuration of the first iteration, and perform performance evaluation on the topology configuration based on the service boundary conditions and the heat treatment digital twin engine to obtain performance evaluation results; wherein, the performance evaluation results include final state performance indicators and manufacturability evaluation indicators; Step S3: Based on the final state performance index and the manufacturability evaluation index in the performance evaluation results, update the topology configuration through sensitivity analysis to obtain the topology configuration for this iteration; Step S4: Repeat steps S2 and S3 until the iteration termination condition is met, and set the topology configuration of the iteration round that meets the iteration termination condition as the final topology configuration; wherein, the iteration termination condition is that the final state performance index meets the service performance requirements and the manufacturability evaluation index meets the manufacturability requirements.

2. The method according to claim 1, characterized in that, The material property data includes thermophysical parameters, phase transformation kinetic parameters, and thermodynamic parameters. Based on the material property data, a heat treatment digital twin engine is constructed, including: Based on the thermophysical parameters, phase transformation kinetic parameters, and thermodynamic parameters of the metal material to be treated, a thermo-metallurgical-mechanical multi-field coupled constitutive model is constructed; wherein, the thermo-metallurgical-mechanical multi-field coupled constitutive model is used to describe the mechanical behavior of the metal material to be treated under the coupled action of temperature field, phase transformation field, and stress field; By discretizing and solving the equations of the thermo-metallurgical-mechanical multi-field coupled constitutive model, a multi-field coupled finite element simulation model of the heat treatment process is generated. Multiple topological configuration samples are input into the multi-field coupled finite element simulation model of the heat treatment process, and the heat treatment deformation field and heat treatment material property field corresponding to each topological configuration sample are output; wherein, the topological configurations have different geometric features; Based on the topological configuration sample, the heat treatment deformation field, and the heat treatment material property field, a training sample set is constructed; Based on the training sample set, a pre-built deep learning agent model is trained to obtain the heat treatment digital twin engine.

3. The method according to claim 1, characterized in that, Based on the design space, the topology configuration of the initial iteration is obtained, and based on the service boundary conditions and the heat treatment digital twin engine, the performance of the topology configuration is evaluated to obtain the performance evaluation results, including: Based on the design space, the topological configuration of the initial iteration is obtained, and the topological configuration is input into the heat treatment digital twin engine to output the final deformation field and the final material property field. Based on the final deformation field, the geometry of the topological configuration is corrected to obtain the corrected topological configuration, and material properties are assigned to the corrected topological configuration based on the final material property field to obtain the analysis model; Based on the service boundary conditions, finite element analysis is performed on the analysis model to obtain the final performance index; Input the topology configuration into the inverse compensation operator and output the pre-compensated print state configuration corresponding to the topology configuration; The feasibility of additive manufacturing process is checked on the pre-compensated printed configuration to obtain manufacturability evaluation index; The final performance indicators and the manufacturability evaluation indicators are combined to obtain the performance evaluation results.

4. The method according to claim 3, characterized in that, The step of inputting the topology configuration into the inverse compensation operator and outputting the pre-compensated print state configuration corresponding to the topology configuration includes: Step S241: Set the topological configuration as the initial guess value of the printing state configuration to obtain the current printing state configuration of this iteration, and initialize the iterative printing state configuration based on the current printing state configuration; Step S242: Input the iterative printing state configuration of the previous second-layer iteration into the heat treatment digital twin engine to obtain the predicted deformation field corresponding to the current printing state configuration; wherein, the iterative printing state configuration of the previous second-layer iteration of the first second-layer iteration is the current printing state configuration; Step S243: Based on the predicted deformation field and the final deformation field, calculate the geometric error between the predicted final configuration obtained after heat treatment of the current printed configuration and the target final configuration; Step S244: When the geometric error is greater than the geometric error threshold, the current printing state configuration is updated by reverse node movement based on the predicted deformation field to obtain the iterative printing state configuration of the second layer iteration in this round. Step S245: Repeat steps S242, S243 and S244 until the geometric error is less than the geometric error threshold, and set the iterative printing state configuration with the geometric error less than the geometric error threshold as the printing state pre-compensation configuration corresponding to the topology configuration.

5. The method according to claim 3, characterized in that, The additive manufacturing process feasibility check of the pre-compensated printed configuration is performed to obtain manufacturability evaluation indicators, including: The pre-compensated printed configuration is subjected to overhang angle detection to obtain the number of overhang violation units and the degree of violation of the overhang violation units. Based on the number and the degree of violation, the overhang angle penalty value is calculated. The original density field of the pre-compensated printed configuration is morphologically processed to obtain a morphologically processed density field, and the feature size penalty value is calculated based on the difference between the original density field and the morphologically processed density field. The manufacturability evaluation index is obtained by weighted summation of the overhang angle penalty value and the feature size penalty value.

6. A topology optimization device for metal additive manufacturing that balances mechanical properties and weight reduction, characterized in that, The device includes: The data acquisition module is used in step S1 to acquire the design space, service boundary conditions, and material property data of the metal material to be processed for the final target configuration, and to construct a heat treatment digital twin engine based on the material property data; wherein, the heat treatment digital twin engine is used to process the topological configuration and output the deformation field and material property field of the topological configuration after undergoing a preset heat treatment process. The performance evaluation module is used in step S2 to obtain the topology configuration of the first iteration based on the design space, and to perform performance evaluation on the topology configuration based on the service boundary conditions and the heat treatment digital twin engine to obtain performance evaluation results; wherein, the performance evaluation results include final state performance indicators and manufacturability evaluation indicators. The configuration update module is used in step S3 to update the topology configuration based on the final state performance index and the manufacturability evaluation index in the performance evaluation results through sensitivity analysis, so as to obtain the topology configuration of this iteration. The configuration determination module is used in step S4 to repeatedly execute steps S2 and S3 until the iteration termination condition is met, and to set the topology configuration of the iteration round that meets the iteration termination condition as the final topology configuration; wherein, the iteration termination condition is that the final state performance index meets the service performance requirements and the manufacturability evaluation index meets the manufacturability requirements.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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