Multi-scale gradient lattice structure design method based on electron beam additive manufacturing

Abstract

The invention provides a multi-scale gradient lattice structure design method based on electron beam additive manufacturing. The multi-scale gradient lattice structure design method comprises the steps that a multi-scale gradient lattice parametric modeling method is constructed, cross-scale mechanical property prediction is carried out, a process simulation and defect prediction technology is developed, and multi-target algorithm collaborative optimization is carried out. According to the method, through parametric modeling and an optimization algorithm, a lattice structure which is more complex and more excellent in performance is designed, and the advantages of the EBM technology are brought into full play; a mechanical property prediction model considering EBM process parameters is established, the mechanical property of the lattice structure is predicted more accurately, and the reliability of a design result is improved; through EBM process simulation and optimization, optimal EBM process parameters are obtained, the manufacturing quality of the lattice structure is improved, and manufacturing defects are avoided; and through integrated design, simulation and optimization processes, the design period of the lattice structure is shortened, and the design efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of additive manufacturing technology, specifically relating to a multi-scale gradient lattice structure design method based on electron beam additive manufacturing. Background Technology

[0002] Lattice structures are lightweight, high-strength structures composed of periodically arranged rods or plates, possessing excellent mechanical, thermal, and acoustic properties, and have broad application prospects in aerospace, biomedicine, and automotive manufacturing. Traditional manufacturing methods for lattice structures mainly include casting, machining, and welding. These methods suffer from long manufacturing cycles, high costs, and low material utilization, making it difficult to meet the manufacturing requirements of complex lattice structures.

[0003] Electron beam additive manufacturing (EBM) is a rapid prototyping technology based on melting metal powder with a high-energy electron beam. It boasts advantages such as high energy density, fast prototyping speed, high material utilization, and the ability to manufacture complex structures. However, existing design methods still have the following limitations: Design freedom is limited, and existing gradient lattices mostly rely on macroscopic size adjustments, lacking cross-scale collaborative design of macro-meso-micro, making it difficult to achieve precise performance control; The accuracy of mechanical property prediction is low. Traditional homogenization theory ignores the microstructure heterogeneity caused by EBM process, such as grain orientation and melt pool morphology, resulting in insufficient accuracy of mechanical model. Optimizing process parameters is difficult. The lack of coupling optimization between structural design and process parameters, such as electron beam power and scanning path, leads to frequent manufacturing defects such as porosity and residual stress.

[0004] Therefore, there is an urgent need to propose a multi-scale gradient lattice structure design method to solve the above problems. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art by providing a multi-scale gradient lattice structure design method based on electron beam additive manufacturing, which solves the problems of limited design freedom, low accuracy of mechanical property prediction, and difficulty in optimizing process parameters in the existing methods.

[0006] The technical solution of this invention is: a multi-scale gradient lattice structure design method based on electron beam additive manufacturing, comprising: Step 1: Perform multi-scale gradient lattice parameterization modeling, including macro-scale modeling, meso-scale modeling and micro-scale modeling, and establish mathematical relationships between parameters at each scale. Step 2: Based on the established multi-scale gradient lattice parameterization model, perform cross-scale mechanical property prediction. The performance prediction includes: predicting the macroscopic mechanical response of the lattice structure based on a macroscopic equivalent model that considers gradient sensitivity factors; quantifying the influence of microstructure caused by electron beam additive manufacturing on the mechanical properties of mesoscopic units based on a mesoscopic-microscopic coupling model that considers crystal plastic constitutive relations and anisotropic yield strength; and realizing cross-scale parameter transfer from microscopic to mesoscopic and then to macroscopic through representative volume units. Step 3: Based on the obtained mechanical property prediction results, simulate the thermodynamic behavior in the electron beam additive manufacturing process through multiphysics coupling simulation, predict potential defects and guide process optimization; Step 4: Establish a multi-objective function that includes mechanical property terms, defect control terms, and residual stress terms, and perform synergistic optimization of gradient coefficient, electron beam power, and scanning speed to obtain the optimal combination of lattice structure design and process parameters.

[0007] Furthermore, in step 1, the macroscopic scale modeling includes: discretizing the geometric model into a grid of fillable lattice units by designing a spatial mapping, and defining geometric boundary conditions.

[0008] Furthermore, in step 1, the mesoscopic scale modeling includes: cell filling, parameter mapping, and transition region generation; The cell filling involves assigning a cell type to each cell; the cell types include uniform cells, hybrid cells, and functional cells. The parameter mapping involves mapping the rod diameter gradient function and density gradient function to the rod diameter and density of each element; the rod diameter gradient function d(z) is: d(z) = d0 + k·z, where z represents the rod diameter in the height direction, d0 is the initial rod diameter, and k is the gradient coefficient, k ∈ [0.01, 0.1]; the density gradient function ρ(x) is: ρ(x) = ρ max ·e -αx x represents the load direction, ρ max Let e ​​be the maximum density, e be the natural constant, and α be the decay coefficient, where α ∈ [0.02, 0.1]. The transition region is generated by using a smoothing function at the boundary of the hybrid units; the smoothing function w(r) is: s is the control rate of gradual change, r is the distance from the center of the transition zone, and r0 is the radius of the transition zone.

[0009] Furthermore, in step 1, the microscale modeling includes: establishing process-melt pool mapping, melt pool-microstructure mapping, and microstructure-property mapping to quantify the influence of process parameters on mechanical properties.

[0010] Furthermore, in step 1, the mathematical relationships between the various scale parameters include: The macroscopic-mesoscopic correlation is achieved through element stiffness contribution decomposition, expressed as:

[0011] in, E t Given the target elastic modulus for the design, E i u For the first i The equivalent modulus of each unit, V i Let i be the volume of the i-th unit. V total This refers to the total volume of the unit. Mesoscopic-microscopic correlation is achieved through local relative density correlation between rod and grain size, expressed as:

[0012] Where d is the diameter of the rod, d g Grain size, For relative density, C is the topological configuration constant.

[0013] Furthermore, in step 3, the multiphysics coupling simulation is based on the heat conduction equation containing latent heat of phase change, the thermo-coupling elastoplastic constitutive equation, and the electron beam heat source input model, and the simulation region is divided into multi-scale meshes.

[0014] Furthermore, in step 3, the potential defects include: warping, porosity, and cracks.

[0015] Furthermore, in step 3, the process optimization includes: scanning path optimization, support structure design, and dynamic adjustment of process parameters; The scanning path optimization specifically involves: using grid scanning in areas with stress higher than a preset value to reduce heat accumulation, and using linear scanning in areas with stress lower than a preset value to improve efficiency; and rotating the scanning direction clockwise or counterclockwise by a set angle during each layer filling to disperse residual stress. The support structure design specifically includes: generating tapered supports in areas with a suspension angle > 45°, with a support diameter ranging from 0.4 to 1.2 mm and a spacing range of 1 to 2 times the support diameter; adding columnar or plate-shaped thermally conductive supports in areas prone to warping, with a support thickness ranging from 0.3 to 0.8 times the wall thickness of the contacting part and a spacing range of 0.5 to 1.2 times the support thickness. The process parameters are dynamically adjusted as follows: the electron beam power is increased to 110%~115% of the rated power in areas prone to porosity; the bottom layer thickness is 30~60μm, and the upper layer thickness is gradually increased to 40~80μm.

[0016] 9. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: in step 4, the objective function is specifically:

[0017] in, E t For the target elastic modulus, E sim The elastic modulus of the lattice structure obtained from multiphysics coupling simulation. Por The porosity is the surface-to-near-surface layer. s r For residual stress, s y For yield stress, w 1, w 2, w 3 is the weighting coefficient, which satisfies w 1+ w 2+ w 3 = 1.

[0018] Furthermore, the method is applied to the design of aerospace load-bearing components, which include face-centered cubic elements for the surface area, body-centered cubic elements for the core area, and hybrid elements; wherein the weighting coefficient in step 4 is taken as... w 1 = 0.6 w 2 = 0.2, w 3 = 0.2.

[0019] The advantages of this invention compared to the prior art are: (1) This invention improves design freedom. Through parametric modeling and optimization algorithms, more complex and higher-performance lattice structures can be designed, giving full play to the advantages of EBM technology.

[0020] (2) This invention improves the accuracy of mechanical property prediction. By establishing a mechanical property prediction model that takes into account EBM process parameters, the mechanical properties of lattice structures can be predicted more accurately, thereby improving the reliability of design results.

[0021] (3) This invention optimizes the EBM process parameters. Through EBM process simulation and optimization, the optimal EBM process parameters can be obtained, thereby improving the manufacturing quality of the lattice structure and avoiding manufacturing defects.

[0022] (4) This invention shortens the design cycle. By integrating design, simulation and optimization processes, the design cycle of lattice structures can be shortened and design efficiency improved. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram of the aerospace load-bearing component structure in an embodiment of the present invention. Detailed Implementation

[0024] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0025] Figure 1 The diagram shown is a schematic flowchart of the multi-scale gradient lattice structure design method based on electron beam additive manufacturing proposed in this invention. The following section will use... Figure 2 The method of the present invention will be introduced using the aerospace load-bearing component shown as an example. Figure 2 In the image, the left side represents the original state aerospace load-bearing component 1, and the right side represents the multi-scale gradient lattice reconstructed aerospace load-bearing component 2, which includes a surface region selected from face-centered cubic (FCC) elements 2-1, a core region selected from body-centered cubic (BCC) elements 2-2, and a hybrid element boundary 2-3. The specific steps of the design method are as follows: (1) Constructing a multi-scale gradient lattice parameterized modeling method The multi-scale gradient lattice parameterized modeling method decomposes the design of the lattice structure into macro-scale modeling, meso-scale modeling, and micro-scale modeling, and establishes mathematical relationships between parameters at each scale, thereby achieving accurate transmission from overall functional requirements to local process parameters.

[0026] Macro-scale modeling mainly focuses on overall functionality and geometric constraints. By designing spatial mapping, the geometric model is discretized into a mesh of fillable lattice elements. The overall performance requirements and geometric boundary conditions of the lattice structure are defined, including geometric dimensions, load conditions, and boundary constraints.

[0027] Mesoscale modeling refers to gradient unit and hybrid topology design, and its main steps are: unit filling, parameter mapping and transition region generation.

[0028] For element filling, based on the macro-mesh division, each node is assigned an element type, including uniform elements, hybrid elements, and functional elements. In this embodiment, hybrid elements are selected, and body-centered cubic (BCC) elements are selected for the core region. d ( z =0.5 + 0.01 z The surface area is selected using face-centered cubic (FCC) cells. d =0.8 mm; Transition zone width d 0 = 5 mm.

[0029] Parameter mapping, applying the bar diameter gradient function d ( z and density gradient function r ( xThe rod diameter and density are mapped to each unit.

[0030] The bar diameter gradient function reflects the linear variation of the bar diameter along the height direction (z-axis) as a function, and its expression is: d ( z )= d 0+ k · z ,in: k These are the gradient coefficients. k ∈[0.01, 0.1]. In this embodiment, k =0.01.

[0031] The density gradient function reflects the exponential decay of the lattice density along the loading direction (x-axis), and its expression is: r ( x )= r max · e -αx ,in: α The attenuation coefficient is... α ∈[0.02, 0.1]. In this embodiment, α =0.05.

[0032] The transition zone is generated at the boundary of the hybrid unit by smoothing the rod diameter and topological connection through the smoothing function w(r).

[0033] The smoothing function controls the gradual change in volume; its expression is: w ( r )= ,in: s To control the rate of change, r The distance from the center of the transition zone. r 0 represents the radius of the transition zone.

[0034] Microscale modeling is used to quantify the impact of process on mechanical properties by correlating process-driven material properties, and to establish simplified process-melt pool mapping, simplified melt pool-microstructure mapping, and simplified microstructure-property mapping.

[0035] Process-Molten Pool Simplified Mapping, including Simplified Mapping of Melt Pool Width: w p = a · P · v -1 + b Interlayer overlap rate or =( w p - h )· w p -1 ,in:P For power, v For scanning speed, h For layer thickness, a , b For example, the power P is initially set to 1800W, the scanning speed v is initially set to 600mm / s, the layer thickness h is 30μm, and a and b are coefficients. For titanium alloy, a=0.015 and b=20μm.

[0036] Simplified mapping of melt pool and microstructure, primarily through grain size. d g The reaction, expressed as: ,in: For cooling rate, c , n For example, c=200 and n=0.5 for titanium alloy.

[0037] The microstructure-property mapping is based on the Hall-Petch formula to link the relationship between grain diameter and yield strength.

[0038] The mathematical correlation of parameters at various scales is achieved, on the one hand, by utilizing the decomposition of element stiffness contributions: Perform macro-meta-correlation, where: E t Given the target elastic modulus for the design, E i u For the first i The equivalent modulus of each unit, V i Let i be the volume of the i-th unit. V total The total volume of the unit cell; on the one hand, the local relative density is used to correlate the size of the bars and grains: Perform mesoscopic-microscopic correlations, where: C is the topological configuration constant.

[0039] (2) Predicting mechanical properties across scales The cross-scale mechanical property prediction includes prediction through macroscopic equivalent models and mesoscopic-microscopic coupling models, and realizes cross-scale data transfer from mesoscopic-microscopic to macroscopic scales.

[0040] The macroscopic equivalent model is used to quickly predict the macroscopic properties of gradient lattice structures, such as the equivalent elastic modulus and yield strength, by using a gradient-sensitive factor. β= 1+ c · r The modified discrete element structure stiffness matrix is ​​obtained by introducing the classic Gibson-Ashby formula: E ( x ,y , z ) / E s = C ( r / r s ) m · β=C ( r ( x , y , z ) / r s ) m ·(1+ c · r Integrating the structural stiffness matrix, we predict the macroscopic mechanical response, including the equivalent elastic modulus and yield strength, where: E s The elastic modulus of a solid material; r s The elastic modulus density of a solid material; m It is the topological configuration constant; r For relative density gradient, r = r / x + r / y + r / z ; c The gradient sensitivity coefficient is determined experimentally.

[0041] The meso-micro coupled model, with crystal plastic constitutive relations and anisotropic yield strength as key equations, quantifies the influence of microstructure (grain orientation, residual stress) caused by EBM process on the mechanical properties of meso-scale units.

[0042] Cross-scale data transfer is achieved by calculating equivalent material properties through representative volume elements (RVEs) to transfer data from the micro to the mesoscopic level. The RVE properties are then assigned to gradient lattice elements to update the parameters of the macroscopic equivalent model, thus achieving the transfer of mesoscopic and macroscopic parameters.

[0043] (3) Develop process simulation and defect prediction technologies The process simulation and defect prediction technology simulates the thermodynamic behavior of electron beam additive manufacturing through multi-physics field coupling simulation, predicts potential defects, and guides process optimization.

[0044] The thermodynamic behavior of electron beam additive manufacturing is simulated by multi-scale mesh generation based on the heat conduction equation containing latent heat of phase change, thermo-coupling elastoplastic constitutive model and electron beam heat source energy input model.

[0045] Potential defects mainly include warping, porosity, and cracks.

[0046] Process optimization mainly includes: scanning path optimization, support structure design, and dynamic adjustment of process parameters.

[0047] Scan path optimization includes a regional strategy: high-stress areas use mesh scanning to reduce heat accumulation, while low-stress areas use linear scanning to speed up the process; contour deflection: the scanning direction of each layer is rotated 67° clockwise / counterclockwise to disperse the direction of residual stress.

[0048] The support structure design includes lattice adaptive supports: tapered supports are generated in areas with a sag angle > 45°, with support diameters ∈ [0.4, 1.2 mm] and spacing ∈ [support diameter, 2·support diameter]; thermal conduction supports: columnar / plate-shaped thermally conductive supports are added in warp-prone areas, with support thicknesses ∈ [0.3·contact part wall thickness, 0.8·contact part wall thickness] and spacing [0.5·support thickness, 1.2·contact part wall thickness]. In this embodiment, tapered supports are generated in areas with a sag angle > 45°, with a support diameter of 1 mm and a spacing of 2 mm; thermal conduction supports: columnar / plate-shaped thermally conductive supports are added in warp-prone areas, with a support thickness of 1 mm and a spacing of 1 mm.

[0049] Dynamic adjustment of process parameters and real-time power modulation: Based on infrared monitoring feedback of the molten pool, the electron beam power is increased to 110%~115% of the rated power in areas prone to porosity; gradient layer thickness: bottom layer thickness ∈[30, 60] μm, ensuring density, with the upper part gradually increasing to h ∈[40, 80] μm, increasing the additive manufacturing speed. In this embodiment, the electron beam power is increased to 110% of the rated power in the porosity-prone region; gradient layer thickness: bottom layer thickness =40μm to ensure density, gradually increasing to 10μm at the top. =80μm, improving additive manufacturing speed.

[0050] (4) Perform multi-objective algorithm collaborative optimization The multi-objective algorithm for collaborative optimization balances multiple conflicting objectives in the design process by establishing an objective function.

[0051] The objective function, consisting of mechanical property terms, defect control terms, and residual stress terms, is expressed as follows: ,in, E simThe elastic modulus of the lattice structure obtained from multiphysics coupling simulation. Por The porosity is the surface-to-near-surface layer. s r For residual stress, s y For yield stress, w 1, w 2, w 3 is the weighting coefficient, which satisfies w 1+ w 2+ w 3 = 1.

[0052] The optimization variables of the objective function are the gradient coefficient k, the electron beam power P, and the scanning velocity v; the boundary conditions are... f ( d ( z ), P , v , Por , s r , s y In this embodiment, the boundary conditions are specifically as follows: f =

[0053] The weighting coefficient should be appropriately increased when mechanical performance is given priority. w The value of 1 can be appropriately increased when dealing with defect sensitivity. w The value of 2. In this embodiment, for aerospace load-bearing components facing a scenario where mechanical performance is prioritized, the weighting coefficient is designed as follows: w 1 = 0.6 w 2 = 0.2, w 3 = 0.2.

[0054] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0055] It is understood that this invention has been described through embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this invention.

Claims

1. A design method for multi-scale gradient lattice structures based on electron beam additive manufacturing, characterized in that, include: Step 1: Perform multi-scale gradient lattice parameterization modeling, including macro-scale modeling, meso-scale modeling and micro-scale modeling, and establish mathematical relationships between parameters at each scale. Step 2: Based on the established multi-scale gradient lattice parameterization model, perform cross-scale mechanical property prediction. The performance prediction includes: predicting the macroscopic mechanical response of the lattice structure based on a macroscopic equivalent model that considers gradient sensitivity factors; quantifying the influence of microstructure caused by electron beam additive manufacturing on the mechanical properties of mesoscopic units based on a mesoscopic-microscopic coupling model that considers crystal plastic constitutive relations and anisotropic yield strength; and realizing cross-scale parameter transfer from microscopic to mesoscopic and then to macroscopic through representative volume units. Step 3: Based on the obtained mechanical property prediction results, simulate the thermodynamic behavior in the electron beam additive manufacturing process through multiphysics coupling simulation, predict potential defects and guide process optimization; Step 4: Establish a multi-objective function that includes mechanical property terms, defect control terms, and residual stress terms, and perform synergistic optimization of gradient coefficient, electron beam power, and scanning speed to obtain the optimal combination of lattice structure design and process parameters.

2. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 1, the macroscopic scale modeling includes: discretizing the geometric model into a grid of fillable lattice units by designing a spatial mapping, and defining geometric boundary conditions.

3. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 1, the mesoscale modeling includes: cell filling, parameter mapping, and transition region generation; The cell filling involves assigning a cell type to each cell; the cell types include uniform cells, hybrid cells, and functional cells. The parameter mapping involves mapping the rod diameter gradient function and density gradient function to the rod diameter and density of each element; the rod diameter gradient function d(z) is: d(z) = d0 + k·z, where z represents the rod diameter in the height direction, d0 is the initial rod diameter, and k is the gradient coefficient, k ∈ [0.01, 0.1]; the density gradient function ρ(x) is: ρ(x) = ρ max ·e -αx x represents the load direction, ρ max Let e ​​be the maximum density, e be the natural constant, and α be the decay coefficient, where α ∈ [0.02, 0.1]. The transition region is generated by using a smoothing function at the boundary of the hybrid units; the smoothing function w(r) is: s is the control rate of gradual change, r is the distance from the center of the transition zone, and r0 is the radius of the transition zone.

4. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 1, the microscale modeling includes: establishing process-melt pool mapping, melt pool-microstructure mapping, and microstructure-property mapping to quantify the influence of process parameters on mechanical properties.

5. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 1, the mathematical relationships between the various scale parameters include: The macroscopic-mesoscopic correlation is achieved through element stiffness contribution decomposition, expressed as: in, E t Given the target elastic modulus for the design, E i u For the first i The equivalent modulus of each unit, V i Let i be the volume of the i-th unit. V total This refers to the total volume of the unit. Mesoscopic-microscopic correlation is achieved through local relative density correlation between rod and grain size, expressed as: Where d is the diameter of the rod, d g Grain size, For relative density, C is the topological configuration constant.

6. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 3, the multiphysics coupling simulation is based on the heat conduction equation containing latent heat of phase change, the thermo-coupling elastoplastic constitutive equation, and the electron beam heat source input model, and the simulation region is divided into multi-scale meshes.

7. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 3, the potential defects include: warping, porosity, and cracks.

8. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 3, the process optimization includes: scanning path optimization, support structure design, and dynamic adjustment of process parameters; The scanning path optimization specifically involves: using grid scanning in areas with stress higher than a preset value to reduce heat accumulation, and using linear scanning in areas with stress lower than a preset value to improve efficiency; and rotating the scanning direction clockwise or counterclockwise by a set angle during each layer filling to disperse residual stress. The support structure design specifically includes: generating tapered supports in areas with a suspension angle > 45°, with a support diameter ranging from 0.4 to 1.2 mm and a spacing range of 1 to 2 times the support diameter; adding columnar or plate-shaped thermally conductive supports in areas prone to warping, with a support thickness ranging from 0.3 to 0.8 times the wall thickness of the contacting part and a spacing range of 0.5 to 1.2 times the support thickness. The process parameters are dynamically adjusted as follows: the electron beam power is increased to 110%~115% of the rated power in areas prone to porosity; the bottom layer thickness is 30~60μm, and the upper layer thickness is gradually increased to 40~80μm.

9. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 1, characterized in that: In step 4, the objective function is specifically: in, E t For the target elastic modulus, E sim The elastic modulus of the lattice structure obtained from multiphysics coupling simulation. Por The porosity is the surface-to-near-surface layer. σ r For residual stress, σ y For yield stress, w 1, w 2, w 3 is the weighting coefficient, which satisfies w 1+ w 2+ w 3 = 1.

10. The multi-scale gradient lattice structure design method based on electron beam additive manufacturing according to claim 9, characterized in that: The method is applied to the design of aerospace load-bearing components, which include face-centered cubic elements for the surface area, body-centered cubic elements for the core area, and hybrid elements; wherein the weighting coefficient in step 4 is taken as... w 1 = 0.6 w 2 = 0.2, w 3 = 0.2.

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