A support structure optimization design method for controlling thermal stress in metal additive manufacturing

Abstract

This invention discloses an optimized design method for support structures to control thermal stress in metal additive manufacturing, relating to the field of metal additive manufacturing. The method includes the following steps: defining a design domain and a non-design domain; initializing design variables; converting design variables into physical variables through density filtering and projection; establishing an interpolation model between the physical variables and the overall structural stiffness; performing finite element simulation on the layer-by-layer additive manufacturing process of the overall structure to obtain the thermal deformation of the overall structure; and calculating the maximum thermal stress σ of the structure. pn The proposed method involves calculating the volume fraction V of the supporting structure and the suspension angle constraint response G; determining the sensitivity; updating the design variables to solve the optimization model; determining whether convergence has occurred; and post-processing the optimization results. The structure designed by this method ensures that the thermal stress of the overall structure is controllable after additive manufacturing, avoiding cracking and delamination caused by excessive thermal stress.

Description

Technical Field

[0001] This invention relates to the field of metal additive manufacturing, and in particular to a method for optimizing the design of support structures to control thermal stress in metal additive manufacturing. Background Technology

[0002] Metal bed additive manufacturing technology uses a high-energy laser beam to heat and melt metal powder layer by layer, followed by cooling and solidification to form a shape. This allows for the rapid fabrication of complex structures and is widely used in the aerospace field. However, during laser additive manufacturing, the high-energy laser beam generates a high temperature gradient, leading to thermal stress within the structure. If the thermal stress is too high during manufacturing, cracking and delamination can occur, resulting in manufacturing failure, material waste, and economic losses.

[0003] By designing a reasonable support structure, thermal stress during the additive manufacturing process can be controlled to a certain extent, ensuring successful component manufacturing. In industry, engineers design support structures based on experience, adjusting their configurations to avoid structural cracking and delamination caused by thermal stress. Simulations or experiments are then used to verify successful component manufacturing. While empirical design methods are relatively easy to implement for simple structures, they may fail to produce complex components. If manufacturing fails, multiple iterations of support structure design are required until the final component is successfully manufactured, which not only prolongs product development time but also wastes materials. In academia, scholars both domestically and internationally have proposed using topology optimization techniques to design additive manufacturing support structures, minimizing material usage and reducing manufacturing costs while satisfying suspension angle constraints. However, support structures that only meet suspension angle constraints struggle to control the thermal stress generated during additive manufacturing. Therefore, considering and controlling additive manufacturing thermal stress in the topology optimization design of the support structure is crucial to prevent structural cracking and delamination due to excessive thermal stress in the formed parts.

[0004] In their paper "On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powderbed metal additive manufacturing," Cheng et al. proposed a topology optimization method for support structures that considers thermal stress constraints. This method aims to minimize the volume of the support structure and incorporates thermal stress constraints in the support structure design, allowing for some control over the thermal stress of the components. However, the layout area of ​​the support structure is already determined before the optimization iteration, and the optimization algorithm can only optimize the volume fraction of lattice unit cells within this area, failing to optimize the macroscopic layout of the support structure.

[0005] Therefore, those skilled in the art are dedicated to developing a support structure optimization design method for controlling thermal stress in metal additive manufacturing. Summary of the Invention

[0006] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is that the existing support structure design method based on engineering experience and trial and error is prone to excessive thermal stress and structural cracking during the additive manufacturing process.

[0007] To achieve the above objectives, the present invention provides a method for optimizing the design of support structures to control thermal stress in metal additive manufacturing, the method comprising the following steps:

[0008] Step 1: Discretize the region surrounding the given solid structure using finite element methods, and define the region containing the solid structure as the non-design domain Ω. * Define the remaining area as the design domain Ω of the supporting structure;

[0009] Step 2: Initialize the design variables μ = (μ1, μ2, ..., μ) that indirectly represent the presence or absence of the structure. n ), where n is the total number of units;

[0010] Step 3: Based on the density filtering function and projection function, the design variable μ, which indirectly represents the presence or absence of a structure, is converted into the physical variable ρ = (ρ1, ρ2, ..., ρ) that directly represents the presence or absence of a structure in a certain unit. n );

[0011] Step 4: Based on the SIMP formula, establish an interpolation model that directly represents the physical variable ρ of a certain unit as having or not having a structure and the stiffness of the overall structure; based on the inherent strain method, perform finite element simulation on the additive manufacturing layer-by-layer processing of the overall structure to obtain the thermal deformation of the overall structure during the layer-by-layer processing.

[0012] Step 5: Calculate the maximum thermal stress σ of the additively manufactured structure. pm , Support structure volume fraction V, Suspension angle constraint response G;

[0013] Step 6: Calculate the sensitivity of each design response to the design variables;

[0014] Step 7: Solve the topology optimization model using the moving asymptote algorithm to obtain the updated design variable μ;

[0015] Step 8: Determine if convergence has occurred. If convergence has occurred, proceed to step 9; otherwise, proceed to step 3.

[0016] Step 9: Post-process the optimization results and establish an optimization structure based on the post-processed ρ.

[0017] Furthermore, in step 1, the finite element used for discretization has a side length of 1 mm. In the initialization phase of step 2, if element i belongs to the non-design domain Ω... * Then the component μ in μ i It is initialized to 1 and remains unchanged in subsequent optimization iterations.

[0018] Furthermore, the density filtering function in step 3 is as follows:

[0019]

[0020] Among them, M e ={i|‖X i -X e ||≤r min} is the unit e with r min For the neighborhood of radius, X i With X e H represents the center coordinates of element i and element e, respectively. ie =max{r min -‖X i -X e ‖,0} represents the weighting coefficients;

[0021] The projection function is as follows:

[0022]

[0023] Where β is the steepness of the projection and η is the projection threshold.

[0024] Furthermore, the SIMP formula in step 4 is:

[0025] E e =E min +ρ e p (E0-Emin )

[0026] Among them, E e E is the Young's modulus obtained by interpolation of element e; min To avoid small values ​​introduced by the singularity of the matrix in the finite element solution, p is the penalty coefficient of the SIMP formula.

[0027] Furthermore, the inherent strain method formula for performing finite element simulation of the additive manufacturing layer-by-layer processing of the overall structure in step 4 is as follows:

[0028] K i U i =F, i=1,2,…,N

[0029] Among them, K i U is the stiffness matrix of the first i-th layer structure; i F represents the structural deformation increment caused by processing the i-th layer. i F represents the equivalent load caused by the inherent strain during the processing of the i-th layer; N represents the total number of layers considered in the simulation of the additive manufacturing layer-by-layer process; in the finite element simulation model of the additive manufacturing layer-by-layer process based on the inherent strain method, the simulation of each layer is independent, and the inherent strain equivalent load F i Only load at level i.

[0030] Furthermore, in step 5, the stress vector σ of unit j when the additive manufacturing process is completed... j for:

[0031]

[0032] Where D is the constitutive matrix, B is the strain-displacement matrix, and l(j) is the layer number where element j is located. To account for the deformation increment of each node in element j caused by processing the i-th layer, L j To obtain from the global displacement vector U i Extracting the element displacement vector The required transformation matrix, ε inh For inherent strain;

[0033] The definition is as follows:

[0034]

[0035] Mises stress σ of element j mj for:

[0036]

[0037] Where R is the Mises stress coefficient matrix, and the specific formula is:

[0038]

[0039] The maximum thermal stress σ of the structure in the completed additive manufacturing state pn Approximate solution using the P-norm formula:

[0040]

[0041] Where p S ρ is the power exponent of the physical variable field interpolation ρ, and P is the power exponent of the P-norm formula;

[0042] The volume fraction V of the supporting structure is calculated based on the physical variable ρ, which represents whether a unit has a structure. The specific formula is as follows:

[0043]

[0044] Where, n Ω The total number of elements in the design domain Ω;

[0045] The suspension angle constraint response G is calculated based on the physical variable ρ, which represents whether a certain element has a structure. The specific formula is as follows:

[0046]

[0047] Where I is a unit vector; ε is the physical variable ρ after additive manufacturing filtering; r This is the allowable error value set to facilitate convergence of the optimization process.

[0048] Furthermore, the maximum thermal stress σ of the additively manufactured structure in its final state. pn For design variable μ e The sensitivity is:

[0049]

[0050] Where, ρ k For the physical variables of unit k, The variable obtained by density filtering for element j;

[0051] It can be obtained from the following formula:

[0052]

[0053] Where, λ i The adjoint vector is obtained using the following formula:

[0054]

[0055] Furthermore, the topology optimization model solved in step 7 is:

[0056] min μ V

[0057] stG≤0 (self-supporting constraint)

[0058] σ pn ≤σ * (Thermal stress constraint)

[0059] K i U i =F i i = 1, 2, ..., N

[0060] 0≤μ e ≤1,e=1,2,…,n

[0061] Where, σ * The yield strength of the material.

[0062] Furthermore, the convergence criterion in step 8 is that both the self-supporting constraint and the thermal stress constraint are satisfied, and the relative change of the objective function in five consecutive steps is less than 0.5%.

[0063] Further, the post-processing step in step 9 specifically involves: performing post-processing on the physical variable ρ representing whether a certain unit has a structure, selecting a threshold, setting elements in ρ that are greater than the threshold to 1, and setting elements in ρ that are not greater than the threshold to 0.

[0064] Compared with the prior art, the present invention has the following beneficial technical effects:

[0065] The proposed method for optimizing the support structure to control thermal stress in metal additive manufacturing does not rely on the experience of engineering designers. By introducing a thermal stress simulation model of the additive manufacturing process and the maximum thermal stress constraint of the components into the structural topology optimization, the method effectively controls the thermal stress of the finished additively manufactured parts during the structural design stage. This results in a support structure design that ensures the overall thermal stress is controllable, avoiding cracking and delamination problems caused by excessive thermal stress.

[0066] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0067] Figure 1 This is a flowchart of the method of the present invention;

[0068] Figure 2 This is a schematic diagram of the design domain of a preferred embodiment of the present invention;

[0069] Figure 3This is a schematic diagram of the parameterized model of the present invention;

[0070] Figure 4 This is a simulation diagram of the additive manufacturing process based on the inherent strain method of the present invention;

[0071] Figure 5 This is the solution result and post-processing result of the optimization model of a preferred embodiment of the present invention. Detailed Implementation

[0072] The preferred embodiments of the present invention are described below with reference to the accompanying drawings to make the technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0073] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0074] like Figure 1 The diagram shown is a flowchart of the method of the present invention, which includes the following steps:

[0075] Step 1, as follows Figure 2 As shown, the method of this invention is used to design a support structure for a cantilever beam structure. The region surrounding the given main structure is discretized using finite elements with a side length of 1 mm, and the region where the main structure is located is defined ( Figure 2 The black area in the diagram represents the non-design domain Ω. * Define the remaining areas ( Figure 2 The area marked with a black diagonal line in the diagram represents the design domain Ω of the supporting structure. The given dimensional parameters for the cantilever beam structure are L1 = 6 mm, L2 = 80 mm, L3 = 30 mm, and L4 = 16 mm. The material properties are set as follows: Young's modulus E0 = 110000 MPa, and Poisson's ratio = 0.34.

[0076] Step 2: Initialize the design variables μ = (μ1, μ2, ..., μ) that indirectly represent the presence or absence of the structure. n Where n is the total number of units, in this embodiment, n = 30 × 80 = 2400.

[0077] During the initialization phase, if element i belongs to the non-design domain Ω * Then the component μ in μ i It is initialized to 1 and remains unchanged in subsequent optimization iterations.

[0078] Step 3, as follows Figure 3As shown, based on density filtering and projection functions, the design variable μ, which indirectly represents the presence or absence of a structure, is transformed into the physical variable ρ = (ρ1, ρ2, ..., ρ) that directly represents the presence or absence of a structure in a certain unit. n ).

[0079] The density filtering formula is as follows:

[0080]

[0081] Where M e ={i|‖X i -X e ||≤r min} is the unit e with r min For the neighborhood of radius, X i With X e H represents the center coordinates of element i and element e, respectively. ie =max{r min -‖X i -X e ‖,0} represents the weighting coefficients.

[0082] The projection function formula is as follows:

[0083]

[0084] Where β is the steepness of the projection and η is the projection threshold.

[0085] Step 4: Based on the SIMP formula, establish an interpolation model that directly represents the physical variable ρ, indicating whether a certain element has a structure, and the overall structural stiffness. Based on the inherent strain method, perform finite element simulation on the additive manufacturing layer-by-layer processing of the overall structure to obtain the thermal deformation of the overall structure during the layer-by-layer processing.

[0086] The SIMP formula is as follows:

[0087] E e =E min +ρ e p (E0-E min )

[0088] Among them, E e E is the Young's modulus obtained by interpolation of element e; min To avoid small values ​​introduced by the singularity of the finite element solution matrix, this embodiment uses 1.1 × 10⁻⁶. -4 MPa; p is the penalty coefficient of the SIMP formula, which is taken as 3 in this embodiment.

[0089] The finite element simulation formula for the additive manufacturing layer-by-layer process based on the inherent strain method is as follows:

[0090] K i Ui =F i i = 1, 2, ..., N

[0091] Among them, K i U is the stiffness matrix of the first i-th layer structure; i F represents the structural deformation increment caused by processing the i-th layer. i The equivalent load caused by the inherent strain when processing the i-th layer structure; N is the total number of layers considered in the simulation of the additive manufacturing layer-by-layer processing process.

[0092] like Figure 4 As shown, in the finite element simulation model of the additive manufacturing layer-by-layer process based on the inherent strain method, the simulations of each layer are independent, and the inherent strain equivalent load F i Only load at level i.

[0093] Step 5: Calculate the maximum thermal stress σ of the additively manufactured structure. pn , Support structure volume fraction V, Suspension angle constraint response G.

[0094] The stress vector σ of element j when additive manufacturing is completed j for:

[0095]

[0096] Where D is the constitutive matrix, B is the strain-displacement matrix, and k(j) is the layer number where element j is located. To account for the deformation increment of each node in element j caused by processing the i-th layer, L j To obtain from the global displacement vector U i Extracting the element displacement vector The required transformation matrix, ε inh This is the inherent strain. The definition is as follows:

[0097]

[0098] Mises stress σ of element j mj for:

[0099]

[0100] Where R is the Mises stress coefficient matrix, and the specific formula is:

[0101]

[0102] Maximum thermal stress σ of additive manufacturing completed structure pn Approximate solution using the P-norm formula:

[0103]

[0104] Where p S ρ is the power exponent of the physical variable field interpolation, which is 0.5 in this embodiment; P is the power exponent of the P-norm formula, which is 8 in this embodiment.

[0105] The volume fraction V of the supporting structure is calculated based on the physical variable ρ, which represents whether a unit has a structure. The specific formula is as follows:

[0106]

[0107] Where, n Ω In this embodiment, n represents the total number of elements in the design domain Ω. Ω =1536.

[0108] The suspension angle constraint response G is calculated based on the physical variable ρ representing whether a certain element has a structure. In this embodiment, a suspension angle constraint based on additive manufacturing filter (AM filter) is used, and the specific formula is as follows:

[0109]

[0110] Where I is a unit vector; ε is the physical variable ρ after additive manufacturing filtering; r The allowable error value is set to facilitate convergence of the optimization process; in this embodiment, it is set to 0.5.

[0111] Step 6: Calculate the sensitivity of each design response to the design variables.

[0112] Maximum thermal stress σ of additive manufacturing completed structure pn For design variable μ e The sensitivity is:

[0113]

[0114] in It can be obtained from the following formula:

[0115]

[0116] Where, λ i The adjoint vector is obtained using the following formula:

[0117]

[0118] Step 7: Solve the topology optimization model using the moving asymptote algorithm to obtain the updated design variable μ.

[0119] The topology optimization model to be solved is:

[0120] minμ V

[0121] stG≤0 (self-supporting constraint)

[0122] σ pn ≤σ * (Thermal stress constraint)

[0123] K i U i =F i i = 1, 2, ..., N

[0124] 0≤μ e ≤1,e=1,2,…,n

[0125] Where σ * The yield strength of the material is taken as 850 MPa in this embodiment.

[0126] Step 8: Convergence check. If both the self-supporting constraint and the thermal stress constraint are satisfied, and the relative change of the objective function over five consecutive steps is less than 0.5%, then proceed to step 9. Otherwise, proceed to step 3.

[0127] Step 9: Post-process the optimization results, such as... Figure 5 As shown.

[0128] The physical variable ρ, which represents whether a unit has a structure, is post-processed. A threshold is selected (0.5 in this embodiment), and elements in ρ that are greater than the threshold are set to 1, while elements in ρ that are not greater than the threshold are set to 0.

[0129] An optimized structure is established based on the post-processed ρ.

[0130] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for optimizing the design of a support structure to control thermal stress in metal additive manufacturing, characterized in that, The method includes the following steps: Step 1: Discretize the region surrounding the given ontological structure using finite element methods, and define the region containing the ontological structure as the non-design domain. Define the remaining area as the design domain of the supporting structure. ; Step 2: Initialize design variables that indirectly represent the presence or absence of the structure. ,in n The total number of units; Step 3: Based on the density filtering function and projection function, the design variables that indirectly represent the presence or absence of the structure are... Converted into physical variables that directly represent whether a certain unit has a structure. ; Step 4: Based on the SIMP formula, establish physical variables that directly represent whether a certain unit has structure or not. An interpolation model for the overall structural stiffness; based on the inherent strain method, finite element simulation of the additive manufacturing layer-by-layer processing of the overall structure is performed to obtain the thermal deformation of the overall structure during the layer-by-layer processing. Step 5: Calculate the maximum thermal stress of the additively manufactured structure. Volume fraction of supporting structure Suspension angle constraint response ; Step 6: Calculate the sensitivity of each design response to the design variables; Step 7: Solve the topology optimization model using the moving asymptote algorithm to obtain updated design variables. ; Step 8: Determine if convergence has occurred. If convergence has occurred, proceed to step 9; otherwise, proceed to step 3. Step 9: Post-process the optimization results, based on the post-processed results... Establish an optimized structure.

2. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, In step 1, the finite element used for discretization has a side length of 1 mm. In the initialization phase of step 2, if the element... i Belonging to the non-design domain Then Components in It is initialized to 1 and remains unchanged in subsequent optimization iterations.

3. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, The density filtering function in step 3 is as follows: in, For unit by The neighborhood of the radius, and Units With unit The center coordinates, These are the weighting coefficients; The projection function is as follows: in, Let be the steepness of the projection. This is the projection threshold.

4. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, The SIMP formula in step 4 is: in, For unit e Young's modulus obtained by interpolation; To avoid small values ​​introduced by matrix singularity in the finite element solution, p This is the penalty coefficient for the SIMP formula.

5. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, The inherent strain method formula for performing finite element simulation of the additive manufacturing layer-by-layer processing of the overall structure in step 4 is as follows: in, For the front Stiffness matrix of layered structure; For processing the first The structural deformation increment caused by the layer; For processing the first The equivalent load caused by the inherent strain in a layered structure; The total number of layers considered in the simulation of the additive manufacturing layer-by-layer process; in the finite element simulation model of the additive manufacturing layer-by-layer process based on the inherent strain method, the simulation of each layer is independent, and the inherent strain equivalent load is... Only loaded in the first i layer.

6. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, When the additive manufacturing process is completed in step 5, the unit... j stress vector for: in The constitutive matrix is The strain-displacement matrix, For unit The floor number, For processing the first Units caused by layers Deformation increment at each node, To obtain from the global displacement vector Extracting the element displacement vector The required transformation matrix, For inherent strain; The definition is as follows: unit Mises stress for: in The Mises stress coefficient matrix is ​​given by the following formula: The maximum thermal stress of the structure in the completed additive manufacturing state Approximate solution using the P-norm formula: in For physical variable fields The power exponent of interpolation, is the power exponent in the P-norm formula; Support structure volume fraction Based on physical variables representing whether a unit has structure The calculation is performed using the following formula: in, For design domain The total number of units; Suspension angle constraint response Based on physical variables representing whether a unit has structure The calculation is performed using the following formula: in, It is a unit vector; For physical variables Variables after additive manufacturing filtration; This is the allowable error value set to facilitate convergence of the optimization process.

7. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, Maximum thermal stress in the finished additive manufacturing structure For design variables The sensitivity is: in, For unit physical variables, For unit The variables obtained after density filtering; It can be obtained from the following formula: in, The adjoint vector is obtained using the following formula: 。 8. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, The topology optimization model solved in step 7 is as follows: Self-supporting constraints Thermal stress constraint in, The yield strength of the material.

9. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 8, characterized in that, The convergence criterion in step 8 is that both the self-supporting constraint and the thermal stress constraint are satisfied, and the relative change of the objective function in five consecutive steps is less than 0.5%.

10. The method for optimizing the design of support structures to control thermal stress in metal additive manufacturing as described in claim 1, characterized in that, The post-processing step in step 9 specifically involves: processing the physical variables representing whether a unit has a structure. Post-processing is performed, a threshold is selected, and... Elements greater than the threshold are set to 1. Elements that are not greater than the threshold are set to 0.

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