Laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing

Abstract

This invention discloses a laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing. This method relates to the field of metal additive manufacturing and includes the following steps: defining a design domain and setting material property parameters; initializing design variables; density filtering and projection; calculating the inherent strain of each unit; simulating thermal deformation during the additive manufacturing process; calculating each design response; sensitivity analysis; solving the optimization model using the MMA algorithm and updating the design variables; determining convergence; and post-processing the optimization results. Through the coordinated optimization design of the support structure and laser path, this invention ensures that the thermal deformation of the overall structure during the layer-by-layer processing of additive manufacturing is controllable, preventing collisions between the structure and the powder spreading device due to excessive thermal deformation. It also reduces the amount of support structure used, reducing manufacturing time and cost.

Description

Technical Field

[0001] The present invention relates to the field of metal additive manufacturing, and in particular to a method for optimizing the design of a laser path and a support structure for controlling thermal deformation in additive manufacturing. Background Art

[0002] Laser metal additive manufacturing (LAM) is an advanced manufacturing technology that builds components by discrete layers and then stacking them one by one. It is widely used in fields such as aviation and aerospace. During the manufacturing process, the high-energy laser beam induces high temperature gradients, causing thermal deformation of the structure. If this deformation is excessive, the formed component may collide with the powder-laying device, leading to manufacturing failure or even damage to the AM equipment, resulting in serious economic losses.

[0003] Support structure and laser path are two major factors that affect the thermal deformation of additively manufactured components.

[0004] In engineering applications, manufacturing engineers typically manually add support structures based on experience and a given laser path. They then verify the component's success through simulation or experimentation. If this fails, multiple adjustments to the support structure and simulation or prototype production are necessary, leading to long and costly trial-and-error cycles.

[0005] The Chinese patent with patent number CN112765865B discloses a method for topological optimization of support structures for controlling thermal deformation in metal powder bed additive manufacturing. This method is based on a given laser path and can optimize the support structure design that reduces the thermal deformation of the component. However, this method only optimizes the support structure and does not consider the influence of the laser path on the thermal deformation of the additively manufactured component. If the laser path is not designed properly, a large number of support structures will need to be added to avoid the problem of collision between the formed structure and the powder spreading device, resulting in greater additive manufacturing and support removal costs. If the laser path is collaboratively optimized while the support structure is being optimized, the amount of support structure used can be further reduced while avoiding collision between the formed structure and the powder spreading device, thereby reducing manufacturing costs.

[0006] Therefore, technical personnel in this field are committed to developing a laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing. Through the coordinated optimization design of the support structure and the laser path, the amount of support structure material is minimized under the premise that the thermal deformation of the overall structure in the additive manufacturing layer-by-layer processing process is controllable, and the problem of collision between the structure of the metal powder bed additive manufacturing layer-by-layer processing device due to excessive thermal deformation is solved. Summary of the Invention

[0007] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to achieve the coordinated optimization design of the support structure and the laser path, and solve the problem of collision between the structure of the metal powder bed additive manufacturing layer-by-layer processing device due to excessive thermal deformation.

[0008] To achieve the above objectives, the present invention provides a method for optimizing the design of a laser path and a support structure for controlling thermal deformation in additive manufacturing, the method comprising the following steps:

[0009] Step 1: Discretize the area surrounding the given main structure with cube units; define the area where the main structure is located as Ω1 and the rest of the area as Ω2; the design domain for laser path optimization is Ω1∪Ω2, and the design domain for support structure optimization is Ω2;

[0010] Step 2: Initialize the design variables μ = (μ1, μ2, ..., μ n ), used to indirectly indicate the presence or absence of the structure; initialize the design variables v = (v1, v2, ..., v n ), used to indirectly represent the relative density of the structure; initialize the design variables d = (d1, d2, ..., d n ), used to indicate the laser scanning direction of each unit; where n is the total number of units;

[0011] Step 3: Based on density filtering and projection function, the design variable μ is converted into a physical variable ρ = (ρ1, ρ2, ..., ρ n ), convert the design variable v into a physical variable φ=(φ1,φ2,…,φ n );

[0012] Step 4: According to the design variables d = (d1, d2, ..., d n ), calculate the inherent strain of each unit ε=(ε1,ε2,...,ε n );

[0013] Step 5: Based on the SIMP formula, establish the overall structural stiffness interpolation model;

[0014] Step 6: Based on the inherent strain method, a finite element simulation model of the layer-by-layer processing of the overall structure is established and solved to obtain the thermal deformation of the overall structure during the additive manufacturing process;

[0015] Step 7: Calculate the design response, including the maximum thermal deformation Q of the top structure during the additive manufacturing process, the volume fraction V of the support structure, and the suspension angle constraint response G.

[0016] Step 8: Calculate the sensitivity of each design response to each design variable;

[0017] Step 9: Establish an optimization model and solve it based on the moving asymptote algorithm to update the design variables μ, v, and d;

[0018] Step 10, determine whether the iteration has converged; if all constraints are satisfied and the relative change of the objective function for 10 consecutive steps is less than 1%, go to step 11, otherwise go to step 3;

[0019] Step 11: Post-process the support structure optimization results; generate the laser scanning path for processing each layer structure based on the optimization results of the design variable d.

[0020] Furthermore, the step 2 further includes: during the initialization process, if the unit i belongs to the region Ω1 where the main structure is located, then the component μ in μ is i 、The component v in v i It is initialized to 1 and remains unchanged throughout the optimization process.

[0021] Furthermore, in step 3, the density filtering formula is as follows:

[0022]

[0023]

[0024] Where M e ={i|||X i -X e ||≤r min} is a unit e with r min is the radius of the neighborhood, X i With X e are the center coordinates of unit i and unit e, respectively, H ie =max{r min -||X i -X e ||, 0} is the weight coefficient;

[0025] The projection function formula is as follows:

[0026]

[0027] Where β is the steepness of the projection, and η is the projection threshold;

[0028] The physical variable representing the relative density of a unit is obtained by the following formula:

[0029]

[0030] Furthermore, the step 4 further includes: the inherent strain of unit i is ε i (d i )=(ε x (di ), ε y (d i ), 0, ε xy (d i ), 0, 0) T , each component is calculated by the following formula:

[0031]

[0032]

[0033]

[0034] in, represents the inherent strain component when the laser scans along the x-axis.

[0035] Furthermore, the overall structural stiffness interpolation model is:

[0036] E e =E min +φ e p (E0-E min )

[0037] Among them, E e is the elastic modulus of unit e obtained after interpolation; E min The minimum value is introduced to avoid singularity of the finite element solution matrix; p is the penalty coefficient.

[0038] Furthermore, the finite element simulation model of the layer-by-layer processing process of the overall structure is:

[0039] K i U i =F i , i=1,2,...,N

[0040] Where N is the total number of layers considered in the simulation of the additive manufacturing layer-by-layer processing process; K i is the stiffness matrix of the first i layers of the structure; U i is the thermal deformation vector caused by processing the i-th layer structure; F i is the inherent strain equivalent load vector when processing the i-th layer structure, which can be calculated by the following formula:

[0041]

[0042] Among them, A i is the i-th layer unit, Y e is the matrix that maps the element load vector of element e to the global load vector, B is the strain-displacement matrix, and D e is the elasticity matrix of unit e, ε eis the inherent strain of element e.

[0043] Furthermore, the maximum thermal deformation Q of the top structure in the additive manufacturing process is approximately solved by the following formula:

[0044]

[0045] Among them, the sum subscript i represents the i-th layer structure; S i is the set of nodes on the top surface of the i-th layer unit; u i，j is the thermal deformation of node j in the manufacturing direction when the i-th layer structure is processed; P is the parameter of the P-norm formula; τ i，j To determine whether the thermal deformation of node j needs to be constrained when the i-th layer structure is processed, the specific formula is:

[0046]

[0047] Among them, B i，j are all the units in the i-th layer with node j as the unit node;

[0048] The support structure volume fraction V is obtained by the following formula:

[0049]

[0050] Where |Ω2| is the number of units contained in Ω2;

[0051] The suspension angle constraint response G is calculated from the physical variable ρ.

[0052] Furthermore, the maximum thermal deformation Q of the top structure in the additive manufacturing process is related to the design variable μ e The sensitivity is:

[0053]

[0054] in It is obtained by the following formula:

[0055]

[0056] Among them, λ i is the adjoint vector, which can be obtained by the following formula:

[0057]

[0058] Among them, L i，j is a vector representing the position of a specific degree of freedom. The degree of freedom position corresponding to the manufacturing direction of node j on the top surface of layer i is 1, and the rest of the positions are 0;

[0059] The maximum thermal deformation Q of the top structure in the additive manufacturing process versus the design variable ve The sensitivity is:

[0060]

[0061] in It is obtained by the following formula:

[0062]

[0063] The maximum thermal deformation Q of the top structure in the additive manufacturing process versus the design variable d e The sensitivity is:

[0064]

[0065] Furthermore, the optimization model is as follows:

[0066]

[0067] stG≤0

[0068] Q≤Q *

[0069] K i U i =F i , i=1,2,...,N

[0070] 0≤μ e ≤1, e=1, 2, …, n

[0071] v min ≤v e ≤1, e=1, 2, ..., n

[0072] 0≤d e <π, e=1, 2, ..., n

[0073] Among them, v min is the minimum value of the volume fraction of the supporting structure unit cell; Q * It is the maximum thermal deformation allowed for the top structure during the manufacturing process.

[0074] Furthermore, step 11 also includes: setting the elements greater than 0.5 in the physical variable ρ to 1, and setting the elements less than 0.5 in the physical variable ρ to 0; calculating the variable φ based on the post-processed physical variable ρ; and establishing a support structure unit cell with a corresponding volume fraction at the unit according to the relative density corresponding to each unit in φ.

[0075] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0076] The laser scanning path and support structure designed in the present invention can ensure that the thermal deformation of the overall structure during the layer-by-layer processing of additive manufacturing is controllable, and avoid collision between the structure and the powder laying device due to excessive thermal deformation. Compared with the method of only optimizing the support structure without optimizing the laser path, the present invention can further reduce the amount of support structure used, thereby reducing manufacturing time and cost.

[0077] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 is a method flow chart of a preferred embodiment of the present invention;

[0079] Figure 2 It is a schematic diagram of the design domain of a preferred embodiment of the present invention;

[0080] Figure 3 This is a support structure optimization result based on unit relative density representation according to a preferred embodiment of the present invention;

[0081] Figure 4 This is the support structure optimization result based on "X-shaped" unit cell reconstruction of a preferred embodiment of the present invention;

[0082] Figure 5 This is the top structure laser scanning path optimization result of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0083] The following describes a preferred embodiment of the present invention with reference to the accompanying drawings to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0084] In the drawings, components with identical structures are denoted by the same reference numerals, and components with similar structures or functions are denoted by similar reference numerals. The size and thickness of each component shown in the drawings are arbitrary and are not limited by the present invention. For clarity, the thickness of components in some places in the drawings is appropriately exaggerated.

[0085] like Figure 1 FIG. 1 is a flow chart of a method according to a preferred embodiment of the present invention, comprising the following steps:

[0086] Step 1:

[0087] like Figure 2As shown in the figure, for a given cantilever beam structure, this method is used to carry out the coordinated optimization design of the laser path and support structure. The area surrounding the given main structure is discretized with cube elements with a side length of 2mm. The area where the main structure is located is defined as Ω1, and the remaining area is defined as Ω2. The design domain for laser path optimization is Ω1∪Ω2, and the design domain for support structure optimization is Ω2. The dimensional parameters of the given cantilever beam structure are: L1=28mm, L2=92mm, L3=20mm, L4=8mm, L5=12mm, and the Young's modulus E0 of the material is set to 70000MPa and the Poisson's ratio is set to 0.33.

[0088] Step 2:

[0089] Initialize the design variables μ=(μ1,μ2,...,μ n ), used to indirectly indicate the presence or absence of the structure; initialize the design variables v = (v1, ν2, ..., v n ), used to indirectly represent the relative density of the structure; initialize the design variables d = (d1, d2, ..., d n ) is used to indicate the laser scanning direction of each unit; n is the total number of units, and in this embodiment, n = (28 / 2) × (92 / 2) × (20 / 2) = 6440.

[0090] During the initialization process, if unit i belongs to the region Ω1 where the main structure is located, the component μ in μ is i 、The component v in v i It is initialized to 1 and remains unchanged throughout the optimization process.

[0091] Step 3:

[0092] Based on density filtering and projection function, the design variables μ and v are transformed into physical variables ρ = (ρ1, ρ2, ..., ρ n ), the physical variable φ directly represents the relative density of the unit = (φ1, φ2, ..., φ n ).

[0093] The density filtering formula is as follows:

[0094]

[0095]

[0096] Among them, M e ={i|||x i -X e ||≤r min} is the neighborhood of unit e with rmin as radius, X i With X e are the center coordinates of unit i and unit e, respectively, Hie =max{r min -||X i -X e ||, 0} is the weight coefficient.

[0097] The projection function formula is as follows:

[0098]

[0099] Where β is the steepness of the projection and η is the projection threshold.

[0100] The physical variable representing the relative density of a unit is obtained by the following formula:

[0101]

[0102] Step 4:

[0103] According to the design variables d=(d1, d2, ..., d n ), calculate the inherent strain of each unit ε=(ε1,ε2,...,ε n ); the inherent strain of element i is ε i (d i )=(ε x (d i ), ε y (d i ), 0, ε xy (d i ), 0, 0) T , each component is calculated by the following formula:

[0104]

[0105]

[0106]

[0107] in, represents the inherent strain component when the laser scans along the x-axis.

[0108] Step 5:

[0109] Based on the SIMP formula, the overall structural stiffness interpolation model is established:

[0110]

[0111] Among them, E e is the elastic modulus of unit e obtained after interpolation; E minIn order to avoid the minimum value introduced by the singularity of the finite element solution matrix, this example takes 10 -6 MPa; p is the penalty coefficient, which is 3 in this example.

[0112] Step 6:

[0113] Based on the inherent strain method, a finite element simulation model of the overall structure layer-by-layer processing process is established and solved to obtain the thermal deformation of the overall structure during the additive manufacturing process:

[0114] K i U i =F i , i=1,2,...,N

[0115] Where N is the total number of layers considered in the simulation of the additive manufacturing layer-by-layer processing process; K i is the stiffness matrix of the first i layers of the structure; U i is the thermal deformation vector caused by processing the i-th layer structure; F i is the inherent strain equivalent load vector when processing the i-th layer structure, which can be calculated by the following formula:

[0116]

[0117] Among them, A i is the i-th layer unit, Y e is the matrix that maps the element load vector of element e to the global load vector, B is the strain-displacement matrix, and D e is the elasticity matrix of unit e, ε e is the inherent strain of element e.

[0118] Step 7:

[0119] Calculate the maximum thermal deformation Q of the top structure, the volume fraction V of the support structure, and the suspension angle constraint response G during the additive manufacturing process.

[0120] The maximum thermal deformation Q of the top structure during the additive manufacturing process is approximately solved by the following formula:

[0121]

[0122] Where, the sum subscript i represents the i-th layer structure; Si is the set of nodes on the top surface of the i-th layer unit; u i，j is the thermal deformation of node j in the manufacturing direction when the i-th layer structure is processed; P is the parameter of the P-norm formula, which is 8 in this example; τ i，j To determine whether the thermal deformation of node j needs to be constrained when the i-th layer structure is processed, the specific formula is:

[0123]

[0124] Among them, B i，j are all the units in the i-th layer with node j as the unit node.

[0125] The volume fraction V of the support structure is obtained by the following formula:

[0126]

[0127] Where |Ω2| is the number of units contained in Ω2;

[0128] In this embodiment, the suspension angle constraint is established using additive manufacturing filtering and the physical variable ρ. The specific formula is as follows:

[0129]

[0130] Where I is a unit vector; is the physical variable ρ after additive manufacturing filtering; ε r is the permissible error value, which is 0.05 in this embodiment.

[0131] Step 8:

[0132] Calculate the sensitivity of each design response to the design variables.

[0133] The maximum thermal deformation Q of the top structure in the additive manufacturing process depends on the design variable μ e The sensitivity is:

[0134]

[0135] in It is obtained by the following formula:

[0136]

[0137] Among them, λ i is the adjoint vector, which can be obtained by the following formula:

[0138]

[0139] Among them, L i，j is a vector representing the position of a specific degree of freedom. The degree of freedom position corresponding to the manufacturing direction of node j on the top surface of the i-th layer is 1, and the other positions are 0.

[0140] The maximum thermal deformation Q of the top structure in the additive manufacturing process versus the design variable v e The sensitivity is:

[0141]

[0142] in It is obtained by the following formula:

[0143]

[0144] The maximum thermal deformation Q of the top structure during additive manufacturing is related to the design variable d e The sensitivity is:

[0145]

[0146] Step 9:

[0147] An optimization model is established and solved based on the moving asymptote algorithm to update the design variables μ, ν, and d.

[0148] The optimization model is as follows:

[0149]

[0150] stG≤0

[0151] Q≤Q *

[0152] K i U i =F i , i=1,2,...,N

[0153] 0≤μ e ≤1, e=1, 2, …, n

[0154] v min ≤ν e ≤1, e=1, 2, …, n

[0155] 0≤d e <π, e=1, 2, ..., n

[0156] Among them, v min is the minimum value of the volume fraction of the supporting structure unit cell, which is 0.18 in this example; Q * The maximum thermal deformation allowed for the top structure during the manufacturing process is 0.03 mm in this example.

[0157] Step 10:

[0158] Determine whether the iteration has converged; if all constraints are satisfied and the relative change of the objective function is less than 1% for 10 consecutive steps, go to step 11; otherwise, go to step 3.

[0159] Step 11:

[0160] The elements with values ​​greater than 0.5 in ρ are set to 1, and the elements with values ​​less than 0.5 in ρ are set to 0. Based on the post-processed ρ, the physical variable φ representing the relative density of each unit is calculated. The support structure optimization results represented by the relative density of the unit in this embodiment are as follows: Figure 3As shown. According to the relative density of each unit in φ, a support structure unit cell with a corresponding volume fraction is established at the unit. The support structure optimization result of this embodiment based on the reconstruction of the "X-shaped" unit cell is shown as follows: Figure 4 shown.

[0161] According to the optimization result of the design variable d, the laser scanning path for processing each layer structure is generated. The laser scanning path of the top layer structure in this embodiment is as follows: Figure 5 shown.

[0162] The preferred embodiments of the present invention have been described in detail above. It should be understood that numerous modifications and variations based on the concepts of the present invention are possible without inventive effort by those skilled in the art. Therefore, any technical solution that can be derived by one skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing, characterized in that: The method comprises the following steps: Step 1: Discretize the area surrounding the given main structure with cube units; define the area where the main structure is located as Ω1 and the rest of the area as Ω2; the design domain for laser path optimization is Ω1∪Ω2, and the design domain for support structure optimization is Ω2; Step 2: Initialize the design variables μ=(μ1,μ2,...,μ n ), used to indirectly indicate the presence or absence of the structure; initialize the design variables ν=(ν1,ν2,...,ν n ), used to indirectly represent the relative density of the structure; initialize the design variables d=(d1,d2,...,d n ), used to indicate the laser scanning direction of each unit; where n is the total number of units; Step 3: Based on density filtering and projection function, the design variable μ is converted into a physical variable ρ = (ρ1, ρ2, ..., ρ n ), converting the design variable ν into a physical variable that directly represents the relative density of the unit Step 4: According to the design variables d = (d1, d2, ..., d n ), calculate the inherent strain of each unit ε=(ε1,ε2,...,ε n ); Step 5: Based on the SIMP formula, establish the overall structural stiffness interpolation model; Step 6: Based on the inherent strain method, a finite element simulation model of the layer-by-layer processing of the overall structure is established and solved to obtain the thermal deformation of the overall structure during the additive manufacturing process; Step 7: Calculate the design response, including the maximum thermal deformation Q of the top structure during the additive manufacturing process, the volume fraction V of the support structure, and the suspension angle constraint response G. Step 8: Calculate the sensitivity of each design response to each design variable; Step 9: Establish an optimization model and solve it based on the moving asymptote algorithm to update the design variables μ, ν, and d; Step 10, determine whether the iteration has converged; if all constraints are satisfied and the relative change of the objective function for 10 consecutive steps is less than 1%, go to step 11, otherwise go to step 3; Step 11: Post-process the support structure optimization results; generate the laser scanning path for processing each layer structure based on the optimization results of the design variable d.

2. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 1, characterized in that: The step 2 also includes: during the initialization process, if the unit i belongs to the region Ω1 where the main structure is located, then the component μ in μ is i , the component ν in ν i It is initialized to 1 and remains unchanged throughout the optimization process.

3. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 1, characterized in that: In step 3, the density filtering formula is as follows: Where M e ={i|||X i -X e ||≤r min } is a unit e with r min is the radius of the neighborhood, X i With X e are the center coordinates of unit i and unit e, respectively, H ie =max{r min -||X i -X e ||,0} is the weight coefficient; The projection function formula is as follows: Where β is the steepness of the projection, and η is the projection threshold; The physical variable representing the relative density of a unit is obtained by the following formula: 。 4. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 3, characterized in that: The step 4 also includes: the inherent strain of unit i is ε i (d i )=(ε x (d i ),ε y (d i ),0,ε xy (d i ),0,0) T , each component is calculated by the following formula: in, represents the inherent strain component when the laser scans along the x-axis.

5. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 4, characterized in that: The overall structural stiffness interpolation model is: Among them, E e is the elastic modulus of unit e obtained after interpolation; E min The minimum value is introduced to avoid singularity of the finite element solution matrix; p is the penalty coefficient.

6. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 5, characterized in that: The finite element simulation model of the overall structure layer-by-layer processing process is: K i U i =F i ,i=1,2,...,N Where N is the total number of layers considered in the simulation of the additive manufacturing layer-by-layer processing process; K i is the stiffness matrix of the first i layers of the structure; U i is the thermal deformation vector caused by processing the i-th layer structure; F i is the inherent strain equivalent load vector when processing the i-th layer structure, which can be calculated by the following formula: Among them, A i is the i-th layer unit, Y e is the matrix that maps the element load vector of element e to the global load vector, B is the strain-displacement matrix, and D e is the elasticity matrix of unit e, ε e is the inherent strain of element e.

7. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 6, characterized in that: The maximum thermal deformation Q of the top structure in the additive manufacturing process is approximately solved by the following formula: Among them, the sum subscript i represents the i-th layer structure; S i is the set of nodes on the top surface of the i-th layer unit; u i,j is the thermal deformation of node j in the manufacturing direction when the i-th layer structure is processed; P is the parameter of the P-norm formula; To determine whether the thermal deformation of node j needs to be constrained when the i-th layer structure is processed, the specific formula is: Among them, B i,j are all the units in the i-th layer with node j as the unit node; The support structure volume fraction V is obtained by the following formula: Where |Ω2| is the number of units contained in Ω2; The suspension angle constraint response G is calculated from the physical variable ρ.

8. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 7, characterized in that: The maximum thermal deformation Q of the top structure in the additive manufacturing process depends on the design variable μ e The sensitivity is: in It is obtained by the following formula: Among them, λ i is the adjoint vector, which can be obtained by the following formula: Among them, L i,j is a vector representing the position of a specific degree of freedom. The degree of freedom position corresponding to the manufacturing direction of node j on the top surface of layer i is 1, and the rest of the positions are 0; The maximum thermal deformation Q of the top structure in the additive manufacturing process versus the design variable ν e The sensitivity is: in It is obtained by the following formula: The maximum thermal deformation Q of the top structure in the additive manufacturing process versus the design variable d e The sensitivity is: 。 9. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 8, characterized in that: The optimization model is as follows: stG≤0 Q≤Q * K i U i =F i ,i=1,2,...,N 0≤μ e ≤1,e=1,2,...,n n min ≤n e ≤1,e=1,2,...,n 0≤d e <π,e=1,2,...,n Among them, ν min is the minimum value of the volume fraction of the supporting structure unit cell; Q * It is the maximum thermal deformation allowed for the top structure during the manufacturing process.

10. The laser path and support structure optimization design method for controlling thermal deformation in additive manufacturing according to claim 9, characterized in that: The step 11 further includes: setting the elements of the physical variable ρ that are greater than 0.5 to 1, and setting the elements of the physical variable ρ that are not greater than 0.5 to 0; calculating the variable based on the post-processed physical variable ρ. ;according to The relative density corresponding to each unit in the is used to establish a support structure unit cell with a corresponding volume fraction at the unit.

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