A two-stage optimized design and manufacturing method for multi-axis 3D printing

Abstract

The present invention relates to a two-stage optimization design and manufacturing method for multi-axis 3D printing, which includes the steps of using topology optimization without overhang constraints to obtain an optimized structure, then dividing the printing sub-area and calculating the local optimal printing direction for the divided different printing sub-areas, taking the local optimal printing direction as the overhang angle constraint of the cell, and adding a constraint term of the cell density in the horizontal neighborhood of the cell to avoid the overhang feature of the optimization process, and using integrated topology optimization to perform integrated topology optimization including angle constraints, and simultaneously perform sensitivity analysis, and perform multi-axis 3D printing manufacturing of a freestanding structure. The beneficial effects of the present invention are to use the step-by-step promotion mode of two-stage optimization design, to solve the problems of dividing the printing sub-area of ​​the design area, the local optimal printing direction and invalid boundary cell processing, to consider the overhang constraint, to take the local optimal printing direction as the printing direction of each cell of the sub-area, and to suppress the non-printable cells to obtain a freestanding structure.

Description

[Technical field]

[0001] The present invention belongs to the technical fields of structural engineering and additive manufacturing, and in particular relates to a two-step optimization design and manufacturing method for multi-axis 3D printing, where multi-axis means that the total number of 3D printing rotation axes, including the rotation axes of the printer head and the rotation axes of the displacement device, is greater than three axes. [Background technology]

[0002] As modern engineering structures become more complex and personalized, the need for 3D printing of complex structural components is constantly increasing, but it is often difficult to achieve using traditional structural design methods. Topology optimization provides an effective solution for this.

[0003] Multi-axis 3D printing technology has been widely used in aerospace, vehicle engineering and other fields. Since the multi-axis 3D printer has a freely rotating base, it can dynamically adjust the printing direction during the printing process to avoid the overhanging effect of the structure during the printing process, effectively solving the problem of the increased volume and significantly reduced performance of the free-standing structure for three-axis 3D printing. Therefore, the rational and effective combination of multi-axis 3D printing manufacturing and the optimization design of the free-standing structure is a key factor for the integrated optimization design and manufacturing of complex structures.

[0004] In the design of a freestanding structure based on multi-axis 3D printing, three main problems need to be solved: (1) how to divide the design domain into different printing regions, (2) how to obtain the optimal printing direction for each sub-region, and (3) how to handle the unprintable cells after changing the printing direction for each sub-region.

[0005] In summary, it is very necessary to study the optimized design and manufacturing methods of multi-axis 3D printing, and realize the optimal structural configuration design and integrated manufacturing of multi-axis 3D printing at any tilt angle. Summary of the Invention [Problem to be solved by the invention]

[0006] The present invention aims to overcome the shortcomings of the prior art and provide a two-stage optimized design and manufacturing method for multi-axis 3D printing. [Means for solving the problem]

[0007] A two-step optimized design and manufacturing method for such multi-axis 3D printing is as follows: S1, first stage design: First, obtain the optimal structure using topology optimization without overhang constraints, then divide the printing sub-area, calculate the local optimal printing direction for different divided printing sub-areas, and check whether the unprintable ratio exceeds the threshold σ r If it is less than the threshold σ, the optimization is terminated. r If so, proceed to step S2. S2, the second stage design: considering the overhang constraint, the locally optimal printing direction is taken as the overhang angle constraint of the cell, and the constraint term of the cell density in the horizontal neighborhood of the cell is added to avoid the overhang feature of the optimization process, and the integrated topology optimization including the angle constraint is performed using the integrated topology optimization, and at the same time, the sensitivity analysis is performed to suppress the non-printable cells and obtain the free-standing structure; S3. Multi-axis 3D printing manufacturing: This includes the steps of extracting and optimizing structural information, establishing a 3D solid model, dividing and slicing to generate printing paths, and performing multi-axis 3D printing manufacturing of the free-standing structure.

[0008] Preferably, in step S1, the method for topology optimization without overhang constraints specifically uses a density-based SIMP model to consider the free form and to calculate the density ρ = ρ1, ρ2, . . . ρ of each cell in the design domain involved in the topology optimization. nele With these as design variables, the structural topology optimization formula is:

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[0009] Preferably, in step S1, the printing sub-region is divided by performing grid discretization on the entire design domain or by using a manual division method, which specifically uses a Harris or SUSAN corner detection algorithm to obtain structural corner points of a simple structure and divide the corner points as vertices of the sub-region, and the obtained rectangular sub-region is the printing sub-region.

[0010] Preferably, in step S1, the optimal printing direction of each printing sub-area is determined by the slant direction of the border cells of the printing sub-area, the border cells being cells with empty cells in adjacent sets, and the criterion for the border cells is:

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[0011] Preferably, the cells adjacent to the base are set as invalid boundary cells, and are also the first layer of the design domain. When a cell that is not printable in the vertical printing direction appears in the i-th layer, the cells in the i-th layer and below are considered as invalid boundary cells, and the cells that satisfy the following formula are also considered as invalid boundary cells:

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[0012] Preferably, in step S2, the degree to which the cell violates the overhang angle constraint is calculated, and the formula for the degree to which the cell violates the overhang angle constraint is:

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[0013] Preferably, in step S2, the formula for considering the structural topology optimization under the linear angle constraint of the cells in each printing sub-region is:

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[0014] Preferably, in step S2, the sensitivity of the objective function to the design variables is solved according to the chain rule, and a stability problem of the optimal solution is solved; For the objective function:

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[0015] Preferably, step S3 specifically includes performing 3D modeling using Rhino software, slicing the solid model obtained by the 3D modeling using Cura software to generate a printing path, and performing multi-axis 3D printing manufacturing. Effect of the Invention

[0016] The present invention obtains the following technical advantages over the prior art: (1) The present invention provides a two-stage optimization design and manufacturing method for multi-axis 3D printing, in which a step-by-step promotion mode of two-stage optimization design is used. In the first stage design, the problems of dividing the printing sub-area of ​​the design area, the locally optimal printing direction and the invalid boundary cell processing are solved. In the second stage design, the overhang constraint is taken into account, and the locally optimal printing direction is the printing direction of each cell in the sub-area, and the unified topology optimization is used to suppress the non-printable cells to obtain a free-standing structure. (2) The two-stage optimization design and manufacturing method for multi-axis 3D printing provided by the present invention combines two-stage optimization design and multi-axis 3D printing manufacturing. Based on the first stage design, an optimal configuration without overhang constraints is obtained, and through corner detection, cell inclination angle, and preprocessing, the division of printing sub-areas, local optimal printing direction, and printing of invalid boundary cells are realized. Based on the second stage design, an integrated optimization design with overhang angle constraints is obtained, and through multi-axis divided 3D printing of the printing head and base rotation axis, the optimal configuration printing of the free-standing structure at any inclination angle is realized. Through division slicing of the 3D solid model and generation of the printing path, the integrated design and manufacturing of multi-axis 3D printing of the optimal configuration of the complex free-standing structure is realized. (3) Based on multi-axis divided 3D printing taking into account the printing head and base rotation axis, the present invention dynamically adjusts the printing direction during the printing process to avoid the overhanging effect of the structure during the printing process, realizes the optimal configuration printing of the free-standing structure at any tilt angle, and realizes the overall optimization design and printing of the under-printed area through the integrated optimization of the angle constraints, effectively solving the problem of volume increase and significant performance degradation when 3D printing the free-standing structure. [Brief description of the drawings]

[0017] [Figure 1] 1 is a specific flowchart of a two-stage optimization design and manufacturing method for multi-axis 3D printing of the present invention. [Figure 2a] FIG. 1 is a schematic diagram of a grid discretization of a rectangular design domain. [Figure 2b] FIG. 1 is a schematic diagram of dividing a rectangular design domain into subdomains by grid discretization. [Figure 3a] FIG. 1 is a schematic diagram of structural corner detection. [Figure 3b] FIG. 1 is a schematic diagram of manually dividing a design domain into subdomains. [Figure 4a] FIG. 2 is a schematic diagram of a cell neighborhood mode. [Figure 4b] FIG. 13 is a schematic diagram of a boundary extension design space for an additional cell. [Diagram 5] FIG. 2 is a schematic diagram of the building direction of the sub-areas. [Figure 6a]FIG. 13 is a schematic diagram of a neighborhood mode of a boundary cell. [Figure 6b] FIG. 13 is a schematic diagram of a neighborhood mode of non-boundary cells. [Figure 7] FIG. 2 is a schematic diagram of a collision occurrence in a printing process. [Figure 8] FIG. 13 is a schematic diagram of locally optimal print directions for adjacent sub-regions. [Figure 9] FIG. 13 is a schematic diagram of a void boundary cell adjacent to a base. [Figure 10] FIG. 13 is a schematic diagram of the process of scanning layer-by-layer to non-printable cells. [Figure 11a] FIG. 13 is a schematic diagram of a printable cell when the base is rotated 0 degrees. [Figure 11b] FIG. 13 is a schematic diagram of a printable cell when the base is rotated. [Figure 11c] FIG. 13 is a schematic diagram of printable cells when the base is rotated. [Figure 12] FIG. 2 is a schematic diagram of the printable areas of different cells. [Figure 13a] FIG. 1 is a schematic diagram of the cantilever beam design domain. [Figure 13b] FIG. 13 is a schematic diagram of the results of the optimal topology configuration of the cantilever beam. [Figure 13c] FIG. 13 is a schematic diagram of the sub-domain division of the cantilever design domain. [Figure 13d] FIG. 13 is a schematic diagram of a cantilever printing curve. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] The present invention will be further described below with reference to examples. The following examples are only for the purpose of helping the reader understand the present invention. However, those skilled in the art can make some improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications are also included in the scope of the present invention.

[0019] Example 1 As an example, as shown in FIG. 1, a two-stage optimization design and manufacturing method for multi-axis 3D printing includes the following steps S1 to S3. S1, first stage design: obtain the optimized structure using topology optimization without overhang constraints, and then obtain a printing scheme including partitioning of printing subregions and local optimal printing directions, so that the unprintable ratio (the ratio of unprintable boundary cells to all boundary cells) is greater than the threshold σ r If it is less than , the optimization is terminated and conversely, the process proceeds to the second stage design in step S2. S1.1, Topology optimization without overhang constraints: Using density-based SIMP model as topology optimization method, we consider free form and set density ρ = ρ1, ρ2, ρ for each cell in the design domain. nele With these as design variables, the structural topology optimization formula is:

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[0020] Example 2 As another example, according to the two-stage optimization design and manufacturing method for multi-axis 3D printing provided in Example 1, this example provides a test example of two-stage optimization design and manufacturing for multi-axis 3D printing of a cantilever model to verify the effectiveness of the method of the present invention.

[0021] As shown in Figure 13a, the design domain is a cantilever model, the length of the beam in this model is 120, the height is 60, the material modulus is 1.0, the volume ratio constraint is 0.3, and the penalty coefficient is 3. As shown in Figure 13b, the left end is the fixed end, and the load is applied to the midpoint of the right boundary of the beam, and the optimal topology configuration is obtained after topology optimization, and the final objective function value after optimization is 121.03. The printing sub-domain division of the cantilever beam and the printing curve of the cantilever beam are shown in Figure 13c and Figure 13d, respectively.

[0022] In this embodiment, after considering multi-axis topology optimization, all cells of the structure can be fully printed without the need for integrated topology optimization. During complex structure design and 3D printing, the problem of having to add supports during the printing process due to the overhang effect caused by gravity, resulting in additional material consumption and the need to remove supports, etc. are solved, and the integrated design and manufacturing of multi-axis 3D printing of the optimal configuration of the free-standing structure is realized.

[0023] During the printing process, the printing direction is dynamically adjusted to avoid the occurrence of overhang effect in the structure printing process, and the integrated optimization of angle constraints is used to realize the overall optimization design and printing of printing areas with insufficient sub-areas, effectively solving the problems of volume increase and significant performance degradation when three-axis 3D printing free-standing structures.

Claims

1. S1, first stage design: first obtain the optimized structure using topology optimization without overhang constraint, then divide the printing sub-area, calculate the local optimal printing direction for different divided printing sub-areas, and check whether the unprintable ratio is within the threshold σ ｒ If it is less than the threshold σ, the optimization is terminated. ｒ If so, proceed to step S2. S2, the second stage design: considering the overhang constraint, the locally optimal printing direction is taken as the overhang angle constraint of the cell, and a constraint term of the cell density in the horizontal neighborhood of the cell is added to avoid the overhang feature of the optimization process, and the integrated topology optimization including the angle constraint is performed using the integrated topology optimization, and at the same time, a sensitivity analysis is performed to suppress the non-printable cells and obtain a free-standing structure; S3. Multi-axis 3D printing manufacturing: A two-stage optimization design and manufacturing method for multi-axis 3D printing, comprising the steps of extracting and optimizing structural information, establishing a 3D solid model, dividing and slicing to generate a printing path, and performing multi-axis 3D printing manufacturing of a free-standing structure.

2. In step S1, the method of topology optimization without overhang constraints specifically uses a density-based SIMP model to consider the free form and calculate the density ρ = ρ of each cell in the design domain involved in the topology optimization. 1 , ρ 2 , ...ρ nele With these as design variables, the structural topology optimization formula is: [0010] and where U is the total displacement vector, F is the total nodal load vector, K is the total stiffness matrix, the objective function C(ρ) is the total strain energy under the action of the external force, and v ｉ The two-stage optimization design and manufacturing method for multi-axis 3D printing according to claim 1, characterized in that, i is the volume of the i-th cell, f is the spatial fraction, and the value of density ρ of each cell in the design space involved in the topology optimization is between 0 and 1.

3. The two-stage optimization design and manufacturing method for multi-axis 3D printing of claim 1, characterized in that in step S1, the printing sub-region is divided by performing grid discretization on the entire design domain or by using a manual division method, in which the manual division method specifically uses a Harris or SUSAN corner detection algorithm to obtain structural corner points of a simple structure, and then divides the corner points as vertices of the sub-region, and the obtained rectangular sub-region is the printing sub-region.

4. In step S1, the optimal printing direction of each printing sub-area is determined by the slant direction of the border cells of the printing sub-area, the border cells are cells with empty cells in adjacent sets, and the criterion for the border cells is: [0025] and During the ceremony, 【number】 The value is used to characterize whether a cell is a border cell or not. If a cell is a border cell, 【number】 The value is 1 if a cell is an interior cell. 【number】 The value is 0, Using a convolution kernel to obtain the cell density gradient direction, converting it to obtain the gradient direction of the boundary cells, and determining a local optimal printing direction for each printing sub-region by considering the printability of the boundary cells in each printing sub-region; A convolution kernel is used to obtain the cell density gradient direction, which is expressed as: [0030] and During the ceremony, 【number】 is the coordinate position of the cell, and the edge-added cells are introduced at the edge of the design domain, the density of the edge-added cells in the design domain adjacent to the base is set to 1, and the density of the edge-added cells in the other design domains is set to 0; The cell density gradient direction is converted into the slope direction of the structure boundary, and the slope direction of the structure boundary is the angle between the structure boundary and the x-axis. The slope direction of the structure boundary is perpendicular to the cell density gradient direction. For the cell density gradient directions of different quadrants, the corresponding slope directions of the structure boundary are [0045] and where φ is the tilt direction of the structure boundary between 0 and π, and φ ｇ The two-stage optimization design and manufacturing method for multi-axis 3D printing of claim 1, characterized in that x is a cell density gradient vector.

5. All cells adjacent to the base are set as invalid boundary cells, and are also the first layer of the design space. If a cell that is not printable in the vertical print direction appears in the i-th layer, all cells in the i-th layer and below are considered as invalid boundary cells, and cells that satisfy the following formula are also considered as invalid boundary cells: [0050] During the ceremony, 【number】 is the allowable rotation angle of the base, and φ allow = 90°, θ is the maximum overhang angle, 【number】 is the coordinate position of the cell, 【number】 The value is used to characterize whether a cell is a border cell or not. If a cell is a border cell, 【number】 The value is 1 if a cell is an interior cell. 【number】 The value is 0, The two-stage optimization design and manufacturing method for multi-axis 3D printing of claim 4, wherein the printing directions of the invalid boundary cells are all adjusted to be vertical after linear optimization.

6. In step 2, the degree to which the cell violates the overhang angle constraint is calculated, and the formula for the degree to which the cell violates the overhang angle constraint is: [006] and In the formula, t ｉ where the value characterizes the degree to which the overhang angle constraint is violated, cos θ is the cosine value of the critical overhang angle of the structure, 【number】 is the cell boundary normal vector, and t ｉ is less than or equal to a tolerance δ, the cell satisfies the overhang angle constraint, with the range of values ​​of δ being 0<δ≦0.001; The inclination direction φ of the structure boundary of each sub-region obtained by the formula (4) ｉ Calculate the local optimal printing direction for each printing sub-region, taking into account the overhang angle of the boundary cells and the avoidance of printing collisions in adjacent regions as constraints according to [0070] where φ is the local optimal print direction vector of the print subregion, O represents the degree vector that the structural cell violates the overhang angle constraint, V is 1 for valid boundary cells and 0 for other boundary cells, and M is a 0-1 mapping matrix; 【number】 is the inclination vector of the structural cell, and φ first and φ next is defined as the printing direction of two adjacent sub-regions, and φ t,max is the maximum allowable deflection angle, and the inclination vector of the structural cell 【number】 If is within the printable range, the value of O is 2φ max Conversely, the value of O is 2φ max Bigger, The objective function is [0080] It is rewritten as: where P is the weight of the penalty function, which is set to 0.01, and the formula for Q is: [0097] and In the formula, φ ｖ 5. The two-stage optimization design and manufacturing method for multi-axis 3D printing of claim 4, wherein x is the angle between the vertical and the x-axis.

7. In step 2, the equation considering the structural topology optimization under the linear angle constraint of the cells in each printing sub-region is: [0010] and During the ceremony, 【number】 is a constraint on the cell density in the horizontal neighborhood of a cell, and γ ｉ is the parameter value of the overhang feature of the structure boundary cell after topology optimization; 【number】 is the linear angle constraint of the local optimal print direction of the subregion, and λ ｉ (φ ｉ ) is a parameter characterizing the local optimal printing direction of the cell and is determined by the overhang angle of the cell, U is the global displacement vector, F is the global nodal load vector, K is the total stiffness matrix, the objective function C(ρ) is the total strain energy under the action of the external force, v ｉ The two-stage optimization design and manufacturing method for multi-axis 3D printing of claim 6, wherein i is the volume of the i-th cell, f is the space fraction, ρ is the density of each cell, and the value of ρ ranges from 0 to 1.

8. In step 2, solve the sensitivity of the objective function to the design variables according to the chain rule, and solve the stability problem of the optimal solution; For the objective function: ##EQU00011## For overhang angle constraints: ##EQU00012## For hanging feature constraints: ##EQU00013## where f is the spatial ratio, h(x) is a sigmoid function, and t ｉ The value characterizes the degree to which the overhang angle constraint is violated, and t ｉｌ and t ｉｒ represent the degree to which the left and right boundaries violate the overhang angle constraint, respectively, and τ ｉｌ and τ ｉｒ represent the degree to which the left and right boundaries respectively violate the hanging feature constraints, and u ｋ is the k-th cell displacement vector, ０ is the stiffness matrix of the initial cell, and E ０ is the Young's modulus of the material, and E min is a parameter close to 0, p is a penalty coefficient, p=3, and v ｉ The two-phase optimization design and manufacturing method for multi-axis 3D printing of claim 6, wherein i is the volume of the i-th cell, ρ is the density of each cell, and ρ values ​​range from 0 to 1.

9. The two-stage optimization design and manufacturing method for multi-axis 3D printing as described in claim 1, characterized in that step S3 specifically includes performing 3D modeling by Rhino software, slicing the solid model obtained by the 3D modeling by Cura software to generate a printing path, and performing multi-axis 3D printing manufacturing.

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