Two-stage optimization 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] This invention relates to the fields of structural engineering and additive manufacturing, and more particularly to a two-stage optimized design and manufacturing method for multi-axis 3D printing. Multi-axis means that the total number of 3D printing rotation axes, including the rotation axis of the printer head and the rotation axis of the displacement device, is greater than three. [Background technology]

[0002] With the increasing complexity and individualization of modern engineering structures, the need for 3D printing of complex structural members is constantly growing. This is often difficult to achieve with conventional structural design methods, and topology optimization provides an effective solution for this purpose.

[0003] Multi-axis 3D printing technology is widely used in fields such as aerospace and vehicle engineering. Because multi-axis 3D printers have a freely rotating base, they can dynamically adjust the printing direction during the printing process, avoiding structural overhang effects and effectively solving the problems of increased volume and significant performance degradation associated with self-supporting structures in 3-axis 3D printing. Therefore, rationally and effectively combining multi-axis 3D printing manufacturing with the optimized design of self-supporting structures is a crucial factor for the integrated optimized design and manufacturing of complex structures.

[0004] Designing self-supporting structures based on multi-axis 3D printing requires solving the following three main problems: (1) How to divide the design area into different printing areas. (2) How to obtain the optimal printing direction for each sub-area. (3) How to handle unprintable cells after changing the printing direction of each sub-area.

[0005] In summary, it is essential to research the optimized design and manufacturing methods for multi-axis 3D printing, and to achieve optimal structural design and integrated manufacturing of multi-axis 3D printed objects at arbitrary tilt angles. [Overview of the Initiative] [Problems that the invention aims to solve]

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

Means for Solving the Problems

[0007] Such a two-stage optimization design and manufacturing method for multi-axis 3D printing is as follows: S1. First-stage design: First, obtain an optimal structure using topology optimization without overhang constraints. Then, divide the printing sub-region, calculate the local optimal printing direction for different divided printing sub-regions, and if the non-printable ratio is less than the threshold value σ r If it is less, end the optimization. If the non-printable ratio is greater than or equal to the threshold value σ r If it is greater than or equal, proceed to step S2. S2. Second-stage design: Considering the overhang constraint, set the local optimal printing direction as the overhang angle constraint of the cell, and add a constraint term for the cell density in the horizontal neighborhood of the cell to avoid the overhang characteristics of the optimization process. Perform integrated topology optimization including angle constraints using integrated topology optimization, and at the same time perform sensitivity analysis to suppress non-printable cells and obtain a self-supporting structure. S3. Multi-axis 3D printing manufacturing: It includes steps of extracting and optimizing structure information, establishing a 3D solid model, dividing and slicing to generate a printing path, and performing multi-axis 3D printing manufacturing of a self-supporting structure.

[0008] Preferably, in step S1, the method of topology optimization without overhang constraints specifically uses a density-based SIMP model, considering free form, and taking the density ρ = ρ1, ρ2, ··· ρ of each cell in the design region involved in topology optimization as design variables. The formula for structural topology optimization is nele Taking the density ρ = ρ1, ρ2, ··· ρ of each cell in the design region involved in topology optimization as design variables, the formula for structural topology optimization is

Equation

[0009] Preferably, in step S1, the entire design area is discretized into a grid or a manual division method is used to divide the print sub-areas. Specifically, the manual division method uses the Harris or SUSAN corner detection algorithm to obtain structural corner points of a simple structure, divides the sub-areas using the corner points as vertices, and the resulting rectangular sub-areas are the print sub-areas.

[0010] Preferably, in step S1, the optimal printing direction for each printing sub-region is determined by the inclination direction of the boundary cell of the printing sub-region, where a boundary cell is a cell that has an empty cell in an adjacent set, and the determination formula for boundary cells is:

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[0011] Preferably, cells adjacent to the base are set as invalid boundary cells, and are also the first layer of the design area. If a cell that cannot be printed in the vertical printing direction appears in the i-th layer, then cells in the i-th layer and below are considered invalid boundary cells, and cells that satisfy the following equation are also considered 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 equation that considers the structural topology optimization of cells within each printed sub-region under linear angular constraints 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 the stability problem of the optimal solution is solved. In the case of the objective function:

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[0015] Preferably, step S3 specifically involves performing 3D modeling using Rhino software, slicing the solid model obtained from the 3D modeling using Cura software to generate print paths, and performing multi-axis 3D printing. [Effects of the Invention]

[0016] The present invention achieves 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, employing a stepwise mode of two-stage optimization design. In the first stage of design, the problems of dividing the design area into print sub-regions, local optimal printing direction, and invalid boundary cell processing are solved. In the second stage of design, overhang constraints are taken into consideration, the local optimal printing direction is set as the printing direction for each cell in the sub-region, and unprintable cells are suppressed using integrated topology optimization to obtain an autonomous 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, and based on the first stage design, an optimal configuration without overhang constraints is obtained, and through corner detection, cell tilt angle, and preprocessing, division of printing sub-regions, locally optimal printing direction, and printing of invalid boundary cells are realized, and based on the second stage design, an integrated optimization design with overhang angle constraints is obtained, and through multi-axis segmented 3D printing of the print head and base rotation axis, optimal configuration printing of self-supporting structures at any tilt angle is realized, and through segmented slicing of the 3D solid model and generation of printing paths, integrated design and manufacturing of multi-axis 3D printing with an optimal configuration of complex self-supporting structures is realized. (3) Based on multi-axis segmented 3D printing that takes into account the print head and base rotation axis, the present invention dynamically adjusts the printing direction during the printing process to avoid the overhang effect of the structure during the printing process, realizes optimal configuration printing of self-supporting structures at any tilt angle, and achieves overall optimized design and printing of underprinted areas by integrally optimizing the angle constraints, thereby effectively solving the problems of increased volume and significant performance degradation when 3D printing self-supporting structures. [Brief explanation of the drawing]

[0017] [Figure 1] This is a specific flowchart of the two-stage optimization design and manufacturing method for multi-axis 3D printing according to the present invention. [Figure 2a] This is a schematic diagram of grid discretization of a rectangular design area. [Figure 2b] This is a schematic diagram showing how a rectangular design area is divided into sub-areas by grid discretization. [Figure 3a] This is a schematic diagram of structural corner detection. [Figure 3b] This is a schematic diagram showing how to manually divide the design domain into subdomains. [Figure 4a] This is a schematic diagram of the cell's neighbor mode. [Figure 4b] This is a schematic diagram of the design region for the boundary extension of the additional cell. [Figure 5] This is a schematic diagram of the building direction for the sub-area. [Figure 6a]This is a schematic diagram of the neighborhood modes of boundary cells. [Figure 6b] This is a schematic diagram of the neighborhood mode for non-boundary cells. [Figure 7] This is a schematic diagram illustrating collision occurrences in the printing process. [Figure 8] This is a schematic diagram of the locally optimal printing direction for adjacent sub-regions. [Figure 9] This is a schematic diagram of an invalid boundary cell adjacent to the base. [Figure 10] This is a schematic diagram of the process of scanning each layer, including cells that cannot be printed. [Figure 11a] This is a schematic diagram of the printable cells when the base is rotated 0 degrees. [Figure 11b] This is a schematic diagram of the printable cells when the base is rotated. [Figure 11c] This is a schematic diagram of the printable cells when the base is rotated. [Figure 12] This is a schematic diagram of the printable areas of different cells. [Figure 13a] This is a schematic diagram of the design area for a cantilever beam. [Figure 13b] This is a schematic diagram showing the result of the optimal topology configuration for a cantilever beam. [Figure 13c] This is a schematic diagram of the sub-domain division of the design area for a cantilever beam. [Figure 13d] This is a schematic diagram of the printed curve of a cantilever beam. [Modes for carrying out the invention]

[0018] The present invention will be further described below with reference to examples. The following description of examples is for the purpose of aiding understanding. Those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications are also included within the scope of the claims of the present invention.

[0019] Example 1 As an example, as shown in Figure 1, a two-step optimization design and manufacturing method for multi-axis 3D printing includes the following steps S1 to S3. S1, First stage design: Obtain an optimized structure using topology optimization without overhang constraints, further obtain a printing scheme including division of the printable sub-region and locally optimal printing direction, and the non-printable ratio (ratio of non-printable boundary cells to all boundary cells) is set to threshold σ r If the result is less than the specified value, the optimization process ends, and the program proceeds to the second stage of design in step S2. S1.1 Topology optimization without overhang constraints: Using a density-based SIMP model as the topology optimization method, the density of each cell in the design domain is ρ = ρ1, ρ2, ... ρ nele With these as design variables, the formula for structural topology optimization is:

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

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

[0022] In this embodiment, after considering multi-axis topology optimization, all cells of the structure can be printed completely without requiring integrated topology optimization. This solves the problem of having to add supports during the printing process due to gravity-induced overhang effects during complex structural design and 3D printing, which leads to additional material consumption and the need to remove supports, thereby realizing integrated design and manufacturing of multi-axis 3D printed structures with optimal configuration.

[0023] During the printing process, the printing direction is dynamically adjusted to avoid overhang effects in the structural printing process. Integrated optimization of angle constraints enables overall optimized design and printing of printing areas with insufficient sub-regions, effectively solving the problems of increased volume and significant performance degradation when 3-axis 3D printing of self-supporting structures.

Claims

1. S1, First stage design: First, obtain the optimized structure using topology optimization without overhang constraints, then divide the printable sub-regions, calculate the locally optimal printing direction for each divided printable sub-region, and the non-printable ratio is the threshold σ r If less than the threshold σ, the optimization is terminated and the unprintable ratio is reached. r If the above conditions are met, proceed to step S2. S2, Second stage design: Considering the overhang constraint, the locally optimal printing direction is set as the overhang angle constraint of cells within the printing sub-region, and a constraint term for cell density near the horizontal of the cell is added to avoid the overhang feature in the optimization process, and integrated topology optimization including the angle constraint is performed using integrated topology optimization, and sensitivity analysis is performed at the same time to suppress unprintable cells and obtain an autonomous structure. S3. Multi-axis 3D printing manufacturing: A two-stage optimization design and manufacturing method for multi-axis 3D printing, characterized by including 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 self-supporting structure.

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

3. In step S1, the printing sub-regions are divided by performing grid discretization on the entire design domain or by using a manual division method, the manual division method specifically involves obtaining structural corner points of a simple structure using the Harris or SUSAN corner detection algorithm, dividing the sub-regions using the corner points as vertices, and the resulting rectangular sub-regions are the printing sub-regions, characterized in that the two-stage optimization design and manufacturing method for multi-axis 3D printing according to claim 1.

4. In step S1, the optimal printing direction for each printing sub-region is determined by the inclination direction of the boundary cells of the printing sub-region. Boundary cells are cells that have empty cells in their adjacent set, and the formula for determining boundary cells is: [Math 2] And, During the ceremony, 【number】 The value is used to characterize whether a cell is a boundary cell or not, and if a cell is a boundary cell, 【number】 The value is 1, and if a cell is an internal cell, then 【number】 The value is 0, Using a convolution kernel, the cell density gradient direction is obtained, transformed to obtain the slope direction of the boundary cells, and the locally optimal printing direction for each printing sub-region is determined by considering the printability of the boundary cells within each printing sub-region. Using a convolution kernel, the direction of the cell density gradient is obtained, and the direction of the cell density gradient is, [Math 3] And, During the ceremony, 【number】 This is the coordinate position of the cell, and edge-adding cells are introduced at the edges of the design area, the density of edge-adding cells in the design area adjacent to the base is set to 1, and the density of edge-adding cells in other design areas is set to 0. The cell density gradient direction is converted to the slope direction of the structural boundary, where the slope direction of the structural boundary is the angle between the structural boundary and the x-axis, and the slope direction of the structural boundary is perpendicular to the cell density gradient direction, and for cell density gradient directions in different quadrants, the corresponding slope direction of the structural boundary is, [Math 4] And, In the formula, φ is the direction of the slope of the structural boundary between 0 and π, g The two-step optimization design and manufacturing method for multi-axis 3D printing according to claim 1, characterized in that 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 area. If a cell that cannot be printed in the vertical printing direction appears in the i-th layer, then all cells in the i-th layer and below are considered invalid boundary cells, and cells that satisfy the following equation are also considered invalid boundary cells. [Math 5] During the ceremony, 【number】 This is the allowable rotation angle of the base, φ allow Let = 90°, and θ be the maximum overhang angle. 【number】 This is the coordinate position of the cell, 【number】 The value is used to characterize whether a cell is a boundary cell or not, and if a cell is a boundary cell, 【number】 The value is 1, and if a cell is an internal cell, then 【number】 The value is 0, The two-stage optimization design and manufacturing method for multi-axis 3D printing according to claim 4, characterized in that the printing direction of invalid boundary cells is all adjusted to the vertical direction 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: [Math 6] And, where \(t\) i characterizes the degree of violation of the overhang angle constraint, \(\cos\theta\) is the cosine value of the critical overhang angle of the structure, and 【number】 is the cell boundary normal vector, and t i If the tolerance δ is less than or equal to the limit, the cell satisfies the overhang angle constraint, and the range of the value of δ is 0 < δ ≤ 0.

001. The slope direction φ of the structural boundary of each sub-region obtained by equation (4) i Accordingly, considering the overhang angle of the boundary cell and the avoidance of printing collisions in adjacent areas as constraints, the locally optimal printing direction for each printing sub-region is calculated. [Number 7] In the formula, φ is the locally optimal printing direction vector of the printing sub-region, O represents the degree vector of the structural cell violating the overhang angle constraint, V is 1 for effective boundary cells and 0 for other boundary cells, and M is the 0-1 mapping matrix. 【number】 φ is the tilt direction vector of the structural cell. first and φ next is defined as the printing direction of two adjacent sub-regions, φ t,max This is the maximum allowable deflection angle and the tilt direction vector of the structural cell. 【number】 If it is within the printable area, the value of O is 2φ max Conversely, if the value of O is 2φ, then the value of O is 2φ. max Larger, The objective function is, [Number 8] It was rewritten as follows: In the equation, P is the weight of the penalty function, set to 0.01, and the equation for Q is: [Number 9] And, In the formula, φ v The two-stage optimization design and manufacturing method for multi-axis 3D printing according to claim 4, characterized in that is the angle between the vertical direction and the x-axis.

7. In step 2, the equation that considers the structural topology optimization of cells within each printed sub-region under linear angular constraints is: [Number 10] And, During the ceremony, 【number】 γ is a constraint term on the cell density in the horizontal vicinity of a cell, i This is the parameter value of the overhang feature of the structural boundary cell after topology optimization. 【number】 λ is a constraint term on the linear angle of the locally optimal printing direction of the sub-region, where λ i (φ i ) is a parameter that characterizes the locally optimal printing direction of the cell, determined by the cell's overhang angle, U is the overall displacement vector, F is the overall nodal load vector, K is the total stiffness matrix, and the objective function C(ρ) is the total strain energy under external force action, v i The two-step optimization design and manufacturing method for multi-axis 3D printing according to claim 6, characterized in that ρ is the volume of the i-th cell, f is the spatial ratio, ρ is the density of each cell, and the value of ρ is between 0 and 1.

8. In step 2, we 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. In the case of the objective function: [Math 11] In the case of overhang angle constraints: [Math 12] In the case of hanging feature constraints: [Number 13] In the formula, f is a spatial ratio, h(x) is a sigmoid function, and t i The value characterizes the degree to which the overhang angle constraint is violated, t il and t ir τ represents the degree to which the left boundary and right boundary violate the overhang angle constraint, respectively. il and τ ir These represent the degree to which the left boundary and right boundary violate the hanging feature constraint, respectively, and u k is the k-th cell displacement vector, and k 0 E is the stiffness matrix of the initial cell. 0 E is the Young's modulus of the material. min is a parameter close to 0, p is the penalty coefficient, and if p = 3, then v i The two-step optimization design and manufacturing method for multi-axis 3D printing according to claim 6, characterized in that ρ is the volume of the i-th cell, ρ is the density of each cell, and the ρ value is between 0 and 1.

9. Step S3 is specifically characterized by performing 3D modeling using 3D modeling software, slicing the solid model obtained from the 3D modeling using slicer software to generate a printing path, and performing multi-axis 3D printing, as described in claim 1, for a two-stage optimization design and manufacturing method for multi-axis 3D printing.

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